1. Rovibronic variational calculations of the nitrate radical
P. Bryan Changala
JILA, National Institute of Standards and Technology and
Department of Physics, University of Colorado, Boulder, CO
Joshua H. Baraban
Department of Chemistry, University of Colorado, Boulder, CO
John F. Stanton
Department of Chemistry, University of Texas, Austin, TX
ISMS 70, UI Urbana-Champaign, IL, 2015

2. Outline Vibronic coupling of the low-lying electronic states of NO3
Extending the Köppel-Domcke-Cederbaum (KDC) quasi-diabatic vibronic Hamiltonian for rotation
Rotational structure of low-lying vibrational levels of the X state
Electronic orbital and spin angular momentum effects

3. The electronic landscape
15000 cm-1
weak coupling
strong coupling
weak
coupling
7000 cm-1
0 cm-1

4. Adiabatic vs. diabatic Hamiltonians
Adiabatic representation:
complicated nuclear coord. derivative operators (bad)
simple scalar functions of nuclear coordinates (good)
KDC quasi-diabatic representation:

5. KDC-DVR rovibronic Hamiltonian
Internal coordinate DVR
Rotational function
exact curvilinear internal coordinate kinetic energy op.
Diabatic KDC-DVR Hamiltonian is extremely sparse
Kinetic op. is most expensive, but cost is linear in # of elec. states

6. Vibronic level structure
5D planar calculation; reproduces results from the EOM-CCSDT vibronic Ham. reported by Simmons, Ichino, and Stanton, J. Phys. Chem. Lett. 3, 1946 (2012).
The well-known 1492 cm-1 level; v3 vs. v3+ν4
(v3+v4)^0 (a1’) is very, very low. The variational internal coordinate wavefunctions seem to indicate that it has a lot of ell = 3 character. Presumably mixed with (3v4)^3 (a1’), which is the only a1’ state nearby.
(4v4)^0 and (v3+v4)^0 (a2’) are also very mixed and the assignment of the 1522/1569 levels could be just as easily flipped.
mixed
mixed
v3+ν4 manifold, very irregular

7. Rovibronic level structure
Fit low-N 5D variational energies to the same oblate top rotational Heff used for experimental energies [Fujimori et al, J. Mol. Spectrosc. 283, 10 (2013)]
Ground vibronic state:
Fits from J=0,1 “NO3vibronic_b” dataset
5D rotational energies weren’t done up to 2v4. But with a 4D calculation (no sym. stretch), the zeta constants for v4 and 2v4^2 are very similar ( vs ), as well as q4 ( vs )

8. Vibronic contributions to
How much vibronic angular momentum comes from z-axis (c-axis) electronic orbital angular momentum in the state?
(small!)
Indeed, a calculation explicitly including Lz results in no significant change to the rotational structure…

9. Other roads to L
The A state can couple with X vibronically via B, or directly via spin-orbit
v. weak quad. coupling
strong lin. coupling
weak lin.
coupling
A2’/E’’ is mainly y (also 14 cm^-1 from x)
E’/E’ is z
X/B SO is vanishing.
E’’/E’’ SO is effectively vanishing (though z is allowed); see Lan’s reasoning

10. Conclusions
KDC diabatic Hamiltonian extended to rovibronic treatment of NO3
3-state X/B model does not account for observed Coriolis coupling in vibronically degenerate modes
HSO and 5-state X/A/B calculation possibly required
Acknowledgements:
Lan Cheng (UT Austin)
NSF GRFP

11. DVR vibrational basis
“Discrete variable representation” (DVR) basis functions for internal vibrational coordinates
highly localized:
functions of coordinates, namely Vij(q), are approximately diagonal: