### Abstract

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫g_{i}(r_{1})g_{k}(r_{2})r 12-1dr_{1}dr_{2}, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.

Original language | English |
---|---|

Pages (from-to) | 1479-1492 |

Number of pages | 14 |

Journal | International Journal of Quantum Chemistry |

Volume | 113 |

Issue number | 10 |

DOIs | |

Publication status | Published - May 15 2013 |

### Fingerprint

### Keywords

- density functional theory
- ground state total electronic energy
- one-electron density
- power series with correct density scaling

### ASJC Scopus subject areas

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

### Cite this

*International Journal of Quantum Chemistry*,

*113*(10), 1479-1492. https://doi.org/10.1002/qua.24345

**Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one-electron density and electronic energy.** / Kristyán, S.

Research output: Contribution to journal › Article

*International Journal of Quantum Chemistry*, vol. 113, no. 10, pp. 1479-1492. https://doi.org/10.1002/qua.24345

}

TY - JOUR

T1 - Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one-electron density and electronic energy

AU - Kristyán, S.

PY - 2013/5/15

Y1 - 2013/5/15

N2 - The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi(r1)gk(r2)r 12-1dr1dr2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.

AB - The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi(r1)gk(r2)r 12-1dr1dr2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.

KW - density functional theory

KW - ground state total electronic energy

KW - one-electron density

KW - power series with correct density scaling

UR - http://www.scopus.com/inward/record.url?scp=84875857016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875857016&partnerID=8YFLogxK

U2 - 10.1002/qua.24345

DO - 10.1002/qua.24345

M3 - Article

AN - SCOPUS:84875857016

VL - 113

SP - 1479

EP - 1492

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 10

ER -