### Abstract

We report the first determination of a "most" diabatic basis for a triatomic molecule based exclusively on ab initio derivative couplings that takes careful account of the limitations imposed by the nonremovable part of those couplings. Baer [Chem. Phys. Lett. 35, 112 (1975)] showed that an orthogonal transformation from adiabatic states to diabatic states cannot remove all the derivative coupling unless the curl of the derivative coupling vanishes. Subsequently, Mead and Truhlar [J. Chem. Phys. 77, 6090 (1982)] observed that this curl does not, in general, vanish so that some of the derivative coupling is nonremovable. This observation and the historical lack of efficient algorithms for the evaluation of the derivative coupling led to a variety of methods for determining approximate diabatic bases that avoid computation of the derivative couplings. These methods neglect an indeterminate portion of the derivative coupling. Mead and Truhlar also observed that near an avoided crossing of two states the rotation angle to a most diabatic basis, i.e., the basis in which the removable part of the derivative coupling has been transformed away, could be obtained from the solution of a Poisson's equation requiring only knowledge of the derivative couplings. Here a generalization of this result to the case of a conical intersection is used to determine a most diabatic basis for a section of the 1^{1}A^{′} and 2^{1}A^{′} potential energy surfaces of HeH_{2} that includes the minimum energy point on the seam of conical intersection.

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

Pages (from-to) | 20-25 |

Number of pages | 6 |

Journal | Journal of Chemical Physics |

Volume | 109 |

Issue number | 1 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**On the adiabatic to diabatic states transformation in the presence of a conical intersection : A most diabatic basis from the solution to a Poisson's equation. I.** / Sadygov, Rovshan; Yarkony, David R.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - On the adiabatic to diabatic states transformation in the presence of a conical intersection

T2 - A most diabatic basis from the solution to a Poisson's equation. I

AU - Sadygov, Rovshan

AU - Yarkony, David R.

PY - 1998

Y1 - 1998

N2 - We report the first determination of a "most" diabatic basis for a triatomic molecule based exclusively on ab initio derivative couplings that takes careful account of the limitations imposed by the nonremovable part of those couplings. Baer [Chem. Phys. Lett. 35, 112 (1975)] showed that an orthogonal transformation from adiabatic states to diabatic states cannot remove all the derivative coupling unless the curl of the derivative coupling vanishes. Subsequently, Mead and Truhlar [J. Chem. Phys. 77, 6090 (1982)] observed that this curl does not, in general, vanish so that some of the derivative coupling is nonremovable. This observation and the historical lack of efficient algorithms for the evaluation of the derivative coupling led to a variety of methods for determining approximate diabatic bases that avoid computation of the derivative couplings. These methods neglect an indeterminate portion of the derivative coupling. Mead and Truhlar also observed that near an avoided crossing of two states the rotation angle to a most diabatic basis, i.e., the basis in which the removable part of the derivative coupling has been transformed away, could be obtained from the solution of a Poisson's equation requiring only knowledge of the derivative couplings. Here a generalization of this result to the case of a conical intersection is used to determine a most diabatic basis for a section of the 11A′ and 21A′ potential energy surfaces of HeH2 that includes the minimum energy point on the seam of conical intersection.

AB - We report the first determination of a "most" diabatic basis for a triatomic molecule based exclusively on ab initio derivative couplings that takes careful account of the limitations imposed by the nonremovable part of those couplings. Baer [Chem. Phys. Lett. 35, 112 (1975)] showed that an orthogonal transformation from adiabatic states to diabatic states cannot remove all the derivative coupling unless the curl of the derivative coupling vanishes. Subsequently, Mead and Truhlar [J. Chem. Phys. 77, 6090 (1982)] observed that this curl does not, in general, vanish so that some of the derivative coupling is nonremovable. This observation and the historical lack of efficient algorithms for the evaluation of the derivative coupling led to a variety of methods for determining approximate diabatic bases that avoid computation of the derivative couplings. These methods neglect an indeterminate portion of the derivative coupling. Mead and Truhlar also observed that near an avoided crossing of two states the rotation angle to a most diabatic basis, i.e., the basis in which the removable part of the derivative coupling has been transformed away, could be obtained from the solution of a Poisson's equation requiring only knowledge of the derivative couplings. Here a generalization of this result to the case of a conical intersection is used to determine a most diabatic basis for a section of the 11A′ and 21A′ potential energy surfaces of HeH2 that includes the minimum energy point on the seam of conical intersection.

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U2 - 10.1063/1.476552

DO - 10.1063/1.476552

M3 - Article

VL - 109

SP - 20

EP - 25

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 1

ER -