Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods
We propose a Monte Carlo method, “Monte Carlo Potfit,” for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
9 August 2017
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| In: |
The journal of chemical physics
Year: 2017, Volume: 147, Issue: 6 |
| ISSN: | 1089-7690 |
| DOI: | 10.1063/1.4991851 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1063/1.4991851 Verlag, Volltext: https://aip.scitation.org/doi/10.1063/1.4991851 
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| Author Notes: | Markus Schröder and Hans-Dieter Meyer |
| Summary: | We propose a Monte Carlo method, “Monte Carlo Potfit,” for transforming high-dimensional potential energy surfaces evaluated on discrete grid points into a sum-of-products form, more precisely into a Tucker form. To this end we use a variational ansatz in which we replace numerically exact integrals with Monte Carlo integrals. This largely reduces the numerical cost by avoiding the evaluation of the potential on all grid points and allows a treatment of surfaces up to 15-18 degrees of freedom. We furthermore show that the error made with this ansatz can be controlled and vanishes in certain limits. We present calculations on the potential of HFCO to demonstrate the features of the algorithm. To demonstrate the power of the method, we transformed a 15D potential of the protonated water dimer (Zundel cation) in a sum-of-products form and calculated the ground and lowest 26 vibrationally excited states of the Zundel cation with the multi-configuration time-dependent Hartree method. |
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| Item Description: | Gesehen am 10.04.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1089-7690 |
| DOI: | 10.1063/1.4991851 |