1. A Tale of Two Controversies
The NO3 Molecule:
A Tale of Two Controversies
( )
John F. Stanton
University of Florida

2. DOE, NSF, Welch Foundation
Acknowledgements
Juergen Gauss
Takatoshi Ichino
Chris Simmons
Anna Krylov
DOE, NSF, Welch Foundation

4. Imaginary non-symmetric frequency Lower energy structures

6. What is the structure of NO3??? D3h? or C2v?
It's C2v!!!
Nelson Pasternak and McDonald JPC 87, 1286 (1983)
Davy and Schaefer JCP 91, 4410 (1989)
Kim, Hammond, Lester and Johnston CPL 161,131 (1990)
Kim, Hunter and Johnston JCP 96, 4067 (1992)
No, it's D3h
Friedl and Sander JPC 91, 2721 (1987)
Kawaguchi, Hirota, Ishiwata and Tanaka JCP 93, 951 (1990)
Kaldor CPL 166, 599 (1990)

9. What is the structure of NO3??? D3h? or C2v?
It's C2v!!!
Nelson Pasternak and McDonald JPC 87, 1286 (1983)
Davy and Schaefer JCP 91, 4410 (1989)
Stanton, Gauss and Bartlett JCP 94, 4084 (1991)
Kim, Hammond, Lester and Johnston CPL 161,131 (1990)
Kim, Hunter and Johnston JCP 96, 4067 (1992)
No, it's D3h
Friedl and Sander JPC 91, 2721 (1987)
Kawaguchi, Hirota, Ishiwata and Tanaka JCP 93, 951 (1990)
Kaldor CPL 166, 599 (1990)
Stanton, Gauss and Bartlett JCP 97, 5554 (1992)

10. Weak
Truly
ferocious
Weak
Diabatic picture of electronic states

12. 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.

17. End of first controversy
Spectroscopically D3h (no doubt)
Equilibrium Structure: ? (but who cares)

18. Beginning of second controversy!

23. Towards accurate and “ab initio” parametrization
of diabatic Hamiltonians and “ab initio” simulations

24. Advances in Vibronic Methods
Highly accurate electronic structure methods suited to coupled
states exist (EOM-CC), and very high level calculations (EOM-CCSDT)
can now be done
Methods for parametrizing vibronic Hamiltonians have evolved
A quasidiabatic ansatz that seems to work very well has been
developed within the context of EOM-CC*
Although the calculations are expensive, we have the technology
to build quantitatively accurate vibronic Hamiltonians
*T. Ichino, J. Gauss and J.F. Stanton JCP 129, (2008).

25. 2009-present: A new era for vibronic Hamiltonians

26. Vibronic Hamiltonian Parametrization:
Potential energy surfaces from EOMIP-CCSDT
Diabatic couplings from EOMIP-CCSD
Large Atomic Natural Orbital Basis Set
Hamiltonian Expanded through Quartic Terms
Intensities in Photoelectron Spectrum:
This is a “new” problem: It requires that we
know the photodetachment cross-sections to
the X and B states. (Takatoshi Ichino)

27. Why do we care about photodetachment cross section. ex
Why do we care about photodetachment cross section? ex. photoelectron spectrum of NO3‾
Interpretation of photoelectron spectra
can be facilitated with knowledge of
cross sections.
Weaver et al., J. Chem. Phys. 94, 1740 (1991)

28. Two approaches to photodetachment cross section calculations
Plane wave approximation of scattering electrons
Transition of the electron from the Dyson orbital obtained with equation-of-motion coupled-cluster theory (EOMIP-CC)
cf. Reed et al., J. Chem. Phys. 64, 1368 (1976).
Öhrn and Born, Adv. Quantum Chem. 13, 1 (1981).
Oana and Krylov, J. Chem. Phys. 131, (2009).
Krylov, Ichino, Stanton, others, JPC Lett, 6, 4532 (2015).
Direct ab initio calculations of electronic transition dipole moments for pseudostates (Stieltjes Imaging)
Equation-of-motion coupled-cluster calculations of oscillator strengths (EOMEE-CC) to obtain the associated moments
cf. Langhoff and Corcoran, J. Chem. Phys. 61, 146 (1976).
Reinhardt, Comp. Phys. Comm. 17, 1 (1979).
Müller-Plathe and Diercksen in “Electronic Structure of Atoms, Molecules and Solids” (1990).

29. First approach: Plane wave approximation
Result 3: Photodetachment from O radical anion
Dyson/partial orthogonalization
Dyson/full orthogonalization
(momentum)
SCF
Dyson/full orthogonalization
(dipole length)
EOMIP-CCSD
aug-pVTZ + diffuse functions
Transition dipole length calculations with the Dyson orbital and the fully
orthogonalized plane wave give an excellent match with the experimental results.
Experiment (dots):
Branscomb et al., Phys. Rev. 111, 504 (1958); J. Chem. Phys. 43, 2906 (1965)

30. Results I:
Energies

33. Empiricism: Scale diabatic coupling
by a factor of

34. Accuracy of e' energy levels from (slightly) fudged Hamiltonian
Level Position
Calculated
Observed
Error
369
365 +4
Kawaguchi
777
772 +5
1069
1152
1173
-21
Jacox
1424
1413
+11
1494
1492 +2
Hirota
1579
1642
1769
1774 -5
1845
1831
+14
Neumark
1931
1927

35. Accuracy of e' energy levels from (slightly) fudged Hamiltonian
Level Position
Calculated
Observed
Error
369
365 +4
Kawaguchi
777
772 +5
1069
1152
1173
-21
Jacox
1424
1413
+11
1494
1492 +2
Hirota
1579
1642
1769
1774 -5
1845
1831
+14
Neumark
1931
1927
new

36. Results II:
Cross-sections

37. Appearance of non-symmetric levels in X state
must be due to vibronic coupling (B state borrowing)

38. Putting it all together: Simulation of PES

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

40. origin

41. Closer inspection of the "v1" feature reveals ...

42. ... that is should be called the "v3" feature!!!!!!!!!

45. Thank You!!!!!!!!!!!!