Preliminary Results for Water Dimer Spectroscopy Simulations

1. 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 STFC, Cosener's House December 15, 2009

2. Contents • I. Motivations • II. Improved Water Monomer Parameters • III. Water Dimer Characteristics • IV. Water Dimer VRT states • V. New Methodology • VI. Summary

3. 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.

4. 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.

5. 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. A110, 445 (2006); X. Huang et al. J. Chem. Phys. 128, 034312 (2008).

6. 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.

7. 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

8. III. Water Dimer Characteristics • Calculating the lowest energy Vibration-Rotation Tunnelling states is a good test for a water dimer potential • Rigid monomer Hamiltonian* • There exists Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), around 5 K. [*] G. Brocks et al. Mol. Phys. 50, 1025 (1983).

9. 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.

10. 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.

11. Water Dimer Characteristics ZPE = 9899 ± 5 cm-1 9854 ± 3 cm-1 * G. S. Tschumper et al. JCP 116, 690 (2002).

12. V. Adiabatic Separation • Adiabatic Separation of Vibrational Modes • Separate intermolecular and intramolecular modes. • m1 = water monomer 1 VibrationalWavefunction • m2 = water monomer 2 VibrationalWavefunction • d = dimer Vibration-Rotation Wavefunction

13. V. New MethodologyFranck-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)

14. 1. Vibrational Band Intensities

15. 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).

16. Calculating Dimer States with New Approach 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. Complete Water Dimer Energy Level Diagram Slightly complicated by Localisation of monomer excitations Intramolecular/ Intermolecular distance

18. Allowed Transitions in our Model Assume excitation localised on one monomer 2. Donor 1. Acceptor Also not between excited monomer states

19. 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

20. 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

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

22. 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

23. 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

24. 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

25. Symmetry • 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

26. Calculating transition energies From monomer DVR3D calculations Etrans Combing monomer DVR3D c alculations and dimer energies

27. 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

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

29. 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

30. 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?)

31. CAVIAR measurements & theory:(1600-8000 cm-1)

32. 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