scholarly journals Analytic construction of Hartree-Fock density matrices

1980 ◽  
Vol 77 (11) ◽  
pp. 6293-6297 ◽  
Author(s):  
P. W. Payne
Keyword(s):  
Density Matrices ◽  
Analytic Construction ◽  
Hartree Fock

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.

Use of Symmetry in Coupled Hartree-Fock Calculations of Non-linear Response Tensors in Molecules

1993 ◽  
Vol 48 (1-2) ◽  
pp. 141-144 ◽  
Author(s):  
P. Lazzeretti ◽  
M. Malagoli ◽  
R. Zanasi
Keyword(s):  
Computer Program ◽  
Electric Dipole ◽  
Linear Response ◽  
Computational Effort ◽  
Second Order ◽  
Basis Functions ◽  
Molecular Symmetry ◽  
Matrix Elements ◽  
Density Matrices ◽  
Hartree Fock

Abstract A new computational scheme for electric dipole hyperpolarizabilities has been devised within the coupled Hartree-Fock method. Only the projection of second-order perturbed orbitals onto the subspace spanned by unperturbed virtual orbitals is computed. The entire molecular symmetry is exploited to reduce computational effort: a reduced two-electron integral file containing only symmetry-distinct matrix elements over the atomic basis functions is processed at each iteration. In addition, only symmetry-independent first-and second-order perturbed density matrices need to be calculated. An efficient computer program implementing the present approach has been developed.

On the density matrices used in hartree-fock calculations

Physica ◽  
1960 ◽  
Vol 26 (12) ◽  
pp. 1041-1044 ◽  
Author(s):  
D. Ter Haar
Keyword(s):  
Density Matrices ◽  
Hartree Fock

The density matrix in many-electron quantum mechanics I. Generalized product functions. Factorization and physical interpretation of the density matrices

1959 ◽  
Vol 253 (1273) ◽  
pp. 242-259 ◽  
Keyword(s):  
Density Matrix ◽  
Matrix Theory ◽  
Particle System ◽  
Intermolecular Forces ◽  
Density Matrices ◽  
Hartree Fock ◽  
Interaction Terms ◽  
The Matrix ◽  
Group Functions ◽  
The One

Many-electron wave functions are usually constructed from antisymmetrized products of one-electron orbitals (determinants) and energy calculations are based on the matrix element expressions due to Slater (1931). In this paper, the orbitals in such a product are replaced by ‘group functions’, each describing any number of electrons, and the necessary generalization of Slater’s results is carried out. It is first necessary to develop the density matrix theory of N -particle systems and to show that for systems described by ‘generalized product functions’ the density matrices of the whole system may be expressed in terms of those of the component electron groups. The matrix elements of the Hamiltonian between generalized product functions are then given by expressions which resemble those of Slater, the ‘coulomb’ and ‘exchange’ integrals being replaced by integrals containing the one-electron density matrices of the various groups. By setting up an ‘effective’ Hamiltonian for each electron group in the presence of the others, the discussion of a many-particle system in which groups or ‘shells’ can be distinguished (e. g. atomic K, L, M , ..., shells) can rigorously be reduced to a discussion of smaller subsystems. A single generalized product (cf. the single determinant of Hartree—Fock theory) provides a convenient first approximation; and the effect of admitting ‘excited’ products (cf. configuration interaction) can be estimated by a perturbation method. The energy expression may then be discussed in terms of the electon density and ‘pair’ functions. The energy is a sum of group energies supplemented by interaction terms which represent (i) electrostatic repulsions between charge clouds, (ii) the polarization of each group in the field of the others, and (iii) ‘dispersion’ effects of the type defined by London. All these terms can be calculated, for group functions of any kind, in terms of the density matrices of the separate groups. Applications to the theory of intermolecular forces and to π -electron systems are also discussed.

The augmented Roothaan–Hall method for optimizing Hartree–Fock and Kohn–Sham density matrices

2008 ◽  
Vol 129 (12) ◽  
pp. 124106 ◽  
Author(s):  
Stinne Høst ◽  
Jeppe Olsen ◽  
Branislav Jansík ◽  
Lea Thøgersen ◽  
Poul Jørgensen ◽  
...  
Keyword(s):  
Density Matrices ◽  
Hartree Fock ◽  
Hall Method
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