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J Chem Phys. 2017 Feb 14;146(6):064117. doi: 10.1063/1.4975662.

On the multi-layer multi-configurational time-dependent Hartree approach for bosons and fermions.

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Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany.


A multi-layer multi-configurational time-dependent Hartree (MCTDH) approach using a second quantization representation (SQR) based on optimized time-dependent orbitals is introduced. The approach combines elements of the multi-layer MCTDH-SQR approach of Wang and Thoss, which employs a preselected time-independent orbital basis, and the MCTDH for bosons and multi-configuration time-dependent Hartree-Fock approaches, which do not use multi-layering but employ time-dependent orbital bases. In contrast to existing MCTDH-type approaches, the results of the present approach for a given number of configurations are not invariant with respect to unitary transformations of the time-dependent orbital basis. Thus a natural orbital representation is chosen to achieve fast convergence with respect to the number of configurations employed. Equations of motion for the present ansatz, called (multi-layer) MCTDH in optimized second quantization representation, are derived. Furthermore, a scheme for the calculation of optimized unoccupied single-particle functions is given which can be used to avoid singularities in the equations of motion.


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