论文标题
平行传输（准） - 绝热基础
The Parallel-Transported (Quasi)-Diabatic Basis
论文作者
论文摘要
本文涉及使用并行运输来创建绝热基础。并行传输基础的优点包括可以在点或歧管附近进行泰勒串联膨胀的设施，例如接缝（电子汉密尔顿电子汉密尔顿的脱整流位置），以及在此基础上衍生耦合和弯曲的衍生耦合和曲率之间的密切关系。这些对于归化邻居中的核schrödinger方程的分析治疗很重要。平行传输基础与奇异价值基础有密切的关系；在本文中，两者都在有关参考点的电源系列中扩展，并且显示它们可以通过二阶同意，但不超越。泰勒级数的扩展是通过投影算子进行的，其扩展不涉及能量分母或任何类型的奇异性，并且在其奇异值基础和平行传输基础方面均可表达。并行运输的基础是PoincaréGauge的一种版本，该版本在电磁方面众所周知，该版本提供了衍生耦合与曲率之间的关系，并且与米德（Mead）的公式一起提供了一种有效的方法来计算Taylor系列的基础状态和衍生物耦合。涵盖了电子哈密顿量中的细胞结构效应的情况。
This article concerns the use of parallel transport to create a diabatic basis. The advantages of the parallel-transported basis include the facility with which Taylor series expansions can be carried out in the neighborhood of a point or a manifold such as a seam (the locus of degeneracies of the electronic Hamiltonian), and the close relationship between the derivative couplings and the curvature in this basis. These are important for analytic treatments of the nuclear Schrödinger equation in a neighborhood of degeneracies. The parallel-transported basis bears a close relationship to the singular-value basis; in this article both are expanded in power series about a reference point and they are shown to agree through second order but not beyond. Taylor series expansions are effected through the projection operator, whose expansion does not involve energy denominators or any type of singularity, and in terms of which both the singular-value basis and the parallel-transported basis can be expressed. The parallel-transported basis is a version of Poincaré gauge, well known in electromagnetism, which provides a relationship between the derivative couplings and the curvature and which, along with a formula due to Mead, affords an efficient method for calculating Taylor series of the basis states and the derivative couplings. The case in which fine structure effects are included in the electronic Hamiltonian is covered.
