1. Towards a Spectroscopically Flexible Water Dimer Potential Energy Surface Ross E. A. Kelly, and Jonathan Tennyson Department of Physics & Astronomy University College London Gerrit C. Groenenboom and Ad van der Avoird Gerrit C. Groenenboom and Ad van der Avoird Theoretical Chemistry, Institute for Molecules and Materials, Radboud University, Nijmegen. Imperial College, December 2008

2. Outline I. Motivations I. Motivations II. The Water Dimer II. The Water Dimer III. Vibration-Rotation Tunnelling III. Vibration-Rotation Tunnelling IV. Dimer Potentials IV. Dimer Potentials V. Theoretical Method V. Theoretical Method VI. VRT States VI. VRT States VII. Monomer Band Origins VII. Monomer Band Origins VIII. Monomer Corrected Surface VIII. Monomer Corrected Surface IX. Conclusions & Further Work IX. Conclusions & Further Work

3. I. Motivations to understand water dimer absorption throughout visible and IR region in the atmosphere. to understand water dimer absorption throughout visible and IR region in the atmosphere. To create a high accuracy water dimer spectra in agreement with experiments. To create a high accuracy water dimer spectra in agreement with experiments. To create a linelist of all possible water dimer transitions. To create a linelist of all possible water dimer transitions.

4. To get all Vibration Rotation Energy Levels Calculations require: To get all Vibration Rotation Energy Levels Calculations require: 1. Some theoretical methodology for solving the Hamiltonian 1. Some theoretical methodology for solving the Hamiltonian 2. High accuracy Potential Energy Surface 2. High accuracy Potential Energy Surface Preferably fully flexible (12D) Preferably fully flexible (12D) 4 O-H distances 4 O-H distances 2 H-O-H Angles 2 H-O-H Angles O-O distance O-O distance 5 Euler Angles 5 Euler Angles II. Water Dimer

5. Extremely Complex Landscape Extremely Complex Landscape X. Huang, B. J. Braams, J. M. Bowman, J. Phys. Chem. A 110, 445 (2006). II. Water Dimer

6. Complicated further by tunnelling effects! Tunnelling between eqiulavent 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 III. Vibration-Rotation Tunnelling

7. 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 III. Labelling Water Dimer States

8. [1] R. Bukowski, K. Szalewicz, G. C. Groenenboom, A. van der Avoird, Science 315, p1249-1252 (2007). [2] X. Huang, B. J. Braams, J. M. Bowman, J. Phys. Chem. A 110, 445 (2006). [3] 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) Benchmark: Benchmark: 6D CC-pol Potential [1] - Rigid Monomers 6D CC-pol Potential [1] - Rigid Monomers New (2) 12D PESs by Huang, Braams & Bowman [2,3] New (2) 12D PESs by Huang, Braams & Bowman [2,3] HBB0 [2] HBB0 [2] and HBB [3] – NEW 12D PES and HBB [3] – NEW 12D PES - All completely ab initio - Good agreement with experiment Many PESs available! Many PESs available! IV. Dimer Potentials Available

9. 30 000 configurations. 30 000 configurations. Calculated at coupled-cluster, single and double and perturbative treatment of triple excitations method. Calculated at coupled-cluster, single and double and perturbative treatment of triple excitations method. augmented, correlation consistent, polarized triple zeta basis set. augmented, correlation consistent, polarized triple zeta basis set. Polynomial fit with 5227 coefficients. Polynomial fit with 5227 coefficients. However, compared to CCpol potential (benchmark): However, compared to CCpol potential (benchmark): Lower relative grid coverage of the surface than benchmark 6D PES. Lower relative grid coverage of the surface than benchmark 6D PES. Not extrapolated to the complete basis set limit (CBS) Not extrapolated to the complete basis set limit (CBS) No bond functions in analytical fit No bond functions in analytical fit Dissociation less accurately described Dissociation less accurately described 12D IV. HBB PES 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).

10. Dissociation Energy = 1665.82 cm -1 / 1757.90 cm -1 Dissociation Energy = 1665.82 cm -1 / 1757.90 cm -1 Other tests? Other tests? Compare with Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), around 5 K. Compare with Low temperature high-resolution Tetrahertz Spectroscopy (prepared in supersonic molecular beams), around 5 K. How can this be done theoretically? How can this be done theoretically? IV. HBB PES for H 4 O 2

11. Rigid monomer Hamiltonian [1]: Only for the Intermolecular modes Used for water dimer previously, detailed account [2] Coupled product of Symmetric rotor functions (Wigner-D functions) for the Angular coordinates Radial basis: sinc Discrete Variable Representation (DVR) [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). V. Theoretical Method for VRT levels

12. VI. Ground State VRT states 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 with: Ground State Tunnelling splittings Rotational Constants Not so good agreement with: Acceptor Tunnelling

13. Excellent agreement with: Ground State Tunnelling splittings Rotational Constants Not so good agreement with: Acceptor Tunnelling [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). VI. Ground State VRT for D 4 O 2

14. In cm -1 Red – ab initio potential Black – experimental GS – ground state DT – donor torsion AW – acceptor wag AT – acceptor twist DT 2 – donor torsion overtone VI. More low level VRT States for H 4 O 2

15. In cm -1 Red – ab initio potential Black – experimental GS – ground state DT – donor torsion AW – acceptor wag AT – acceptor twist DT 2 – donor torsion overtone VI. More low level VRT States for D 4 O 2

16. VII. Monomer Band Origins New 12D Huang et al. PES seems to work well: New 12D Huang et al. PES seems to work well: –for low-level dimer VRT states How about for H2O monomer energy levels? How about for H2O monomer energy levels? Use DVR3D [1] for Water monomer levels: Use DVR3D [1] for Water monomer levels: 1. J. Tennyson et al., Comp. Phys. Comm. 2004, 163, 85-116.Excite Fix 100 bohr 1. J. Tennyson et al., Comp. Phys. Comm. 2004, 163, 85-116.

17. Comparison is not so good. Comparison is not so good. VII. Monomer Band Origins Blue HBB dimer Blue HBB dimer Green HBB0 Green HBB0 Red Shirin 2008. Red Shirin 2008.(Monomer).

18. VIII. Adding Monomer Correction Correction 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.

19. VIII. Monomer Corrected Surface CharacteristicHBBHBB+MC DeDeDeDe-1657.12-1665.82 Point 2 198.47193.46 Point 3 243.98241.09 Point 4 340.60358.06 Point 5 1178.921181.76 Point 6 588.19590.19 Point 7 894.83898.27 Not Particularly worse than HBB potential.

20. Still a very good agreement with exp. Still a very good agreement with exp. Nothing is changed significantly. Nothing is changed significantly. VIII. Ground State VRT levels for H 4 O 2

21. VIII. More VRT States for HBB+MC surface Again, agreement is not significantly worse. Again, agreement is not significantly worse.

22. IX. Conclusions & Further Work Introduction of monomer correction makes PES more transferable for spectroscopic purposes. Introduction of monomer correction makes PES more transferable for spectroscopic purposes. Little effect on dimer characteristics. Little effect on dimer characteristics. Monomer band origins significantly improved. Monomer band origins significantly improved. We are working towards a model which incorporates monomer excitations into the dimer states, so spectra can be produced. We are working towards a model which incorporates monomer excitations into the dimer states, so spectra can be produced.