On the numerical solution of the exact factorization equations
On the numerical solution of the exact factorization equations
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DOI：
10.1063/1.5090802
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发表时间：
2019-04-21
影响因子：
4.4
通讯作者：
Maitra, Neepa T.
中科院分区：
文献类型：
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作者：
Gossel, Graeme H.;Lacombe, Lionel;Maitra, Neepa T.
精确因式分解（EF）方法耦合电子-离子动力学重铸的含时分子薛定谔方程为两个耦合方程，一个为核波函数和一个为条件电子波函数。这些方程中出现的势提供了对非绝热过程的深入了解，并从这些方程出发制定了新的实用非绝热动力学方法。在这里，我们提供了一个自洽的精确方程的解的第一个演示，其稳定性和收敛性的初步分析。这些方程有一个前所未有的数学形式，包含了一个在时间传播中通常遇到的厄米哈密顿量之外的哈密顿量，因此当以直接的方式应用于EF方程时，通常的含时薛定谔数值方法失败了。我们找到了一种方法，使稳定的传播足够长的时间来见证非绝热行为的模型系统之前，非平凡的不稳定性接管。EF为基础的方法的发展和分析的影响进行了讨论。由ATP Publishing授权出版。
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schrodinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic wavefunction. The potentials appearing in these equations have provided insight into non adiabatic processes, and new practical non adiabatic dynamics methods have been formulated starting from these equations. Here, we provide a first demonstration of a self-consistent solution of the exact equations, with a preliminary analysis of their stability and convergence properties. The equations have an unprecedented mathematical form, involving a Hamiltonian out side the class of Hermitian Hamiltonians usually encountered in time-propagation, and so the usual numerical methods for time-dependent Schrodinger fail when applied in a straightforward way to the EF equations. We find an approach that enables stable propagation long enough to witness non-adiabatic behavior in a model system before non-trivial instabilities take over. Implications for the development and analysis of EF-based methods are discussed. Published under license by ATP Publishing.