Prediction of many-electron wavefunctions using atomic potentials: extended basis sets and molecular dissociation

The Brillouin theorem has been generalized for the extended non-relativistic electronic Hamiltonian (HÑ+ Hne+ aHee) in relation to coupling strength parameter (a), as well as for the configuration interactions (CI) formalism in this respect. For a computation support, we have made a particular modification of the SCF part in the Gaussian package: essentially a single line was changed in an SCF algorithm, wherein the operator rij-1 was overwritten as rij-1 ® arij-1, and “a” was used as input. The case a=0 generates an orto-normalized set of Slater determinants which can be used as a basis set for CI calculations for the interesting physical case a=1, removing the known restriction by Brillouin theorem with this trick. The latter opens a door from the theoretically interesting subject of this work toward practice.

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Generalization of Brillouin theorem for the non-relativistic electronic Schrödinger equation in relation to coupling strength parameter, and its consequences in single determinant basis sets for configuration interactions

10.26434/chemrxiv.5371498.v1 ◽

2017 ◽

Author(s):

Sandor Kristyan

Keyword(s):

Schrödinger Equation ◽

Coupling Strength ◽

Schrodinger Equation ◽

Basis Set ◽

Basis Sets ◽

Single Line ◽

Strength Parameter ◽

Physical Case ◽

Ci Calculations

The Brillouin theorem has been generalized for the extended non-relativistic electronic Hamiltonian (HÑ+ Hne+ aHee) in relation to coupling strength parameter (a), as well as for the configuration interactions (CI) formalism in this respect. For a computation support, we have made a particular modification of the SCF part in the Gaussian package: essentially a single line was changed in an SCF algorithm, wherein the operator rij-1 was overwritten as rij-1 ® arij-1, and “a” was used as input. The case a=0 generates an orto-normalized set of Slater determinants which can be used as a basis set for CI calculations for the interesting physical case a=1, removing the known restriction by Brillouin theorem with this trick. The latter opens a door from the theoretically interesting subject of this work toward practice.

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Solution of the Schrödinger torsion equation in the basis set of Mathieu functions: verification by numerical experiment

Journal of Physics Conference Series ◽

10.1088/1742-6596/2052/1/012004 ◽

2021 ◽

Vol 2052 (1) ◽

pp. 012004

Author(s):

A N Belov ◽

V V Turovtsev ◽

Yu A Fedina ◽

Yu D Orlov

Keyword(s):

Schrödinger Equation ◽

Numerical Experiment ◽

Numerical Solution ◽

Schrodinger Equation ◽

Periodic Potential ◽

Plane Waves ◽

Basis Set ◽

Basis Sets ◽

Mathieu Functions ◽

Computational Stability

Abstract The efficiency of the algorithm for the numerical solution of the Schrödinger torsion equation in the basis of Mathieu functions has been considered. The computational stability of the proposed algorithm is shown. The energies of torsion transitions determined in the basis sets of plane waves and Mathieu functions have been compared with the results of spectroscopy. A conclusion about the applicability of the algorithm using the basis set of Mathieu functions to the solution of the Schrödinger equation with a periodic potential has been derived.

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