Towards Theoretical Spectroscopy of the Water Dimer

1. Towards Theoretical Spectroscopy of the Water Dimer 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 University of Leicester September 2009

2. Franck-Condon Type Approx for IR spectra • Transition: • Approximation: (Franck Condon type). 0th Order Model =1 • (1) Monomer Vibrational Band Intensity • (2) Franck Condon Factor • (square of overlap integral)

3. 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).

4. Calculating Dimer States Solve eigenproblems Obtain energies and wavefunctions Create Monomer band origins in the dimer (with DVR3D) Create dot products between eigenvectors to get FC factors Vibrationally average potential on Condor machine (large jobs!) Combine with Matt’s Band intensities to get spectra Create G4 symmetry Hamiltonian blocks

5. Complete Water Dimer Energy Level Diagram Slightly complicated by Localisation of monomer excitations Intramolecular/ Intermolecular distance

6. Allowed Transitions Assume excitation localised on one monomer 2. Donor 1. Acceptor Also not between excited monomer states

7. Adiabatic Surfaces 1. Acceptor bend 2. Donor bend Have perturbed monomer wavefunctions from these DVR3D calculations Monomer well 1597.5 1608.2 1594.8 1594.8

8. Calculating Dimer States Solve eigenproblems Obtain energies and wavefunctions Create Monomer band origins in the dimer (with DVR3D) Create dot products between eigenvectors to get FC factors Vibrationally average potential on Condor machine (large jobs!) Combine with Matt’s Band intensities to get spectra Create G4 symmetry Hamiltonian blocks

9. Averaging Technique • 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 Now we averaged the potential, we can start the dimer energy level (and wavefunction) calculations

10. Calculating Dimer States Solve eigenproblems Obtain energies and wavefunctions Create Monomer band origins in the dimer (with DVR3D) Create dot products between eigenvectors to get FC factors Vibrationally average potential on Condor machine (large jobs!) Combine with Matt’s Band intensities to get spectra Create G4 symmetry Hamiltonian blocks

11. Allowed Permutations with excited monomers 2 2 6 6 4 3 1 1 5 5 3 4 1 1 2 6 2 6 3 4 5 5 4 3 1 2 1 2 6 6 3 3 5 5 4 4 2 2 1 1 6 6 4 4 5 5 3 3

12. Symmetry • 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

13. Calculating transition energies From monomer DVR3D calculations Etrans Combing monomer DVR3D calculations and dimer energies

14. Calculating Dimer States Solve eigenproblems Obtain energies and wavefunctions Create Monomer band origins in the dimer (with DVR3D) Create dot products between eigenvectors to get FC factors Vibrationally average potential on Condor machine (large jobs!) Combine with Matt’s band intensities to get spectra Create G4 symmetry Hamiltonian blocks

15. Donor and Acceptor Bend FC factors G4 symmetry so each dimer state has 4 similar transitions but with different energy Dimer VRT Ground State

16. Calculating Dimer States Solve eigenproblems Obtain energies and wavefunctions Create Monomer band origins in the dimer (with DVR3D) Create dot products between eigenvectors to get FC factors Vibrationally average potential on Condor machine (large jobs!) Combine with Matt’s band intensities to get spectra Create G4 symmetry Hamiltonian blocks

17. Strongest absorption on bend – difficult to distinguish from monomer features Looks like area of interest – lots going on between 6000-9000cm-1 Full Vibrational Stick Spectra (low T ~100K?)

18. 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