The density matrix, density, and Fermi hole in Hartree–Fock theory

2009 ◽  
pp. 823-827
Author(s):  
K. A. Dawson ◽  
N. H. March
Keyword(s):  
Density Matrix ◽  
Matrix Density ◽  
Hartree Fock ◽  
Fermi Hole

The density matrix, density, and Fermi hole in Hartree–Fock theory

1984 ◽  
Vol 81 (12) ◽  
pp. 5850-5854 ◽  
Author(s):  
K. A. Dawson ◽  
N. H. March
Keyword(s):  
Density Matrix ◽  
Matrix Density ◽  
Hartree Fock ◽  
Fermi Hole

Is it Reasonable to Obtain Information on the Polarizability and Hyperpolarizability Only from the Electron Density?

2018 ◽  
Vol 71 (4) ◽  
pp. 295 ◽  
Author(s):  
Dylan Jayatilaka ◽  
Kunal K. Jha ◽  
Parthapratim Munshi
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Ground State ◽  
Density Functional ◽  
Particle Density ◽  
Density Matrices ◽  
Hartree Fock ◽  
Electron Density Matrix ◽  
Ground State Electron ◽  
Side Result

Formulae for the static electronic polarizability and hyperpolarizability are derived in terms of moments of the ground-state electron density matrix by applying the Unsöld approximation and a generalization of the Fermi-Amaldi approximation. The latter formula for the hyperpolarizability appears to be new. The formulae manifestly transform correctly under rotations, and they are observed to be essentially cumulant expressions. Consequently, they are additive over different regions. The properties of the formula are discussed in relation to others that have been proposed in order to clarify inconsistencies. The formulae are then tested against coupled-perturbed Hartree-Fock results for a set of 40 donor-π-acceptor systems. For the polarizability, the correlation is reasonable; therefore, electron density matrix moments from theory or experiment may be used to predict polarizabilities. By constrast, the results for the hyperpolarizabilities are poor, not even within one or two orders of magnitude. The formula for the two- and three-particle density matrices obtained as a side result in this work may be interesting for density functional theories.

Hartree–Fock density matrix equation

1976 ◽  
Vol 65 (10) ◽  
pp. 4234-4238 ◽  
Author(s):  
Leon Cohen ◽  
C. Frishberg
Keyword(s):  
Density Matrix ◽  
Matrix Equation ◽  
Hartree Fock ◽  
Density Matrix Equation

Direct optimization of the AO density matrix in Hartree–Fock and Kohn–Sham theories

2000 ◽  
Vol 327 (5-6) ◽  
pp. 397-403 ◽  
Author(s):  
Trygve Helgaker ◽  
Helena Larsen ◽  
Jeppe Olsen ◽  
Poul Jørgensen
Keyword(s):  
Density Matrix ◽  
Direct Optimization ◽  
Hartree Fock
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