Simulating the spectrum of the water dimer in the far infrared and visible

1. Simulating the spectrum of the water dimerin the far infrared and visible Ross E. A. Kelly, Matt J. Barber, Jonathan Tennyson Department of Physics and Astronomy University College London Thanks to: Gerrit C. Groenenboom, Ad van der Avoird Theoretical Chemistry Institute for Molecules and Materials Radboud University CAVIAR Consortium UCL Lab & Theory Meeting 30th April 2010

2. Lab observations in the visible (broad band CRDS) For dimer spectroscopy Need accurate description of water monomer contribution Including weak lines A.J.L. Shillings, S.M. Ball, M.J. Barber, J. Tennyson & R.L. Jones, Atmos. Chem. Phys. (to be submitted)

3. Improved Water Dimer Characteristics • Monomer corrected HBB potential • Corrects for monomer excitation R.E.A. Kelly, J. Tennyson, G C. Groenenboom, A. Van der Avoird, JQRST, 111, 1043 (2010).

4. Water Dimer Characteristics • Lowest Vibration-Rotation Tunnelling (VRT) states: good test for a water dimer potential • Rigid monomer Hamiltonian • Compare with 5 K Tetrahertz Spectra. G. Brocks et al. Mol. Phys. 50, 1025 (1983).

5. 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, 111, 1043 (2010).

6. Model for high frequency absorption • Approximate separation between monomer and dimer modes • Assume monomers provide chromophores • Franck-Condon approximation for vibrational fine structure • Rotational band model (so far)

7. Adiabatic Separation • Adiabatic Separation of vibrational Modes • Separate intermolecular and intramolecular modes. • m1 = water monomer 1 vibrational wavefunction • m2 = water monomer 2 vibrational wavefunction • d = dimer VRT wavefunction

8. Allowed Transitions in our Model Assume excitation localised on one monomer 2. Donor 1. Acceptor All transitions from ground monomer vibrational states

9. Franck-Condon Approx for overtone spectra Assume monomer m1 excited, m2 frozen m2i = m2f I a

10. Franck-Condon Approx for overtone spectra (1) Monomer vibrational band Intensity (2) Franck-Condon factor (square of overlap integral): Gives dimer vibrational fine structure

11. Calculating dimer spectra with FC 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 parallel machine (large jobs!) Combine with Band intensities Simulate spectra Create G4 symmetry Hamiltonian blocks

12. Vibrational band intensities • Calculate from (perturbed) monomer vibrationalwavefunctions • Requires Eckart embedding of axis frame • Use HBB 12 D dipole moment surface (DMS) corrected with accurate monomer DMS CVR: L. Lodi et al, J Chem Phys., 128, 044304 (2008) Issues: • PES used to generate monomer wavefunctions • (Cut) through 12 D DMS used

13. Vibrational band intensities: m at equilibrium

14. Vibrational band intensities: m at R < Req

15. 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. Adiabatic Surfaces 1. Acceptor bend 2. Donor bend Monomer well 1597.5 1608.2 1594.8 1594.8

17. Outline of full problem • Calculate states for donor • Calculate states for acceptor • Vibrationally average potential for each state-state combination • Really only |0j> and |i0> • Need to ultimately solve (6D problem) • H=K+Veff • Veff sampled on a 6D grid

18. Averaging Technique Need effective 6D PES, dependent on monomer state

19. Averaging Technique (a) 6D averaging: (b) 3D+3D averaging: C Leforestier et al, J Chem Phys, 117, 8710 (2002)

20. Vibrational Averaging: 6D • 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 • 1,0802 = 1,166,400 points for both monomers • 1,166,400 x 2,894,301 intermolecular points = 3,374,862,926,400 points • Same monomer wavefunctions for all grid points • Distributed computing: Condor 1000 computers, 10 days

21. Problems with Fixed Wavefunction approach (6D method) • Donor bend

22. Problems with Fixed Wavefunction approach (6D method) • (Donor) Free OH stretch • (Donor) Bound OH stretch

23. Problems with Fixed Wavefunction approach (6D method) • (Donor) Free OH stretch • (Donor) Bound OH stretch

24. Vibrational Averaging: 3D+3D • Energies up to 16,000 cm-1 sufficient. • Computation “reduced” • typical number of DVR points with different Morse Parameters: • {9,9,24} gives 1,080 points for monomer • 2 x 1,080 = 2 160 points for both monomers • 2 160 x 2,894,301 intermolecular points = ‘only’ 624 890 160 points • But requires monomer wavefunctions at each r • Parallel computing: Legion 60 computers, 16 days

25. Allowed Permutations with excited monomers 2 2 6 6 4 3 1 1 5 5 3 4 • G16 Symmetry of Hamiltonian for GS monomers • > replaced with G4 • Dimer program modified: • Hamiltonian in G4 symmetry blocks • Separate eigensolver to obtain energy levels and dimerwavefunctions

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

27. Strongest absorption on bend – difficult to distinguish from monomer features More structure between 6000-9000 cm-1 Full Vibrational Stick Spectra (low T ~100K?)

28. Estimating transition frequencies Band centre from monomer DVR3D calculation Blue/red shift from calculation on perturbed PES Vibrational fine structure from dimer  dimer transitions

29. Simulate spectra at “295 K” • Assume 4.5% dimer concentration • Rotational band profile 30 cm-1 (too narrow?) • Predictions give absolute intensities • 6D averaging But: Vibrational substructure still only for low T (8 J=0 states per symmetry) Results preliminary (main calculations in progress)

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

36. Conclusions • Careful treatment of weak monomer spectra essential • Preliminary spectra for up to 10,000 cm-1 produced. • Band profile comparisons show some encouraging signs.. • Effects of the sampling of the potential being investigated. • New averaging job (3D+3D) running for input for spectra up to 16,000 cm-1. • Need all states up to dissociation • Only 8 states per symmetry here • It is a challenge for a much higher number of states