论文标题
基于第二定量电子的非绝热量子动力学无势能表面：在MCTDH方法的框架内应用
Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: application within the framework of the MCTDH method
论文作者
论文摘要
基于电子运动的第二个量化表示（SQR）与核坐标的通常表示，以描述电子和核的非绝热动力学的第一原理量子形式主义。该程序规避了势能表面和非绝热耦合的引入，为出生的近探针近似提供了替代方案。分子哈密顿量在核的混合第一个量化表示和电子的SQR表示中的一个重要特征是，所有自由度，核位置和电子职业的所有程度都是可区分的。这使得该方法与各种张量分解\ emph {ansätze}兼容，以传播核电子波函数。在这里，我们描述了这种形式主义的应用在多符合时间依赖性的Hartree（MCTDH）框架中及其多层概括，分别对应于塔克和分层的塔克张量分解，分别是波函数的分解。该方法适用于在极端紫外线照射下HEH $^+$分子的光解离横截面的计算，该分子在两个可能的片段化通道之间具有非绝热效应和量子干扰，He+H $^+$和HE HE HE HE HE HE $^+$+H。将这些计算与基于AB \ emph {ab intio}势能表面和非绝热耦合矩阵元素的通常描述进行了比较，这完全同意。原理证明的计算旨在说明这种形式主义的优势和缺点，并详细讨论了这些形式主义，以及克服它们的可能方法。
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.
