P. Gill: New Ways to Think about Electronic Excited States

For historical reasons, the ground state retains a privileged position in many descriptions of excited states and I will argue that this bias is unhelpful, both conceptually and computationally. To remedy the situation, we are pursuing a hierarchy of excited-state models which are rooted, like their groundstate analogs, in the mean-field, orbital-based picture that has proven so fertile for chemists of all persuasions. I will introduce two Maximum Overlap Methods (MOM) that enable us to compute such state-specific models and I will use low-lying excited states of small atoms and molecules to demonstrate both the strengths and weaknesses of the approach [1 - 4]. What am I asserting if I claim that a molecule is in a “singly-excited electronic state” state? Or, for that matter, a doubly- or triply-excited state? Do these descriptions correspond to an experimentally observable feature of the molecule? If not, do they correspond to a universally agreed theoretical definition? If not, which definition have we been using and are we confident that it’s a good one? I will argue that these questions have been either ignored or treated superficially by many researchers and that, as a result, it is likely that some states have been incorrectly classified in the past. I will propose a simple definition [5] of an excitation number η that is easy to calculate and easy to interpret for electronic excited states which have been obtained using the MOM approach. We have computed η for a variety of excited states of a selection of organic and inorganic molecules and we find that it is almost always close to an integer. The rounded form of η provides clean and compelling answers to the questions above in all the cases that we have investigated.

[1] A. T. B. Gilbert, N. A. Besley and P. M. W. Gill, J. Phys. Chem. A 112, 13164 (2008).

[2] N. A. Besley, A. T. B. Gilbert and P. M. W. Gill, J. Chem. Phys. 130, 124308 (2009).

[3] G. M. J. Barca, A. T. B. Gilbert and P. M. W. Gill, J. Chem. Phys. 141, 111104 (2014).

[4] G. M. J. Barca, A. T. B. Gilbert and P. M. W. Gill, J. Chem. Theory Comput. 14, 1501 (2018).

[5] G. M. J. Barca, A. T. B. Gilbert and P. M. W. Gill, J. Chem. Theory Comput. 14, 9 (2018).