First Ionization Energy as the Asymptotic Limit of the Average Local Electron Energy

• Amer M. El-Samman
, 
• Egor Ospadov
, and 
• Viktor N. Staroverov*

 

 ABSTRACT:

 The first vertical ionization energy of an atom or molecule isencoded in the rate of exponential decay of the exact natural orbitals. For natural orbitals represented in terms of Gaussian basis functions, this property does nothold even approximately. We show that it is nevertheless possible to deduce thefirst ionization energy from the long-range behavior of Gaussian-basis-set wavefunctions by evaluating the asymptotic limit of a quantity called the average localelectron energy (ALEE), provided that the most diffuse functions of the basis sethave a suitable shape and location. The ALEE method exposes subtle qualitativedifferences between seemingly analogous Gaussian basis sets and complementsthe extended Koopmans theorem by being robust in situations where the one-electron reduced density matrix is ill-conditioned.

 

https://sci-hub.se/https://pubs.acs.org/doi/10.1021/acs.jctc.0c00806