# Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B

## Abstract

Accurate densities were determined from configuration interaction wave functions for atoms and ions of Li, Be, and B with up to four electrons. Exchange-correlation potentials, V{sub xc}(r), and functional derivatives of the noninteracting kinetic energy, δK[ρ]/δρ(r), obtained from these densities were used to examine their discontinuities as the number of electrons N increases across integer boundaries for N = 1, N = 2, and N = 3. These numerical results are consistent with conclusions that the discontinuities are characterized by a jump in the chemical potential while the shape of V{sub xc}(r) varies continuously as an integer boundary is crossed. The discontinuity of the V{sub xc}(r) is positive, depends on the ionization potential, electron affinity, and orbital energy differences, and the discontinuity in δK[ρ]/δρ(r) depends on the difference between the energies of the highest occupied and lowest unoccupied orbitals. The noninteracting kinetic energy and the exchange correlation energy have been computed for integer and noninteger values of N between 1 and 4.

- Authors:

- Department of Chemistry, East Carolina University, Greenville, North Carolina 27858 (United States)

- Publication Date:

- OSTI Identifier:
- 22415448

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AFFINITY; ATOMS; BERYLLIUM; BERYLLIUM IONS; BORON; BORON IONS; CONFIGURATION INTERACTION; ELECTRON CORRELATION; ELECTRON EXCHANGE; ELECTRONS; KINETIC ENERGY; LITHIUM; LITHIUM IONS; POTENTIALS; WAVE FUNCTIONS

### Citation Formats

```
Morrison, Robert C.
```*Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B*. United States: N. p., 2015.
Web. doi:10.1063/1.4905235.

```
Morrison, Robert C.
```*Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B*. United States. doi:10.1063/1.4905235.

```
Morrison, Robert C. Wed .
"Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B". United States.
doi:10.1063/1.4905235.
```

```
@article{osti_22415448,
```

title = {Discontinuity of the exchange-correlation potential and the functional derivative of the noninteracting kinetic energy as the number of electrons crosses integer boundaries in Li, Be, and B},

author = {Morrison, Robert C.},

abstractNote = {Accurate densities were determined from configuration interaction wave functions for atoms and ions of Li, Be, and B with up to four electrons. Exchange-correlation potentials, V{sub xc}(r), and functional derivatives of the noninteracting kinetic energy, δK[ρ]/δρ(r), obtained from these densities were used to examine their discontinuities as the number of electrons N increases across integer boundaries for N = 1, N = 2, and N = 3. These numerical results are consistent with conclusions that the discontinuities are characterized by a jump in the chemical potential while the shape of V{sub xc}(r) varies continuously as an integer boundary is crossed. The discontinuity of the V{sub xc}(r) is positive, depends on the ionization potential, electron affinity, and orbital energy differences, and the discontinuity in δK[ρ]/δρ(r) depends on the difference between the energies of the highest occupied and lowest unoccupied orbitals. The noninteracting kinetic energy and the exchange correlation energy have been computed for integer and noninteger values of N between 1 and 4.},

doi = {10.1063/1.4905235},

journal = {Journal of Chemical Physics},

number = 1,

volume = 142,

place = {United States},

year = {Wed Jan 07 00:00:00 EST 2015},

month = {Wed Jan 07 00:00:00 EST 2015}

}