Adaptable Gaussian Bases for Quantum Dynamics of the Nuclei
Adaptable Gaussian Bases for Quantum Dynamics of the Nuclei
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DOI：
10.1007/978-3-030-67262-1_8
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发表时间：
2021
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影响因子：
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通讯作者：
Sophya Garashchuk
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作者：
Sophya Garashchuk
波函数表示的紧性是高维分子系统量子动力学的核心实际问题之一，因为对于一般的粒子间相互作用，波函数的复杂性随系统大小呈指数增长。虽然在电子结构理论和计算中已经很好地建立了根据标准预定义基组扩展波函数，但在原子核的量子动力学中却不是这样。一个“族”的方法是基于高斯函数，其参数以某种方式定制为随时间演变的波函数的形状，或与感兴趣的系统相关的能量和空间范围;基参数的选择通常来自经典动力学、半经典参数或耦合变分方程，各有其优缺点。在本章中，我们详细回顾了几种构造紧致高斯基的方法，这些方法可扩展到多维系统，并且在原则上产生精确的量子动力学：解冻的高斯波包动力学，与时间无关的准随机分布高斯基，以及由量子轨迹引导的与时间相关的高斯基。这些方法的非变分特性和它们对目标波函数的适应性，结合最近的进展，在飞行中的电子结构计算，使它们实际应用于大分子系统。
Compactness of the wavefunction representation is one of the central practical questions in quantum dynamics of high-dimensional molecular systems, because, for general inter-particle interactions, the complexity of a wavefunction grows exponentially with the system size. While expanding the wavefunctions in terms of standard predefined basis sets is well established in the electronic structure theory and computations, it is not so in the quantum dynamics of the nuclei. One ‘family’ of approaches is based on Gaussian functions whose parameters are tailored in some way to the shape of a wavefunction evolving in time, or to the energy and spatial range relevant to the system of interest; the choice of the basis parameters often comes from classical dynamics, semiclassical arguments, or from coupled variational equations, all with their pros and cons. In this chapter, we review in detail several approaches to constructing compact Gaussian bases, scalable to multidimensional systems and, in principle, yielding exact quantum dynamics: thawed Gaussian wavepacket dynamics, time-independent quasi-random distributed Gaussian bases, and time-dependent Gaussian bases guided by quantum trajectories. The non-variational character of these methods and their adaptability to target wavefunctions, combined with recent advances in the on-the-fly electronic structure calculation, make them practical for applications to large molecular systems.