1. Theoretical Studies of the Fundamental and Overtone Spectrum of the Water Dimer D. A. Matthews J. F. Stanton J. Vázquez The University of Texas at Austin D. A. Matthews J. F. Stanton J. Vázquez The University of Texas at Austin

2. The Water Dimer  Simple system to study hydrogen bonding.  The first step to understanding bulk liquid water.  Important in atmospheric processes such as formation of H 2 SO 4 (i.e. acid rain).  Plays some role in absorption of solar radiation in atmosphere.  Simple system to study hydrogen bonding.  The first step to understanding bulk liquid water.  Important in atmospheric processes such as formation of H 2 SO 4 (i.e. acid rain).  Plays some role in absorption of solar radiation in atmosphere.

3. VPT2  Force field may be expressed as a Taylor expansion about the equilibrium geometry:  Both Rayleigh-Schrödinger and van Vleck approaches give the same “dressed” Hamiltonian in second order:  The diagonal terms of this operator give the VPT2 energies.  Force field may be expressed as a Taylor expansion about the equilibrium geometry:  Both Rayleigh-Schrödinger and van Vleck approaches give the same “dressed” Hamiltonian in second order:  The diagonal terms of this operator give the VPT2 energies.

4. VPT2  An example is F 2 : a local approximation to the force field using CCSD(T) give reasonable levels for both methods…  Gives better results than “exact” variational methods for truncated polynomial force fields. E R F-F

5. VPT2  Also, VPT2 is exact for a Morse oscillator, so it is ideal for stretching modes.  But when using the global CCSD(T) force field, the “exact” variational method falls apart. E R F-F !

6. Resonance  Artifact of perturbation theory.  Fermi Resonances:  Affect states coupled by cubic force constants (e.g. 2 1 and 1 + 3 + 8 in the water dimer).  Darling-Dennison Resonances:  Affect states coupled by quartic force constants and coriolis coupling constants (e.g. 2 1 and 2 3 in water).  Artifact of perturbation theory.  Fermi Resonances:  Affect states coupled by cubic force constants (e.g. 2 1 and 1 + 3 + 8 in the water dimer).  Darling-Dennison Resonances:  Affect states coupled by quartic force constants and coriolis coupling constants (e.g. 2 1 and 2 3 in water).

7. Resonance a 2 b c d + e  a ≈ 2  b  c ≈  d +  e First, Fermi resonances are found, and resonant states are added to the effective Hamiltonian. The off-diagonal elements (first order interactions) are given by multiples of the cubic force constants.  abb K aaac, K accc  ade  bbc K bbde  cde

8. Resonance 2  e ≈ 2  c  c +  b ≈ 2  d Second, Darling-Dennison resonances are found and states added to the effective Hamiltonian. The diagonal and off-diagonal elements between these states include second order quartic, bicubic, and coriolis contributions as in the dressed Hamiltonian, except that terms involving cubic constants between Fermi states are removed. 2 e 2 c c + b 2 d K eecc K eecb K eedd K cccb, K cbbb K ccdd K cbdd

9. Resonance Fermi First and second order interactions between Fermi and Darling- Dennison resonant states may be non-zero, leading to mixing of these states. When the effective Hamiltonian is fully formed, it is diagonalized to give the final levels.  aee,  acb, K bbcc, K decc, etc. Darling- Dennison

10. Results: Fundamentals aug-cc-pVTZ a ANO1 a Experiment b Mode (cm -1 ) I (km/mol) (cm -1 ) I (km/mol) (cm -1 ) I (km/mol) v1371162373746373549 v2363453654536603 v3359114836201313601100 v4161439162847161913 v5160368161163159927 v6304730821311 v71446414738143 v8121163108189103 v9372558374849374545 v104957750190523 v11122113110111108 v128554865788 a) Using CCSD(T) frozen core, and VPT2. b) Experimental frequencies from J. Phys. Chem. A, 109 (17), 4005 (2005), Intensities from Ne matrix: Y. Bouteiller and J. P. Perchard, Chem. Phys. 305, 1 (2004).

11. Results: Two-quantum OH Levels aug-cc-pVTZ a ANO1 a Experiment b Dominant State (cm -1 ) I (km/mol) (cm -1 ) I (km/mol) (cm -1 ) Assignment v1+v274120.0174620.02 2v973780.0374240.01 v1+v373110.0673580.07 v2+v372360.8572860.857282no assignment v1+v3/2v271622.0372072.0871932v2 or v1+v3 2v271320.0371740.00 2v370260.0970860.07 v1+v974430.1774910.19 v3+v973110.0173630.10 7240resonance? v2+v971933.0972343.047250 given as 2v1, but probably v2+v9 a) Using CCSD(T) frozen core, VPT2, and diagonalizing Darling-Dennison resonances. b) Gas phase frequencies from Nesbitt et al., J. Chem. Phys. 122, 194316 (2005).

12. Acknowledgements John Stanton Juana Vázquez The Robert A. Welch Foundation The Camille and Henry Dreyfus Foundation John Stanton Juana Vázquez The Robert A. Welch Foundation The Camille and Henry Dreyfus Foundation