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We propose a pruned multi-configuration time-dependent Hartree (MCTDH) method with systematically expanding nondirect product bases and use it to solve the time-independent Schrödinger equation. No pre-determined pruning condition is required to select the basis functions. Using about 65 000 basis functions, we calculate the first 69 vibrational eigenpairs of acetonitrile, CH3CN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions. In addition, we compare the new pruned MCTDH method with the established multi-layer MCTDH (ML-MCTDH) scheme and determine that although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required. In our largest calculation, the vast majority of the energies have errors smaller than 0.01 cm-1. [ABSTRACT FROM AUTHOR]

In this paper, we propose a pruned, nondirect product multi-configuration time dependent Hartree (MCTDH) method for solving the Schrödinger equation. MCTDH uses optimized 1D basis functions, called single particle functions, but the size of the standard direct product MCTDH basis scales exponentially with D, the number of coordinates. We compare the pruned approach to standard MCTDH calculations for basis sizes small enough that the latter are possible and demonstrate that pruning the basis reduces the CPU cost of computing vibrational energy levels of acetonitrile (D = 12) by more than two orders of magnitude. Using the pruned method, it is possible to do calculations with larger bases, for which the cost of standard MCTDH calculations is prohibitive. Pruning the basis complicates the evaluation of matrix-vector products. In this paper, they are done term by term for a sum-of-products Hamiltonian. When no attempt is made to exploit the fact that matrices representing some of the factors of a term are identity matrices, one needs only to carefully constrain indices. In this paper, we develop new ideas that make it possible to further reduce the CPU time by exploiting identity matrices. [ABSTRACT FROM AUTHOR]

A rigorous and efficient approach for the calculation of eigenstates in polyatomic molecular systems with potentials displaying multiple wells is introduced. The scheme is based on the multi-configurational time-dependent Hartree (MCTDH) approach and uses multiple MCTDH wavefunctions with different single-particle function bases to describe the quantum dynamics in the different potential wells. More specifically, an iterative block Lanczos-type diagonalization scheme utilizing state-averaged MCTDH wavefunctions localized in different wells is employed to obtain the energy eigenvalues and eigenstates. The approach does not impose any formal restriction on the symmetry of the potential or the number of wells. A seven-dimensional model system of tetrahedral symmetry, which is inspired by A·CH4 type complexes and displays four equivalent potential minima, is used to study the numerical performance of the new approach. It is found that the number of configurations in the MCTDH wavefunctions required to obtain converged results is decreased by roughly one order of magnitude compared to standard MCTDH calculations employing a block-relaxation scheme. [ABSTRACT FROM AUTHOR]

A schemeto efficiently calculate ro-vibrational (J> 0)eigenstates within the framework of the multiconfigurational time-dependentHartree (MCTDH) approach is introduced. It employsa basis of MCTDH wave packets which is generated in the calculationof vibrational (J= 0) eigenstates via existing MCTDH-basediterative diagonalization approaches. The subsequent ro-vibrationalcalculations for total angular momenta J> 0 usedirect products of these wave packets and the Wigner rotation matrices.In this ro-vibrational basis, the Hamiltonian matrix can be computedand diagonalized with minor numerical effort for any value of J. Accurate ro-vibrational states are obtained if the numberof iterations in the J= 0 calculations and the basisset sizes in the MCTDH wave function representation are converged.Test calculations studying CH2D show that ro-vibrationaleigenstates for moderately large Jcan be convergedwithin wavenumber accuracy with the same MCTDH basis sets and onlyslightly increased iteration counts compared to purely vibrational(J= 0) calculations. If large J’s are considered or very high accuracies are required, thenumber of iterations required to obtain convergence increases significantly.Comparing the theoretical results with experimental data for the out-of-planebend, symmetric stretch, and antisymmetric stretch fundamentals, theaccuracy of the ab initio potential energy surface employed is investigated. [ABSTRACT FROM AUTHOR]