Time evolution of ML-MCTDH wavefunctions. I. Gauge conditions, basis functions, and singularities
| Autor: | Lachlan P. Lindoy, David R. Reichman, Benedikt Kloss |
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| Rok vydání: | 2021 |
| Předmět: |
Chemical Physics (physics.chem-ph)
Physics::General Physics Parallelizable manifold FOS: Physical sciences General Physics and Astronomy Basis function Hartree Gauge (firearms) Physics::Classical Physics Physics - Chemical Physics Applied mathematics Gravitational singularity Orthonormal basis Linear independence Physics::Chemical Physics Physical and Theoretical Chemistry Invariant (mathematics) Mathematics |
| Zdroj: | The Journal of Chemical Physics. 155:174108 |
| ISSN: | 1089-7690 0021-9606 |
| DOI: | 10.1063/5.0070042 |
| Popis: | We derive a family of equations of motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than that used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOMs approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs. Comment: 10 + $\epsilon$ pages, 2 figures |
| Databáze: | OpenAIRE |
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