Erratum: Accurate determination of the total electronic energy of the Be ground state

1978 ◽  
Vol 17 (1) ◽  
pp. 486-486 ◽  
Author(s):  
Carlos F. Bunge
Keyword(s):  
Ground State ◽  
Accurate Determination ◽  
Electronic Energy ◽  
Total Electronic Energy

scholarly journals Quasi-Linear Buildup of Coulomb Integrals via the Coupling Strength Parameter in the Non-Relativistic Electronic Schrödinger Equation

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Ground State ◽  
Coupling Strength ◽  
Virial Theorem ◽  
Slater Determinant ◽  
Electronic Energy ◽  
Strength Parameter ◽  
Total Electronic Energy ◽  
Repulsion Energy ◽  
Physical Case ◽  
Coulomb Integrals

The non-relativistic electronic Hamiltonian, Hkin+Hne+aHee, is linear in coupling strength parameter (a), but its eigenvalues (electronic energies) have only quasi-linear dependence on it. Detailed analysis is given on the participation of electron-electron repulsion energy (Vee) in total electronic energy (Etotal electr,k) in addition to the wellknown virial theorem and standard algorithm for vee(a=1)=Vee calculated during the standard- and post HF-SCF routines. Using a particular modification in the SCF part of the Gaussian package, we have analyzed the ground state solutions via the parameter “a”. Technically, with a single line in the SCF algorithm, operator was changed as 1/rij-> a/rij with input “a”. The most important findings are, 1, vee(a) is quasi-linear function of “a”, 2, the extension of 1st Hohenberg-Kohn theorem (PSI0(a=1) <=> Hne <=> Y0(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant Y0 is the accurate form) to the physical case a=1. Moreover, we have generalized the emblematic Hund’s rule, virial-, Hohenberg-Kohn- and Koopmans theorems in relation to the coupling strength parameter.

scholarly journals Quasi-Linear Buildup of Coulomb Integrals via the Coupling Strength Parameter in the Non-Relativistic Electronic Schrödinger Equation

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Ground State ◽  
Coupling Strength ◽  
Virial Theorem ◽  
Slater Determinant ◽  
Electronic Energy ◽  
Strength Parameter ◽  
Total Electronic Energy ◽  
Repulsion Energy ◽  
Physical Case ◽  
Coulomb Integrals

The non-relativistic electronic Hamiltonian, Hkin+Hne+aHee, is linear in coupling strength parameter (a), but its eigenvalues (electronic energies) have only quasi-linear dependence on it. Detailed analysis is given on the participation of electron-electron repulsion energy (Vee) in total electronic energy (Etotal electr,k) in addition to the wellknown virial theorem and standard algorithm for vee(a=1)=Vee calculated during the standard- and post HF-SCF routines. Using a particular modification in the SCF part of the Gaussian package, we have analyzed the ground state solutions via the parameter “a”. Technically, with a single line in the SCF algorithm, operator was changed as 1/rij-> a/rij with input “a”. The most important findings are, 1, vee(a) is quasi-linear function of “a”, 2, the extension of 1st Hohenberg-Kohn theorem (PSI0(a=1) <=> Hne <=> Y0(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant Y0 is the accurate form) to the physical case a=1. Moreover, we have generalized the emblematic Hund’s rule, virial-, Hohenberg-Kohn- and Koopmans theorems in relation to the coupling strength parameter.

Quasi-linear dependence of Coulomb forces on coupling strength parameter in the non-relativistic electronic Schrödinger equation and its consequences in Hund’s rule, Mølle -Plesset perturbation- , virial - , Hohenberg-Kohn - and Koopmans theorem

2017 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Linear Dependence ◽  
Ground State ◽  
Coupling Strength ◽  
Virial Theorem ◽  
Slater Determinant ◽  
Electronic Energy ◽  
Strength Parameter ◽  
Total Electronic Energy ◽  
Repulsion Energy ◽  
Koopmans Theorem

<p> The extended non-relativistic electronic Hamiltonian, H<sub>Ñ</sub>+ H<sub>ne</sub>+ aH<sub>ee</sub>, is linear in coupling strength parameter (a), but its eigenvalues (interpreted as electronic energies) have only quasi-linear dependence on “a”. No detailed analysis has yet been published on the ratio or participation of electron-electron repulsion energy (V<sub>ee</sub>) in total electronic energy – apart from virial theorem and the highly detailed and well-known algorithm for V<sub>ee</sub>, which is calculated during the standard HF-SCF and post-HF-SCF routines. Using a particular modification of the SCF part in the Gaussian package we have analyzed the ground state solutions via the parameter “a”. Technically, this modification was essentially a modification of a single line in an SCF algorithm, wherein the operator r<sub>ij</sub><sup>-1</sup> was overwritten as r<sub>ij</sub><sup>-1</sup> ® ar<sub>ij</sub><sup>-1</sup>, and used “a” as input. The most important finding beside that the repulsion energy V<sub>ee</sub>(a) is a quasi-linear function of “a”, is that the extended 1<sup>st</sup> Hohenberg-Kohn theorem (Y<sub>0</sub>(a=1) Û H<sub>ne</sub> Û Y<sub>0</sub>(a=0)) and its consequences in relation to “a”. The latter allows an algebraic transfer from the simpler solution of case a=0 (where the single Slater determinant is the accurate form) to the realistic wanted case a=1. Moreover, we have generalized the emblematic theorems in the title in relation to the coupling strength parameter. </p>

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