Calculation of ionization potentials from density matrices and natural functions, and the long-range behavior of natural orbitals and electron density

1975 ◽  
Vol 62 (2) ◽  
pp. 549 ◽  
Author(s):  
Marilyn M. Morrell
Keyword(s):  
Electron Density ◽  
Long Range ◽  
Ionization Potentials ◽  
Density Matrices ◽  
Natural Orbitals

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.

The ' Variable Electronegativity ' Method. III. The Pyrrole Anion and Electronegativity Reversal

1959 ◽  
Vol 12 (3) ◽  
pp. 330 ◽  
Author(s):  
RD Brown ◽  
ML Heffernan
Keyword(s):  
Electron Density ◽  
Electron Distribution ◽  
Ionization Potentials ◽  
Alternative Methods ◽  
Electron Densities ◽  
Tertiary Nitrogen

The π-electron distribution in the pyrrole anion has been evaluated by the VESCF method using two alternative methods of estimating core attraction terms. The results indicate that the π-electron distribution around the conjugated system is very nearly uniform, supporting previous speculations that the relative attracting powers of tertiary nitrogen and carbon reverse when their π-electron densities exceed a certain value, suspected to be not too much greater than unity. The present calculations indicate that the critical π-electron density is around 1.2. The VESCF estimates of ionization potentials of the pyrrole anion are also reported.

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