scholarly journals Solving the Non-Relativistic Electronic Schrödinger Equation with Manipulating the Coupling Strength Parameter over the Electron-Electron Coulomb Integrals

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Coupling Strength ◽  
Correlation Effect ◽  
Electronic Energy ◽  
Basis Set ◽  
Strength Parameter ◽  
Repulsion Energy ◽  
Consistent Field ◽  
Self Consistent Field ◽  
Moller Plesset ◽  
Coulomb Integrals

The non-relativistic electronic Hamiltonian, H(a)= Hkin+Hne+aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution of real (physical) a=1 case is generated thereafter from it to calculate the total electronic energy (Etotal electr,K) mainly for ground state (K=0). This strategy is worked out with utilizing generalized Moller-Plesset (MP), square of Hamiltonian (H2) and Configuration interactions (CI) devices. Applying standard eigensolver for Hamiltonian matrices (one or two times) buys off the needs of self-consistent field (SCF) convergence in this algorithm, along with providing the correction for basis set error and correlation effect. (SCF convergence is typically performed in the standard HF-SCF/basis/a=1 routine in today practice.)

scholarly journals Solving the Non-Relativistic Electronic Schrödinger Equation with Manipulating the Coupling Strength Parameter over the Electron-Electron Coulomb Integrals

2019 ◽  
Author(s):  
Sandor Kristyan
Keyword(s):  
Coupling Strength ◽  
Correlation Effect ◽  
Electronic Energy ◽  
Basis Set ◽  
Strength Parameter ◽  
Repulsion Energy ◽  
Consistent Field ◽  
Self Consistent Field ◽  
Moller Plesset ◽  
Coulomb Integrals

The non-relativistic electronic Hamiltonian, H(a)= Hkin+Hne+aHee, extended with coupling strength parameter (a), allows to switch the electron-electron repulsion energy off and on. First, the easier a=0 case is solved and the solution of real (physical) a=1 case is generated thereafter from it to calculate the total electronic energy (Etotal electr,K) mainly for ground state (K=0). This strategy is worked out with utilizing generalized Moller-Plesset (MP), square of Hamiltonian (H2) and Configuration interactions (CI) devices. Applying standard eigensolver for Hamiltonian matrices (one or two times) buys off the needs of self-consistent field (SCF) convergence in this algorithm, along with providing the correction for basis set error and correlation effect. (SCF convergence is typically performed in the standard HF-SCF/basis/a=1 routine in today practice.)

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>

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>

Basis set convergence of atomic axial tensors obtained from self‐consistent field calculations using London atomic orbitals

1994 ◽  
Vol 100 (9) ◽  
pp. 6620-6627 ◽  
Author(s):  
Keld L. Bak ◽  
Poul Jo/rgensen ◽  
Trygve Helgaker ◽  
Kenneth Ruud ◽  
Hans Jo/rgen Aa. Jensen
Keyword(s):  
Basis Set ◽  
Set Convergence ◽  
Atomic Orbitals ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Universal Gaussian basis functions in relativistic quantum chemistry: atomic Dirac–Fock–Coulomb and Dirac–Fock–Breit calculations

1992 ◽  
Vol 70 (6) ◽  
pp. 1822-1826 ◽  
Author(s):  
G. L. Malli ◽  
A. B. F. Da Silva ◽  
Yasuyuki Ishikawa
Keyword(s):  
Relativistic Quantum ◽  
Basis Set ◽  
Basis Sets ◽  
Interaction Energies ◽  
Gaussian Basis Sets ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Gaussian Basis Set ◽  
Good Agreement

Matrix Dirac–Fock–Coulomb and Dirac–Fock–Breit self-consistent field calculations are performed for a number of neutral atoms. He (Z = 2) through Xe (Z = 54), using the universal Gaussian basis set (18s, 12p, 11d) reported recently by Da Silva etal. The total Dirac–Fock–Coulomb, the Dirac–Fock–Breit, and the Breit interaction energies calculated with this universal Gaussian basis set are in good agreement with the corresponding values obtained by using an extensive well-tempered Gaussian basis set for the He through Ca (Z = 20) atoms. Although this universal Gaussian basis set is inadequate for the calculation of total Dirac–Fock–Coulomb and Dirac–Fock–Breit energies for the Kr, Sr, and Xe atoms, the Breit interaction energies calculated with this basis for these three atoms are in very good agreement with the corresponding Breit interaction energies obtained by using the extensive well-tempered Gaussian basis sets. Work is in progress to generate a more extensive and energetically better universal Gaussian basis set for He through Xe for its use in non-relativistic Hartree–Fock as well as Dirac–Fock self-consistent field calculations on polyatomics involving heavy atoms.

1,n-Radical ions: the nature of the one-electron two-centre bond in cyclopropane radical cations. An abinitio SCF MO approach

1983 ◽  
Vol 61 (10) ◽  
pp. 2310-2315 ◽  
Author(s):  
Danial D. M. Wayner ◽  
Russell J. Boyd ◽  
Donald R. Arnold
Keyword(s):  
Radical Cations ◽  
Basis Set ◽  
Radical Ions ◽  
Mo Calculations ◽  
Activation Barriers ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The One ◽  
Spin Distributions

The nature of the one-electron two-centre bond in the cyclopropane and 1,2-divinylcyclopropane radical cations is elucidated by use of abinitio self consistent field (SCF) molecular orbital (MO) calculations. The charge and spin distributions in the 90,90 and 90,0 conformations are compared at the STO-3G and 4-31G basis set levels. From energy differences between the radical cations in the 90,90 conformation and the 90,0 (transition state) conformation, the activation barriers for cis–trans isomerization in the 2A1 state of C3H6,+ and of the 1,2-divinylcyclopropane radical cation are estimated. These results are compared to previous calculations and experimental data where possible.

Theoretical electronic investigation of the low-lying electronic states of the LuF molecule

2009 ◽  
Vol 87 (11) ◽  
pp. 1163-1169 ◽  
Author(s):  
Y. Hamade ◽  
F. Taher ◽  
M. Choueib ◽  
Y. Monteil
Keyword(s):  
Ground State ◽  
Electronic States ◽  
Electronic Energy ◽  
Wave Number ◽  
Spectroscopic Constants ◽  
Complete Active Space ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Calculated Potential Energy

The theoretical electronic structure of the LuF molecule is investigated, using the Complete Active-Space Self-Consistent Field CASSCF and the MultiReference Configuration Interaction MRCI methods. These methods are performed for 26 electronic states in the representation 2s+1Λ(+/−), neglecting spin–orbit effects. Spectroscopic constants including the harmonic vibrational wave number ωe (cm–1), the relative electronic energy Te (cm–1) referred to the ground state and the equilibrium internuclear distance Re (Å) are predicted for all the singlet and triplet electronic states situated below 50 000 cm–1. Calculated potential energy curves are also reported.

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