1. Ohio State (Current): Charlotte E. HinkleSamantha Horvath Annie LesiakAndrew Petit Sara E. Ray Former group members who were involved in DMC development and applications: Hee-Seung Lee (UNC-Willmington)John M. Herbert (OSU) Benjamin Auer (postdoc at Penn State) Helena Masso (Senet group visitor)Lindsay M. Johnson GENERATING SPECTRA FROM GROUND STATE WAVE FUNCTIONS: UNRAVELING ANHARMONIC EFFECTS IN THE OH -. H 2 O AND H 5 O 2 + VIBRATIONAL PREDISSOCIATION SPECTRA

2. harmonic oscillator treatment of molecular vibrations Can define a set of normal coordinates so that: This leads to a solution to H  =E  that is a product of 1-d harmonic oscillator functions The intensity of a transition is given by If we truncate  at first order, the resulting matrix elements are non-zero when n = 1.

3. How well does this work for H 5 O 2 + ? Scaled harmonic spectrum (from the HBB PES/DMS) When the mass of the bridging hydrogen is infinite Spectrum: N. I. Hammer, E. G. Diken, …, MAJ, JCP 122, 244301 (2005) PES: X. Huang, B. J. Braams and J. M. Bowman Combination of OO/ HOH wags – H.-D. Meyer H5O2+H5O2+

4. Harmonic spectrum of H 3 O 2 -

5. How can we go beyond the harmonic treatment for frequencies/transition intensities? 2 nd order perturbation theory

6. Spectrum: N. I. Hammer, E. G. Diken, …, MAJ, JCP 122, 244301 (2005) PES: X. Huang, B. J. Braams and J. M. Bowman What about other regions of the spectrum? Scaled harmonic spectrum (from the HBB PES/DMS) When the mass of the bridging hydrogen is infinite Combination of OO/ HOH wags – H.-D. Meyer H5O2+H5O2+ HarmonicAnharmonic 901 cm -1 -952cm -1 1796 cm -1 1909 cm -1 [MP2/6-311+G(p,d)] Need to be more Sophisticated in our Treatment of the low-frequency modes

7. How can we go beyond the harmonic treatment for frequencies/transition intensities? 2 nd order perturbation theory Are there other models we could use?

8. Fixed-Node Diffusion Monte Carlo* Use Quantum Monte Carlo to obtain the ground state wave function (and probability distribution), based on a potential surface Statistical approach that is ideally suited for ground state calculations of energies; wave functions and probability amplitudes – excited states provide challenges (V. Buch, S. J. Singer, ABM, …) At the end one has a Monte Carlo sampling of the ground state probability distributions and a value for the zero-point energies Excited states are obtained by a “fixed node” approximation * See Andrew Petit and Charlotte Hinkles’ talks on Thursday

9. Calculating excited states 1) Divide the potential with an infinite barrier 2) Calculate the ground states for both halves of the potential 3) Combine two halves of the wave function to form the excited state

10. RESULTS FOR H 3 O 2 - ABM, X. Huang, S.Carter and J.M.Bowman, JCP 123 064317/1-14 (2005)

11. How can we go beyond the harmonic treatment for frequencies/transition intensities? 2 nd order perturbation theory Are there other models we could use? Can we combine the DMC and ideas of harmonic treatments?

12. What is meant by “simple harmonic oscillator/rigid rotor treatment”? Can define a set of normal coordinates so that: This leads to a solution to H  =E  that is a product of 1-d harmonic oscillator functions The intensity of a transition is given by If we truncate  at first order, the resulting matrix elements are non-zero when n = 1. Can we exploit the fact that in the harmonic treatment,  n = N n f n (q)  0 (q) to approximate excited state wave functions, energies and tansition intensities?

13. Proof of principle for H 3 O 2 - Run DMC calculations so the walkers remain in an Eckart frame Obtain a ground state probability distribution Approximatewhere the s mode that is being excited – use hermite polynomials for higher excited states Use expressions for E and matrix elements for the dipole moment operator, expressed as integrals of multiplicative operators averaged over the ground state probability amplitude ABM, E. G. Diken and M. A. Johnson, in press JPCA [R.B. Gerber Festschrift].

15. Harmonic spectrum of H 3 O 2 - JPCA 109, 1487-90 (2005).

16. Comparing frequencies (H 3 O 2 - ): Mode ModelMultimode * DMC 136563634.03610.0 236673641.03610.0 3487515.0505.0 4610576.0588.0 5548465.0479.0 613431299.01102.0 714931473.0 8763741.0644.0 9169132.0131.0 * (ABM), Xinchuan Huang Stuart Carter and J. M. Bowman, 123, 064317/1-14 (2005).

17. Spectrum E. G. Diken, MAJohnson, and ABM, JPCA 109, 1487-90 (2005).

18. Spectrum ABM, E. G. Diken and M. A. Johnson, JPCA on line ASAP

19. harmonic calculations for H 5 O 2 + Scaled harmonic spectrum (from the HBB PES/DMS) When the mass of the bridging hydrogen is infinite X. Huang, B. J. Braams and J. M. Bowman

20. Comparison of Expt / theory for H 5 O 2 + : L. R. McCunn, J. R. Roscioli, MAJ and ABM, JPCB 112, 321 (2008)

21. Outlooks and challenges Often we can gain important insights from harmonic treatments. With a potential surface, fixed node DMC is more effective for determining excited state energies and wave functions than we would have expected at the outset The difficulty is we need a potential There are also challenges around the determination of spectra, and the model approach described here looks promising Other DMC applications: Based on preliminary studies, we find that we can obtain excited rotational states with DMC and analysis of these functions provides insights into rotation/vibration coupling in these molecules. [Andrew Petit/Charlotte Hinkle RJ03/4] The reaction path approach looks promising for deciphering the kinetics and dynamics of very floppy intermediates [Charlotte Hinkle WF11]

22. Acknowledgements: DMC development : Hee-Seung Lee (PhD; Assistant professor at UNC-Willmington) John M. Herbert (REU student – 1998; UW PhD 2003; Assist. Prof. at OSU) Benjamin M. Auer (Undergraduate – 2000-2003; Postdoc with S.H-S at PSU) Ion/water clusters (Expt.): Current Group members: Mark A. Johnson (Yale) Annie Lesiek Joseph R. Roscioli Charlotte E. Hinkle Eric DikenSamantha Horvath Ben Elliot George GardenierLindsay M. Johnson Theory/potentials: Joel M. Bowman (Emory) Stuart Carter Xinchuang Huang Funding:NSF Andrew Petit, Charlotte Hinkle Annie Lesiek, Samantha Horvath + Sara Ray MI13 WF10 RJ03 RJ04;WF11