THz-TDS Studies of Low Frequency Modes in … Studies of Low Frequency Modes in Organic Molecular...

THz-TDS Studies of Low Frequency Modes in Organic Molecular Crystals and Progress

Toward THz Vibrational Optical Activity

Charles A. Schmuttenmaer

Department of Chemistry, Yale University225 Prospect St., New Haven, CT 06520-8107

Schmuttenmaer LabBecky Milot, Michael WilliamsDan AschaffenburgRebecca Allred, Stafford Sheehan

Solar Energy CollaborationVictor Batista, et al. Theory

Gary Brudvig, et al. Biophysical & PSII

Bob Crabtree, et al. Inorganic & Catalysis

Coworkers and $$$

http://thz.yale.edu

THz Time-Domain Spectroscopy(THz-TDS)

Advantages:

Very sensitive to intermolecular interactions (H-bonding, Coulombic forces, etc.).

Most sensitive broadband far-infrared method at frequencies below 33 cm-1.

Many opaque substances (in the visible or infrared) are transparent in the far-IR.

Absorption coefficient and refractive index are obtained “automatically”.

Kramers-Kronig analysis is not required.

Opens up largely unexplored region of the spectrum: 0.2 to 4 THz (6 to 130 cm-1).

Disadvantages:

Somewhat limited spectral coverage compared to Raman or Fourier Transform-IR.

P. U. Jepsen and S. J. Clark, "Precise ab-initio prediction of terahertz vibrational modes in crystalline systems," Chem. Phys. Lett. 442, 4-6 275-280 (2007).

THz Spectra of OMCs are Rich

Possible Spectroscopic Measurements

THz spectraRaman spectraTemperature dependencePressure dependenceSingle crystal orientation dependenceIsotope dependenceFamily of related compoundsTHz optical activityX-ray diffraction & powder XRD

Theoretical ConsiderationsLevel of theory: Empical, semi-empirical, ab initio, DFTDFT: Plane-wave vs. atom-centeredvan der Waals interactions: R-6 term vs. vdW functionalUnit cell relaxation (or not)Anharmonicity0 K

To Obtain…Vibrational frequencies and intensitiesIntensities along a, b, and c crystallographic axesPressure dependenceTemperature dependence (not really)VCD & VORDIsotope dependence

1. THz Studies of Organic Molecular Crystals1. Range of interactions2. Experimental considerations3. Calculations4. Describing vibrational modes5. Comparing calculations with measurements

2. THz Optical Activity1. CD and ORD2. Experimental considerations3. Spirals4. Molecules (future studies…)

Outline

L-valine crystal lattice

Isolated L-valine molecule

THz-TDS of Molecular Crystals

+ --

---

-

-- -

--

-

+ +

+++

+ ++

+ ++ +

+---

Types of Interactions in a Molecular Crystal

Molecules We Have Studied Over the Years

Materials are purchased from Sigma and used as received. They are polycrystalline “powders” –polarizing microscope. They are pressed into pellets (~2 – 5 mm thick). Typically, no filler material is used.

Experimental Schematic & Representative Data

General ApproachUse THz spectroscopy, Raman scattering, powder XRD, and ab initio (DFT) calculations to fully understand THz spectra of organic molecular crystals (OMCs): Which modes correspond to which peaks???1. Measure THz and Raman spectra of L, D, and DL-racemates of polycrystalline amino acids.

2. Verify polymorph using XRD.

3. Assign low frequency intermolecular phonon modes.- If crystal structure is known: Calculate modes. - If not: Determine it ourselves, and then calculate modes.

4. Understand the different phonon modes in the different crystals.

5. Verify interpretation with isotope substitution, temperature dependence, pressure dependence, and THz vibrational optical activity.

Frequency (THz)0.0 0.5 1.0 1.5 2.0 2.5P

ower

abs

orpt

ion

coef

. (cm

-1)

0

50

100

150

200

250

D-histidine L-histidine DL-histidine

Frequency (THz)0.0 0.5 1.0 1.5 2.0 2.5

0

50

100

150

200

250a) b)

Frequency (THz)0.0 0.5 1.0 1.5 2.0 2.5

Pow

er a

bsor

ptio

n co

ef. (

cm-1

)

020406080

100120140160 c)

Polymorphism

As received Recrystallized

Recrystallized (same data as part b)

50/50 linear combination of D- and L-histidine in part (a).

Powder XRD: Histidines

angle (2)10 15 20 25 30

log

inte

nsity

0

1

2

3

Recrystallized L-histidine (both phases)50/50 linear combination of D & L

a) L-histidine, as received

b) Calculated, orthorhombic

c) D-histidine, as received

d) Calculated, monoclinic

e) 50/50 linear combination of D & L

angle (2)10 15 20 25 30

Log

inte

nsity

0

5

10

15

e)

d)

c)

b)

a)

D- and L-histidine can exist in two stable polymorphs: orthorhombic and monoclininc.

P. U. Jepsen and S. J. Clark, Chem. Phys. Lett. 442, 275-280 (2007).

Alp

ha (c

m-1

)

050

100150200250

Frequency (THz)0.5 1.0 1.5 2.0 2.5

Alp

ha (c

m-1

)

0

50

100

150

200D-tyrosineL-tyrosine

DL-tryosine

CHARMM(empirical)

Karen Siegrist,† Christine R. Bucher,† Idan Mandelbaum,† Angela R. Hight Walker,† Radhakrishnan Balu,‡ Susan K. Gregurick,‡ and David F. Plusquellic*,† J. AM. CHEM. SOC. 2006, 128, 5764-5775

THz spectroscopy definitely reveals interesting absorption features. These low-frequency vibrations are strongly influenced by intermolecular interactions.

But what are they?

Harmonic frequencies are calculated which means they are WRONG!

Pote

ntia

l Ene

rgy

r

Anharmonicity: Diatomic MoleculeRed-shifts at higher temperatures.

Urea calculations

Mode v1:

Harmonic frequency: 30.44 cm-1 (shown in gray)

Anharmonic:0 1: 62.9 cm-1

1 2: 82.9 cm-1

2 3: 93.1 cm-1

It is significantly anharmonicand blue-shifts at higher temperatures.

(shown in blue)

NH2H2N

O

Name AC vs. PW Price vdW functional?

Crystal09 Atom-centered $$$ ?DMol3 Plane Waves $$$ ??VASP Plane Waves $$$ ??GPAW Plane Waves Free ?ABINIT Plane Waves Free ?CASTEP Plane Waves $$$ ?SIESTA Atom-centered Free YESGaussian Atom-centered $$$ No

and many, many, many more…http://dft.sandia.gov/Quest/DFT_codes.html

Density Functional Theory (DFT) Calculations

Begin calculation with experimental XRD coordinates.

1200 eV 0.35 Å

Plane wave

s

p

d

f

Atom-centered

Basis functions

Korter et al., J. Phys. Chem. A 113, 13013 (2009).

Comparing different DFT calculationsCurrently, people compare calculated spectra to experimental ones, and use their judgment to decide which is the “best” fit.

1. Quantify vibrational mode character.

2. Vibrational mode eigenvector projection.

We need a way to more rigorously compare different calculations.

Experiment & CalculatedL-leucine

L-valine

L-isoleucine

DL-leucine

DL-valine

DL-isoleucine

L-enantiomers: High line density DL-racemates: Low line density

Small Molecules

Describing vibrations

Michael Denk, http://131.104.156.23/Lectures/CHEM_207/vibrational_spectroscopy

Medium Sized Molecules (alanine)

27-carbon CH stretch

33OH stretch

1 3

Medium Sized Molecules (alanine)

Large Molecules and/or Organic Molecular Crystals

Tim Korter, Syracuse University, Department of Chemistry

Quantifying Intermolecular Vibrational Character

4 molecules per unit cell

For each molecule in unit cell:

= Total displacement

Displace along vibrational mode eigenvector:

2rms

1

1TotalN

i ii

mN

where i is displacement vector for each atom and 1, 0,i i ir r

Quantifying Intermolecular Vibrational Character

Calculate C.O.M. displacement:

= Translational Component

2rms rms 0, , 1, ,

1

1Trans TotalN

i com i com ii

m r rN

Finally:

Intermolecular = Total – Intra

Rotational = Inter - Trans

We obtain:

Total displacement

Intramolecular

IntermolecularRotationalTranslational

Overlap C.O.M.s. & Rotatefor maximum overlap.

20, , 1, ,

1

N

i com i com ii

m r r

U

2rms 0, , 1, ,

1

1IntraN

i com i min com ii

m r rN

U

Quantifying Intermolecular Vibrational Character

Remaining displacements:= Intramolecular Component

Rigorous Convergence in DL-Valine Calculations

Calculation methods have a plenitude of settings

How to check convergence?

Energy

Calculated Vibrations

Character of the Modes

DL-Valine: Fixed vs. Optimized Unit Cell

Begin calculation with experimental XRD coordinates. Calculation is at 0 K, crystal structure is not. Therefore, one should NOT fix unit cell dimensions at experimental values.

DL-Valine: Fixed vs. Optimized Unit Cell

L-valine

Atomic coordinates are optimized (otherwise, imaginary frequencies are obtained). So why not unit cell parameters as well?

If unit cell remains fixed, then it is under an indeterminate amount of stress during the calculation. Therefore, one should NOT fix unit cell dimensions at experimental values.

DL-Valine Frozen Unit Cell

Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode character.

DL-Valine Fixed vs. Optimized Unit Cell

DL-Valine Frozen Unit Cell

Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode character.

DL-Valine Fixed vs. Optimized Unit Cell

DL-Valine Frozen Unit Cell

Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode characters.

DL-Valine Fixed vs. Optimized Unit Cell

DL-Valine Frozen Unit Cell

Example of a case where choice of calculation parameters makes a small difference on calculated spectrum, but a big change in mode character.Phys. Chem. Chem. Phys. 13, 11719 (2011)

DL-Valine Fixed vs. Optimized Unit Cell

??

Looking at Convergence (again)

Vibrational mode eigenvector projection.

56

6

5

789

9

8

7

Looking at Convergence (again)Vibrational mode eigenvector projections from one calculation onto another. 6-31G(d,p) is considered the best basis set (that we used), so express the eigenvectors of the other calculations as linear combinations of the 6-31G(d,p) results.

6-31G(d) is converged

DL-Valine Fixed vs. Optimized Unit Cell

DL-Valine Fixed vs. Optimized Unit Cell

SIESTA DZDP is Converged

Double ZetaTriple Zeta

Need to use a van der Waals functional!

The Perdew–Burke–Ernzerhof (PBE) functional does NOT treat dispersion, i.e., van der Waals interactions.

c

Compare Gaussian and SIESTA Results

No vdW No vdW No vdW vdW No vdWvdW

NH3+-O2C

CHH

H3C CH3

L-Valine

DL-valine (triclinic)

1

2

3

4

5

6

7

8

9

10

11

12

Tx Ty Tz RA RB RC O1-C1 -

O2O1-C

1 -C2

O2-C1 -

C2N1-C

2 -C1

N1-C2 -

C3C1-C

2 -C3

C2-C3 -

C4C2-C

3 -C5

C4-C3 -

C5O1-C

1 -C2 -

N1

O1-C1 -

C2 -C3

O2-C1 -

C2 -N1

O2-C1 -

C2 -C3

N1-C2 -

C3 -C4

N1-C2 -

C3 -C5

C1-C2 -

C3 -C4

C1-C2 -

C3 -C5

DL-leucine

1

2

3

4

5

6

7

8

9

10

11

12

Tx Ty Tz RA RB RC O1-C1 -

O2O1-C

1 -C2

O2-C1 -

C2N1-C

2 -C1

N1-C2 -

C3C1-C

2 -C3

C2-C3 -

C4C3-C

4 -C5

C4-C3 -

C6

O1-C1 -

C2 -N1

O1-C1 -

C2 -C3

O2-C1 -

C2 -N1

O2-C1 -

C2 -C3

N1-C2 -

C3 -C4

C1-C2 -

C3 -C4

C2-C3 -

C4 -C5

C2-C3 -

C4 -C6

C4-C3 -

C6

1. Isotope Substitution2. Temperature Dependence3. Pressure Dependence4. Selection Rules (Raman vs. IR)5. Related Molecules6. THz Optical Activity (VCD & VORD)

Experimental Variables

Isotope Substitution

Another way to verify that calculation is correct. Even if the frequencies are not perfect, they should shift in correct direction.

THz Optical Activity:

Optical activity in an artificial chiral media: a terahertz time-domain investigation of Karl F. Lindman’s 1920 pioneering experiment.

A. Y. Elezzabi* and S. Sederberg, 13 April 2009 / Vol. 17, No. 8 / OPTICS EXPRESS 6600.

Circular Dichroism (CD) & Optical Rotatory Dispersion (ORD) areRelated through Kramers-Kronig

http://www.answersingenesis.org/images/chirality-rgb.jpg

http://www.georgehart.com/rp/chiral-2-layer-sphere.html http://www.georgehart.com/rp/rp.html

http://scienceblogs.com/pharyngula/upload/2009/04/nodal_spiral.jpeg

http://www.nanotech-now.com/images/nanotube-chiral-large.jpg

Chirality makes it all possible.

Polarized Light

http://en.wikipedia.org/wiki/File:Linear_polarization_schematic.png

http://en.wikipedia.org/wiki/File:Circular_polarization_schematic.png

http://en.wikipedia.org/wiki/File:Elliptical_polarization_schematic.png

Linear Circular Elliptical

Also, Linear = RCP ± LCP

http://commons.wikimedia.org/wiki/File:Circular_dichroism.png http://www.imb-jena.de/ImgLibDoc/cd/images/lucepolarizzata3.jpg

Time = t a little later

Circular Dichroism

On average, VCD spectrum is 300 / 5000 times weaker than UV CD spectrum.

A (1/.

Circular Dichroism

http://www.nsm.buffalo.edu/~jochena/research/opticalactivity.html

Hexahelicene (M)HexahelieceneCD spectrum of (M)-Hexahelicene.Green: Experiment, Red: Computed

http://www.brukeroptics.com/uploads/pics/enantiom1_02.jpg

Vibrational Circular Dichroism (VCD)

http://www.chem.uic.edu/takgroup/Research/Warwick/Slide91.JPG

Optical Rotatory (Dispersion)Analogous to birefringence (no & ne)

http://www.star.le.ac.uk/~rw/courses/lect4313_fig48.jpghttp://sirius.ucsc.edu/demoweb/images/optics/birefrigent.jpg

nLCP > nRCP (or vice versa)

http://chemed.chem.purdue.edu/genchem/topicreview/bp/1organic/graphics/24_19.gif

Making Circularly Polarized THz LightLinear Quarter wave-plate with optic axis @ 45o

PCA-40-05-10-800-0

Frequency (THz)

0 1 2 3 4 5 6

Spe

ctra

l Am

plitu

d (a

rb. u

nits

)

1

10

100

1000

10000

/4 /2 /4 /4

SampleInput pulse(vertically polarized)

DetectorRotatablePolarizerat 45o

Si prism inducesπ/2 phase shift

Making Circularly Polarized THz Light

Fresnel Rhombhttp://spie.org/Images/Graphics/Publications/FG05_P49_f1.jpg

Phase Shift upon total internal reflection in Si (n = 3.417)(c = 17 degrees)

Reflection angle (degrees)40 41 42 43 44 45

Pha

se s

hift

betw

een

p- a

nd s

-pol

ariz

atio

ns (d

egre

es)

86

88

90

92

94

20 30 40 5050

70

90

110

2 2 2tan 2 cos sin 1 / sinn n

(Masahiko Tani, Fukui University)

“XY-antenna” to generate THz pulse

at 45o

Electronically Rotating THz Linear Polarization (Faster than Mechanical)

Use lockin amplifier to Either measure ARCP – ALCP(With either mechanical or electronic modulation).

Michael Johnston, Oxford University

Experimental Apparatus and Sample(Measure CD and ORD simultaneously)

cos cosA A

Sample rotates light by , polarizer angle is .

cos cosA A

cos( ) cos( ) cos( ) sin( ) sin( ) cos( )xA A sin( )yA A

2cos ( ) cos( )sin( )x yA A A

cos 2 cos2 2A AA

2 2

2tan 2 ( ) cosx y

x y

A AA A

cos sinixe x i x cos 1 2 ix ixx e e

Can Analyze Data in Frequency Domain…

Rotation angle

Sample rotates light by , polarizer angle is .

D. J. Aschaffenburg, M. R. C. Williams, D. Talbayev, D. F. Santavicca, D. E. Prober, and C. A. Schmuttenmaer, “Efficient Measurement of Broadband Terahertz Optical Activity.” J. Appl. Phys., 100, 241114 (2012). DOI: 10.1063/1.4729148

2 2 2 2 2

2 2 2 2 2

cos sin 2 cos cos sin

sin cos 2 cos cos sinx y x y

x y x y

a A A A A

b A A A A

Or Time Domain

Rotation angle only Rotation angle and ellipticity

2 2 2cos 2 cos2 2f f fA AA f t

Thanks to Diyar Talbayev!!

Axcos()cos(-) for -180 <= <= 0

2f (phase angle of lockin, in degrees, when detecting second harmonic)

-180-150-120 -90 -60 -30 0 30 60 90 120 150 180

THz

Am

plitu

de (a

rb. u

nits

)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Axcos()cos(-) for 0 <= <= 180

2f (phase angle of lockin, in degrees, when detecting second harmonic)

-180-150-120 -90 -60 -30 0 30 60 90 120 150 180TH

z A

mpl

itude

(arb

. uni

ts)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

= 2f

o o

* *0

* *1

2 45 45

3

1

cos 2 cos 2

2 cos cos 2 sin 2

2 sin sin 2

x y x x y y

x y x x y y

x y

RHCP LHCP x y

S I I A A A A

S I I A A A A

S I I A A

S I I A A

Stokes Parameters

1. Tiny metal helices (watch springs, other ideas?)THz Vibrational Optical Activity

2. Hexahelicene (hard to obtain material… )Intramolecular modes shown.Intermolecular could be even stronger.

Frequency (cm-1)0 200 400 600 800 1000

(c

m-1

)

0

500

1000

1500

2000

IR absorption coefficient

Frequency (cm-1)0 200 400 600 800 1000

(cm

-1)

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

VCD “absorption coefficient”

Can be positive or negative!

3. (R)-(+)-1,1′-bi-2-naphtholThings to Study (cont.)

Claire Niezborala and Francois Hache, J. AM. CHEM. SOC. 2008, 130, 12783–12786

P. Fischer, F. W. Wise, and A. C. Albrecht, J. Phys. Chem. A 2003, 107, 8232-8238

$100 for 5 g (S enantiomer).

Hexahelicene

$467 for 2 mg!

Things to Study (cont.)

P. U. Jepsen and S. J. Clark, "Precise ab-initio prediction of terahertz vibrational modes in crystalline systems," Chem. Phys. Lett. 442, 4-6 275-280 (2007).

Alp

ha (c

m-1

)

050

100150200250

Frequency (THz)0.5 1.0 1.5 2.0 2.5

Alp

ha (c

m-1

)

0

50

100

150

200D-tyrosineL-tyrosine

DL-tryosine

CHARMM(empirical)

3. Organic molecular crystals (help assign spectrum)

Things to Study (cont.)4. Helix-rich proteins (albumin and hemoglobin )

Albumin

THz CD will (hopefully) be more sensitive to tertiary structure than CD in the visible/UV or VCD in the infrared.

Hemoglobin

General Approach in Summary

1. Measure THz and Raman spectra of L, D, and DL-racemates of polycrystalline amino acids.

2. Verify polymorph using XRD.

3. Assign low frequency intermolecular phonon modes.- If crystal structure is known: Calculate modes. - If not: Determine it ourselves, and then calculate modes.

4. Understand the different phonon modes in the different crystals.

5. Verify interpretation with isotope substitution, temperature dependence, pressure dependence, and THz vibrational optical activity.

Use THz spectroscopy, Raman scattering, powder XRD, and ab initio (DFT) calculations to fully understand THz spectra of organic molecular crystals (OMCs): Which modes correspond to which peaks???