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Theoretical Simulations of Optical Rotation and Raman Optical Activity of Molecules in Solution
by
Parag Mukhopadhyay
Department of ChemistryDuke University
Date:_______________________
Approved:
___________________________Prof. David N. Beratan, Supervisor
___________________________Prof. Weitao Yang
___________________________Prof. Jie Liu
___________________________Prof. Terrence G. Oas
Dissertation submitted in partial fulfillment ofthe requirements for the degree of
Doctor of Philosophy in the Department ofChemistry in the Graduate School
of Duke University
2008
ABSTRACT
Theoretical Simulations of Optical rotation and Raman Optical Activity of Molecules in Solution
by
Parag Mukhopadhyay
Department of ChemistryDuke University
Date:_______________________
Approved:
___________________________Prof. David N. Beratan, Supervisor
___________________________Prof. Weitao Yang
___________________________Prof. Jie Liu
___________________________Prof. Terrence G. Oas
An abstract of a dissertation submitted in partialfulfillment of the requirements for the degree of
Doctor of Philosophy in the Department ofChemistry in the Graduate School
of Duke University
2008
Copyright byParag Mukhopadhyay
2008
iv
Abstract
Chiroptical spectroscopic techniques such as optical rotation (OR), electronic circular
dichroism (ECD), and Raman optical activity (ROA) provide the means to probe molecular
dissymmetry, which is the arrangement of atoms that is not superimposable on its mirror image.
However, the application of chiroptical methods for conformational and configurational analysis
of molecules (or molecular stereochemistry) requires the accurate and efficient computation of
chiroptical response properties. Access to a battery of accurate methods, especially for OR, have
just emerged over the last decade. A combination of quantum chemical electronic structure
methods and chiroptical spectroscopy can now be used to establish a comprehensive
understanding of molecular stereochemistry. A key challenge in stereochemical analysis is to
compute the chiroptical response of molecules in solution, which is the focus of our research in
optical activity.
Although the common perception is that chiroptical responses are solely determined by a
chiral solute’s electronic structure in its environment, we demonstrate that chiral imprinting
effects on media, and molecular assembly effects can dominate chiroptical signatures. Both these
effects are strongly influenced by intermolecular interactions that are essential to accurately
describe chiroptical signatures of molecules. Chiroptical response of molecules spans a range of
large positive and negative values, and hence, the measured chiroptical response represents an
ensemble average of orientations. Thus, accurate prediction of chiroptical properties requires
adequate conformational averaging. Here we show that OR and ROA of molecules in solution
can be modeled using a combination of structure sampling and electronic structure methods.
Method for computing chiroptical response in the condensed phase using continuum solvation
models and point charge solvent model, although more efficient than explicit solvent treatments,
are often inadequate for describing induced chirality effects. The lack of a priori knowledge of
v
solvent-solute interactions and their influence on the chiroptical signature demands exploration of
thermally averaged solute-solvent clusters and comparison with simpler solvent studies.
vi
Contents
Abstract ................................................................................................................................................. iv
Contents ................................................................................................................................................ vi
List of Tables ...................................................................................................................................... viii
List of Figures....................................................................................................................................... ix
List of Abbreviations ........................................................................................................................... xii
Acknowledgements............................................................................................................................. xiii
1 Optical signature of molecular dissymmetry: Combining theory with experiments to addressstereochemical puzzles ........................................................................................................................ 14
1.1 Overview............................................................................................................................ 14
1.2 Introduction........................................................................................................................ 14
1.3 Molecular dissymmetry and the electric dipole-magnetic dipole polarizability tensor .. 15
1.4 Utilizing the G′(ω) tensor to probe molecular dissymmetry............................................ 19
1.4.1 Configuration and conformation analysis of molecules using chiropticalspectroscopy................................................................................................................................ 19
1.4.2 Chiroptical signatures of intra- and inter-molecular interactions. .......................... 21
1.5 Summary............................................................................................................................ 23
2 Solvent effect on optical rotation: A case study of Methyloxirane in water ............................ 25
2.1 Overview............................................................................................................................ 25
2.2 Introduction........................................................................................................................ 25
2.3 Results and Discussion...................................................................................................... 28
2.4 Conclusions........................................................................................................................ 36
2.5 Materials and methods....................................................................................................... 37
2.5.1 Experimental Procedure ........................................................................................... 37
2.5.2 Molecular dynamics simulation setup and procedure............................................. 37
2.5.3 Computation of optical rotation ............................................................................... 38
vii
3 Contribution of a solute’s chiral solvent imprint to optical rotation......................................... 39
3.1 Overview............................................................................................................................ 39
3.2 Introduction........................................................................................................................ 39
3.3 Results and Discussion...................................................................................................... 41
3.4 Conclusions........................................................................................................................ 45
3.5 Materials and Methods ...................................................................................................... 46
3.5.1 Monte Carlo simulation setup and procedure.......................................................... 46
3.5.2 Calculation of optical rotation.................................................................................. 47
4 Characterizing aqueous solution conformations of a peptide backbone using Raman opticalactivity computation ............................................................................................................................ 48
4.1 Overview............................................................................................................................ 48
4.2 Introduction........................................................................................................................ 49
4.3 Results................................................................................................................................ 52
4.3.1 Low-energy conformations of Ala dipeptide in water ............................................ 52
4.3.2 Structures of H2O-Ala dipeptide clusters ................................................................ 54
4.3.3 ROA and Raman spectra of H2O- and D2O- Ala dipeptide clusters....................... 57
4.4 Discussion.......................................................................................................................... 74
4.5 Conclusions........................................................................................................................ 80
4.6 Methods ............................................................................................................................. 81
4.6.1 MC simulations ........................................................................................................ 81
4.6.2 TD-DFT calculations of ROA.................................................................................. 82
5 Epilogue ...................................................................................................................................... 85
Bibliography ........................................................................................................................................ 88
Biography............................................................................................................................................. 98
viii
List of Tables
Table 4-1 The peptide backbone dihedral angles (φ, ψ) of alanine dipeptide-water clusterstructures from the Monte Carlo simulations used in the quantum mechanical energyminimization. ....................................................................................................................................... 56
ix
List of Figures
Figure 2.1 Optical rotatory dispersion of methyloxirane in the gas phase and in water computedusing an implicit solvent model (A) and a combination of implicit and explicit solvent models(B). Calculations used the TD-DFT/BP86 functional and aug-cc-pVDZ basis set. The conductor-like screening model (COSMO) was used as the implicit solvent model. The vertical bars showthe error estimate of the average optical rotation calculated using the blocking method 71.............. 28
Figure 2.2 Radial distribution function of hydrogen atoms for water around the methyloxiraneoxygen atom......................................................................................................................................... 30
Figure 2.3 Optical rotatory dispersion of (S)-methyloxirane in water computed with an increasingnumber of solvent molecules. Calculations used the TD-DFT/BP86 functional and aug-cc-pVDZbasis sets. The conductor-like screening model (COSMO) was used as the implicit solvent model.The error bars were calculated using the blocking method 71. ........................................................... 31
Figure 2.4 Variation in the dipole-length and dipole-velocity form of calculated optical rotationsusing TD-DFT/BP86 correlation-exchange functional. The specific rotation was averaged for1700 structure snapshots from a molecular dynamic simulation to generate the ORD of (S)-methyloxirane in water. The conductor-like screening model (COSMO) was used as the implicitsolvent model. The vertical bars show the error estimate of the average optical rotation calculatedusing the blocking method 71. .............................................................................................................. 32
Figure 2.5 Computed optical rotatory dispersion of (S)-methyloxirane with the first explicithydration shell. Calculations used different combinations of TD-DFT/BP86/B3LYP functionalsand aug-cc-pVDZ/aug-cc-pVTZ basis sets as described in the text. The conductor-like screeningmodel (COSMO) was used as the implicit solvent model. The bars indicate error estimatescomputed using the blocking method 71.............................................................................................. 33
Figure 2.6 Average optical rotation of (S)-methyloxirane at 589 nm, [α]D, as a function of thenumber of MD simulation snapshots. Calculations used the TD-DFT/BP86 functional and aug-cc-pVDZ basis set. A combination of explicit water molecules (within 0.40 nm of the methyloxiraneoxygen atoms) and an implicit solvent model (COSMO) were used in the calculations. The errorestimate of the average optical rotation was calculated using the blocking method 71. .................... 34
Figure 2.7 Distribution of the optical rotation of (S)-methyloxirane at 589 nm, [α]D, as a functionof water molecule positions defined by the angle τ, in the first hydration shell. The insets showstructures with water molecules on the same or opposite sides from the methyl group ofmethyloxirane, defined as the syn- or anti-configurations, respectively. Water on the opposite sidedominated the explicit solvent contribution to [α]D. .......................................................................... 35
Figure 3.1 Optical rotatory dispersion (ORD) of (S) ()- and (R) ()-methyloxirane-benzeneclusters (shown in the MC structure snapshot), and the solvent imprint () computed usingexplicit solvent models. Calculations used TD-DFT/BP86 functional and SVP basis set; and animplicit solvent () based on the COSMO model. The error bars are calculated using theblocking method 71. .............................................................................................................................. 41
x
Figure 3.2 Optical rotatory dispersion (ORD) of (S)-methyloxirane in benzene () and thecomputed ORD of the chiral solvent imprint (;;;). Calculations used varied TD-DFT/BP86/BLYP correlation-exchange functionals with RI-J and SV/SVP/aug-cc-pVDZ basissets. The specific rotation was averaged over 1000 structure snapshots from a Monte-Carlosimulation to generate the ORD of the chiral solvent structure. ........................................................ 43
Figure 3.3 Optical rotatory dispersion of ethylene oxide in benzene computed using explicitsolvent model. Calculations used TD-DFT/BP86 correlation-exchange functionals with RI-J andaug-cc-pVDZ basis set. The specific rotation was averaged over 1000 structure snapshots from aMonte-Carlo simulation to generate the ORD of ethylene oxide and (S)-mehtyloxirane () inbenzene................................................................................................................................................. 44
Figure 3.4 Optical rotatory dispersion of (S)-methyloxirane in alkylbenzenes................................. 45
Figure 4.1 . A. Ball and stick model for the N-acetylalanine-N′-methylamide (Ala dipeptide). Thepeptide backbone structure in Ala dipeptide is defined by φ and ψ dihedral angles. B. Free energydifferences of Ala dipeptide conformations in water computed using Monte Carlo simulations.αR, αL, β, and PPII conformational regions are shown on the Ramachandran map. Figure 4.1Cshows the computed φ and ψ distribution (yellow) resembles the empirically derived φ, ψdistribution of amino acid residues (black) not in either canonical helix or sheet secondarystructures in protein X-ray crystal structures 127. ................................................................................ 53
Figure 4.2 Ramachandran map of φ, ψ pairs for Ala dipeptide-water cluster structures taken fromthe Monte Carlo simulations. Figure 4.2A shows a collection of Ala dipeptide-water clusterstructures (black) that have the same peptide backbone conformation with different waterarrangements. Figure 4.2B shows the distribution of φ, ψ values for the alanine dipeptide-waterclusters optimized using quantum mechanical energy minimization. Green arrows show that eachpeptide conformation, before and after energy minimization, occupies the same region on theRamachandran map. ............................................................................................................................ 55
Figure 4.3 SCP backscattering ROA (A, C) and Raman (B, D) spectra of H2O-Ala dipeptideclusters. The computed spectra shown in blue and red are averaged over a collection of dipeptideconformations from PPII (inset in A) and αR (inset in C) regions of the Ramchandran map. Theexperimental spectra (green; in arbitrary units) are from reference 126.............................................. 58
Figure 4.4 ROA spectra computed using Ala dipeptide-H2O cluster from the low-energy region ofthe Ramachandran map. The computed spectra shown are averaged over a collection of dipeptideconformations from regions D, E, F and G of the Ramchandran map (inset in A). Theexperimental spectrum (in arbitrary units) is from reference 126. ....................................................... 60
Figure 4.5 ROA spectra computed using Ala dipeptide-H2O cluster from the low-energy region ofthe Ramachandran map. The computed spectra shown are averaged over a collection of dipeptideconformations from regions D, E, F and G of the Ramchandran map (inset in A). Theexperimental spectrum (in arbitrary units) is from reference 126. ....................................................... 62
Figure 4.6 SCP backscattering ROA (A, C) and Raman (B, D) spectra of D2O-Ala dipeptideclusters. The computed spectra shown in blue and red are averaged over a collection of dipeptideconformations from PPII (inset in A) and αR (inset in C) regions of the Ramchandran map. Theexperimental spectra (green; in arbitrary units) are from reference 126.............................................. 63
xi
Figure 4.7 ROA spectra computed using Ala dipeptide-D2O cluster from the low-energy region ofthe Ramachandran map. The computed spectra shown are averaged over a collection of dipeptideconformations from regions A, B and C of the Ramchandran map (inset in A). The experimentalspectrum (in arbitrary units) is from reference 126. ............................................................................. 65
Figure 4.8 ROA spectra computed using Ala dipeptide-D2O cluster from the low-energy region ofthe Ramachandran map. The computed spectra shown are averaged over a collection of dipeptideconformations from regions D, E, F and G of the Ramchandran map (inset in A). Theexperimental spectrum (in arbitrary units) is from reference 126. ....................................................... 66
Figure 4.9 SCP backscattering ROA (A, C) and Raman (B, D) spectra of Ala dipeptide in H2O.The computed spectra shown in orange and pink are averaged over a collection of dipeptideconformations from αL (inset in A) and β (inset in C) regions of the Ramchandran map. Theexperimental spectrum (in arbitrary units) is from reference 126. ....................................................... 68
Figure 4.10 SCP backscattering ROA (A, C) and Raman (B, D) spectra of Ala dipeptide in D2O.The computed spectra shown in orange and pink are averaged over a collection of dipeptideconformations from αL (inset in A) and β (inset in C) regions of the Ramchandran map. Theexperimental spectrum (in arbitrary units) is from reference 126. ....................................................... 69
Figure 4.11 ROA (A, C) and Raman (B, D) scattering cross sections contributions of Aladipeptide (red), water (blue), and peptide-water interactions (black) to the total ROA and Ramanscattering cross sections of Ala dipeptide-water clusters (green). These computed spectra areaveraged over a collection of dipeptide conformations from PPII (A, B) and αR (C, D) regions ofthe Ramachandran map. ...................................................................................................................... 70
Figure 4.12 SCP backscattering ROA spectra computed for a representative PPII (φ = -68° andψ = 135°; blue) and a αR conformation of Ala dipeptide (φ = -73° and ψ = −30°; red).Experimental spectra (green; in arbitrary units) in H2O (A, B) and D2O (C, D) are from reference126. ......................................................................................................................................................... 71
Figure 4.13 ROA intensity differences associated with the vibrations in the low wavenumberrange decomposed into contributions from groups of atoms in Ala dipeptide for a PPII (φ = -68°and ψ = 135°; A) and a αR (φ = -73° and ψ = −30°; B) conformation of Ala dipeptide. The groupsof atoms in Ala dipeptide are shown in panel I. Positive and negative ROA intensity differencesare shown as red and yellow circles, respectively. ............................................................................. 73
xii
List of Abbreviations
OR: Optical rotation
ORD: Optical rotatory dispersion
ROA: Raman optical activity
DFT: Density functional theory
TD-DFT: Time dependent density functional theory
MD: Molecular dynamics simulations
MC: Monte Carlo simulations
xiii
Acknowledgements
First and foremost, I thank my advisor Prof. David N. Beratan for his guidance,
encouragement and support throughout my graduate studies. I also thank my committee members
Prof. Weitao Yang, Prof. Jie Liu, and Prof. Terrence G. Oas for insightful discussions. Prof. Oas
also introduced me to the interdisciplinary training program in Structure Biology and Biophysics,
and I express my sincere gratitude for his constant support for my academic and professional
development.
I thank various past and present members of the Beratan group: Dr. Gerard Zuber, Dr.
Michael Rock Goldsmith, Dr. Michael Peterson, Dr. Alexander Balaeff, and Dr. Ilya Balabin, for
insightful discussions.
Last, but not least, I thank my wife Dr. Pooja Arora, my parents and sister for their
support and constant encouragement.
14
1 Optical signature of molecular dissymmetry: Combining
theory with experiments to address stereochemical puzzles
1.1 Overview
Modern chemistry emerged from a quest to understand the rules governing the shapes of
objects at the molecular level. An immediate consequence of van’t Hoff’s description of carbon’s
tetravalency is molecular dissymmetry. Chiroptical spectroscopy, including optical rotatory
dispersion (ORD), electronic circular dichroism (ECD), and Raman optical activity (ROA)
provide means to probe the dissymmetric arrangement of atoms in space. However, deciphering
the molecular shape information encoded in chiroptical response properties requires the accurate
and efficient theoretical simulation of these response properties. Indeed, access to a battery of
accurate theoretical methods has just emerged over the last decade and these methods are forging
strong links between chiroptical spectroscopy and molecular structure. Thus, this chapter briefly
describes the applications of chiroptical spectroscopy to molecular structure analysis, and is
organized as follows: in the introduction we give a brief historical perspective of the advent of
molecular stereochemistry, in 1.3 we review the physical origins of chiroptical phenomena, the
optical activity tensor, G′′(ω), and then in 1.4 we explore the value of linking theory to
experiment in order to correlate chiroptical response to molecular stereochemistry. Finally, in the
summary we briefly describe our research finding in optical activity of molecules in solution.
1.2 Introduction
In 1815 Biot found that plane-polarized light is rotated by a characteristic angle when it
passes through some organic liquids. This behavior became known as optical activity. In 1848
Pasteur separated crystals of the salts of tartaric acid into right- and left-handed hemihedral
crystals. Solutions of these crystals rotated polarized light in opposite directions, leading him to
conclude that molecular dissymmetry results in optical activity 1,2. Molecular dissymmetry is
15
arrangement of atoms in a manner that is not superimposable on their mirror image, a necessary
condition for optical activity. Subsequently, in 1874 van’t Hoff showed that the tetrahedral
geometry of a carbon atom attached to four different atoms (or groups of atoms) is dissymmetric
and hence optically active. During the same time Joseph Achille Le Bel 3, independently showed
that for a molecule of type XY4, where X is an atom or group of atoms joined to four univalent
atoms Y, if the three Ys are replaced by different substituents, then from a purely geometrical
consideration the resulting molecule is dissymmetric and hence optically active. Thus, van’t Hoff
and Le Bel’s investigations of molecular optical activity laid the foundation of modern molecular
stereochemistry 4.
The quantum mechanical (QM) description of optical activity 5-8 followed just a few years
after the emergence of the Schrödinger equation yet, reliable computational methods to predict
OR are just ten years old! 9,10. Following the first accurate ab initio calculation of OR 11, advances
in computational methods for the reliable prediction of OR were reported 9,12. However, the use of
OR for structural analysis of chiral molecules has been limited because of the lack of a direct
intuitive connection between observed rotations and molecular structure. Indeed, no general rules
even exist to predict the sign of the OR for a given structure. Our aim is to compute molecular
chiroptical signatures so that the data may be used in combination with experiments to assign and
interpret the stereochemistry (both conformation and configuration) of the molecule.
1.3 Molecular dissymmetry and the electric dipole-magneticdipole polarizability tensor
Rosenfeld and Condon formulated a modern description for the propagation of polarized
radiation in optically active media 6. Based on a semiclassical theory, they showed that the optical
rotatory parameter β, describes the response of a chiral molecule to polarized radiation. The
specific rotation [α]λ (in deg [dm(g/cm3)]-1) of a chiral molecule is related to its optical rotatory
parameter β:
€
α[ ]λ =−1.3423×10−4 ×β × ˜ ν 2
3M (1)
16
where M is the molar mass (g/mol),
€
˜ ν is the radiation frequency in cm-1 and β is in atomic units
(bohr).
The optical rotatory parameter β is an isotropic average derived from the trace of the electric
dipole-magnetic dipole tensor (or the optical activity tensor), G′′(ω):
€
β = −′ G xx (ω) + ′ G yy (ω) + ′ G zz(ω)
3ω= −
13ω
Tr ′ G (ω)[ ] (2)
G′′(ω) is a second rank tensor and the QM expression for G′′(ω) is:
€
′ G αβ ω( ) = −4πh
ωω j 0
2 −ω 2j≠0∑ Im 0 ˆ µ α j j ˆ m β 0{ } (3)
where h is Planck’s constant,
€
0 and
€
j are the ground and excited states, respectively;
€
ˆ µ α and
€
ˆ m β are electric and magnetic dipole moment operators;
€
ω0 j is the angular transition frequency
(
€
ω = 2πc ˜ ν ;
€
˜ ν is frequency in cm-1) and
€
ω is the angular frequency of the incident radiation. The
rotational strength is
€
R0 j = −i 0µ j • j m 0{ } (
€
µ and
€
m are electric and magnetic transition
moment vectors, respectively) and defines the intensity of ECD bands.
€
R0 j and β (equation 2) are
related by:
€
β = −2π3h
1ω0 j2 −ω 2
j≠0∑ R0 j (4)
Thus, OR can be computed from ECD spectrum. In achiral systems Tr [G′′(ω)] cancels. The
optical rotatory parameter β is small because Tr [G′′(ω)] nearly cancels in chiral systems 13. As a
consequence, small changes in the electronic distribution can produce large OR changes. In a QM
calculation, changing basis set, level of electron correlation, solvent, molecular geometry, or
treatment of vibrational contributions can have a large influence on β. Indeed, it remains
challenging to predict OR accurately for chiral molecules. Recently, coupled-cluster (CC) and
time dependent density functional theory (TD-DFT) methods have been used to predict OR 9,
although the computational efficiency of TD-DFT methods favors their use in many OR
calculations 12.
17
ROA measures the intensity difference of Raman scattered right- and left-circularly polarized
light 14. Scattered light originates from the radiation field generated by the oscillating electric and
magnetic multipole moments induced in a molecule by the incident light wave 15. The interference
between light waves scattered via the molecular polarizability (α) and optical activity response
(G′′ and A) yields a dependence of the scattered intensity on the degree of circular polarization of
the incident light and to the circular component on the scattered light, which is the physical basis
of ROA 16. The electric dipole-electric dipole (α) and electric dipole-electric quadrupole (A)
tensors are 15:
€
ααβ ω( ) =4πh
ω j 0
ω j 02 −ω 2
j≠0∑ Re 0 ˆ µ α j j ˆ µ β 0{ } (5)
€
Aαβγ ω( ) =4πh
ω j 0
ω j 02 −ω 2
j≠0∑ Re 0 ˆ µ α j j ˆ Θ βγ 0
(6)
where
€
ˆ Θ βγ is the quadrupole moment operator.
Zuber et al. recently demonstrated accurate and efficient prediction of ROA spectra using
TD-DFT methods 17. The approach avoids calculating the four-center Coulomb integrals and
omits contributions of the electric dipole-electric quadrupole tensor (A) to the ROA differential
scattering cross-section. We used the same scheme in the off-resonance approximation 16 to
calculate the circular difference differential scattering cross-sections per unit solid angle
€
−Δndσ π( )SCPdΩ
for back scattered circular polarization (SCP) 18 with naturally polarized (n)
incident light:
€
−Δndσ π( )SCP
dΩ≈
Kc48β( ′ G )2 (7)
c is the speed of light,
€
β( ′ G )2 is the anisotropic ROA invariant , and K is:
€
K =107
9π 2µo
2c 4 ˜ ν oωo
200πc−Δ ˜ ν p
3
(8)
18
€
ωo = 2πν o is the frequency of the incident light,
€
Δ ˜ ν p is the Raman frequency shift (in cm-1), c is
the speed of light (in m s-1), and
€
µo is the permittivity of vacuum.
Placzek polarizability theory writes 19
€
β( ′ G )2 =12
3αµν ′ G µν −αµµ ′ G νν( )µν
∑ (9)
where
€
αµν ′ G µν is
€
αµν ′ G µν =h
8π 2cΔ ˜ ν p i, j∑
∂αµνe
∂xiα
0α ,β∑
∂ ′ G µνe
∂x jβ
0
Lαi,px Lβj ,p
x (10)
€
Lαi,px is the ith component of the Cartesian displacement vector of nucleus α for normal mode p.
€
αµνe and
€
′ G µνe are the elements of the electronic components of the electric dipole-electric dipole
tensor and the imaginary part of the electric dipole-magnetic dipole tensor, respectively. The
index 0 indicates that the derivatives of the electronic tensors are evaluated at the equilibrium
nuclear geometry.
In order to explore how G′′ tensor is used to address stereochemical puzzles, we have
divided the following section into two topics: (1) The configurational and conformational analysis
of molecules using chiroptical spectroscopy, and (2) The chiroptical response of molecular
assemblies. These sections also include an overview of the computer simulations of the solvent
effects on OR and ROA, which is the focus of our research, and the details of these simulations
are described in chapters 2, 3 and 4.
19
1.4 Utilizing the G′(ω) tensor to probe molecular dissymmetry
1.4.1 Configuration and conformation analysis of molecules usingchiroptical spectroscopy.
The applications of OR, ECD, and ROA to molecular structure analysis requires the
accurate and efficient computation of chiroptical response properties. We now describe how the
prediction of chiroptical properties in concert with experiments is a productive approach to probe
and to establish links between molecular stereochemistry and chiroptical response.
Determining the absolute configuration (AC) of a chiral molecule is often a considerable
challenge. Common tools to determine the AC of natural products include X-ray crystallography,
ECD 20, nuclear magnetic resonance (NMR) analysis of Mosher ester and relative derivates 21,
chemical degradation and total synthesis 22,23. Chemical degradation and total synthesis are time
consuming, costly, and error prone 24. Comparison of calculated and experimental OR data, in
contrast, provides a straightforward and less expensive strategy to assign AC. Kondru et al.
reported the first ab initio theoretical AC assignment of a natural product (Hennoxazole A) by
computing the molar rotation of its fragments and using van’t Hoff’s superposition principle to
combine the fragment results 25. This approach divided the flexible natural product into weakly
interacting fragments, computed the Boltzmann-averaged molar OR for each fragment, and
summed the contributions to obtain a composite molecular value for comparison with experiment.
Prior experimental studies had validated the use of the additivity principle for this natural product26. This approach was also successfully applied to determine the AC of the natural product
Pitiamide A 27. Recently, Zuber et al. combined NMR NOEs, chemical shift, and J-coupling
measurements with both OR and ECD data to determine the AC of the marine natural product
Bistramide C. Bistramide C has 10 stereogenic carbons with, 1024 possible stereoisomers 28. The
Bistramide C study demonstrates that the judicious use of electronic structure analysis and
spectroscopic data can be used to accomplish successful AC assignment of complex flexible
natural products with a large numbers of stereogenic carbons. Other groups have also noted the
20
utility of using multiple chiroptical methods, including ORD, ECD, VCD, and ROA to determine
the AC of chiral species 29.
The reliability of computational methods for predicting OR was demonstrated by assigning
the yet undetermined stereochemistry of several molecules. For example, Zuber et al. used TD-
DFT, OR calculations to assign (+) and (-) OR signs to trans-(S)- and trans-(R)-ladderane
configurations, respectively 30. Recently, Mascitti and Corey carried out the enantioselective
synthesis of pentacycloanammoxic acid with a trans-(S)-ladderane constituent 31, which was
indeed found to have a positive [α]D, consistent with our prediction.
The development of computational methods to describe chiroptical response is enabling the
examination of molecular conformations and assemblies via these responses. Kondru, Beratan
and Wipf defined atomic and chemical group contributions to OR to establish an intuitive link
between structure and OR 32. Atomic contribution maps indicate that OR calculations are
sensitive to molecular geometry, and thus, reliable prediction of molar rotation for flexible
molecules requires extensive conformational averaging 33. Indeed, Vaccaro and co-workers find a
strong dependence of computed OR on molecular conformations in 2-substituted butanes 34,
similar to earlier analysis of OR in twisted “molecular wires” 35.
The availability of commercial ROA spectrometer and corresponding computational methods
has made ROA spectroscopy a useful tool for configuration and conformation analysis of chiral
molecules 14,17. We have demonstrated the utility of ROA by predicting the distribution of
dominant N-acetylalanine-N′-methylamide (Ala dipeptide) conformations in aqueous solution 36
(see chapter four for more details).
The conformational heterogeneity of Ala dipeptide has been probed using multiple
spectroscopic methods in addition to ROA. Despite extensive study, there is no consensus for Ala
dipeptide’s structure in aqueous solution. For example, the 13C NMR spectra of Ala dipeptide in
water and in liquid-crystalline media suggest that the structure in these two media is similar, and
that the structure is dominated by extended left-handed PPII helical conformations 37,38. Following
these NMR studies, Mehta et al. used 13C NMR 39 to show that Ala dipeptide in water exists in a
21
mixture of PPII and the compact right-handed αR helical conformations. Kim et al. probed the
conformational heterogeneity of Ala dipeptide in aqueous solution using 2D-IR 40 and reported
the presence of PPII-like conformations, and ruling out αR helical conformations in water. Raman
spectroscopy, in contrast, suggests that PPII, αR and the intra-molecular hydrogen bonded C7eq
conformations coexist in aqueous solution 41.
The significant variation of proposed Ala dipeptide conformations warrants further analysis,
and suggests the utility of linking chiroptical simulations to experimental data. ROA has been
used to characterize aqueous solution conformations of the peptide backbone in polypeptides and
proteins 42. The ROA spectrum reports a weighted superposition of spectra arising from molecular
conformations 42. We analyzed the ROA spectra of Ala dipeptide in H2O and D2O using TD-DFT
on Monte Carlo (MC) sampled geometries. We thus explore the consistency of MC generated
structures with experimental ROA data. Our analysis of the Raman and ROA spectra of Ala
dipeptide indicate that it is dominated by αR and PPII conformations in aqueous solution 36.
1.4.2 Chiroptical signatures of intra- and inter-molecular interactions.
Atomic and chemical group contributions to OR indicate that functional groups far from
stereogenic centers can dominate the OR of chiral species. For example, Kondru et al. found that
the large difference in the OR of the marine natural products Calyculin A and B, which differs
only by the (E)- vs (Z)-configuration of a terminal double bond in a tetraene unit distant from the
stereogenic center, arises from the polarizability of the terminal cyanide (CN) substituent rather
than by direct perturbation of the stereogenic carbons 43. The Calyculin case demonstrates that π-
mediated intramolecular electronic communication between the stereocenter and a distant CN
group dominates the OR.
A key challenge in stereochemical analysis is to compute chiroptical responses accurately
for molecules in solutions. Indeed, OR in solution is known in many instances to be very different
from the response in the gas phase 44. Condensed phase effects arise from 1) the chiral solvent
imprint, 2) the perturbation of the chiral species by solvent, 3) molecular assembly, and 4) the
22
influence of solvation on the population of molecular conformers and concominant changes in
electronic structures.
Our studies have shown that the solvent effects on ORD can be modeled using a
combination of structure sampling and electronic structure methods (see chapter two and three for
model details). We demonstrated the validity of this approach in studies of the solvent
dependence of ORD for methyloxirane, a particularly difficult and relevant case that has
confounds some of the highest-level computational methods. (S)-methyloxirane has a positive
ORD spectrum in water and a negative spectrum in benzene in the long wavelength regime 45. A
hydrogen bonded methyloxirane-water adduct dominates the ORD in water 46. For methyloxirane
in benzene, the chiral imprint on the benzene cluster dominates the ORD spectrum 47. That is,
removing the methyloxirane and computing the ORD of the imprinted benzene snapshots
reproduces the observed ORD spectra.
Xu and coworkers have recently studied the solvation of methyloxirane in water using
VCD, OR, and simulation 48. They concluded that the methyloxirane-water binary complex
dominates the chiroptical signature in aqueous solution at room temperature, and the anti
conformation is preferred over the syn conformation, consistent with our predictions 46. The OR
of (R)-pantolactone is also controlled by noncovalent association via hydrogen bonding. Indeed,
(R)-pantolactone in carbon tetrachloride at room temperature was shown to have [α]D that arises
from a combination of monomers and dimers 49.
The ORD signature of methyloxirane in benzene arises from a chiral imprint on the
solvent, not from perturbation of methyloxirane by the solvent 47. The methyloxirane-benzene
case demonstrates that a chiral solvent cluster seeded by a chiral solute may dominate the
chiroptical response. Indeed, chiral solutes are known to induce chiral solvent ordering that
contributes to the chiroptical response. Fidler et al. showed that dissymmetric solvent
organization around a chiral solute accounts for 10-20% of the total CD intensity attributable to
an optically active chromophore 50. Yet, the dominance of an induced chirality signature was
shown for the first time using the theoretical computation of methyloxirane’s ORD in benzene 51.
Wang and Cann have recently studied the extent of induced chirality in achiral solvent by chiral
23
solute using MD simulations 52. They concluded that chirality transfer is most pronounced for
solvents that are hydrogen bonded to solutes, and the dissymmetric solvent shell around the solute
at specific positions also contributes to the extent of chirality transfer.
The chirality of metals or nanocluster with chiral adsorbates is the subject of intense
interest because of potential applications in enantioselective catalysis 53, enantiodiscrimination 54,
enantioselective crystallization 55 and photonics 56. Theoretical analysis indicates that the chiroptic
response of metal clusters with chiral adsorbates may arise from an intrinsically chiral core
structure of the metal cluster 57, a chiral surface or chiral adsorbates. Goldsmith et al. employed
simple model calculations using a dissymmetrically-perturbed particle-in-a-box model to probe
chiral imprinting of nanoparticles. The authors found that CD may be induced in a nanoparticle
by a chiral monolayer as in Au28(SG)16 glutathione passivated gold nanoclusters 58. Similar to
solution chiral imprints, the analysis of the CD spectra suggests that the chiroptical response of
the chiral monolayer protected cluster can arise from the imprinted core lattice with dissymmetric
adsorbates. Gautier and Bürgi recently showed, using thiolate-for-thiolate ligand exchange
experiments on gold nanoparticles, that the optical activity of gold nanoparticles is indeed
dictated by the chirality of the adsorbed thiolates 59, consistent with theoretical predictions 58.
1.5 Summary
Three-dimensional shape is a key determinant of molecular function. Theoretical
calculations of OR, ORD, ECD, and ROA, when combined with experiments, can be used to
assign stereochemistry (both conformation and configuration) for natural products and
biomolecules.
A key challenge in stereochemical analysis is to compute the chiroptical response of
molecules in solution, which is the focus of our research in optical activity. Our theoretical
studies of methyloxirane in water and benzene, which are described in chapters 2 and 3, show that
hydrogen bond and dispersion interactions strongly influence the chiroptical responses 46,47.
Although the common perception is that chiroptical responses are solely determined by a chiral
24
solute’s electronic structure in its environment, we demonstrate that chiral imprinting effects on
media, and molecular assembly effects can dominate chiroptical signatures. Both these effects are
strongly influenced by intermolecular interactions that are essential to accurately describe
chiroptical signatures of molecules. Chiroptical response of molecules spans a range of large
positive and negative values 46,47,60, and hence, the measured chiroptical response represents an
ensemble average of orientations. Thus, accurate prediction of chiroptical properties requires
adequate conformational averaging. Methods for computing chiroptical response in the
condensed phase using continuum solvation models and point charge solvent model, although
more efficient than explicit solvent treatments, are often inadequate for describing induced
chirality effects 47. The lack of a priori knowledge of solvent-solute interactions and their
influence on the chiroptical signature demands exploration of thermally averaged solute-solvent
clusters and comparison with simpler solvent studies.
25
2 Solvent effect on optical rotation: A case study ofMethyloxirane in water
2.1 Overview
In order to understand solvent effects on optical rotation (OR), the solvent dependence of
the ORD for methyloxirane was studied. The figure above shows the measured (dashed line) and
computed (solid line) ORD of (S)-methyloxirane in water () and benzene (). The hydrogen
bonded methyloxirane-water adduct (top structure) dominates the ORD in aqueous solution. In
contrast, the chiral benzene cluster (bottom structure) dominates the ORD in benzene (also see
chapter 3 for more details). Here we show that including explicit solute-solvent interactions is
essential to describe the influence of the solvent on the OR of methyloxirane in water.
2.2 Introduction
A long-standing challenge in molecular stereochemistry is to assess the contributions of
the solvent surrounding chiral organic molecules. The observed specific rotation angles and ORD
are strongly influenced by solvent-solute interactions. For example, (S)-methyloxirane has a
positive OR in water and a negative OR in benzene 45. The vapor phase and condensed phase
26
optical rotations of chiral molecules are also known to differ in large and nonintuitive ways 61.
Access to experimental gas phase optical rotation data 44 and to modern linear-response OR
calculations 11,13,25,33,34,49,62-67 provides the tools needed to analyze and predict the contributions of
solute-solvent interactions to OR. Wilson et al. recently reported the OR for a series of organic
molecules in the vapor phase using cavity ring-down polarimetry 44. These authors compared the
solution and vapor phase OR to assess the influence of the condensed phase environment on
ORD. They concluded: (a) for flexible solute molecules, solvent stabilization of individual
conformers can influence the optical rotation strongly; (b) solvation of rigid molecules like
methyloxirane causes changes in the static and dynamic distribution of molecular electron
densities; and (c) surprisingly, OR under solvent-free conditions can resemble OR measured in a
highly polar solvent. We find that, for methyloxirane in high-polarity solvents such as water, it is
essential to include explicit solute-solvent interactions in the theoretical analysis to describe the
observed ORD.
Recently, coupled-cluster (CC) and time dependent density functional theory (TD-DFT)
methods have been used to predict OR 9. However, the substantially greater computational
efficiency of TD-DFT methods has led to their favored use in current OR calculations. The
solvent dependence of OR for chiral molecules has been computed using TD-DFT and an implicit
continuum solvent model. Kongested et al. recently used CC methods combined with a
continuum solvent description to calculate the influence of solvent on the OR of (S)-
methyloxirane 68. The authors concluded that continuum models do not reproduce the
experimentally observed solvent shifts in the ORD as a function of solvent. Moreover, implicit
solvent models do not predict the sign change in the ORD of methyloxirane in aqueous solution at
wavelengths longer than 400 nm. Accordingly, the inclusion of explicit solvent effects appears to
be essential for further progress. Here, we show that ORD calculations using explicit solvent
models, combined with continuum models, such as the conductor-like screening model
(COSMO) 69, can capture the sign and relative magnitude of the ORD of methyloxirane in water.
More importantly, explicit solvent studies allow elucidation of the solvent contributions to the
observed OR spectrum. Comparison of the total computed OR (solute + solvent) with the OR
27
computed for the solvent shell (solvent with the chiral solute removed from the electronic
structure analysis) allows us to determine when explicit solute-solvent interactions have a critical
effect on the ORD.
Ruud and Zanasi 70 have shown that it is important to include molecular vibrational
effects to correctly predict the experimental gas phase OR values of (S)-methyloxirane
successfully. Ruud et al, however, showed that vibrational corrections in dimethyloxirane
decrease the accuracy of the calculated OR values, which was attributed to the absence of solvent
effects 66. More recently, Mort and Autschbach 67 showed that including vibrational corrections
results in a small percentile difference between the experimental solution phase numbers and the
calculated gas phase values with or without the vibrational effects in a series of rigid molecules.
They attributed this behavior to the absence of solvent effects in their OR calculations. Rather
than making vibrational corrections to our OR calculations, we focused entirely on the influence
of solvent effects. As discussed by Mort and Autschbach, OR calculations incorporating both
vibrational and solvent effects might result in a further improved quantitative agreement between
theory and experiment.
28
2.3 Results and Discussion
Figure 2.1 Optical rotatory dispersion of methyloxirane in the gas phase and inwater computed using an implicit solvent model (A) and a combination of implicit andexplicit solvent models (B). Calculations used the TD-DFT/BP86 functional and aug-cc-pVDZ basis set. The conductor-like screening model (COSMO) was used as the implicitsolvent model. The vertical bars show the error estimate of the average optical rotation
calculated using the blocking method 71.
29
Figure 2.1 shows the computed ORD of (S)- and (R)-methyloxirane in water and in the
gas phase. The ORD were calculated using the BP86 functional with an aug-cc-pVDZ basis set.
Each structure had explicit water molecules within a cut-off distance of 0.35 nm from the
methyloxirane oxygen atom and a dielectric continuum for large distances based on the COSMO
model (water dielectric constant equal to 78.4). The computed ORD of (S)- and (R)-
methyloxirane in water were related by a simple reversal of sign, as expected. The ORD
predictions with explicit solvent were very close to the experimental values, especially for
wavelengths >400 nm. Calculations using the implicit solvent model only (Figure 2.1 A) predict
the wrong sign for the OR of methyloxirane at 400 nm and longer wavelengths, while
calculations using a combination of explicit and implicit solvent models (Figure 2.1 B) correctly
predict the sign of the OR at all wavelengths. Interestingly, in the water-methyloxirane system
(Figure 2.1 B), the OR of the pure solvent shell (water + COSMO without the chiral solute) is a
minor fraction of the total OR system (solute + water + COSMO) at all wavelengths. Thus, the
water-methyloxirane interactions in an aqueous methyloxirane solution constitute the major
contribution to the observed ORD.
Solvent significantly influences the OR of chiral molecules. For example, Gottarelli et al.
showed that chiral biaryls show significant variation in OR in biphenyl-type solvents 72. Based on
a statistical theory of dielectric susceptibility and optical activity of isotropic liquids the authors
described three different solvent effects on OR. First, the solvent manifests itself as a continuous
dielectric medium characterized by its refractive index. Second, the induction of chiral
conformations in the neighbouring solvent molecules contributes to the OR. And third, short-
range interactions between solute and solvent influence the OR in solution. Craig and
Thirunamachandran showed that intermolecular interactions between chiral and achiral molecules
results in the modification of the optical rotatory tensor of the chiral molecule, such that it
displays changed chiroptical properties 73. Here we show that the optical response of
methyloxirane in water derives from hydrogen bonded methyloxirane-water adduct and not from
methyloxirane alone. Goldsmith et. al. showed that in order to compute the correct optical
rotation of pantolactone, it is important to compute the optical rotation of the pantolactone dimer,
30
which exists in equilibrium with the monomer in solution, and the response originates from the
dimer adduct and not just the individual monomer 49. Thus, we emphasize that it is important to
include explicit solvent models in order to describe solvation effects on optical rotation properly,
because the optical response may arise from the solute-solvent adduct (as in the case of aqueous
solution methyloxirane), which is a very different chemical species than the chiral solute alone.
Figure 2.2 Radial distribution function of hydrogen atoms for water around themethyloxirane oxygen atom.
Figure 2.2 shows the calculated radial distribution function of the hydrogen atoms of
water molecules around the methyloxirane oxygen atom. This function shows a well-defined
minimum at 0.25 nm. We included explicit solvent molecules within a cut-off distance of 0.25 nm
from the oxygen atom of methyloxirane to model the first solvation shell. Subsequently, more
water molecules were added to our calculations with cut-off distances of 0.35 and 0.40 nm. Thus,
we also computed OR values with different numbers of water molecules in the quantum
mechanical analysis. The total number of water molecules within the cut-off distances was 1-2
(0.25 nm), 3-5 (0.35 nm) and 6-9 (0.40 nm).
31
Figure 2.3 shows the variations of the computed OR of (S)-methyloxirane as a function of
the number of solvent molecules. These ORD spectra were calculated using the BP86 functional
and an aug-cc-pVDZ basis set. Apart from the OR at 365 nm, we found no significant variation in
the computed ORD of the aqueous methyloxirane solution with the number of solvent molecules
included. The OR at 365 nm approaches the experimental value as more water molecules are
included in the calculation up to the maximum cut-off distance of 0.40 nm. We also emphasize
that the computed average OR with explicit water molecules within a cut-off distance of 0.40 nm
from the methyloxirane oxygen atom, with and without the implicit solvent model (COSMO) at
589 nm, [α]D , was 8.3 and 7.3, respectively.
Figure 2.3 Optical rotatory dispersion of (S)-methyloxirane in water computed withan increasing number of solvent molecules. Calculations used the TD-DFT/BP86 functionaland aug-cc-pVDZ basis sets. The conductor-like screening model (COSMO) was used as the
implicit solvent model. The error bars were calculated using the blocking method 71.
Previous theoretical studies suggested that TD-DFT methods with the B3LYP functional
and (at least) an aug-cc-pVDZ basis set are required to make reliable OR predictions 74. Thus, we
also compared the results of our OR calculations with different combinations of BP86/B3LYP
correlation-exchange functionals and aug-cc-pVDZ /aug-cc-pVTZ basis sets. We included only
the first solvation shell around methyloxirane in the comparison, as we found no significant
32
change (except at 365 nm) in the computed ORD as a function of the number of solvent
molecules included (see Figure 2.3).
Figure 2.4 Variation in the dipole-length and dipole-velocity form of calculatedoptical rotations using TD-DFT/BP86 correlation-exchange functional. The specific rotation
was averaged for 1700 structure snapshots from a molecular dynamic simulation togenerate the ORD of (S)-methyloxirane in water. The conductor-like screening model
(COSMO) was used as the implicit solvent model. The vertical bars show the error estimateof the average optical rotation calculated using the blocking method 71.
33
Figure 2.4 shows the computed ORD of (S)-methyloxirane with the first hydration shell,
which includes explicit solvent molecules within a cut-off distance of 0.25 nm from
methyloxirane oxygen atom. The dipole-length (L) and dipole-velocity (V) forms (see Method
section for details) of the TD-DFT results with BP86/aug-cc-pVDZ (or aug-cc-pVTZ) are very
similar. Thus we expect the L and V forms of the results with B3LYP/aug-cc-pVDZ (or aug-cc-
pVTZ) will also be very similar.
Figure 2.5 Computed optical rotatory dispersion of (S)-methyloxirane with the firstexplicit hydration shell. Calculations used different combinations of TD-DFT/BP86/B3LYP
functionals and aug-cc-pVDZ/aug-cc-pVTZ basis sets as described in the text. Theconductor-like screening model (COSMO) was used as the implicit solvent model. The bars
indicate error estimates computed using the blocking method 71.
Figure 2.5 shows that the computed ORD spectra of (S)-methyloxirane with the
BP86/aug-cc-pVDZ (or aug-cc-pVTZ) and B3LYP/aug-cc-pVDZ (or aug-cc-pVTZ) analysis are
very similar, especially at wavelengths longer than 400 nm We emphasize that the L form of TD-
DFT, as implemented in Turbomole5.6 with the B3LYP exchange-correlation functional, was
used to compute the OR. However, the L and V forms of the TD-DFT results with BP86/aug-cc-
pVDZ (or aug-cc-pVTZ) are very similar (see Figure 2.4). Thus, we expect the computed L- and
34
V- based values with B3LYP/aug-cc-pVDZ (or aug-cc-pVTZ) also to be very similar. These
results show that the computed ORD of (S)-methyloxirane with the BP86/aug-cc-pVDZ (or aug-
cc-pVTZ) and B3LYP/aug-cc-pVDZ (or aug-cc-pVTZ) analysis are very similar, especially at
wavelengths longer than 400 nm.
Figure 2.6 Average optical rotation of (S)-methyloxirane at 589 nm, [α]D, as afunction of the number of MD simulation snapshots. Calculations used the TD-DFT/BP86functional and aug-cc-pVDZ basis set. A combination of explicit water molecules (within
0.40 nm of the methyloxirane oxygen atoms) and an implicit solvent model (COSMO) wereused in the calculations. The error estimate of the average optical rotation was calculated
using the blocking method 71.
Figure 2.6 shows the average computed [α]D value as a function of the number of MD
simulation snapshots. Each structure had explicit water molecules within a cut-off distance of
0.40 nm from methyloxirane oxygen atom with a dielectric continuum description based on the
COSMO model with the water dielectric constant of 78.4. The average [α]D value converged to
+8.4 as the number of snapshots were increased.
35
Figure 2.7 Distribution of the optical rotation of (S)-methyloxirane at 589 nm, [α]D,as a function of water molecule positions defined by the angle τ, in the first hydration shell.
The insets show structures with water molecules on the same or opposite sides from themethyl group of methyloxirane, defined as the syn- or anti-configurations, respectively.
Water on the opposite side dominated the explicit solvent contribution to [α]D.
In order to understand the physical origin of the positive OR for methyloxirane in water,
we computed the OR at 589 nm and displayed [α]D as a function of the angular position of the
water molecules, defined by the angle τ (see inset in Figure 2.7), in the first hydration shell (there
is only a minor dependence of the computed [α]D on the number of solvent molecules, see Figure
2.3). Structures with water molecules adjacent to or opposite to the methyl group of
methyloxirane are defined as syn- or anti-configurations, respectively (see insets in Figure 2.7).
Figure 2.7 shows the τ histogram for 14,000 MD structure-snapshots. The [α]D values were
calculated with the BP86 functional and the aug-cc-pVTZ basis set. The distribution shows that
the syn-configurations make a nearly equal number of positive and negative [α]D contributions,
while the anti-configurations make a predominantly positive contribution to [α]D contributions.
Based on the MD simulations, therefore, the positive [α]D value for methyloxirane in water arises
36
from the greater number of water anti-configurations with positive [α]D. It is also important to
note that the average [α]D values for 14,000 and 1,700 structure snapshots are +10.4 and +9.8,
respectively.
Su and Xu recently showed that for methyloxirane-(water)2 ternary cluster in the gas
phase, the anti conformer is more populated than the syn conformer 75. In contrast, the syn
conformer is more populated for the methyloxirane-water binary cluster in the gas phase 76. The
authors suggested that the secondary hydrogen-bonding of the methyl group and water, which
results in the syn conformational preference for methyloxirane-water binary cluster, do not
contribute to the stability of the methyloxirane-(water)2 ternary cluster. For the ternary cluster,
maximizing the interactions between the second water and methyloxirane results in the
conformational preference of anti conformer, which is consistent with our theoretical prediction.
Following our OR calculation of methyloxirane aqueous solution, Xu and coworkers also studied
the solvation of methyloxirane in water using VCD, OR and computer simulations 48. Those
authors concluded that the methyloxirane-water binary complex is the dominating species in
aqueous solution at room temperature, which is also consistent with our prediction 46.
2.4 Conclusions
Molecular dynamics simulations and time-dependent density functional theory (TD-DFT)
methods were used to determine the solvent dependence of the optical rotatory dispersion (ORD)
spectrum for methyloxirane in water. The off-resonance ORD spectrum was calculated using both
explicit and conductor-like screening solvent models (COSMO). TD-DFT ORD calculations at
the BP86/aug-cc-pVDZ (or aug-cc-pVTZ) and B3LYP/aug-cc-pVDZ (or aug-cc-pVTZ) levels
using explicit water molecules reveal excellent agreement between experiment and theory in both
sign and magnitude; the COSMO model alone does not adequately describe the influence of
solvent on the ORD spectrum of methyloxirane. The positive OR at 589 nm, i.e. the [α]D value, is
attributed to the greater number of MD snapshots with water molecules on the side of the
methyloxirane ring opposite to the methyl group. We conclude that including explicit solute-
solvent interactions is essential to describe the influence of the solvent on the OR of
37
methyloxirane in water and that MD simulations provide a suitable means to analyze and predict
chiroptical solvation effects.
2.5 Materials and methods
2.5.1 Experimental Procedure
Optical rotation (α) was measured with an AUTOPOL IV digital polarimeter. Optical
rotation of (S)-methyloxirane (Alfa Aesar) in water and benzene at 0.05 g/mL was measured at
six different wavelengths. The specific rotation at a given wavelength [α]λ was calculated using:
€
α[ ]λ =αVml
α is the optical rotation in degrees, V is the volume (ml) containing a mass m (g) of the
optically active substance, and l is the path length (dm).
2.5.2 Molecular dynamics simulation setup and procedure
Molecular dynamics (MD) simulations of (S) and (R)-methyloxirane oxide in a pre-
equilibrated box of 2175 water molecules were done in a NPT ensemble using Gromacs 3.1.4. 77
In all simulations a leapfrog integrator was used with a 2-fs time step 78. All bonds were
constrained to their equilibrium value with the SETTLE algorithm 79 for water and the LINCS
algorithm 80 for all other bonds. In all simulations, a DFT/B3LYP/6-311G** optimized fixed
geometry of (S)-methyloxirane was used. A twin-range cutoff was used for the Lennard-Jones
interactions, with interactions within 0.9 nm evaluated every step and interactions between 0.9
and 1.4 nm evaluated every 5 steps. A neighbor list was used and updated every five steps. For
electrostatic interactions, a reaction field with a Coulomb cutoff of 1.4 nm was used with
dielectric constants of 78.4 for water beyond the cutoff. The pressure was held at 1 bar using the
weak-coupling scheme with a coupling constant of 1.0 ps and an isothermal compressibility of
4.5 ×10-5 bar-1. Each component of the system (i.e. (S)-methyloxirane and water) was coupled
separately to a temperature bath at 300 K, using the Berendsen thermostat 81, with a coupling
38
constant of 0.1 ps. The SPC water model was used 82. The OPLS-AA force field 83 was used and
partial charges on (S)-methyloxirane were calculated in Gaussian03 at the DFT/B3LYP level with
the 6-31G* basis set and charge partitioning using the chelpg method 84. Simulations in water
were carried out for 40 ns.
2.5.3 Computation of optical rotation
Structures from the MD trajectories were used for optical rotation (OR) calculations. The
specific rotation was averaged for 1700 structure snapshots at each wavelength to generate the
ORD spectrum of methyloxirane in water. Specific rotations for each structure were calculated
according to the equation:
€
α[ ]λ =−1.34229 ×10−4Tr ′ G ω( )[ ]ν 2
3Mω
where Tr [G (ω)] is the trace of frequency dependent electric-dipole magnetic-dipole
polarizability tensor,
€
ν (=λ-1=ω/2πc) is the radiation wavenumber, and M is the combined molar
mass of (S)-methyloxirane and the number of solvent molecules in each snapshot. Thus, by
including the mass of the water molecules we are properly normalizing [α]λ with respect to the
total number of water molecues. [α]λ, is an intensive property independent of the number of
solvent molecules. The dipole-length (L) and dipole-velocity (V) formulation of time dependent
density functional response theory (TD-DFT) as implemented in Turbomole5.6 85 with B3LYP
and BP86 exchange-correlation functional, respectively, was used for the calculation of [G’ (ω)].
39
3 Contribution of a solute’s chiral solvent imprint to opticalrotation
3.1 Overview
Solvent or solute dissymmetry? Dissymmetric solvent ordering around a chiral molecule
(see Figure) in solution contributes to the chiroptical signature. Indeed, the solvent can dominate
the chiroptical response, as shown for (S)-methyloxirane in benzene.
3.2 Introduction
A long-standing challenge in molecular stereochemistry is to assess the “chiral imprint”
of a chiral solute on the surrounding solvent. The solute’s influence on ordering the solvation
sphere should contribute to the optical rotatory dispersion (ORD). The magnitude of this
contribution, however, has never been assessed. We now show that for (S)-methyloxirane in
benzene, the chiral imprint in the solvent sphere dominates the optical rotation (OR). To the best
of our knowledge, this is the first evidence in support of a chiroptical property dominated by the
dissymmetry induced in the solvent.
The observed specific OR angles and ORD of chiral molecules in solution are well
known to be strongly influenced by solvent-solute interactions. For example, (S)-methyloxirane
has a positive OR in water and a negative OR in benzene 45. Thus, theoretical modelling to
understand both the sign and magnitude of OR is of interest. Access to experimental gas and
40
solution phase OR data 61 and to modern linear-response OR calculations 11,13,25,33,34,49,62-67 provide
the tools needed to dissect solute and solvent contributions to OR. In the preceding chapter, we
showed that water-methyloxirane interactions in an aqueous solution dominate the observed ORD46; in contrast, for methyloxirane in benzene, we show here that the chiral solvent ordering is the
dissymmetry that dominates the ORD.
The solvent dependence of OR for chiral molecules has been computed recently using
coupled-cluster (CC) and time dependent density functional theory (TD-DFT) using implicit
continuum solvent methods 9. Kongested et al. used CC combined with a continuum solvent
description to calculate the influence of solvent on the OR of (S)-methyloxirane 68. The authors
concluded that continuum models: (a) do not reproduce the experimentally observed solvent
shifts of the ORD spectra as a function of solvent; and (b) cannot describe the contribution of the
chiral solvent structure induced by the chiral solute to the observed OR. Explicit solvent models
capture solvent/sign anomalies in the OR and allow attribution of contributions to OR arising
from a solute’s chiral imprint on its environment as shown below.
41
3.3 Results and Discussion
Figure 3.1 Optical rotatory dispersion (ORD) of (S) ()- and (R) ()-methyloxirane-benzene clusters (shown in the MC structure snapshot), and the solventimprint () computed using explicit solvent models. Calculations used TD-DFT/BP86
functional and SVP basis set; and an implicit solvent () based on the COSMO model. Theerror bars are calculated using the blocking method 71.
Figure 3.1 shows the computed ORD spectra of (S)- and (R)-methyloxirane in benzene
using explicit and implicit solvent models. The ORD spectra were calculated using the BP86
functional with the SVP basis set. Calculations using a dielectric continuum based on the
COSMO model 69 (an implicit solvent model) with a benzene dielectric constant of 2.0 incorrectly
predict the sign of the OR approaching resonance from long wavelengths. Explicit solvent,
however, correctly predicts the sign of the OR at these wavelengths.
The computed ORD spectra of (S)- and (R)-methyloxirane based on explicit solvent
models are related by a simple reversal of sign, as expected. Interestingly, in the methyloxirane-
benzene system, the OR of the solvent imprint (benzene cluster without the chiral solute) is
comparable to the total OR of the system (solute + benzene) at all wavelengths (Figure 3.1).
Thus, the chiral solvent ordering of benzene, or the chiral imprint, dominates the ORD. Chiral
solutes are known to induce chiral solvent ordering. Fidler et al., for example, showed that
42
dissymmetric solvent organization around a chiral solute accounts for 10-20% of the total circular
dichroism intensity attributable to an optically active chromophore 50,86. Our ORD calculations for
methyloxirane in benzene attribute the chiroptical signature to the dissymmetric benzene cluster
around the methyloxirane. Morimoto et al. recently showed that the attractive interactions
between benzene rings results in the formation of a cyclic trimeric dissymmetric benzene cluster
in solution, which is reminiscent of the assembles seen in our MC simulations 87.
Computed OR values are very sensitive to molecular conformation 33,34. Thus, the
difference in the computed and experimental OR values (Figure 3.1) might arise from the
approximations in the description of molecular interactions in the MC simulation of
methyloxirane in benzene arising from the force field limitations as well as approximations in the
quantum mechanical calculations.
43
Figure 3.2 Optical rotatory dispersion (ORD) of (S)-methyloxirane in benzene ()and the computed ORD of the chiral solvent imprint (;;;). Calculations used varied
TD-DFT/BP86/BLYP correlation-exchange functionals with RI-J and SV/SVP/aug-cc-pVDZ basis sets. The specific rotation was averaged over 1000 structure snapshots from a
Monte-Carlo simulation to generate the ORD of the chiral solvent structure.
The ORD spectra of the chiral solvent imprint were also computed using different
combinations of BP86/BLYP correlation-exchange functionals and SV/SVP/aug-cc-pVDZ basis
sets. We found no significant variation in the computed ORD spectra with the choice of
functional/basis set. Figure 3.2 shows that the computed ORD spectra of the chiral solvent
imprint with varied correlation-exchange functionals and basis sets are very similar. Previous
theoretical studies suggested that TD-DFT methods with the B3LYP functional and (at least) an
aug-cc-pVDZ basis set are required to produce reliable gas phase OR predictions 74. We
emphasize that using a non-hybrid DFT functional, such as BP86/BLYP, permits use of the RI-J
approximation implemented in Turbomole5.6 to reduce the computational time by six orders of
magnitude compared to calculations with hybrid functionals such as B3LYP; this is especially
important for performing 20,000 OR calculations of benzene-methyloxirane clusters (with 106-
130 atoms) using varied functionals and basis sets. Ensemble averaged calculation of OR for
chiral molecules in solution gives similar results with pure and hybrid functionals, as previously
44
shown for ORD calculations of methyloxirane in aqueous solution 46. Recently, Hassey et al. used
single-molecule spectroscopy to show that the chiroptical response of molecules spans a range of
large positive and negative values, and hence suggested that in the solution phase, the measured
chiroptical response represents an ensemble average of orientations and solvent interactions 60.
Figure 3.3 Optical rotatory dispersion of ethylene oxide in benzene computed usingexplicit solvent model. Calculations used TD-DFT/BP86 correlation-exchange functionals
with RI-J and aug-cc-pVDZ basis set. The specific rotation was averaged over 1000structure snapshots from a Monte-Carlo simulation to generate the ORD of ethylene oxide
and (S)-methyloxirane () in benzene.
In order to show that the predicted chiral solvent structure in methyloxirane-benzene
solution is not an artifact of the methodology, we exemplify it by correctly predicting an average
OR value close to zero for an achiral ethylene oxide-benzene solution. Figure 3.3 shows the OR
of an achiral ethylene oxide-benzene solution. The ORD was calculated using MC simulation and
TD-DFT (with BP86/aug-cc-pVDZ), as described above for the methyloxirane-benzene system.
Each ethylene oxide-benzene structure snapshot from the MC simulation is dissymmetric, with a
nonzero contribution to the OR: the ensemble averaged OR value, however, is close to zero, as
expected.
45
Figure 3.4 Optical rotatory dispersion of (S)-methyloxirane in alkylbenzenes.
In order to probe methyloxirane’s chiral solvent imprint in solutions of benzene
derivatives, we measured the ORD of (S)-methyloxirane in alklybenzenes (Figure 3.4). Figure 3.4
shows that in methyloxirane-alkylbenzene systems, the magnitude of OR in solution decreases as:
Benzene > Toluene > ortho-Xylene > meta-Xylene > 1,2,4 trimethylbenzene > para-Xylene.
Thus, increasing the number of alkyl groups in benzene decreases the OR value of methyloxirane
in alkylbenzenes. The intermolecular steric hindrance between the methyl groups of
alkylbenzenes could decrease the number of solvents in the chiral solvent structure around
methyloxirane, and hence decrease the chiroptical response originating from the chiral solvent
imprint.
3.4 Conclusions
Our results indicate that the contribution to OR of a dissymmetric solvent imprint can
exceed the OR contribution of the solute itself. Implicit solvent models are not sufficient to
describe the imprint effects because they lack explicit inclusion of the solvent electronic structure.
A judicious choice of solvent modelling is essential to describe the chiroptical signature of
molecules in solution.
46
3.5 Materials and Methods
In our study, Monte Carlo (MC) simulation of solute and solvent combined with TD-DFT
methods were used to compute the OR of (S)- and (R)-methyloxirane. Thus, the off-resonance
ORD of methyloxirane in benzene was calculated using an explicit solvent model. MC
simulations of (S)- and (R)-methyloxirane in an equilibrated box of benzene were performed in a
NPT ensemble, using BOSS 88. The all-atom OPLS-AA force-field 83was used in the MC
simulations. OR calculations were performed using TD-DFT implemented in Turbomole5.6 85
with different combinations of the BP86/BLYP correlation-exchange functionals and
SV/SVP/aug-cc-pVDZ basis sets at four wavelengths. All calculations were performed with the
resolution of identity approximation (RI-J) 89. Grimme showed that accurate TD-DFT predictions
of frequency dependent OR for large molecules can be achieved efficiently with the RI-J
approximation 90; structures used in the TD-DFT analysis were taken from the MC simulations.
Each structure had benzene molecules within a cut-off distance of 0.5 nm from the center-of-mass
of methyloxirane. The total number of benzene molecules within the cut-off distance was 8-10.
The specific rotation was averaged over an ensemble of 1,000 structures at each wavelength to
generate the ORD of (S)- and (R)-methyloxirane in benzene. The error estimate of the average
OR was calculated using a renormalization group blocking method 71.
3.5.1 Monte Carlo simulation setup and procedure
Monte Carlo (MC) simulations of (S)- and (R)-methyloxirane in a pre-equilibrated box of
500 benzene molecules were done using BOSS. Simulations were done with a constant number of
molecules at 25° and 1 atm (NPT ensemble) with the Metropolis algorithm. Calculations were
performed with the periodic boundary condition, and long-range electrostatic interactions were
evaluated by the Ewald method. The OPLS-AA force field with flexible solute and solvent
geometries were used in the simulations. AM1 91 based CM1A 92partial charges scaled by 1.14 for
the solute and solvent were used in the MC simulations. A more detailed description of the MC
move and the atomic charge partitioning scheme can be found in 88.
47
3.5.2 Calculation of optical rotation
Structures from the MC trajectories were used for optical rotation (OR) calculations.
Each structure had benzene molecules within a cut-off distance of 0.5 nm from the center-of-mass
of methyloxirane. The total number of benzene molecules within the cut-off distance was 8-10.
The specific rotation was averaged for 1000 structure snapshots at each wavelength to generate
the ORD spectrum of (S)- and (R)-methyloxirane in benzene. Specific rotations for each structure
were calculated according to the equation:
€
α[ ]λ =−1.34229 ×10−4Tr ′ G ω( )[ ]ν 2
3Mω
where Tr [G (ω)] is the trace of frequency dependent electric-dipole magnetic-dipole
polarizability tensor,
€
ν (=λ-1=ω/2πc) is the radiation wavenumber, and M is the combined molar
mass of (S)-methyloxirane and the number of solvent molecules in each snapshot. Thus, by
including the mass of the water molecules we are properly normalizing [α]λ with respect to the
total number of water molecues. [α]λ, is an intensive property independent of the number of
solvent molecules. The dipole-length (L) and dipole-velocity (V) formulation of time dependent
density functional response theory (TD-DFT) as implemented in Turbomole5.6, with B3LYP and
BP86 exchange-correlation functional, respectively, was used for the calculation of [G’ (ω)].
48
4 Characterizing aqueous solution conformations of a peptidebackbone using Raman optical activity computation
1.1 Overview
Mounting spectroscopic evidence indicates that alanine predominantly adopts extended
polyproline II (PPII) conformations in short polypeptides. Here we analyze Raman optical
activity (ROA) spectra of N-acetylalanine-N′-methylamide (Ala dipeptide) in H2O and D2O
using density functional theory on Monte Carlo (MC) sampled geometries in order to examine the
propensity of Ala dipeptide to adopt compact right- (αR) and left-handed (αL) helical
conformations. The computed ROA spectra based on MC sampled αR and PPII peptide
conformations contain all the key spectral features found in the measured spectra. However, there
is no significant similarity between the measured and computed ROA spectra based on the αL and
β conformations sampled by the MC methods. This analysis suggests that Ala dipeptide in water
populates αR and PPII conformations but no substantial population of αL or β structures, despite
sampling αL and β structures in our MC simulations. Thus, ROA spectra combined with the
theoretical analysis allow us to determine the dominant populated structures. Including explicit
solute-solvent interactions in the theoretical analysis is essential for the success of this approach.
49
4.2 Introduction
Conformational analysis of alanine containing polypeptides suggests that the polyproline
II (PPII) is the major backbone conformation in aqueous solution. For example, Kallenbach and
coworkers recently showed that alanine containing peptides possess over 90% extended
conformations (i.e. PPII and β structures) 93. The authors, however, did not rule out the possibility
of the presence of compact (αR, αL) conformations of alanine in aqueous solution, and suggested
that such compact structures are present, albeit not dominant. Here, we use Raman optical activity
(ROA) to examine the propensity of Ala dipeptide, which contains a peptide backbone with a
single alanine, to adopt compact structures like the right- (αR) and left-handed (αL) helical
conformations in aqueous solution. We find that Ala dipeptide adopts both the extended PPII and
compact αR conformations, which are the dominant conformations in aqueous solution.
Experimental and theoretical studies of polypeptides 94 suggest that short polypeptides
can adopt secondary structures in aqueous solution. For example, the hepta-alanine polypeptide
Ac-X2A7O2-NH2 (XAO, X and O denote diaminobutyric acid and ornithine, respectively) in
aqueous solution was suggested to be an ensemble of β-turn, β-strand and PPII conformations 95-
97. A combination of Fourier transform infrared (FTIR), vibrational circular dichroism (VCD),
electronic circular dichroism (ECD), Raman, and NMR spectroscopic studies probed shorter
alanine-based cationic peptides (e.g., trialanine, tetraalanine, and H-AAKA-OH). These studies
indicated that these shorter peptides have a higher fraction of PPII than β-strand or αR
conformations 98. ROA studies of a series of A2-A5 peptides suggest that the PPII population
increases with the number of alanines 99. Taken together, these results provide compelling
evidence that alanine containing peptides in water populates PPII conformations. Molecular
dynamics (MD) simulations of alanine containing peptides in water indicate the sampling of αR
motifs, in addition to the PPII and β conformations 100. Graf’s combined MD and NMR studies,
however, show that there is no detectable population of the αR conformation in aqueous solutions
of A3-A7 peptides and that these short polyalanine peptides in water populate the PPII
50
conformation almost exclusively 101. Following Graf’s conformational analysis of A3-A7 peptides,
Hummer and co-worker studied polyalanine peptide (A5) conformations in aqueous solution using
MD simulations in order to address the question of whether the commonly used force fields
overpopulate the α-helical conformations of polyalanine peptides 102. They concluded that the
NMR data are consistent with force fields that give a small α-helical population of polyalanine
peptide and do not require exclusive formation of the PPII structure. Our combined MC and ROA
studies of Ala dipeptide show that the shortest alanine-containing peptide exists as a mixture of
PPII and αR conformations in aqueous solution.
Chiroptical properties are sensitive to molecular geometry and to solvation 33,46,47. ROA is
a chiroptical spectroscopy that measures the difference in the intensity of Raman scattered right-
and left-circularly polarized light, and is utilized to characterize aqueous solution conformations
of the peptide backbone in polypeptides and proteins 42,103. ROA studies of polypeptides suggest
that water promotes structural fluctuations between αR, PPII, and β conformations 104. The ROA
spectrum is the superposition of spectra arising from all conformations of polypeptides in solution42, and thus, ROA analysis can be used to characterize solution conformations of peptide units in
polypeptides.
The theoretical framework for ROA is well known 15,65,105. Accurate time dependent DFT
(TD-DFT) calculations of ROA are accessible using the resolution of identity approximation (RI-
J) 17,90,106 and the BLYP functional with the rDPS basis set 107. ROA spectra are predicted to be
very sensitive to both molecular conformation 14,108-111 and solvation, which were studied
previously using continuum solvent models 112. Herrmann et al. and Pecul et al. analyzed ROA
spectra of polypeptides using a single conformation in the gas phase 113 and in an implicit solvent112, respectively. Since ROA studies of polypeptides indicate that water facilitates conformational
fluctuations 104, modeling polypeptide conformations in explicit solvent, and subsequently
utilizing modelled structures to compute ROA spectra, may improve the effectiveness of ROA
simulations for polypeptides.
Despite extensive experimental and theoretical study, there is no consensus on Ala
dipeptide’s structure in aqueous solution. NMR studies are consistent with both: (1) an equal
51
population of PPII and αR conformations 39,114 and (2) a dominant PPII conformation 37,38. The
later composition is supported by two-dimensional (2D) IR spectroscopy 40. However, Raman
spectroscopy suggests that C7eq, PPII, and αR conformations all exist in aqueous solution 41. MC
and MD simulations of Ala dipeptide indicate either (1) PPII 100,115,116 and αR structures dominate
117-120 or (2) a comparable population of PPII and αR structures dominates 121-123, depending on the
force field used. Thus, a debate remains as to whether PPII is the dominant conformation of Ala
dipeptide in aqueous solution. The significant variation in the description of Ala dipeptide
conformations warrants further analysis, and suggests the utility of linking chiroptical simulations
with experimental studies. Our ROA simulations combined with experimental data show that Ala
dipeptide populates both the αR and PPII conformations in aqueous solution, and hence, it is
erroneous to ascribe all experimental signal to one dominant conformation, namely the PPII.
We present TD-DFT calculations of back-scattered circular polarization (SCP) ROA
based on MC simulation of Ala dipeptide in aqueous solution. Simulated Raman and ROA
spectra constructed using the collection of H2O-Ala clusters (see methods section for more
details) with αR and PPII conformations of Ala dipeptide are consistent with experiments.
However, there is no significant similarity between the measured and computed Raman or ROA
spectra for the set of H2O-Ala clusters with αR and β conformations of Ala dipeptide. Thus, these
calculations facilitate assignment of the observed ROA spectral features to corresponding
secondary structures that characterize the populated conformations of the peptide in aqueous
solution.
Previous ROA analysis using four Ala dipeptide conformations (β, αR, αL, PPII), each
hydrogen bonded to four water molecules and embedded in an implicit solvent model, showed
that the computed spectra of the PPII structure best explained the experimental ROA spectrum 124.
It was also suggested that αR, αL, and “other conformations” of Ala dipeptide may be present in
aqueous solution 124. Those ROA calculations were performed using restricted Hartree-Fock
theory with a split valence plus basis set, and neglected the effects of explicit water on the
chiroptical response tensor. Pecul et al. showed recently that solvent influences on the chiroptical
52
response tensor should be included when computing solvent effects on ROA 112. Jalkanen et al.
recently computed the ROA spectra of a single (H2O)4-Ala dipeptide cluster, with the PPII
conformation of the dipeptide, embedded in implicit solvent models using the B3PW91/B3LYP
exchange correlation functionals with the aug-cc-pVDZ basis set 125. Those simulated ROA
spectra 124-126 were in qualitative agreement with the experimental spectra, which provided the
impetus for computing the ROA spectrum with improved accuracy for aqueous Ala dipeptide
solutions using geometry sampling as an explicit part of the calculation. We now show that
including explicit solute-solvent interactions is essential for computing the ROA of Ala dipeptide
in water, and that TD-DFT computation (with the RI-J approximation and rDPS basis set) using
MC sampled geometries in aqueous solution provides a suitable means to analyze the ROA
spectra of peptides and determine the dominant populated conformations of peptides in solution.
4.3 Results
4.3.1 Low-energy conformations of Ala dipeptide in water
Figure 4.1 shows the difference in free energy (ΔG) of Ala dipeptide conformations in
water computed using MC simulations. The αR, αL, β, and PPII conformational regions are
populated by the dipeptide (Figure 4.1B), in agreement with previous molecular mechanics force
field simulations 116,121. Figure 4.1C shows that the computed distribution of φ and ψ dihedral
angles (for Ala dipeptide conformations with ΔG < 0) also resembles the φ, ψ distribution of
amino acid residues that are not found in either canonical helix or sheet secondary structures in
protein X-ray crystal structures 127. Ala dipeptide explores both the right- (αR) and left- (αL)
handed helical conformations in agreement with previous MD and MC simulation studies 68,116,121.
Thus, our MC simulations of aqueous Ala dipeptide indicate that the α-helical conformations are
stabilized by solvation.
53
Figure 4.1 . A. Ball and stick model for the N-acetylalanine-N′-methylamide (Aladipeptide). The peptide backbone structure in Ala dipeptide is defined by φ and ψ dihedralangles. B. Free energy differences of Ala dipeptide conformations in water computed using
Monte Carlo simulations. αR, αL, β, and PPII conformational regions are shown on theRamachandran map. Figure 4.1C shows the computed φ and ψ distribution (yellow)
resembles the empirically derived φ, ψ distribution of amino acid residues (black) not ineither canonical helix or sheet secondary structures in protein X-ray crystal structures 127.
54
4.3.2 Structures of H2O-Ala dipeptide clusters
H2O-Ala dipeptide clusters from the MC simulations, corresponding to the low-energy
regions (αR, αL, β, and PPII; Figure 4.1B) of the Ramachandran map, were optimized using
quantum mechanical energy minimization (see computational method section for details). Figure
4.2 shows the Ramachandran map for Ala dipeptide structures taken from the MC simulations
prior to geometry optimization. Each φ, ψ pair (black) represents a cluster of H2O-Ala dipeptide
clusters that have the same peptide backbone dihedral angles with different water geometries. The
φ, ψ values correspond to peptide geometries from low-energy regions 1, 2, and 3 of the
Ramchandran map (Figure 4.2A). The φ, ψ values for H2O-Ala dipeptide structures, and the
number of structures for each φ, ψ pair, appear in Table 1 (360 total structures). Figure 4.2B
shows a wider distribution of φ, ψ values for the structures of H2O-Ala dipeptide clusters,
optimized using quantum mechanical energy minimization. The peptide backbone dihedral angles
changes upon geometry optimization. However, each peptide conformation, before and after
geometry optimization, occupies the same region of the Ramachandran map. Following geometry
optimization of the H2O-Ala dipeptide cluster, the structures were used for computing ROA and
Raman spectra using TD-DFT (see method section for details).
55
Figure 4.2 Ramachandran map of φ, ψ pairs for Ala dipeptide-water clusterstructures taken from the Monte Carlo simulations. Figure 4.2A shows a collection of Ala
dipeptide-water cluster structures (black) that have the same peptide backboneconformation with different water arrangements. Figure 4.2B shows the distribution of φ, ψvalues for the alanine dipeptide-water clusters optimized using quantum mechanical energyminimization. Green arrows show that each peptide conformation, before and after energy
minimization, occupies the same region on the Ramachandran map.
56
Table 4-1 The peptide backbone dihedral angles (φ, ψ) of alanine dipeptide-watercluster structures from the Monte Carlo simulations used in the quantum mechanical
energy minimization.
φ, ψ values
(deg)
Number of structures
with explicit water
-150, 150 30
-140, 135 30
-120, 115 30
-90, 120 30
-120, 150 30
-105, 150 30
-80, 145 30
-60, 165 30
-60, 135 30
-145, 80 30
-65, -45 20
-60, -30 10
55, 65 30
57
4.3.3 ROA and Raman spectra of H2O- and D2O- Ala dipeptideclusters
Figure 4.3 shows the computed ROA (A, C) and the Raman (B, D) spectra using H2O-
Ala dipeptide clusters. The computed spectra are averaged (see discussion for details) over 30
H2O-Ala dipeptide structures from PPII (inset in Figure 4.3A) and αR (inset in Figure 4.3C)
conformational regions of the Ramachandran map. The ROA spectra computed using both the
PPII and αR conformations, taken together, contain all the key spectral features found in the
measured spectrum. For example, ROA bands (a-f in Figure 4.3A) at 395 cm-1 (a), 940 cm-1 (b),
1140 cm-1 (c), 1560 cm-1 (e, amide II), 1665 cm-1 (f, amide I), and the couplet centered at ~1300
cm-1 (d, extended amide III) are predicted in the computed spectrum using a set of Ala dipeptide
conformations with -80° ≤ φ ≤ -60° and 130° ≤ ψ ≤ 150° (blue, inset in Figure 4.3A), which is the
set of structures from the PPII conformational region on the Ramachandran map. Thus, these
ROA bands are attributed to the H2O-Ala dipeptide structures with PPII conformations. The range
of φ, ψ values (-80° ≤ φ ≤ -60° and 130° ≤ ψ ≤ 150°) for the PPII conformations of Ala dipeptide
in aqueous solution determined from our ROA analysis is consistent with the range of values (-
95° ≤ φ ≤ -45° and 95° ≤ ψ ≤ 145°) determined by 2D IR spectroscopy 40. Barron and co-workers
have shown that positive ROA bands at ~1318 cm-1 and ~1670 cm-1 characterize PPII
conformations of polypeptides 42,128, also consistent with our ROA analysis.
58
Figure 4.3 SCP backscattering ROA (A, C) and Raman (B, D) spectra of H2O-Aladipeptide clusters. The computed spectra shown in blue and red are averaged over a
collection of dipeptide conformations from PPII (inset in A) and αR (inset in C) regions ofthe Ramchandran map. The experimental spectra (green; in arbitrary units) are from
reference 126.
Figure 4.3C shows that the ROA bands (a-f) at 395 cm-1 (a), 940 cm-1 (b), 1140 cm-1 (c),
1380 cm-1 (e, Cα-H bend), 1450 cm-1 (f), and the positive-negative couplet centered at ~1300 cm-1
(d, extended amide III) are predicted in the computed spectrum using a set of Ala dipeptide
59
conformations (-50° ≤ φ ≤ -100° and -50° ≤ ψ ≤ 0°) from the αR region of the Ramachandran map
(red, inset in Figure 4.3C). Thus, these ROA bands can be attributed to the H2O-Ala dipeptide
structures with αR conformations of the dipeptide. Interestingly, the ROA spectrum computed
using the set of αR structures show a sequence of -/- bands in the frequency range of 300 cm-1 to
400 cm-1 (Figure 4.3C), consistent with the measured spectra. In contrast, the ROA spectrum
computed using the set of PPII structures show a sequence of +/- bands in the same frequency
range of 300 cm-1 to 400 cm-1 (Figure 4.3A). Thus, the difference in the signs of the predicted
ROA bands for the αR and PPII conformations suggests that the ROA bands in the frequency
range of 300 cm-1 to 400 cm-1 can be used to differentiate between the right-handed αR and left-
handed helical PPII conformations of Ala dipeptide (see discussion section for more detail). The
Raman spectra computed using the PPII (Figure 4.3B) and αR (Figure 4.3D) structures are also in
good agreement with the measured spectrum. Figures 4.3B and 4.3D show only subtle differences
in the computed Raman spectra using the PPII and αR conformations. For example, Raman bands
at ~1140 cm-1 (Figure 4.3B) and ~1540 cm-1 (Figure 4.3D) are predicted for the PPII and αR
conformations, respectively. Thus, ROA is a better probe of the secondary structure of peptides in
aqueous solution than Raman scattering experiments.
60
Figure 4.4 ROA spectra computed using Ala dipeptide-H2O cluster from the low-energy region of the Ramachandran map. The computed spectra shown are averaged over a
collection of dipeptide conformations from regions A, B, and C of the Ramchandran map(inset in A). The experimental spectrum (in arbitrary units) is from reference 126.
Figure 4.4 and 4.5 show a more detailed analysis of the dependence of the computed
ROA spectra on the φ and ψ dihedral angles of Ala dipeptide in H2O. The computed spectra
correspond to Ala dipeptide-water clusters from the low-energy regions of the Ramchandran map.
For example, Figures 4.4 A, 4.5 E and 4.5 F show the computed ROA spectra using sets of Ala
dipeptide conformations from the β, PPII and αR conformational region of the Ramchandran map
(insets in Figures 4.4 and 4.5), respectively. The computed spectra are averaged over sets of Ala
61
dipeptide conformations on 50° × 50° grids of φ and ψ. The ROA spectral features in the
computed spectra using peptide-water clusters with the PPII (Figure 4.5E), αR (Figure 4.5F) and
β (Figure 4.4A) conformations of Ala dipeptide are very different, which originate from different
peptide and water geometries of the Ala dipeptide-water clusters.
62
Figure 4.5 ROA spectra computed using Ala dipeptide-H2O cluster from the low-energy region of the Ramachandran map. The computed spectra shown are averaged over acollection of dipeptide conformations from regions D, E, F and G of the Ramchandran map
(inset in D). The experimental spectrum (in arbitrary units) is from reference 126.
63
Figure 4.6 SCP backscattering ROA (A, C) and Raman (B, D) spectra of D2O-Aladipeptide clusters. The computed spectra shown in blue and red are averaged over a
collection of dipeptide conformations from PPII (inset in A) and αR (inset in C) regions ofthe Ramchandran map. The experimental spectra (green; in arbitrary units) are from
reference 126.
Figure 4.6 shows the computed ROA (A, C) and the Raman (B, D) spectra using D2O-
Ala dipeptide clusters. The computed ROA spectra using both the PPII and αR conformations
(insets in Figure 4.6A and 4.6C) taken together contain all the key spectral features found in the
64
measured spectrum in D2O. For example, ROA bands (peaks a-h in Figure 4.6A) at 340 cm-1 (a),
395 cm-1 (b), 500 cm-1 (c), 950 cm-1 (d), 1050 cm-1 (e), 1280 cm-1 (f, extended amide III), 1440
cm-1 (g), and 1650 cm-1 (h, amide I), are predicted in the computed spectrum using the set of PPII
conformations. Similarly, ROA bands (peaks a-e in Figure 4.6C) at 340 cm-1 (a), 395 cm-1 (b),
500 cm-1 (c), 1150 cm-1 (d), and 1440 cm-1 (e) are predicted in the computed spectrum using the
set of αR conformations. Interestingly, the measured ROA spectrum of Ala dipeptide in D2O
shows a sequence of +/-/- bands in the frequency range of 300 cm-1 to 400 cm-1. In contrast, the
measured ROA spectrum in H2O (Figure 4.3) shows a sequence of -/- bands between 300 cm-1
and 400 cm-1. Thus, the ROA spectrum of Ala dipeptide in D2O has an additional positive band in
the frequency range of 300 cm-1 to 400 cm-1. The ROA spectra computed using the set of PPII
(Figure 4.6A) and αR (Figure 4.6C) structures in D2O show a sequence of +/(-) and -/(-) bands in
the frequency range of 300 cm-1 to 400 cm-1, respectively. The sign in the parenthesis, (-),
indicates the common negative ROA band predicted in the frequency range of 300 cm-1 to 400
cm-1 for the PPII and αR conformations. Thus, the computed ROA spectra based on PPII and αR
dipeptide conformations taken together contain the +/(-)/- spectral feature found in the frequency
range of 300 cm-1 to 400 cm-1 of the measured spectrum in D2O. The Raman spectra computed
using the PPII (Figure 4.6B) and αR (Figure 4.6D) structures are also in good agreement with the
measured spectrum in D2O.
65
Figure 4.7 ROA spectra computed using Ala dipeptide-D2O cluster from the low-energy region of the Ramachandran map. The computed spectra shown are averaged over a
collection of dipeptide conformations from regions A, B and C of the Ramchandran map(inset in A). The experimental spectrum (in arbitrary units) is from reference 126.
66
Figure 4.8 ROA spectra computed using Ala dipeptide-D2O cluster from the low-energy region of the Ramachandran map. The computed spectra shown are averaged over acollection of dipeptide conformations from regions D, E, F and G of the Ramchandran map
(inset in D). The experimental spectrum (in arbitrary units) is from reference 126.
67
Figure 4.7 and 4.8 show a more detailed analysis of the dependence of the computed
ROA spectra on the φ and ψ dihedral angles of Ala dipeptide in D2O. The computed spectra
correspond to Ala dipeptide-water clusters from the low-energy regions of the Ramchandran map.
The ROA spectral features in the computed spectra using peptide-water clusters with the PPII
(Figure 4.8E), αR (Figure 4.8F) and β (Figure 4.7A) conformations of Ala dipeptide in aqueous
solution are very different. Thus, similar to the H2O results, different ROA spectra originate from
very different peptide and water geometries of the peptide-water clusters.
68
Figure 4.9 SCP backscattering ROA (A, C) and Raman (B, D) spectra of Aladipeptide in H2O. The computed spectra shown in orange and pink are averaged over a
collection of dipeptide conformations from αL (inset in A) and β (inset in C) regions of theRamchandran map. The experimental spectrum (in arbitrary units) is from reference 126.
69
Figure 4.10 SCP backscattering ROA (A, C) and Raman (B, D) spectra of Aladipeptide in D2O. The computed spectra shown in orange and pink are averaged over a
collection of dipeptide conformations from αL (inset in A) and β (inset in C) regions of theRamchandran map. The experimental spectrum (in arbitrary units) is from reference 126.
Figures 4.9 and 4.10 show that there is no significant similarity between the measured
and computed ROA and Raman spectra using the αL (with 45° ≤ φ ≤ 65° and 25° ≤ ψ ≤ 55°) and
β (with -180° ≤ φ ≤ -125° and 150° ≤ ψ ≤ 180°) conformations of H2O-Ala dipeptide and D2O-
70
Ala dipeptide clusters. Thus, our ROA analysis suggests that Ala dipeptide in water populates αR
and PPII conformations without substantial αL and β populations.
Figure 4.11 ROA (A, C) and Raman (B, D) scattering cross sections contributions ofAla dipeptide (red), water (blue), and peptide-water interactions (black) to the total ROA
and Raman scattering cross sections of Ala dipeptide-water clusters (green). Thesecomputed spectra are averaged over a collection of dipeptide conformations from PPII (A,
B) and αR (C, D) regions of the Ramachandran map.
Figure 4.11 shows the relative contributions of the peptide, water and peptide-water
coupling to the ROA (A, C) and Raman (B, D) intensities computed using the αR (A, B) and PPII
71
(C, D) conformations of Ala dipeptide. The ROA and Raman scattering cross sections are
influenced by water in the low frequency range of 300 cm-1-1100 cm-1 and for the amide I and II
bands. However, water makes no contribution to the Raman and ROA intensities from 1200 cm-1
to 1500 cm-1. Kapitán et al. recently showed that ROA bands in the 800 cm-1-1600 cm-1 range for
the proline zwitterion in aqueous solution are not influenced by water 129, which is consistent with
our ROA analysis that also predicts the presence of ROA bands (1200 cm-1-1500 cm-1) for Ala
dipeptide in aqueous solution that are not influenced by the solvent.
Figure 4.12 SCP backscattering ROA spectra computed for a representative PPII (φ= -68° and ψ = 135°; blue) and a αR conformation of Ala dipeptide (φ = -73° and
ψ = −30°; red). Experimental spectra (green; in arbitrary units) in H2O (A, B) and D2O (C,D) are from reference 126.
72
Figure 4.12 shows the dipeptide contributions of the total ROA and Raman scattering
cross sections of Ala dipeptide-water cluster (see equations 5 and 6 in the method section for
more detail), computed using a PPII (φ = -68 and ψ = 135°; A, C) and a αR (φ = -73° and ψ = -
30°; B, D) conformation of Ala dipeptide. The computed ROA spectrum using both of these
conformations show spectral features found in the measured spectrum in both H2O (A, B) and
D2O (C, D). For example, Figures 4.12B and 4.12D show that ROA bands a-i (including amide I,
II III and the low frequency vibrational modes in the 300 cm-1 to 400 cm-1 range) predicted in the
computed spectra using the αR conformations of Ala dipeptide conformation are observed in the
measured spectra in H2O and D2O.
In order to understand the origin of the ROA intensity differences associated with the
molecular vibrations in the low frequency range (300 cm-1-400 cm-1), we decomposed those
intensity differences into contributions from groups of atoms in Ala dipeptide. As proposed by
Hug 19,130, the ROA intensity decompositions is illustrated using the group coupling matrices for a
PPII (φ = -68 and ψ = 135°; Figure 4.13A) and an αR (φ = -73° and ψ = -30°; Figure 4.13B)
conformation of Ala dipeptide (Figure 4.13I). The group coupling matrices show that the ROA
intensity differences at ~364 cm-1 (Figure 4.13C) for the PPII (Figure 4.13A) and at ~325 cm-1
(Figure 4.13D) for the αR (Figure 4.13B) are both dominated by the vibrational coupling of
groups 1 and 2 (Figure 4.13I), which is positive (red) and negative (yellow) for the PPII and αR
conformations, respectively. Figure 4.13 also show that the ROA intensity differences associated
with molecular vibrations at ~401 cm-1 (13G) for the PPII and at ~395 cm-1 (13H) for the αR are
both dominated by the vibrational couplings of groups 1 and 3 (Figure 4.13I), and is negative for
both of these conformations. Thus, the ROA spectral decomposition describe the physical basis
for the pattern of +/− and −/− ROA bands in the frequency range of 300 cm-1 to 400 cm-1 that are
predicted for the PPII and αR helical conformations of Ala dipeptide, respectively. Figures 4.13E
and 4.13F show the ROA intensity differences associated with molecular vibrations at ~352 cm-1
for the PPII and at ~338 cm-1 for the αR conformation.
73
Figure 4.13 ROA intensity differences associated with the vibrations in the lowwavenumber range decomposed into contributions from groups of atoms in Ala dipeptidefor a PPII (φ = -68° and ψ = 135°; A) and a αR (φ = -73° and ψ = −30°; B) conformation of
Ala dipeptide. The groups of atoms in Ala dipeptide are shown in panel I. Positive andnegative ROA intensity differences are shown as red and yellow circles, respectively.
74
4.4 Discussion
The aim of this study is to characterize Ala dipeptide conformations that are consistent
with the measured ROA spectra in H2O and D2O. The ROA spectra were computed for H2O- and
D2O-Ala dipeptide clusters with the PPII, αR, αL and β conformations of the dipeptide (Figure
4.1B) because the MC simulations found these structures in aqueous solution. Agreement
between the measured and averaged computed ROA spectra (based on overlay of spectra) is used
to characterize the populated conformations of Ala dipeptide in aqueous solution. The computed
ROA spectra for the H2O- and D2O-Ala dipeptide clusters with the PPII and αR conformations
contain spectral features that are observed in the measured spectra (Figures 4.3 and 4.6).
However, there is no significant similarity between the measured and predicted ROA spectra for
the αL and β conformations. Thus, our analysis of ROA of Ala dipeptide in aqueous solution
suggests that Ala dipeptide populates both the αR and PPII conformations, but no substantial
population of αL and β structures, despite the fact that αL and β structures are found in the MC
simulations.
The computed “average” ROA spectra are arithmetic averages, which implies that we are
assuming an equal population of Ala dipeptide structures within the PPII, αR, αL and β
conformational regions on the Ramachandran map (insets in Figures 4.3, 4.6 and 4.9). In other
words, the φ, ψ pairs of Ala dipeptide structures within the PPII, αR, αL and β conformational
regions are assumed to be equally probable. A quantitative comparison of the predicted and
observed ROA spectra requires the Boltzmann distribution of Ala dipeptide conformations, and
the population-weighted average computed ROA spectrum. In principle, we could use the energy
of each Ala dipeptide-water cluster (from the DFT geometry optimization calculation, see
methods for details) to determine the Boltzmann distribution of Ala dipeptide-water cluster
geometries, and hence a population-weighted average computed ROA spectrum. The
experimental observable, i.e. the ROA spectrum of Ala dipeptide in aqueous solution, is an
ensemble average over both solvent positions and peptide geometries. However, each Ala
dipeptide-water cluster used in our ROA calculations constitutes specific peptide-water geometry,
75
and not an ensemble average. Hence, a population-weighted average computed using the set of
Ala dipeptide-water clusters would still not be an accurate prediction of the experimental
observable. Thus, we resort to the assumption of an equal probability of Ala dipeptide structures
within the PPII, αR, αL and β conformational regions, and compare the computed average ROA
spectrum of each of these conformational regions to the observed spectrum.
The conformational heterogeneity of Ala dipeptide has been probed using other
spectroscopic methods. For example, the 13C NMR spectra of Ala dipeptide in water and in
liquid-crystalline media suggest that its structures in aqueous solution and in the liquid-crystalline
state are very similar, and that the structure is dominated by PPII conformations 37,38. However,
these studies could not rule out the existence of αR helical conformations in water. Following
these NMR studies, Mehta et al. used 13C NMR to show that Ala dipeptide in water exists in a
mixture of PPII and αR conformations 39, consistent with our ROA analysis. Kim et al. used 2D-
IR to probe the conformational heterogeneity of Ala dipeptide in aqueous solution 40. Those
authors concluded that the 2D-IR experimental data and simulations are consistent with PPII-like
conformations of Ala dipeptide in aqueous solution, and ruled out the possibility of αR helical
conformations for Ala dipeptide in water. We emphasize that the 2D-IR experiments were
performed in D2O, which stabilizes PPII conformations compared to H2O. For example,
Chellgren and Creamer have also shown that D2O stabilizes PPII conformations of alanine
containing peptides relative to H2O 131. Those authors therefore suggested that conformational
analysis of peptides using NMR, VCD, IR, and Raman spectroscopy of peptides in D2O is biased
towards increased PPII populations.
Deng et al. suggested that the two negative ROA bands observed in the frequency range
of 300 cm-1 to 400 cm-1 in the measured spectra of Ala dipeptide in H2O and D2O are indicative of
its predominant conformation in aqueous solution 126. Our ROA computations predict the
sequence of +/- and -/- ROA bands in the frequency range of 300 cm-1 to 400 cm-1 for the PPII
and αR helical conformations of Ala dipeptide, respectively (Figure 4.12). Thus, the ROA
analysis suggests that the two negative ROA bands observed in the frequency range of 300 cm-1
76
to 400 cm-1 in the measured spectra in H2O and D2O are characteristics of αR helical
conformations of Ala dipeptide. The measured ROA spectrum of Ala dipeptide in D2O (Figures
4.12C and 4.12D) also shows a positive ROA band at ~320 cm-1 in addition to the two negative
peaks in the frequency range of 300 cm-1 to 400 cm-1. Our ROA spectrum computed using the
PPII conformation of Ala dipeptide in D2O (Figures 4.12C) predicts a positive ROA band in the
frequency range of 300 cm-1 to 400 cm-1, which consistent with the measured ROA spectrum in
D2O. Thus, the positive ROA band in the frequency range of 300 cm-1 to 400 cm-1 is a
characteristic of the PPII conformations of Ala dipeptide. Since, D2O stabilizes PPII
conformations of peptides relative to H2O (see discussion in preceding paragraph), the positive
ROA band observed in D2O, is not observed in the measured spectrum in H2O. The predicted
ROA spectra using PPII and αR helical conformations of Ala dipeptide have common spectral
features found in the measured spectra in H2O and D2O, which indicate that Ala dipeptide in
aqueous solution displays both conformations. We emphasize that the differential ROA response
of Ala dipeptide in H2O and D2O, such as the key experimental spectral feature of -/- and +/-/-
bands in the frequency range of 300 cm-1 to 400 cm-1 in H2O and D2O, respectively, predicted by
our calculations demonstrates that ROA can also differentiate the PPII and αR dominant
populated structures of Ala dipeptide in aqueous solution.
Han et al. also computed the ROA spectra of Ala dipeptide in H2O and their theoretical
analysis of the ROA spectra suggests that PPII is the dominant conformation in aqueous solution124. In contrast, our theoretical analysis of the ROA spectra of Ala dipeptide suggests that αR is the
dominant conformation in H2O. If PPII dominated the conformational ensemble of Ala dipeptide
in H2O then a positive ROA band in the frequency range of 300 cm1 to 400 cm-1 would
characterize it (see discussion in preceding paragraph). However, the measured ROA spectrum in
H2O (Figure 4.12B) shows two negative bands in that frequency range. The simulated ROA
spectrum based on the H2O-Ala dipeptide cluster with the αR conformation of the dipeptide
(Figure 4.12B) shows negative ROA bands between 300 cm-1 and 400 cm-1, in agreement with the
measured spectrum. Thus, our ROA calculations suggest a dominant population of αR
77
conformation of Ala dipeptide in H2O, which is also consistent with 13C NMR studies 39. The
measured ROA spectrum of Ala dipeptide in D2O (Figure 4.12C) shows a positive ROA band
between 300 cm-1 and 400 cm-1 that is characteristic of the PPII conformation (see discussion in
preceding paragraph), which is accurately predicted in our ROA computation using D2O-Ala
dipeptide cluster with the PPII conformation of the dipeptide (Figure 4.12C).
Similarities between the observed and computed spectra (Figures 4.3, 4.6, 4.12) using the
PPII and αR conformations of Ala dipeptide suggest that the pattern of +/− and −/− ROA bands in
the frequency range of 300 cm-1 to 400 cm-1 are characteristic of the PPII and αR helical
conformations for Ala dipeptide, respectively. In order to assign these spectral features to
molecular structural elements, we decomposed the ROA intensity differences associated with
vibrations in the frequency range of 300 cm-1 to 400 cm-1 into contributions from nuclei in groups
of atoms in Ala dipeptide for a αR and a PPII conformation. For example, the ROA band at ~364
cm-1 (Figure 4.13A) and ~325 cm-1 (Figure 4.13B) for the PPII and αR, respectively, both
originate from the relative motions of the nuclei in groups 1 and 2 (Figure 4.13I). ROA bands that
are dominated by the relative motions of the nuclei in groups 1 and 2 in Ala dipeptide (Figure
4.13I) are also a probe of its secondary structure, since both of these groups contain the planar
amide bonds that determine the φ and ψ dihedral angles. Thus, the ROA spectral features in the
low frequency range of 300 cm-1 to 400 cm-1 provide structural information of the predominant
conformations of Ala dipeptide in aqueous solution.
The ROA solvent dependence for chiral molecules was computed recently using DFT.
Pecul et al. used DFT combined with a continuum solvent description to examine the influence of
solvent on the ROA spectra of rigid molecules 112. The authors concluded that the solvent
influence on the molecular geometry, the molecular Hessian, and the optical tensors should be
included when computing solvent effects on ROA. Our computation of the geometry
optimization, vibrational frequencies, normal modes, and derivatives of electric dipole-electric
dipole polarizability and electric dipole-magnetic dipole polarizability tensors (Equation 4 in
method section) were carried out using Ala dipeptide-water cluster structures. Thus, including
78
explicit water in our ROA calculations accounts for the necessary solvent effects. We also find
that the ROA and Raman scattering cross sections in the low frequency range of 300 cm-1-1100
cm-1 and for the amide I and II bands are influenced by water, in contrast, the ROA and Raman
bands in the frequency range of 1200 cm-1 to 1500 cm-1 are not affected by water (Figure 4.11).
This result is consistent with a recent ROA study of proline zwitterion in aqueous solution, which
also showed the presence of ROA bands that are not influenced by water 129. ROA computation of
polypeptides including explicit solute-solvent interactions becomes extremely time consuming as
the number of atoms grows. Efficient ROA computations of polypeptides may be achieved by
excluding the water contribution to the Cartesian gradients of the electric dipole-electric dipole
polarizability and electric dipole- magnetic dipole polarizability. However, the solvent influence
on the geometry optimization of the solute and on the molecular Hessian must be included for
predicting of the ROA in solution.
The accurate prediction of ROA spectra of peptides in aqueous solution requires
averaging over both solvent positions and peptide geometries 108. The average ROA spectra
(Figures 4.3, 4.6) computed using H2O- and D2O-Ala dipeptide clusters with the PPII and αR
peptide conformations predict ROA spectral features of Ala dipeptide in aqueous solution.
Figures 4.12B and 4.12D show that the ROA spectra computed using a single peptide
conformation with φ = -73° and ψ = -30° agrees better with the observed spectrum than the
computed spectrum averaged over a collection of Ala dipeptide structures with a wide range of φ
and ψ values (-50° ≤ φ ≤ -100° and -50° ≤ ψ ≤ 0°; Figures 4.3C, 4.6C) from the αR
conformational region of the Ramachandran map. This suggests that a better agreement between
the observed and computed average ROA spectrum of the αR conformational region might be
achieved using a narrow distribution of peptide geometries around φ = -73° and ψ = -30°, rather
than the broader distribution of structures with -50° ≤ φ ≤ -100° and -50° ≤ ψ ≤ 0°.
Our calculations show that the predicted ROA spectra using both the PPII and αR
conformations of Ala dipeptide in H2O and D2O are in very good agreement with the measured
spectra (Figures 4.3 and 4.6) based on the overlap between the measured and computed spectra.
79
Herrmann et al. recently showed that the ROA of helical peptides are dominated by the chirality
associated with the peptide backbone conformation 113,132. Thus, based on the good agreement
between the measured and computed spectra using the helical PPII and αR conformations of Ala
dipeptide, we suggest that the backbone conformation of Ala dipeptide in aqueous solution is
characterized by the compact αR and extended PPII conformations, both of which are present in
aqueous solution.
Conformational analysis of Ala dipeptide is of fundamental importance to the question of
the local conformational preference of unfolded polypeptides. Our ROA computational method
could be used to interpret the ROA spectra of longer unfolded polypeptides in aqueous solution,
and to characterize their solution conformations. In order to characterize conformations of
unfolded polypeptides, one has to determine residue-specific Ramachandran maps of the
polypeptides. We demonstrate that ROA probes of molecular chirality can be used to determine
the Ramachandran map of the shortest alanine-containing peptide. The accurate description of the
conformational heterogeneity of Ala dipeptide backbone is an important step towards defining the
residue-specific conformational preferences in unfolded polypeptides. In addition to the
biological significance of dipeptide conformational analysis, combined experiments and
simulations on short peptides can be used to determine the accuracy of commonly used force
fields in MD and MC simulations. For example, our MC and ROA studies of Ala dipeptide show
that the shortest alanine-containing peptide exists as a mixture of PPII and αR conformations in
aqueous solution, without substantial population of left-handed αL or β structures, despite
sampling αL and β structures in force field based MC simulations. Best et al. recently studied
polyalanine peptide A5 conformations in aqueous solution using MD simulations in order to
address the question of whether the commonly used force fields overpopulate the α-helical
conformations of polyalanine peptides102. They concluded that the NMR data are consistent with
force fields that produce α-helical populations of polyalanine peptides and that the data do not
require exclusive formation of the PPII structure, consistent with our conformational analysis of
Ala dipeptide in aqueous solution.
80
Growing access to commercial ROA spectrometers (http://www.btools.com) and
improved efficiency of ROA calculations 133, such as implementation of analytical derivative
procedures for the computation of ROA, are likely to motivate further ROA analysis of aqueous
polypeptide solutions. A combined conformational analysis and ROA study of polypeptides
should be helpful for understanding more fully the relationship between peptide conformations
and ROA spectra. A link of this kind may provide further insights into the connection between
structure and dynamics.
4.5 Conclusions
Backscattered circular polarization ROA analysis for Ala dipeptide based on TD-
DFT/DFT calculations and MC sampled peptide-water clusters were used with experimental
ROA and Raman data to assign the dominant conformations of Ala dipeptide in aqueous solution.
Agreement of observed and simulated ROA spectral features indicate the viability of screening
plausible MC structures based on ROA data. We find that the computed ROA spectra using a
PPII conformations with φ = -68° and ψ = 135° and an αR conformations with φ = -73° and ψ = -
30° are in agreement with the observed spectra. Thus, our ROA analysis shows that Ala dipeptide
adopts both αR and PPII conformations in aqueous solution, which are the dominant
conformations in aqueous solution.
We also find that including explicit solute-solvent interactions is required for: (a)
adequate quantum mechanical geometry optimization of the solute conformations in solution, (b)
computation of the molecular Hessian and (c) computation of the solvent influence on the optical
tensor for predicting the ROA spectra of peptides in solution. The qualitative agreement between
the observed and computed spectra using the PPII and αR conformations of the dipeptide in H2O
and D2O suggest that our ROA computational method could be used to interpret measured ROA
spectra of longer polypeptides in aqueous solution and to characterize their solution
conformations.
81
4.6 Methods
Two sets of MC computer simulations of Ala dipeptide in H2O were performed using the
OPLS force field 83 and TIP4P water model 134. First, low-energy conformations of Ala dipeptide
in H2O were identified that characterize potentially populated regions of the Ramachandran map
using MC free-energy simulations. Second, H2O configurations were sampled with fixed
backbone dihedral angles (φ and ψ; Figure 4.1A) for the dipeptide. The fixed peptide geometries
were selected from low-energy regions of the Ramachandran map. H2O-Ala dipeptide cluster
structures from the second set of MC simulations (sampling water configuration with fixed-
peptide geometry) were optimized using DFT. Each H2O-Ala dipeptide cluster has ten water
molecules within a cut-off distance of 0.5 nm from the hydrogen bond donor (NH) and acceptor
(O, N) atoms of Ala dipeptide (Figure 4.1A). Following geometry optimization of the H2O-Ala
dipeptide cluster, the structures were used for computing the back-scattering ROA and Raman
spectra using TD-DFT with RI-J approximation, the BLYP functional and the rDPS basis set.
4.6.1 MC simulations
Free energy perturbation theory 88 was used to calculate the potential of mean force
(PMF) that describes the relative free energy difference between Ala dipeptide conformations as a
function of the peptide backbone dihedral angles. One-dimensional (1D) PMFs were calculated
first with φ fixed and ψ varied from 0° to 360° in 5° increments. Then ψ was fixed and φ was
varied from 0° to 360° in 5° increments. A 2D plot of the free energy difference for φ = 80°, ψ =
80°, the reference conformation, and all φ, ψ pairs were calculated from the 1D PMFs. Thus, the
2D plot identifies low-energy conformations of Ala dipeptide in water.
MC simulations of Ala dipeptide in a box of 500 water molecules were performed using
BOSS 88 at 25°C and 1 atm (NPT ensemble) with periodic boundary conditions. Long-range
electrostatic interactions were evaluated by the Ewald method 135. The AM1 91 based CM1A 92
partial atomic charges for the solute and solvent were used in the MC simulations. A more
detailed description of the MC move and the atomic charge-partitioning scheme appears in 88.
82
4.6.2 TD-DFT calculations of ROA
Zuber et al. recently demonstrated accurate and efficient prediction of ROA spectra
using DFT 17. The approach avoids calculating the four-center Coulomb integrals and omits
contributions of the electric dipole-electric quadrupole polarizability tensor to the ROA
differential scattering cross-section. Luber et al. also showed recently that the contribution of the
electric dipole-electric quadrupole polarizability tensor to the ROA intensities can be neglected
for the amide I, amide II, amide III vibrational modes for peptides (below 2000 cm-1) 136. We use
the same scheme in the off-resonance approximation 16 to calculate the circular difference
differential scattering cross-sections per unit solid angle
€
−Δndσ π( )SCPdΩ
for back scattered
circular polarization 137 (SCP) with naturally polarized (n) incident light:
€
−Δndσ π( )SCPdΩ
≈Kc48βG
2( ) (1)
c is the speed of light,
€
βG2 is the anisotropic ROA invariant , and K is:
€
K =107
9π 2µo
2c 4 ˜ ν oωo
200πc−Δ ˜ ν p
3
(2)
€
ωo = 2πν o is the frequency of the incident light,
€
Δ ˜ ν p is the Raman frequency shift (in cm-1), c is
the speed of light (in m s-1), and
€
µo is the permittivity of vacuum.
Placzek polarizability theory writes 19
€
βG2 =
12
3αµν ′ G µν −αµµ ′ G νν( )µν
∑ (3)
where
€
αµν ′ G µν is
€
αµν ′ G µν =h
8π 2cΔ ˜ ν p i, j∑
∂αµνe
∂xiα
0α ,β∑
∂ ′ G µνe
∂x jβ
0
Lαi,px Lβj ,p
x (4)
83
€
Lαi,px is the ith component of the Cartesian displacement vector of nucleus α for normal mode p.
€
αµνe and
€
′ G µνe are the elements of the electric dipole-electric dipole polarizability tensor and the
imaginary part of the electric dipole-magnetic dipole polarizability tensor, respectively. The index
0 indicates that the derivatives of the electronic tensors are computed at the equilibrium nuclear
geometry.
The geometries of H2O-Ala dipeptide clusters from the second set of MC simulations
were optimized using DFT implemented in Turbomole (Version 5.6) 85 with the BLYP
correlation-exchange functional and the SVP basis set. The normal coordinates of the H2O-Ala
dipeptide clusters were computed from the molecular Hessian, which was determined for the
optimized geometry. Optimizations of some of the H2O-Ala dipeptide cluster structures lead to
imaginary frequencies and hence such structures were not included in the ROA calculations. 532
nm incident laser frequency was used for tensor calculations, which were performed using TD-
DFT with the BLYP functional, the rDPS basis set, and the [7s3p3d1f]/[3s2p1d] auxiliary basis
set 138. All of the calculations were performed in a gauge-independent dipole-velocity formulation
using the RI-J approximation. The Cartesian gradients of the polarizability tensors were evaluated
numerically using the 6N-displaced geometries, where N is the number of atoms. The 6N
geometries were obtained from the optimized geometries of the H2O-Ala dipeptide clusters using
a displacement of ± 10-3 atomic units along the Cartesian coordinates.
The molecular hessian of the optimized geometry of H2O-Ala dipeptide clusters were
used to compute the vibrational frequencies and normal coordinates of D2O-Ala dipeptide
structures. Thus, we used the H2O-Ala dipeptide structures from the MC simulations to compute
the ROA and Raman spectra of D2O-Ala dipeptide clusters. The ROA and Raman spectra of the
D2O-Ala dipeptide clusters were then computed using equation 4.
The total Raman
€
(ndσ ) and ROA
€
(−Δndσ ) scattering cross sections of a Ala dipeptide-
water cluster is the sum of scattering cross sections of the peptide
€
(ndσ p ,−Δndσ p ) , water
€
(ndσW ,−ΔndσW ) , and peptide-water interactions
€
(ndσ pWI ,−Δndσ pWI ) . Hence, the total Raman
and ROA scattering cross sections is:
84
€
ndσ=ndσ p+ndσW +ndσ pWI (5)
€
−Δ ndσ = −(Δ ndσ p +Δ ndσW +Δ ndσ pWI ) (6)
Thus, the relative contributions of the Raman and ROA scattering cross sections of the
dipeptide, water, and peptide-water interactions can be compared to the total ROA and Raman
scattering cross sections of Ala dipeptide-water cluster.
85
5 Epilogue
In this dissertation we describe computer simulations of the solvent effects on optical
rotation (OR) and Raman optical activity (ROA) of molecules. Our aim is to compute molecular
chiroptical signatures so that the data may be used in combination with experiments to assign and
interpret the conformations and configurations of molecules.
Theoretical OR predictions depend strongly on the quantum mechanical (QM) methods
used, and the results are often strongly geometry dependent. The significant variation in predicted
OR values (sign and magnitude) arise from the small Tr [G′(ω)] (see equations 1 and 2), which is
1-3 order of magnitude smaller than the largest tensor element G′αβ. Thus, in a QM calculation,
changing basis set, level of electron correlation, solvent, molecular geometry, or treatment of
vibrational contributions that slightly change G′ tensor elements can lead to sign inversion in OR.
Hence, theoretical predictions of OR demands QM calculations with different combinations of
basis sets and level of electron correlation in order to check the consistency of the predictions.
Zuber, Beratan and Wipf recently showed that the anisotropic component of Rayleigh optical
activity (RayOA) scattering has a weak dependence on the theoretical methods 139. Hence,
accurate RayOA calculations combined with experiments could be developed into a powerful
chiroptical spectroscopic tool to probe molecular stereochemistry that would complement existing
methods.
Our theoretical studies of methyloxirane in benzene show that the solute’s chiral solvent
imprint can dominate the OR in solution. It will be interesting to determine if chirality transfer
from a chiral solute to an achiral solvent in isotropic phase is a general effect that also occurs in
other chiral systems or for other chiroptical properties. For example, Xu and coworkers recently
showed chirality transfer from methyl lactate 140,141 and methyloxirane 48 to hydrogen-bonded
water using vibrational circular dichroism spectroscopy. Chiral solvent structure around a chiral
solute can influence chemical processes such as asymmetric organic synthesis and chiral
chromatography. Chiral chromatographic techniques are the principal methods for the analysis
and separation of chiral organic and biomolecules, as evidenced by their extensive use throughout
86
the scientific community. However, despite such wide spread use, the molecular mechanisms of
chromatographic separation processes are poorly understood. For example, the chiral solvent
imprint of the chiral surface (stationary phase) could influence the stereoselectivity of the
separation process, and hence, the retention characteristic of solute molecules. A detailed
understanding of the molecular mechanisms of chiral chromatographic separation processes
would help in predicting retention properties of any solute, which can also provide insights into
developing combinations of stationary-mobile phase systems with improved retention
characteristics.
The solution conformations of polypeptides are the subject of increasing attention,
although their ensemble of geometries is difficult to characterize 94. Recent studies suggest that
ROA can be used to characterize backbone conformations of polypeptides in aqueous solution.
ROA is especially useful in cases when assignment of polypeptide conformations by electronic
circular dichroism is difficult, as has been reported recently 142. We show that ROA calculations
based on density functional theory and Monte Carlo (MC) simulations can be used to identify
populated conformations of a peptide in aqueous solution. These calculations facilitate
assignment of the observed ROA spectral features to corresponding secondary structures that
characterize the populated conformations of the peptide in aqueous solution. Thus, the
interpretation of the experimental data enabled by the calculations helps in understanding the
relationship between peptide conformations and ROA spectra. In addition to the agreement
between the theoretical results and the experimental data, our calculations also provide substantial
predictive value. For example, our calculations show that ROA can be used to distinguish
between left-(αL) and right-handed (αR) helical conformations of a peptide backbone in aqueous
solution. To the best of our knowledge this is the first evidence in support of ROA to distinguish
the chirality associated with the handedness of helical conformations of peptides.
The accurate and efficient prediction of ROA suggests that ROA analysis could be used
to identify ROA spectral features that characterize secondary structures (αR, αL, β, PPII) in
proteins and polypeptides. Arora and coworkers recently reported the atomic structure of a short
αR polypeptide stabilized by a main chain hydrogen bond surrogate 143, and Wennermers and
87
coworker showed that Azidopolyproline polypeptide have a single dominant PPII conformation
in aqueous solution 144. ROA analysis of those polypeptide sequences can be used to identify
ROA fingerprints of the αR, β, and PPII conformations. Characterization of the peptide backbone
conformations of intrinsically disordered proteins (IDPs), which do not fold into well-defined
three-dimensional structure under physiological conditions, is the subject of intense interest as
their disorder structures are implicated in important biological functions in cell regulation and
signaling 145,146. The intrinsic disorder of IDPs restricts the utility of X-ray and NMR techniques
for probing their solution conformations. Thus, the ensemble of conformations of IDPs is difficult
to characterize. MC or MD simulations combined with ROA analysis of IDPs may provide the
means to probe for secondary structures of IDPs, and thus, characterize their solution
conformations.
88
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Biography
Parag Mukhopadhyay earned a B.Sc. with honors in chemistry from the University of
Delhi, India and M.Sc. degrees in chemistry and biological sciences from the Indian Institute of
Technology, Delhi, India, and the University of Calgary, Canada, respectively. He conducted his
doctoral research in theoretical and experimental probes of molecular chirality at Duke
University, and published the following articles:
I. P. Mukhopadhyay, P. Wipf, D.N. Beratan. “Optical signatures of molecular
dissymmetry: Combining theory with experiments to address stereochemical
puzzles”, to be submitted, Accounts of Chemical Research.
II. P. Mukhopadhyay, G. Zuber, D.N. Beratan. “Characterizing aqueous solution
conformations of a peptide backbone using Raman optical activity computation”,
Biophysical Journal, 2008. In press.
III. P. Mukhopadhyay, G. Zuber, P. Wipf, D.N. Beratan. “Contribution of a solute’s
chiral solvent imprint to optical rotation”, Angewandte Chemie International
Edition, 46:6450-6452, 2007. The work was also highlighted in Science (2007,
317:725), Chemical and Engineering News (6 August, 2007) and Angewandte
Chemie, International Edition (2007, 46:7738-7740).
IV. P. Mukhopadhyay, G. Zuber, M.R. Goldsmith, P. Wipf, D.N. Beratan. “Solvent
effects on optical rotation: A case study of methyloxirane in water”,
ChemPhysChem, 7:2483-2486, 2006.
