1. ENERGY LEVELS OF THE NITRATE RADICAL BELOW 2000 CM -1 Christopher S. Simmons, Takatoshi Ichino and John F. Stanton Molecular Spectroscopy Symposium, June 2012 Thanks to: NSF, DOE, Welch Foundation Dan Neumark

2. Overview: 1.Qualitative vibronic coupling Hamiltonian results 2.Construction of quantitative vibronic coupling Hamiltonian 3.A rat's nest of states 4.Comparison of level positions with experiment 5.A truly ab initio simulation of the photodetachment spectrum of NO 3 -

3. Reminder about why NO 3 is so complicated...

4. Before 2009-Qualitative Vibronic Hamiltonians Used linear vibronic coupling KDC Hamiltonian of Mayer et al. Semiquantitative at best, much empiricism in construction Engineered to fit aspects of nitrate PES Described other spectra well, too. Suggested that it contains the essential physics.

5. but...

6. Experiments have been unsuccessful* in observing v 3 between 900-1100 cm -1, the region suggested. A variational (Born-Oppenheimer) calculation suggests that v 3 is extremely weak This can be understood by a destructive interference effect between the intrinsic (diabatic) vibrational transition moment and an electronic contribution due to the strong X/B mixing (also seen in p-benzoquinone) JFS Mol. Phys. 107, 1059 (2009).

7. 2009-present: A new era for vibronic Hamiltonians

8. Challenging example for this new technology Electronic structure calculations done at EOMIP-CCSDT with a large atomic natural orbital basis (computational aspects of getting this done constituted the bulk of a PhD thesis) Diabatic coupling constants calculated with new ``quasidiabatic” CC model Treatment of the JT splitting in the B state on the symmetry properties of the potential provided fodder for some nontrivial algebraic analysis

10. Quantum numbers: Domains of Sensibility

11. Forget it

12. Level Position CalculatedObservedError 369365+4Kawaguchi 777758+19Neumark 10691057+12Neumark 11521173-21Jacox 14241413+11Kawaguchi 14941492+2Hirota 1579 1642 17691774-5Jacox 18451831+14Neumark 19311927+4Hirota Accuracy of e' energy levels from Hamiltonian

13. First Spectroscopic Application of the Hamiltonian: The ab initio simulation of the nitrate PES

14. What do we mean by a truly "ab initio" simulation? Hamiltonian (potential energy surfaces, coupling) from quantum chemistry calculations Relative cross sections (A 2 ' and E') from theory Calculation of cross sections with EOM-CC theory Krylov: Dyson orbitals (Feynman-Dyson amplitudes) Recent work: Stieltjes imaging and Dyson orbitals (T. Ichino MI11)

16. A. Weaver, D.W. Arnold, S.E. Bradforth and D.M. Neumark J. Chem. Phys. 94, 1740 (1991) origin Experimental photodetachment spectrum

17. C.S. Simmons, T. Ichino and J.F. Stanton, submitted to JPC Lett origin Ab initio photodetachment simulation a 2 ' symmetry e ' symmetry

18. origin

20. Closer inspection of the "v 1 " feature reveals...

21. ... that is should be called the "v 3 " feature!!!!!!!!!

22. Conclusions Quantitative vibronic Hamiltonian gives excellent agreement with known e' level positions in NO 3 Assignment of quantum numbers becomes problematic above 1500 cm -1 In conjunction with calculated cross sections, experimental photodetachment spectrum of nitrate reproduced almost quantitatively There IS (!!!!) an e' level at about 1065 cm -1 that is best called "v 3 " and this feature is the dominant one underlying the second-strongest band in the experimental PES spectrum of NO 3 anion Nodal structure of 1492 cm -1 level is not consistent with it being a fundamental vibration h opeless