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

Transition: Approximation: (Franck Condon type). 0 th Order Model =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) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matt’s Band intensities to get spectra

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

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 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) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matt’s Band intensities to 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 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) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matt’s Band intensities to get spectra

Allowed Permutations with excited monomers

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 E trans From monomer DVR3D calculations

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

Donor and Acceptor Bend FC factors Dimer VRTGround 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) Create G4 symmetry Hamiltonian blocks Solve eigenproblems Obtain energies and wavefunctions Create dot products between eigenvectors to get FC factors Combine with Matt’s band intensities to get spectra

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