Manthe Uwe
Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitatsstr. 25, 33615 Bielefeld, Germany.
J Chem Phys. 2009 Feb 7;130(5):054109. doi: 10.1063/1.3069655.
The multiconfigurational time-dependent Hartree (MCTDH) approach facilitates multidimensional quantum dynamics calculations by employing a layered representation: in the upper layer of the representation the multidimensional wave function is expanded in a basis of time-dependent single-particle functions, in the lower layer then these single-particle functions are represented in a larger time-independent basis. This two layer approach can be generalized to a multilayer MCTDH representation to further increase the numerical efficiency. In recent work [U. Manthe, J. Chem. Phys. 128, 164116 (2008)], a quadrature scheme has been introduced which facilitates multilayer MCTDH calculations for Hamiltonians with general potential energy functions. Based on time-dependent discrete variable representation (DVR) grids corresponding to the single-particle function bases the scheme employs the correlation DVR (CDVR) approach. The present work shows that serious problems arise when this original multilayer CDVR approach is applied for accurate calculations of vibrational states. A solution to these problems is presented which uses a revised scheme to define the time-dependent DVR grids entering into the CDVR scheme. Applications studying the vibrational states of CH(3) demonstrate that the resulting revised multilayer MCTDH/CDVR approach yields smoothly convergent and accurate results.
多组态含时 Hartree（MCTDH）方法通过采用分层表示来促进多维量子动力学计算：在表示的上层，多维波函数在含时单粒子函数的基中展开，在下层，这些单粒子函数则在更大的与时间无关的基中表示。这种两层方法可以推广到多层 MCTDH 表示，以进一步提高数值效率。在最近的工作[U. Manthe, J. Chem. Phys. 128, 164116 (2008)]中，引入了一种求积方案，该方案便于对具有一般势能函数的哈密顿量进行多层 MCTDH 计算。基于与单粒子函数基对应的含时离散变量表示（DVR）网格，该方案采用了关联 DVR（CDVR）方法。目前的工作表明，当将这种原始的多层 CDVR 方法应用于振动状态的精确计算时会出现严重问题。本文提出了这些问题的解决方案，即使用一种修正方案来定义进入 CDVR 方案的含时 DVR 网格。对 CH(3)振动状态的研究应用表明，由此产生的修正后的多层 MCTDH/CDVR 方法能产生平滑收敛且准确的结果。
