### Abstract

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Original language | English (US) |
---|---|

Article number | 224317 |

Journal | The Journal of Chemical Physics |

Volume | 124 |

Issue number | 22 |

DOIs | |

State | Published - Jun 14 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.** / Bubin, Sergiy; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 124, no. 22, 224317. https://doi.org/10.1063/1.2204605

}

TY - JOUR

T1 - Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

AU - Bubin, Sergiy

AU - Adamowicz, Ludwik

PY - 2006/6/14

Y1 - 2006/6/14

N2 - In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

AB - In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

UR - http://www.scopus.com/inward/record.url?scp=33745151414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745151414&partnerID=8YFLogxK

U2 - 10.1063/1.2204605

DO - 10.1063/1.2204605

M3 - Article

VL - 124

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 22

M1 - 224317

ER -