基于二次量子化电子的无势能面非绝热量子动力学：在MCTDH方法框架内的应用
Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: application within the framework of the MCTDH method
摘要：
介绍了一种基于电子运动的第二量子化表示（SQR）和通常的核坐标表示的第一性原理量子形式主义来描述电子和原子核的非绝热动力学。这一过程避免了引入势能面和非绝热耦合，提供了一种替代玻恩-奥本海默近似。在原子核的混合第一量子化表示和电子的SQR表示中，分子哈密顿量的一个重要特征是所有的自由度，原子核位置和电子占据，都是可区分的。这使得该方法与用于核电子波函数传播的各种张量分解\emph{ansätze}兼容。在这里，我们描述的应用程序中的多配置时间相关的哈特里（MCTDH）框架和多层的推广，对应于塔克和分层塔克张量分解的波函数，分别这种形式主义。计算了HeH $^+$分子在极紫外光照射下的光解离截面，结果表明，该解离截面具有非绝热效应和He+H $^+$和He $^+$ +H两个可能的解离通道之间的量子干涉.这些计算进行了比较与通常的描述的基础上ab \emph{ab initio}势能面和非绝热耦合矩阵元素，完全同意。的证明的原则计算，以说明这种形式主义，这是详细讨论的优点和缺点，以及可能的方法来克服它们。
英文摘要：
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear coordinates is introduced. This procedure circumvents the introduction of potential energy surfaces and non-adiabatic couplings, providing an alternative to the Born-Oppenheimer approximation. An important feature of the molecular Hamiltonian in the mixed first quantized representation for the nuclei and the SQR representation for the electrons is that all degrees of freedom, nuclear positions and electronic occupations, are distinguishable. This makes the approach compatible with various tensor decomposition \emph{ansätze} for the propagation of the nuclear-electronic wavefunction. Here, we describe the application of this formalism within the multi-configuration time-dependent Hartree (MCTDH) framework and its multilayer generalization, corresponding to Tucker and hierarchical Tucker tensor decompositions of the wavefunction, respectively. The approach is applied to the calculation of the photodissociation cross-section of the HeH$^+$ molecule under extreme ultraviolet irradiation, which features non-adiabatic effects and quantum interferences between the two possible fragmentation channels, He+H$^+$ and He$^+$+H. These calculations are compared with the usual description based on ab \emph{ab initio} potential energy surfaces and non-adiabatic coupling matrix elements, which fully agree. The proof-of-principle calculations serve to illustrate the advantages and drawbacks of this formalism, which are discussed in detail, as well as possible ways to overcome them.
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