Progress Towards Theoretical Spectra of the Water Dimer Ross E. A. Kelly, Matt Barber, & Jonathan Tennyson Department of Physics & Astronomy University College London Gerrit C. Groenenboom & Ad van der Avoird Gerrit C. Groenenboom & Ad van der Avoird Theoretical Chemistry, Institute for Molecules & Materials, Radboud University, Nijmegen. Imperial College, December 2008

Contents I. A Spectroscopically Flexible Water Dimer Potential Energy Surface I. A Spectroscopically Flexible Water Dimer Potential Energy Surface II. Dimer Absorption Model Recap II. Dimer Absorption Model Recap III. Dimer States within the FC-type Model III. Dimer States within the FC-type Model IV. Some Dimer States IV. Some Dimer States V. Conclusions & Further Work V. Conclusions & Further Work

I. A Spectroscopically Flexible Water Dimer Potential Energy Surface 12D Huang et al. PES seems to work well for dimer VRT states Not so well for Monomer Modes. Correction for monomer modes: New Potential Expression: Tests for Potential Evaluation of the saddle points. Evaluation of the saddle points. Evaluation of the monomer & dimer VRT states. Evaluation of the monomer & dimer VRT states.

II. Dimer Absorption Model Recap Adiabatic Separation of Vibrational Modes Adiabatic Separation of Vibrational Modes Separate intermolecular and intramolecular modes. Separate intermolecular and intramolecular modes. m 1 = water monomer 1 Vibrational Wavefunction m 1 = water monomer 1 Vibrational Wavefunction m 2 = water monomer 2 Vibrational Wavefunction m 2 = water monomer 2 Vibrational Wavefunction d = dimer Vibration-Rotation Wavefunction d = dimer Vibration-Rotation Wavefunction

Transition: Transition: Approximation: Approximation: (Franck Condon type). 0 th Order Model =1 Franck Condon Factor Franck Condon Factor (square of overlap integral) Monomer Vibrational Band Intensity Monomer Vibrational Band Intensity II. Franck Condon Type Approx

II. Computational realisation Monomer Vibrational Band intensities Monomer Vibrational Band intensities –Matt has made those. Franck-Condon factors: 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).

III. Dimer States For each monomer, monomer state For each monomer, monomer state –need E level calculations To do this, we wanted to vibrationally average the corrected potential for monomer modes. To do this, we wanted to vibrationally average the corrected potential for monomer modes. –A big job, as discussed previously! –Billions up to trillions of function evaluations required! Done this on Condor system at UCL. Done this on Condor system at UCL. –Pool of 1,400 computers.

DVR3D Calculation of grid {n r1,n r2,n θ }. DVR3D Calculation of grid {n r1,n r2,n θ }. Condor Run for evaluating all the points. Condor Run for evaluating all the points. Average points for each dimer point. Average points for each dimer point. Average monomer states to get E shifts. Average monomer states to get E shifts. Find minimum on averaged surface for dimer input. Find minimum on averaged surface for dimer input. Dimer calculations. Dimer calculations. III. Creating Dimer States

III. Vibrational Averaging Runs Two Grids done so far: Two Grids done so far: –{6,6,18} –{7,7,24}, just finished! {6,6,18} Grid. {6,6,18} Grid. –A snip at 413 billion function calls. –Reliable up to 3,657 cm-1. –Simply for testing the method. {7,7,24} Grid. {7,7,24} Grid. –Slightly more expensive at 1.3 trillion function calls. –Reliable up to 11, cm-1. –Good for first real results. Also, convergence can be tested by comparing these 2 grids. Also, convergence can be tested by comparing these 2 grids.

IV. Some States Closer Look at some of these levels

IV. 07,07,24 State Convergence with 06,06,18 (0.1 cm -1 ) Good comparison with HBB+MC only. E levels slightly underestimated as before.

IV. 07,07,24 State Tunnelling levels Convergence with 06,06,18 (0.1 cm -1 ) Good comparison with HBB+MC only. Tunnelling levels slightly overestimated.

IV. Some States Closer Look at some of these levels

IV. 07,07,24 State Similar levels but not exactly the same. Levels change in this region between 0.1 -> 2 cm -1 Dissociation energy is larger: De = cm -1 De (0 0) = cm -1

V. Conclusions & Further Work Method seems to be working. Method seems to be working. E level calculations to be performed over 0- 10,000 cm -1 range for low temp. E level calculations to be performed over 0- 10,000 cm -1 range for low temp. Then all possible transitions to be computed: Then all possible transitions to be computed: –Work started with initial results. –First computed FC factor Stick Spectra first for low temp, 0-10,000cm -1. Stick Spectra first for low temp, 0-10,000cm -1. New Condor Runs can be performed now. New Condor Runs can be performed now.