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Preliminary Results for Water Dimer Spectroscopy Simulations. Ross E. A. Kelly , Matt J. Barber, and Jonathan Tennyson Department of Physics and Astronomy UCL Gerrit C. Groenenboom, Ad van der Avoird Theoretical Chemistry Institute for Molecules and Materials Radboud University CAVIAR AGM - PowerPoint PPT Presentation
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Preliminary Results for Water Dimer Spectroscopy Simulations
Ross E. A. Kelly, Matt J. Barber, and Jonathan TennysonDepartment of Physics and Astronomy
UCL
Gerrit C. Groenenboom, Ad van der AvoirdTheoretical Chemistry Institute for Molecules and Materials
Radboud University
CAVIAR AGMSTFC, Cosener's House
December 15, 2009
Contents
• I. Motivations
• II. Improved Water Monomer Parameters
• III. Water Dimer Characteristics
• IV. Water Dimer VRT states
• V. New Methodology
• VI. Summary
I. Motivations
• to understand water dimer absorption throughout visible and IR region in the atmosphere.
• To create a high accuracy water dimer spectra in agreement with experiments.
• To create a linelist of all possible water dimer transitions.
0.0E+00
5.0E-09
1.0E-08
1.5E-08
2.0E-08
2.5E-08
3.0E-08
3.5E-08
4.0E-08
4.5E-08
5.0E-08
606 608 610 612 614 616 618 620 622
Wavelength / nm
Ab
sorp
tio
n C
oef
fici
ent
/ cm
-1
Measured
UCL '08
0.0E+00
5.0E-09
1.0E-08
1.5E-08
2.0E-08
2.5E-08
3.0E-08
3.5E-08
4.0E-08
4.5E-08
5.0E-08
606 608 610 612 614 616 618 620 622
Wavelength / nm
Ab
so
rpti
on
Co
eff
icie
nt
/ c
m-1
Measured
HITRAN '06
II. Improved Water Monomer Parameters
• To get the water dimer spectroscopy correct we need an accurate understanding of the water monomer contribution to the observed experimental spectra
[*] Courtesy of R. L. Jones & A. J. L. Shillings, University of Cambridge.
III. Improved Water Dimer Characteristics
• May exist in various configurations
• Has feasible tunnelling between equivalent geometries
• Has a complex potential energy landscape
• Full dimensional potential exists*
[*] X. Huang et al. J. Phys. Chem. A 110, 445 (2006); X. Huang et al. J. Chem. Phys. 128, 034312 (2008).
III. Improved Water Dimer Characteristics• Monomer corrected
Bowman dimer potential used*.
• Corrects for monomer excitation
[*] R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. Van der Avoird, JQRST. Submitted.
III. Water Dimer Characteristics
• Dimer VRT states complicated by tunnelling effects• Tunnelling between equivalent states in the PES is
feasible!• Acceptor Tunnelling:
– No bond breaking here– Lowest tunnelling barrier
• Also, by breaking the Hydrogen bond, other tunnelling paths possible: – Donor-Acceptor interchange– Donor Bifurcation Tunnelling
III. Water Dimer Characteristics
• Calculating the lowest energy Vibration-Rotation Calculating the lowest energy Vibration-Rotation Tunnelling states is a good test for a water dimer Tunnelling states is a good test for a water dimer potentialpotential– Rigid monomer Hamiltonian*Rigid monomer Hamiltonian*
• There exists Low temperature high-resolution Tetrahertz There exists Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), Spectroscopy (prepared in supersonic molecular beams), around 5 K.around 5 K.
[*] G. Brocks et al. Mol. Phys. 50, 1025 (1983).
IV. Water Dimer VRT Levels
• In cm-1• Red – ab initio potential• Black – experimental
• GS – ground state
• DT – donor torsion
• AW – acceptor wag
• AT – acceptor twist
• DT2 – donor torsion overtone
[*] R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. Van der Avoird, JQRST. Submitted.
IV. Water Dimer VRT Levels
• Very good agreement with:– Ground State
Tunnelling splittings
– Rotational Constants
• Not so good agreement with:– Acceptor
Tunnelling[*] R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. Van der Avoird, JQRST. Submitted.
Water Dimer Characteristics
ZPE = 9899 ± 5 cm-1
9854 ± 3 cm-1
Structure Symmetry HBB HBB+SHI08 Benchmark*1Cs 0.0 0.0 02C1 161.4 159.6 1813Cs 198.5 193.5 1984Ci 244.0 241.1 2455C2 329.3 323.9 3236C2h 348.1 340.6 3487Cs 603.0 601.3 6358C2h 1181.8 1178.9 12499C2v 590.2 588.2 625
10C2v 898.3 894.8 948* G. S. Tschumper et al. JCP 116, 690 (2002).
V. Adiabatic Separation
Adiabatic Separation of Vibrational Modes Adiabatic Separation of Vibrational Modes Separate intermolecular and intramolecular Separate intermolecular and intramolecular
modes.modes.
mm11 = water monomer 1 Vibrational Wavefunction = water monomer 1 Vibrational Wavefunction
mm22 = water monomer 2 Vibrational Wavefunction = water monomer 2 Vibrational Wavefunction
d = dimer Vibration-Rotation Wavefunctiond = dimer Vibration-Rotation Wavefunction
dmm 21
• Transition:
• Approximation:(Franck Condon type).0th Order Model
2
2121
2fffiii
fi dmmdmmI
fi mm
mExcite
22
1
22
1122
fifi
mmddmmfi
=1
• (2) Franck Condon Factor
(square of overlap integral)
• (1) Monomer Vibrational Band Intensity
V. New MethodologyFranck-Condon Type Approx for IR spectra
1. Vibrational Band Intensities
2. Franck-Condon factors
– Overlap between dimer states on adiabatic potential energy surfaces for water monomer initial and final states
– Need the dimer states (based on this model).
Calculating Dimer States with New Approach
Vibrationally average potential on
Condor machine(large jobs!)
Create Monomer band origins in the
dimer (with DVR3D)
CreateG4 symmetry
Hamiltonian blocks
Solve eigenproblemsObtain energies
and wavefunctions
Create dot productsbetween eigenvectors
to get FC factors
Combine with Matt’sBand intensitiesto get spectra
Complete Water Dimer Energy Level Diagram
Intramolecular/ Intermolecular distance
Slightly complicated byLocalisation of monomerexcitations
Allowed Transitions in our Model
1. Acceptor 2. Donor
Also not between excited monomer states
Assume excitation localised on one monomer
Adiabatic Surfaces
1. Acceptor bend 2. Donor bend
1597.5 1608.21594.8 1594.8
Monomer well
Have perturbed monomer wavefunctions from these DVR3D calculations
Calculating Dimer States
Vibrationally average potential on
Condor machine(large jobs!)
Create Monomer band origins in the
dimer (with DVR3D)
CreateG4 symmetry
Hamiltonian blocks
Solve eigenproblemsObtain energies
and wavefunctions
Create dot productsbetween eigenvectors
to get FC factors
Combine with Matt’sBand intensitiesto get spectra
• Large grid calculations performed with these new perturbed monomer wavefunctions
• For each dimer geometry on 6D grid (~3 million points)
• Up to 10,000 cm-1 • Took around 2 weeks on 500 machines• New run up to 16,000 cm-1 running
Averaging Technique
);,()()(
)()(|);,(|)()(
212
222
11
2211212211
rqqqq
qqrqqqq
Vmm
mmVmm
Now we averaged the potential, we can start the dimer energy level (and wavefunction) calculations
Vibrational Averaging larger calculations
• Energies up to 16,000 cm-1 sufficient.
• Computation:
– typical number of DVR points with different Morse Parameters:
– {9,9,24} gives 1,080 points for monomer (cf. 17,864)
– 1,0802 = 1,166,400 points for the dimer (cf. 319,122,496)
– 1,166,400 * 2,894,301 intermolecular points
= 3,374,862,926,400 points
Calculating Dimer States
Vibrationally average potential on
Condor machine(large jobs!)
Create Monomer band origins in the
dimer (with DVR3D)
CreateG4 symmetry
Hamiltonian blocks
Solve eigenproblemsObtain energies
and wavefunctions
Create dot productsbetween eigenvectors
to get FC factors
Combine with Matt’sBand intensitiesto get spectra
Allowed Permutations with excited monomers
1 15 5
2 26 6
4
4
3
3
1 1
5 5
2 26 6
6 6
6 6
5
5 5
5
4
4
3
3
3 3
3 3
4
4
4
4
1 1
1 1
2
2 2
2
• G16 Symmetry of Hamiltonian for GS mononers– > replaced with G4
• Dimer program modified substantially to print Hamiltonian into G4 symmetry blocks
• Separate eigensolver to obtain energy levels and dimer wavefunctions
Symmetry
Calculating transition energies
Combing monomer DVR3D calculations and dimer energies
Etrans
From monomer DVR3D calculations
Calculating Dimer States
Vibrationally average potential on
Condor machine(large jobs!)
Create Monomer band origins in the
dimer (with DVR3D)
CreateG4 symmetry
Hamiltonian blocks
Solve eigenproblemsObtain energies
and wavefunctions
Create dot productsbetween eigenvectors
to get FC factors
Combine with Matt’sband intensitiesto get spectra
Donor and Acceptor Bend FC factors
Dim
er VR
T
Ground
State
G4 symmetry so each dimer state has 4 similar transitions but with different energy
Calculating Dimer States
Vibrationally average potential on
Condor machine(large jobs!)
Create Monomer band origins in the
dimer (with DVR3D)
CreateG4 symmetry
Hamiltonian blocks
Solve eigenproblemsObtain energies
and wavefunctions
Create dot productsbetween eigenvectors
to get FC factors
Combine with Matt’sband intensitiesto get spectra
Full Vibrational Stick Spectra (low T ~100K?)
1.00E-56
1.00E-50
1.00E-44
1.00E-38
1.00E-32
1.00E-26
1.00E-20
1.00E-14
1.00E-08
1.00E-02
1000 4000 7000 10000
Frequency (cm-1)
Ab
sorp
tio
n (
Hit
ran
un
its)
1.00E-281.00E-271.00E-261.00E-251.00E-241.00E-231.00E-221.00E-211.00E-201.00E-191.00E-181.00E-171.00E-16
1000 4000 7000 10000
Strongest absorption on bend – difficult todistinguish from monomer features
Looks like area of interest – lots going on between 6000-9000cm-1
CAVIAR measurements & theory: (1600-8000 cm-1)
1300 1400 1500 1600 1700 1800 19000.0
0.2
0.4
0.6
0.8
1.0
1.2Keq=0.039 atm-1, HWHM=30 cm-1
17.85 mb pure H2OThreshold=3; Grad.=0.05
Cs
(1
0-20
cm
2 m
ole
c-1a
tm-1
)
Wavenumber (cm-1)
MT_CKD RAL (2007) /295K, 128m/ Tobin et al. 1996 /296 K/ Burch, 1981 /308K/ WD (S&K, 2003) WD (KjSaGaVi-2009) WD (UCL-2009 v1) / 48 WD (UCL-2009 v2) / 48
3400 3500 3600 3700 3800 39000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Wavenumber, cm-1
/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/
Keq=0.041 atm-1, hwhm=25 cm-1
15.3 mb purer H2O
Cs,
10
-20 c
m2 *
mo
lec
-1at
m-1
CKD-2.4 MT_CKD WD (S&K-2003) MSF (RAL-2007) Burch cont. corr. to Hit04 WD (KjSaGaVi-2009) WD (UCL-2009 v1) / 24 WD (UCL-2009 v2) / 24
5000 5100 5200 5300 5400 5500 56000.0
0.2
0.4
0.6
0.8
1.0
1.2
/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/
Keq=0.041 atm-1, hwhm=30 cm-115.3 mb pure H2O
opt.depth/273.15*293/2.69e19/0.0151^2/51275
Everything (excluding Burch data) is with the 'Base term' subtracted !!!
Wavenumber, cm-1
/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/
Cs,
1
0-21
cm
2 *m
ole
c-1a
tm-1
WD (S&K-2003) MSF (RAL-2007) Ptashnik et al. (2004) 299K CKD 2.4, 293K MT_CKD 1.10, 293K WD (KjSaGaVi-2009) WD (UCL-2009 v.1) / 48 WD (UCL-2009 v.2) / 48
6900 7000 7100 7200 7300 7400 75000.0
0.1
0.2
0.3
0.4
0.5
0.6/Res. 0.01 cm-1; 293K; 512.75m; 1.15mm apert., f=418.0mm/
Keq=0.041 atm-1, hwhm=30 cm-1
Wavenumber, cm-1
15.3 mb pure H2O
Cs,
10
-21 c
m2
mo
lec
-1at
m-1
CKD-2.4 MT_CKD MSF RAL (2007), 293K WD (S&K-2003) WD (KjSaGaVi-2009) WD (UCL-2009 v.1) / 24 WD (UCL-2009 v.2) / 24
VII. Conclusions
• Preliminary Stick spectra for up to 10,000cm-1 produced.– Band profiles provided by Igor show some encouraging signs.– Larger calculations were performed to check convergence.– Effects of the sampling of the potential being investigated.
• New averaging job running for input for spectra up to 16,000cm-1.
• All states up to disociation– Only 8 states here
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