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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
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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
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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).
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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
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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
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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
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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.
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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).
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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.
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IV. Franck-Condon Type Approximation Recap – FC approx: BO approx: Assume Transition is vertical: Franck-Condon Factor (square of overlap integral) Electronic Band intensity
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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
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Transition: Approximation: (Franck-Condon type). 0 th Order Model =1 Franck-Condon Factor Monomer Vibrational Band Intensity IV. Franck-Condon Type Approx
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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
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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.
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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!
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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)
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Discussion Work in Progress. Comments welcome.
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