scholarly journals Fourier–Legendre expansion of the one-electron density matrix of ground-state two-electron atoms

2008 ◽  
Vol 129 (12) ◽  
pp. 124117 ◽  
Author(s):  
Sébastien Ragot ◽  
María Belén Ruiz
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Ground State ◽  
Electron Density Matrix ◽  
The One ◽  
Legendre Expansion

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.

Properties of Aromaticity Indices Based on the One-Electron Density Matrix†

2007 ◽  
Vol 111 (28) ◽  
pp. 6521-6525 ◽  
Author(s):  
Jerzy Cioslowski ◽  
Eduard Matito ◽  
Miquel Solà
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Electron Density Matrix ◽  
The One

Direct calculation of the one-electron density matrix for closed-shell systems

2000 ◽  
Vol 113 (13) ◽  
pp. 5179 ◽  
Author(s):  
Osamu Matsuoka ◽  
Takaharu Matsufuji ◽  
Tatsuji Sano
Keyword(s):  
Density Matrix ◽  
Electron Density ◽  
Direct Calculation ◽  
Closed Shell ◽  
Electron Density Matrix ◽  
The One
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