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