1. Theoretical Modelling of the Water Dimer: Progress and Current Direction 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. NPL, June 2008

2. Contents  I. Review of previous work  II. Characterising more states  III. New Potential Energy Surface  IV. Franck-Condon Type Approach  V. Vibrational Averaging of the PES

3. I.1. Brocks et al. Hamiltonian  Water Dimer Vibration-Rotation Tunneling (VRT) levels from the Rigid Dimer Hamiltonian by Brocks et al. [1].  Only for the Intermolecular modes  Used for water dimer previously, detailed account [2].  Dependent on V (6D). We used new 12D Potential Energy Surface (PES).  Compared with Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), around 5 K. [1] G. Brocks, A. van der Avoird, B. T. Sutcliffe, J. Tennyson, Mol. Phys. 50, 1025 (1983). [2] G. C. Groenenboom, et al., JCP 113, 6702 (2000).

4.  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 I.2. Vibration-Rotation Tunnelling

5. I.3. Labelling Water Dimer States  Can be represented by Permutation-Inversion Group G 16. 1 1 11 5 5 5 5 2 2 22 66 6 6 6 6 6 6 5 55 5 4 4 4 4 3 3 3 3 3 3 3 3 4 4 4 4 1 1 1 1 2 2 2 2  Isomorphic to D 4h with Irreducible Elements: A 1 +, A 2 +, A 1 -, A 2 -, B 1 +, B 2 +, B 1 -, B 2 -, E +, E - -> Water Dimer Spectroscopic Labels

6. I.4. Ground State VRT Levels for H 4 O 2 [1] X. Huang, B. J. Braams, J. M. Bowman, R. E. A. Kelly, J. Tennyson, G. C. Groenenboom, A. van der Avoird, J. Chem. Phys. 128, 034312 (2008). Very good agreement:  Ground State Tunnelling splittings  Rotational Constants Not so good agreement:  Acceptor Tunnelling

7. II. Characterising States up to 60cm-1  J=0,…,8, K=0,..,J.  J=0,…,20, K=0,1,2.  E states are not included because they are very large calculations – UCL LEGION facility.  Actually many more states included, should be relatively simple to go up to say 100-200cm-1.  Helped with a new 64GB RAM computer. –Large Hamiltonians can be stored in memory.

8. III. Modified water dimer PES  New 12D Huang et al. PES seems to work well for low-level dimer VRT states  Not so well for Monomer Modes.  Correction for monomer modes:  New Potential Expression:  Tests for Potential  Revaluation of the saddle points.  Revaluation of the dimer VRT states. Picture from: X. Huang, B. J. Braams, J. M. Bowman, J. Phys. Chem. A 110, 445 (2006).

9. Dimer Absorption Model  to calculate water dimer absorption throughout visible and IR region in the atmosphere ab initio.  Direct Computation impossible!  We have developed a new model.

10. IV. Franck-Condon Type Approximation  Recap – FC approx:  BO approx:  Assume Transition is vertical:  Franck-Condon Factor (square of overlap integral)  Electronic Band intensity

11. Adiabatic Separation of Vibrational Modes  Separate intermolecular and intramolecular modes.  m 1 = water monomer 1 Vibrational Wavefunction  m 2 = water monomer 2 Vibrational Wavefunction  d = dimer Vibration-Rotation Wavefunction

12.  Transition:  Approximation: (Franck-Condon type). 0 th Order Model =1  Franck-Condon Factor  Monomer Vibrational Band Intensity IV. Franck-Condon Type Approx

13. Comp realisation  Monomer Vibrational Band intensities –> Matt.  Franck-Condon factors: –Overlap between dimer states on adiabatic potential energy surfaces for water monomer initial and final states

14. V. Vibrational Averaging  Modify van der Avoird et al. methodology to implement 12D flexibility for VRT levels.  Since only 6D code.  Separate intermolecular and intramolecular modes.  For each monomer state and calculate VRT levels.  We want to vibrationally average the potential for monomer modes.  In this way, we can create a 12D effective PES.

15. V. Vibrational Averaging  Very many potential energy points need to be evaluated.  Example: –typical number of DVR points: –{28, 28, 44} gives 17,864 points for monomer –17,864 2 = 319,122,496 points for the dimer –319,122,496 * 2,894,301 intermolecular points = 923,349,349,048,896 points - one bad headache!

16.  Energies up to 16,000 cm-1 sufficient.  Use simpler monomer wavefunctions.  Easier Computation: –typical number of DVR points with different Morse Parameters: –{9,9,24} gives 1,080 points for monomer (cf. 17,864) –1,080 2 = 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 - one not so bad headache! (cf. 923,349,349,048,896) V. Vibrational Averaging Calculations to be done on UCL condor service (pool of 1,400 UCL computers)

17. Discussion  Work in Progress.  Comments welcome.