Direct Calculation of Approximate Natural Orbitals and Natural Expansion Coefficients of Atomic and Molecular Electronic Wavefunctions. II. Decoupling of the Pair Equations and Calculation of the Pair Correlation Energies for the Be and LiH Ground States

1968 ◽  
Vol 48 (4) ◽  
pp. 1819-1832 ◽  
Author(s):  
Reinhart Ahlrichs ◽  
Werner Kutzelnigg
Keyword(s):  
Pair Correlation ◽  
Ground States ◽  
Direct Calculation ◽  
Molecular Electronic ◽  
Natural Orbitals ◽  
Electronic Wavefunctions ◽  
Expansion Coefficients ◽  
Natural Expansion

Eine Approximation der Löwdinschen natürlichen Orbitale für Moleküle mit einer Green-Funktion-Methode

1972 ◽  
Vol 27 (4) ◽  
pp. 545-552 ◽  
Author(s):  
R. Albat
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Mass Operator ◽  
Ground States ◽  
Present Form ◽  
Many Body ◽  
Natural Orbitals ◽  
First Order ◽  
The Many ◽  
Closed Shells

Abstract An Approximation of Löwdin's Natural Orbitals for Molecules with a Green's Function Method The many-body-pertubation theorie of the single-particle Green's function is used to get an approximate first-order density matrix. Slightly modified SCF-orbitals form the basis for the expansion. The mass-operator in Dyson's equation is considered up to second order in the Perturbation. In the present form the method is only applicable to ground states with closed shells. The ground states of the molecules LiH and NH3 serve as examples to demonstrate the usefulness of the directly calculated natural orbitals for application in the C I-method. The natural orbitals give a much better convergence of the C I-expansion than the SCF-orbitals do.

scholarly journals Independent Sources of Information-Theoretic Descriptors of Electronic States

2020 ◽  
pp. 106-115
Author(s):  
Roman F. Nalewajski
Keyword(s):  
Information Sources ◽  
Electronic States ◽  
The State ◽  
Sources Of Information ◽  
Molecular Electronic ◽  
Information Theoretic ◽  
State Entropy ◽  
Phase Current ◽  
Electronic Wavefunctions ◽  
Information Order

The need for resultant measures of the Information-Theoretic (IT) content of molecular electronic wavefunctions, combining the information contributions due to the probability and phase/current distributions, is reemphasized. Complementary measures of the state entropy (disorder) and information (order) contents are reexamined, the continuities of wavefunction components are summarized, and the probability acceleration concept is used to determine the current and information sources. The experimental elimination of the state uncertainties is discussed and limitations in this information-acquirement process imposed by the Heisenberg indeterminacy principle are commented upon.

The direct calculation of the first-order density matrix for atoms

1965 ◽  
Vol 283 (1393) ◽  
pp. 194-202 ◽  
Keyword(s):  
Perturbation Theory ◽  
Density Matrix ◽  
Ground State ◽  
Direct Calculation ◽  
Molecular Orbitals ◽  
Natural Orbitals ◽  
Mean Values ◽  
First Order ◽  
Order Contribution

The theory of isoelectronic sequences of atoms has been developed as a perturbation theory and is extended here to the calculation of the first-order density matrix. It is shown that the calculation of the first-order contribution to this matrix can be reduced to the solution of a number of one-electron equations. These equations have been solved for the helium ground state, the helium 3 S state and the lithium ground state. From the density matrix, mean values of one-electron operators can be derived by integration. A variety of these mean values is quoted and the significance of the stable values discussed. From the density matrix the natural orbitals can be derived and these are found to be identical with the unrestricted molecular orbitals to terms of zero and first order.

Are atoms intrinsic to molecular electronic wavefunctions? I. The FORS model

1982 ◽  
Vol 71 (1) ◽  
pp. 41-49 ◽  
Author(s):  
Klaus Ruedenberg ◽  
Michael W. Schmidt ◽  
Mary M. Gilbert ◽  
S.T. Elbert
Keyword(s):  
Molecular Electronic ◽  
Electronic Wavefunctions

Are atoms intrinsic to molecular electronic wavefunctions? III. Analysis of FORS configurations

1982 ◽  
Vol 71 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Klaus Ruedenberg ◽  
Michael W. Schmidt ◽  
Mary M. Gilbert ◽  
S.T. Elbert
Keyword(s):  
Molecular Electronic ◽  
Electronic Wavefunctions
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