### Abstract

The Curl equations (Baer, M. Chem Phys Lett 1975, 35, 112) are applied to calculate the nonadiabatic coupling terms, τ _{ij}, subject to ab initio boundary conditions. As an example we consider a two-state, planar system characterized by two (polar) coordinates, θ and q, and treat the corresponding components of τ, namely, T _{θ}(q, θ) and τ _{q}(q, θ). The main difficulty that we encounter is that the vectorial Curl equation supplies, for this case, only one differential equation although we have two unknown functions. To overcome this difficulty we employ a gauge transformation that leads to a divergence equation-the missing equation. Next, the two Curl-divergence equations are treated with the aim of forming two decoupled second-order differential equations for the two components of a vector potential A(q, θ) [which is related to τ(q, θ) through a gauge transformation], namely, one for A _{θ}(q, θ) [related to τ _{θ}(q, θ)] and one for A _{q}(q, θ) [related to τ _{q}(q, θ)], The main achievement of the theory is a relation, for a given q ^{1}, between the Fourier coefficients of τ _{q}(q, θ) and those of τ _{θ}(q, θ). This approach is applied to three cases: an analytic model and two ab initio treatments-one for the C _{2}H molecule and one for the H + H _{2} molecular system. In all three cases encouraging agreements were obtained between the ab initio-calculated values of τ _{q}(q, θ) values and the ones that follow from the present approach.

Original language | English |
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Pages (from-to) | 594-604 |

Number of pages | 11 |

Journal | International Journal of Quantum Chemistry |

Volume | 99 |

Issue number | 5 SPEC. ISS. |

DOIs | |

Publication status | Published - Sep 15 2004 |

### Keywords

- Conical intersection
- Curl equations
- Nondiabetic coupling terms
- Topological phase

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Condensed Matter Physics
- Physical and Theoretical Chemistry

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## Cite this

_{2}H molecule and the H

_{2}+ H system.

*International Journal of Quantum Chemistry*,

*99*(5 SPEC. ISS.), 594-604. https://doi.org/10.1002/qua.10840