# Average local ionization energy generalized to correlated wavefunctions

## Abstract

The average local ionization energy function introduced by Politzer and co-workers [Can. J. Chem. 68, 1440 (1990)] as a descriptor of chemical reactivity has a limited utility because it is defined only for one-determinantal self-consistent-field methods such as the Hartree–Fock theory and the Kohn–Sham density-functional scheme. We reinterpret the negative of the average local ionization energy as the average total energy of an electron at a given point and, by rewriting this quantity in terms of reduced density matrices, arrive at its natural generalization to correlated wavefunctions. The generalized average local electron energy turns out to be the diagonal part of the coordinate representation of the generalized Fock operator divided by the electron density; it reduces to the original definition in terms of canonical orbitals and their eigenvalues for one-determinantal wavefunctions. The discussion is illustrated with calculations on selected atoms and molecules at various levels of theory.

- Authors:

- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada)
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7 (Canada)

- Publication Date:

- OSTI Identifier:
- 22419822

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ATOMS; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; EIGENVALUES; ELECTRIC UTILITIES; ELECTRON DENSITY; ELECTRONS; GAS UTILITIES; HARTREE-FOCK METHOD; IONIZATION; MOLECULES; SELF-CONSISTENT FIELD

### Citation Formats

```
Ryabinkin, Ilya G., and Staroverov, Viktor N., E-mail: vstarove@uwo.ca.
```*Average local ionization energy generalized to correlated wavefunctions*. United States: N. p., 2014.
Web. doi:10.1063/1.4893424.

```
Ryabinkin, Ilya G., & Staroverov, Viktor N., E-mail: vstarove@uwo.ca.
```*Average local ionization energy generalized to correlated wavefunctions*. United States. doi:10.1063/1.4893424.

```
Ryabinkin, Ilya G., and Staroverov, Viktor N., E-mail: vstarove@uwo.ca. Thu .
"Average local ionization energy generalized to correlated wavefunctions". United States.
doi:10.1063/1.4893424.
```

```
@article{osti_22419822,
```

title = {Average local ionization energy generalized to correlated wavefunctions},

author = {Ryabinkin, Ilya G. and Staroverov, Viktor N., E-mail: vstarove@uwo.ca},

abstractNote = {The average local ionization energy function introduced by Politzer and co-workers [Can. J. Chem. 68, 1440 (1990)] as a descriptor of chemical reactivity has a limited utility because it is defined only for one-determinantal self-consistent-field methods such as the Hartree–Fock theory and the Kohn–Sham density-functional scheme. We reinterpret the negative of the average local ionization energy as the average total energy of an electron at a given point and, by rewriting this quantity in terms of reduced density matrices, arrive at its natural generalization to correlated wavefunctions. The generalized average local electron energy turns out to be the diagonal part of the coordinate representation of the generalized Fock operator divided by the electron density; it reduces to the original definition in terms of canonical orbitals and their eigenvalues for one-determinantal wavefunctions. The discussion is illustrated with calculations on selected atoms and molecules at various levels of theory.},

doi = {10.1063/1.4893424},

journal = {Journal of Chemical Physics},

number = 8,

volume = 141,

place = {United States},

year = {Thu Aug 28 00:00:00 EDT 2014},

month = {Thu Aug 28 00:00:00 EDT 2014}

}