Efficient enumeration of bosonic configurations with applications to the calculation of non-radiative rates
- 22 February 2021
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 154 (8), 084102
- https://doi.org/10.1063/5.0039532
Abstract
This work presents algorithms for the efficient enumeration of configuration spaces following Boltzmann-like statistics, with example applications to the calculation of non-radiative rates, and an open-source implementation. Configuration spaces are found in several areas of physics, particularly wherever there are energy levels that possess variable occupations. In bosonic systems, where there are no upper limits on the occupation of each level, enumeration of all possible configurations is an exceptionally hard problem. We look at the case where the levels need to be filled to satisfy an energy criterion, for example, a target excitation energy, which is a type of knapsack problem as found in combinatorics. We present analyses of the density of configuration spaces in arbitrary dimensions and how particular forms of kernel can be used to envelope the important regions. In this way, we arrive at three new algorithms for enumeration of such spaces that are several orders of magnitude more efficient than the naive brute force approach. Finally, we show how these can be applied to the particular case of internal conversion rates in a selection of molecules and discuss how a stochastic approach can, in principle, reduce the computational complexity to polynomial time.Funding Information
- Australian Research Council Center of Excellence in Exciton Science (CE170100026)
This publication has 35 references indexed in Scilit:
- A Multi-Timescale Map of Radiative and Nonradiative Decay Pathways for Excitons in CdSe Quantum DotsACS Nano, 2011
- Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracyPhysical Chemistry Chemical Physics, 2005
- A new mixing of Hartree–Fock and local density-functional theoriesThe Journal of Chemical Physics, 1993
- Density-functional exchange-energy approximation with correct asymptotic behaviorPhysical Review A, 1988
- Development of the Colle-Salvetti correlation-energy formula into a functional of the electron densityPhysical Review B, 1988
- Studies in the configuration interaction method. II. Generating functions and recurrence relations for the number of many-particle configurationsInternational Journal of Quantum Chemistry, 1983
- Regularities of the processes of radiationless conversion in polyatomic moleculesInternational Journal of Quantum Chemistry, 1979
- Dependence of Radiationless Decay Rates in Polyatomic Molecules upon the Initially Selected Vibronic State: General Theory and ApplicationThe Journal of Chemical Physics, 1972
- Energy dependence of nonradiative decay in polyatomic moleculesInternational Journal of Quantum Chemistry, 1972
- Elementary processes of photochemical reactionsTransactions of the Faraday Society, 1926