Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate MCTDH calculations with general potential energy surfaces.

We propose a new collocation multi-configuration time-dependent Hartree (MCTDH) method. It reduces point-set error by using more points than basis functions. Collocation makes it possible to use MCTDH with a general potential energy surface without computing any integrals.

A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces.

We introduce a collocation-based multi-configuration time-dependent Hartree (MCTDH) method that uses more collocation points than basis functions. We call it the rectangular collocation MCTDH (RC-MCTDH) method. It does not require that the potential be a sum of products.

A collocation-based multi-configuration time-dependent Hartree method using mode combination and improved relaxation.

Although very useful, the original multi-configuration time-dependent Hartree (MCTDH) method has two weaknesses: (1) its cost scales exponentially with the number of atoms in the system; (2) the standard MCTDH implementation requires that the potential energy surface (PES) be in the sum-of-product (SOP) form in order to reduce the cost of computing integrals in the MCTDH basis. One way to deal with (1) is to lump coordinates into groups. This is mode combination (MC).

A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface.

Standard multiconfiguration time-dependent Hartree (MCTDH) calculations use a direct product basis and rely on the potential being a sum of products (SOPs). The size of the direct product MCTDH basis scales exponentially with the number of atoms. Accurate potentials may not be SOPs.

A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation with a general potential energy surface.

We present a new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation required to compute (ro-)vibrational spectra, photodissociation cross sections, reaction rate constants, etc., that can be used with general potential energy surfaces. Collocation obviates the need for quadrature and facilitates using complicated kinetic energy operators.

Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH.

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, CHCN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions.

Using a pruned, nondirect product basis in conjunction with the multi-configuration time-dependent Hartree (MCTDH) method.

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.

CH+5: Symmetry and the Entangled Rovibrational Quantum States of a Fluxional Molecule.

Protonated methane, CH5+, is the prototypical example of a fluxional molecular system. The almost unconstrained angular motion of its five hydrogen atoms results in dynamical phenomena not found in rigid or semirigid molecules. Here it is shown that standard concepts to describe rotational quantum states of molecules can not be applied to CH5+ or any other fluxional system of the type ABn or Bn with n > 4 due to fundamental symmetry reasons.

Iterative diagonalization in the multiconfigurational time-dependent Hartree approach: ro-vibrational eigenstates.

A scheme to efficiently calculate ro-vibrational (J > 0) eigenstates within the framework of the multiconfigurational time-dependent Hartree (MCTDH) approach is introduced. It employs a basis of MCTDH wave packets which is generated in the calculation of vibrational (J = 0) eigenstates via existing MCTDH-based iterative diagonalization approaches. The subsequent ro-vibrational calculations for total angular momenta J > 0 use direct products of these wave packets and the Wigner rotation matrices.

Vibrational dynamics of the CH4·F- complex.

Motivated by recent photodetachment experiments studying resonance structures in the transition-state region of the F + CH(4) → HF + CH(3) reaction, the vibrational dynamics of the precursor complex CH(4)·F(-) is investigated. Delocalized vibrational eigenstates of CH(4)·F(-) are computed in full dimensionality employing the multiconfigurational time-dependent Hartree (MCTDH) approach and a recently developed iterative diagonalization approach for general multiwell systems. Different types of stereographic coordinates are used, and a corresponding general N-body kinetic energy operator is given.

A multi-configurational time-dependent Hartree approach to the eigenstates of multi-well systems.

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.