### Abstract

We elaborate on the theory for the variational solution of the Schrödinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schrödinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H _{2} ^{+} and H _{2}, three bound states of the positronium molecule, Ps _{2}, and the ground and two excited states of the ^{7}Li atom.

Original language | English |
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Article number | 024104 |

Journal | The Journal of Chemical Physics |

Volume | 137 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jul 14 2012 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*137*(2), [024104]. https://doi.org/10.1063/1.4731696

**Molecular structure calculations : A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation.** / Mat́yus, E.; Reiher, Markus.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 137, no. 2, 024104. https://doi.org/10.1063/1.4731696

}

TY - JOUR

T1 - Molecular structure calculations

T2 - A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

AU - Mat́yus, E.

AU - Reiher, Markus

PY - 2012/7/14

Y1 - 2012/7/14

N2 - We elaborate on the theory for the variational solution of the Schrödinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schrödinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H 2 + and H 2, three bound states of the positronium molecule, Ps 2, and the ground and two excited states of the 7Li atom.

AB - We elaborate on the theory for the variational solution of the Schrödinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schrödinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H 2 + and H 2, three bound states of the positronium molecule, Ps 2, and the ground and two excited states of the 7Li atom.

UR - http://www.scopus.com/inward/record.url?scp=84863900634&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863900634&partnerID=8YFLogxK

U2 - 10.1063/1.4731696

DO - 10.1063/1.4731696

M3 - Article

C2 - 22803525

AN - SCOPUS:84863900634

VL - 137

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

M1 - 024104

ER -