### Abstract

In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N -particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

Original language | English |
---|---|

Article number | 114107 |

Journal | Journal of Chemical Physics |

Volume | 128 |

Issue number | 11 |

DOIs | |

Publication status | Published - 2008 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*128*(11), [114107]. https://doi.org/10.1063/1.2894866

**Energy and energy gradient matrix elements with N -particle explicitly correlated complex Gaussian basis functions with L=1.** / Bubin, Sergiy; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 128, no. 11, 114107. https://doi.org/10.1063/1.2894866

}

TY - JOUR

T1 - Energy and energy gradient matrix elements with N -particle explicitly correlated complex Gaussian basis functions with L=1

AU - Bubin, Sergiy

AU - Adamowicz, Ludwik

PY - 2008

Y1 - 2008

N2 - In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N -particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

AB - In this work we consider explicitly correlated complex Gaussian basis functions for expanding the wave function of an N -particle system with the L=1 total orbital angular momentum. We derive analytical expressions for various matrix elements with these basis functions including the overlap, kinetic energy, and potential energy (Coulomb interaction) matrix elements, as well as matrix elements of other quantities. The derivatives of the overlap, kinetic, and potential energy integrals with respect to the Gaussian exponential parameters are also derived and used to calculate the energy gradient. All the derivations are performed using the formalism of the matrix differential calculus that facilitates a way of expressing the integrals in an elegant matrix form, which is convenient for the theoretical analysis and the computer implementation. The new method is tested in calculations of two systems: the lowest P state of the beryllium atom and the bound P state of the positronium molecule (with the negative parity). Both calculations yielded new, lowest-to-date, variational upper bounds, while the number of basis functions used was significantly smaller than in previous studies. It was possible to accomplish this due to the use of the analytic energy gradient in the minimization of the variational energy.

UR - http://www.scopus.com/inward/record.url?scp=41049100529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41049100529&partnerID=8YFLogxK

U2 - 10.1063/1.2894866

DO - 10.1063/1.2894866

M3 - Article

C2 - 18361554

AN - SCOPUS:41049100529

VL - 128

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

M1 - 114107

ER -