High Accuracy Treatment of NO 3 Energy Levels (not really), Not Exactly the Talk I Had Envisioned John F. Stanton Christopher Simmons Takatoshi Ichino Kerstin Klein

Spectroscopic problem Adiabatic Picture Hard work Quantitative Agreement Quantitative Agreement Rationalize Results Rationalize Results Qualitative Insight

Spectroscopic problem Adiabatic Picture Hard work Quantitative Agreement Quantitative Agreement Rationalize Results Rationalize Results Qualitative Insight Diabatic Picture Diabatic Picture Simple Model Elaborate Model

Spectroscopic problem Adiabatic Picture Hard work Quantitative Agreement Quantitative Agreement Rationalize Results Rationalize Results Qualitative Insight Diabatic Picture Diabatic Picture Simple Model Elaborate Model

A 2 E’’ a 2 2 3, 4 X2A2’X2A2’ A 2 E’’ b B 2 E’ a B 2 E’ b ˜˜˜˜˜ X 2 A 2 ’ A 2 E’’ a A 2 E’’ b B 2 E’ a B 2 E’ b ˜ ˜ ˜ ˜ ˜

Diabatic/quasidiabatic Hamiltonian approach and NO 3 (Longuet-Higgins, Gouterman, Köppel, Domcke, Cederbaum) Effective in qualitative investigation of X-band negative ion photoelectron spectrum (Mayer, Cederbaum and Köppel JCP 100, 899 (1994)) Effective in qualitative investigation of dispersed fluorescence spectra Reinterpretation of ν 3 : 1492 cm -1 to ca cm -1 (Stanton JCP 126, (2007)) Effective in qualitative investigation of B-X excitation spectra (Stanton and Jacox, unpublished) Ineffective in qualitative investigation of A-band negative ion photoelectron spectrum (Mahapatra, Eisfeld and Köppel CPL 441, 7 (2007))

The Good

Simulation of NO 3 - Photodetachment Spectrum to X State ~ T=450 K

Simulation of X B Absorption Spectrum of NO 3 ~ ~ Hot bands

Simulation of cm -1 dispersed fluorescence of NO 3 (X B) ~ ~ wrt ground level

The Ugly

Simulation of NO 3 - Photodetachment Spectrum to A State ~

The Less Ugly Partial quartic parametrization Faraji, Köppel, Eisfeld and Mahapatra 347, 110 (2008)

Can the KDC approach be made sufficiently quantitative to be useful for this problem?

Pros and Cons of the LVC model in this parametrization: Extremely simple and outstanding qualitative model that has been used for nearly thirty years to identify vibronic coupling in molecular systems. Calculations are straightforward. But… Does not account for either anharmonicity or Duschinsky mixing in the symmetric modes. Two state model approach for coupling coordinates relies on assumption that “quasidiabatic force constants” for coupling modes are similar in the two states. This is chemically reasonable (unlike similar assumptions about adiabatic force constants), but at best qualitatively accurate. And there are cases where this assumption clearly fails (wagging mode of HCO 2 ). There are potential problems when the number of states involved in the coupling is greater than two (cyclopentadienyl radical)

How can we make this quantitative? How “good” can it be? Totally symmetric modes can be treated by a higher-order Taylor series. quadratic has been done sometimes (the so-called QVC) model, but we have gone up to quartic terms. Typical parametrizations are such that the adiabatic and ab initio potentials are identical at the origin of the coordinate system (vertical parametrization). We have developed a parametrization method such that the adiabatic model potentials agree exactly with the ab initio potentials at the minima of the final states (adiabatic parametrization*). By making an ansatz for the quasidiabatic states, we have recently come up with an analytic method for calculating the coupling constants**. This allows us to extend the coupling to nonlinear terms. * T. Ichino, A.J. Gianola, W.C. Lineberger and J.F. Stanton, JCP 125, (2006). **T. Ichino, J. Gauss and J.F. Stanton, JCP 130, (2009).

The “adiabatic” parametrization (Ichino, et al.) neutral Nothing new, in a sense. Same idea used in Franck-Condon simulations for decades. D

Some new terminology VP1Vertical parametrization (LVC model) VP2Vertical parametrization (QVC) VPnVertical parametrization, potentials expanded to n th order AP2Adiabatic parametrization (through quadratic terms) AP4Adiabatic parametrization (through quartic terms)

AP4 AP2

AP4 AP2

Minimum Pseudorotation barrier Conical Intersection

A rather gross (and unpalatable) assumption: Treat the A state as a C 2v molecule (ignore pseudorotation) Other computational minutae: Adiabatic parametrization (AP2) in conjunction with large basis set Jahn-Teller coupling treated by EOMIP-CCSD theory Ignore coupling between A state and B state Totally symmetric force field treated with CCSD(T) Truncate parametrization as quadratic

ANO1/CCSD(T) Vertical Parametrization (Jahn-Teller Spectrum) Very promising (and preliminary) result!

Coming later this summer: Full-blown AP4 treatment of NO 3 Thank you!