### Abstract

An algorithm for variational calculations of molecules with one π electron performed with all-electron explicitly correlated Gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the Born-Oppenheimer electronic energy determined with respect to the ECG exponential parameters and the coordinates of the Gaussian centers. The availability of the gradient greatly accelerates the variational energy minimization. The algorithm is tested in calculations of four electronic excited states, c^{3}Π_{u}, C^{1}Π _{u}, i^{3}Π_{g}, and I^{1}Π_{g}, of the hydrogen molecule at a single internuclear distance specific to each state. With the use of the analytical energy gradient, the present calculations yield new, lowest-to-date, variational energy upper bounds for all four states.

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

Article number | 124101 |

Journal | The Journal of Chemical Physics |

Volume | 138 |

Issue number | 12 |

DOIs | |

State | Published - Mar 28 2013 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*The Journal of Chemical Physics*,

*138*(12), [124101]. https://doi.org/10.1063/1.4795094

**Analytical energy gradient used in variational Born-Oppenheimer calculations with all-electron explicitly correlated Gaussian functions for molecules containing one π electron.** / Tung, Wei Cheng; Pavanello, Michele; Sharkey, Keeper L.; Kirnosov, Nikita; Adamowicz, Ludwik.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 138, no. 12, 124101. https://doi.org/10.1063/1.4795094

}

TY - JOUR

T1 - Analytical energy gradient used in variational Born-Oppenheimer calculations with all-electron explicitly correlated Gaussian functions for molecules containing one π electron

AU - Tung, Wei Cheng

AU - Pavanello, Michele

AU - Sharkey, Keeper L.

AU - Kirnosov, Nikita

AU - Adamowicz, Ludwik

PY - 2013/3/28

Y1 - 2013/3/28

N2 - An algorithm for variational calculations of molecules with one π electron performed with all-electron explicitly correlated Gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the Born-Oppenheimer electronic energy determined with respect to the ECG exponential parameters and the coordinates of the Gaussian centers. The availability of the gradient greatly accelerates the variational energy minimization. The algorithm is tested in calculations of four electronic excited states, c3Πu, C1Π u, i3Πg, and I1Πg, of the hydrogen molecule at a single internuclear distance specific to each state. With the use of the analytical energy gradient, the present calculations yield new, lowest-to-date, variational energy upper bounds for all four states.

AB - An algorithm for variational calculations of molecules with one π electron performed with all-electron explicitly correlated Gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the Born-Oppenheimer electronic energy determined with respect to the ECG exponential parameters and the coordinates of the Gaussian centers. The availability of the gradient greatly accelerates the variational energy minimization. The algorithm is tested in calculations of four electronic excited states, c3Πu, C1Π u, i3Πg, and I1Πg, of the hydrogen molecule at a single internuclear distance specific to each state. With the use of the analytical energy gradient, the present calculations yield new, lowest-to-date, variational energy upper bounds for all four states.

UR - http://www.scopus.com/inward/record.url?scp=84875783128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875783128&partnerID=8YFLogxK

U2 - 10.1063/1.4795094

DO - 10.1063/1.4795094

M3 - Article

C2 - 23556703

AN - SCOPUS:84875783128

VL - 138

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 12

M1 - 124101

ER -