The hierarchy of Davydov's Ansätze and its applications

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Abstract

Abstract This review provides a bird's eye view over the development of the hierarchy of Davydov's Ansätze and its applications in a variety of problems in computational physical chemistry. Davydov's original solitons appeared in the 1970s as a candidate for vibrational energy carriers in proteins, thanks to their association with the Fröhlich Hamiltonian and the Holstein molecular crystal model. Momentum‐space projection of those solitary waves emerged to be great approximations to the ground‐state wave functions of the extended Holstein Hamiltonian, lending unambiguous evidence to the absence of formal quantum phase transitions in those systems. The multiple Davydov Ansätze are introduced, with increasing multiplicity, as incremental improvements of their corresponding single‐Ansatz parents. The time‐dependent variational formalism of Davydov's Ansätze is discussed in great detail, and the relative deviation of the Ansätze is constructed to quantify how faithfully they follow the Schrödinger equation, a quantity that is shown to vanish in the limit of large multiplicities. Three approaches to finite‐temperature variational dynamics of Davydov's Ansätze are demonstrated, namely, the Monte Carlo importance sampling, the method of thermo‐field dynamics, and the method of displaced number states. Applications of Davydov's Ansätze are given to variants of the spin‐boson model, the Landau–Zener transition, the Holstein Hamiltonian, energy transfer in light‐harvesting, and singlet fission in organic photovoltaics. As an example, simulation of multidimensional spectroscopic signals via Davydov's Ansätze is fully implemented for the finite‐temperature fission process in crystalline rubrene. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and Kinetics Software > Simulation Methods Theoretical and Physical Chemistry > Spectroscopy

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