Multi-configuration time-dependent Hartree (MCTDH) is a prominent approach for solving the Schroedinger equation to study the dynamics of nuclei. The original MCTDH method has two important weaknesses. First, because MCTDH uses a direct product basis, both the memory and the time costs of an MCTDH calculation scale exponentially with the number of nuclei. Second, calculating matrix-vector products in the MCTDH basis is, when the potential energy surface is not a sum of products, costly. The collocation-MCTDH (C-MCTDH) methods presented in this talk mitigate both these weaknesses. The original C-MCTDH method [J. Chem. Phys. 148, 044115 (2018)] uses, as is also true in standard MCTDH, a direct product basis. I shall present two solutions to the basis size problem. First, by using generalized hierarchical basis functions, that span the same space as the single particle functions we introduced in the first C-MCTDH paper, and a Smolyak grid, we have developed a C-MCTDH approach that makes it possible to prune both the basis and the grid. Second, by using multivariate single particle functions and a collocation grid made from a simultaneous diagonalization discrete variable representation or Leja points, the memory and time costs can be significantly reduced. In both methods, there is no need to compute matrix elements of the PES in a MCTDH basis and it is therefore straightforward to use a non-sum-of-products PES. To use a collocation method, it is only necessary to evaluate basis functions, derivatives of basis functions, and the PES at collocation points. We test both approaches by calculating the first 36, 80, and 69 vibrational eigenpairs of CH3, CH4, and CH3CN, respectively. It is shown that using rectangular collocation, i.e. more points than basis functions, is advantageous.

Using collocation with the multi-configuration time-dependent Hartree method

ACS Spring Meeting 2021

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.