### Abstract

In this article, we discuss the electronic nonadiabatic coupling matrix, τ, which under certain conditions is characterized by two interesting features: (1) its components fulfill an extended Curl equation (Chem. Phys. Lett. 1975, 35, 112, (see Appendix 1)) and (2) it is quantized in the sense that the topological D matrix, presented as an exponentiated line integral over the τ matrix, is a unitary diagonal matrix (Chem. Phys. Lett. 2000, 319, 489). These features can be shown to exist if the relevant group of states forms a Hilbert subspace, namely, a group of states that are strongly coupled with each other but are only weakly coupled with all other states. The numerical study is carried out applying the eigenfunctions of the Mathieu equation.

Original language | English |
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Pages (from-to) | 7189-7196 |

Number of pages | 8 |

Journal | Journal of Physical Chemistry A |

Volume | 107 |

Issue number | 37 |

DOIs | |

Publication status | Published - Sep 18 2003 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Journal of Physical Chemistry A*,

*107*(37), 7189-7196. https://doi.org/10.1021/jp030214d

**The electronic non-adiabatic coupling matrix : A numerical study of the curl condition and the quantization condition employing the Mathieu equation.** / Vértesi, T.; Vibók, A.; Halász, G.; Yahalom, A.; Englman, R.; Baer, M.

Research output: Contribution to journal › Article

*Journal of Physical Chemistry A*, vol. 107, no. 37, pp. 7189-7196. https://doi.org/10.1021/jp030214d

}

TY - JOUR

T1 - The electronic non-adiabatic coupling matrix

T2 - A numerical study of the curl condition and the quantization condition employing the Mathieu equation

AU - Vértesi, T.

AU - Vibók, A.

AU - Halász, G.

AU - Yahalom, A.

AU - Englman, R.

AU - Baer, M.

PY - 2003/9/18

Y1 - 2003/9/18

N2 - In this article, we discuss the electronic nonadiabatic coupling matrix, τ, which under certain conditions is characterized by two interesting features: (1) its components fulfill an extended Curl equation (Chem. Phys. Lett. 1975, 35, 112, (see Appendix 1)) and (2) it is quantized in the sense that the topological D matrix, presented as an exponentiated line integral over the τ matrix, is a unitary diagonal matrix (Chem. Phys. Lett. 2000, 319, 489). These features can be shown to exist if the relevant group of states forms a Hilbert subspace, namely, a group of states that are strongly coupled with each other but are only weakly coupled with all other states. The numerical study is carried out applying the eigenfunctions of the Mathieu equation.

AB - In this article, we discuss the electronic nonadiabatic coupling matrix, τ, which under certain conditions is characterized by two interesting features: (1) its components fulfill an extended Curl equation (Chem. Phys. Lett. 1975, 35, 112, (see Appendix 1)) and (2) it is quantized in the sense that the topological D matrix, presented as an exponentiated line integral over the τ matrix, is a unitary diagonal matrix (Chem. Phys. Lett. 2000, 319, 489). These features can be shown to exist if the relevant group of states forms a Hilbert subspace, namely, a group of states that are strongly coupled with each other but are only weakly coupled with all other states. The numerical study is carried out applying the eigenfunctions of the Mathieu equation.

UR - http://www.scopus.com/inward/record.url?scp=0141793998&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141793998&partnerID=8YFLogxK

U2 - 10.1021/jp030214d

DO - 10.1021/jp030214d

M3 - Article

VL - 107

SP - 7189

EP - 7196

JO - Journal of Physical Chemistry A

JF - Journal of Physical Chemistry A

SN - 1089-5639

IS - 37

ER -