### Abstract

An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.

Original language | English |
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Journal | International Journal of Quantum Chemistry |

DOIs | |

Publication status | Accepted/In press - 2017 |

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### Keywords

- Kinetic energy density
- Kinetic energy density functionals
- Large-scale calculations
- Orbital-free density functional theory

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

### Cite this

**Kinetic energy density for orbital-free density functional calculations by axiomatic approach.** / Alharbi, Fahhad; Kais, Sabre.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Kinetic energy density for orbital-free density functional calculations by axiomatic approach

AU - Alharbi, Fahhad

AU - Kais, Sabre

PY - 2017

Y1 - 2017

N2 - An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.

AB - An axiomatic approach is herein used to determine the physically acceptable forms for general D-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By statistically training the KEDF forms on a model problem of noninteracting kinetic energy in 1D (six terms only), the mean relative accuracy for 1000 randomly generated potentials is found to be better than the standard KEDF by several orders of magnitudes. The accuracy improves with the number of occupied states and was found to be better than 10-4 for a system with four occupied states. Furthermore, we show that free fitting of the coefficients associated with known KEDFs approaches the exactly analytic values. The presented approach can open a new route to search for physically acceptable kinetic energy density functionals and provide an essential step toward more accurate large-scale orbital free density functional theory calculations.

KW - Kinetic energy density

KW - Kinetic energy density functionals

KW - Large-scale calculations

KW - Orbital-free density functional theory

UR - http://www.scopus.com/inward/record.url?scp=85015162769&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015162769&partnerID=8YFLogxK

U2 - 10.1002/qua.25373

DO - 10.1002/qua.25373

M3 - Article

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

ER -