Towards Theoretical Spectroscopy of the Water Dimer

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

University of LeicesterSeptember 2009

• 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

Franck-Condon Type Approx for IR spectra

FC type Approach

• 2. Franck-Condon (FC) 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

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

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

• New condor potential 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 started, for 20 weeks

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

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 1

1 1

5 5

5 5

2 2

2 2

6 6

6 6

6 6

6 6

5

5 5

5

4

4

4

4

3

3

3

3

3 3

3 3

4

4

4

4

1 1

1 1

2

2 2

2

• G16 Symmetry of Hamiltonian has to be replaced with G4

• Dimer code modified substantially to break Hamiltonian into G4 symmetry blocks

• Separate code created 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

1.00E-28

1.00E-261.00E-24

1.00E-22

1.00E-20

1.00E-181.00E-16

1.00E-14

1.00E-121.00E-10

1.00E-08

1.00E-06

1.00E-041.00E-02

1.00E+00

1450 1500 1550 1600 1650 1700 1750

Acceptor bend

Donor Bend

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

VII. Conclusions

• Preliminary Stick spectra for up to 10,000cm-1 produced.– Need to add band profiles– Also larger calculations need to be performed to increase accuracy

(jamax basis =8 was used, 10 is desirable)– Also state FC factors should be checked!

• New condor job running for input for spectra up to 16,000cm-1 running. 500 machines for 2 months.

• Needs of the group?– Room temperature calcs require parallelisation of water dimer

eigensolver program– Also slightly modified potential, therefore additional condor jobs