### Abstract

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H _{3} ^{+} ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H _{3} ^{+} rovibrational spectrum is reproduced at the 0.1 cm ^{-1} accuracy level up to 16 600 cm ^{-1} above the ground state.

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

Pages (from-to) | 5001-5013 |

Number of pages | 13 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 370 |

Issue number | 1978 |

DOIs | |

State | Published - Nov 13 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)
- Engineering(all)

### Cite this

**Progress in calculating the potential energy surface of H _{3} ^{+} .** / Adamowicz, Ludwik; Pavanello, Michele.

Research output: Contribution to journal › Article

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*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 370, no. 1978, pp. 5001-5013. https://doi.org/10.1098/rsta.2012.0101

}

TY - JOUR

T1 - Progress in calculating the potential energy surface of H 3 +

AU - Adamowicz, Ludwik

AU - Pavanello, Michele

PY - 2012/11/13

Y1 - 2012/11/13

N2 - The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H 3 + ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H 3 + rovibrational spectrum is reproduced at the 0.1 cm -1 accuracy level up to 16 600 cm -1 above the ground state.

AB - The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H 3 + ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H 3 + rovibrational spectrum is reproduced at the 0.1 cm -1 accuracy level up to 16 600 cm -1 above the ground state.

UR - http://www.scopus.com/inward/record.url?scp=84867507228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867507228&partnerID=8YFLogxK

U2 - 10.1098/rsta.2012.0101

DO - 10.1098/rsta.2012.0101

M3 - Article

C2 - 23028149

AN - SCOPUS:84867507228

VL - 370

SP - 5001

EP - 5013

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 1978

ER -