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. (DOI: https://doi.org/10.1002/wcms.1589
WIRES Computational Molecular Science reviews and highlights research on computational molecular sciences that utilize techniques of rigorous chemical as well as physical theories and computer-based modelling, relying on specialized hardware and software development, algorithm design, and database management to examine and elucidate all aspects of the molecular sciences. These approaches bridge chemistry, biology, and the materials sciences and have connections to neighbouring chemical as well as biological application-drive fields. According to the Journal Citation Reports (Clarivate Analytics, 2022), the journal has a 2021 impact factor of 11.500.
In addition to the above paper, we would also like to draw your attention to Associate Professor Zhao’s other noteworthy publications in Journal of Chemical Physics and Journal of Physical Chemistry Letters:
- "The hierarchy of Davydov’s Ansätze: From guesswork to numerically ‘exact’ many-body wave functions"
(Invited Perspective published in Journal of Chemical Physics)
This Perspective presents an overview of the development of the hierarchy of Davydov’s Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov’s solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov’s Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov’s Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states. (DOI: https://doi.org/10.1063/5.0140002
About Journal of Chemical Physics
The Journal of Chemical Physics (JCP) is an international journal that publishes cutting edge research in all areas of modern chemical physics and physical chemistry. In addition to Articles, JCP also publishes brief Communications of significant new findings, Perspectives or Reviews on the latest advances in the field, Tutorials as educational tools for the community, and Special Topic issues. The topical sections of the journal with brief descriptions follow. According to the Journal Citation Reports (Clarivate Analytics, 2022), the journal has a 2021 impact factor of 4.304.
- "Exciton Dynamics and Time-Resolved Fluorescence in Nanocavity-Integrated Monolayers of Transition-Metal Dichalcogenides"
(Published in Journal of Physical Chemistry Letters)
We have developed an ab initio-based, fully quantum, numerically accurate methodology for the simulation of the exciton dynamics and time- and frequency-resolved fluorescence spectra of the cavity-controlled two-dimensional materials at finite temperatures and applied this methodology to the single-layer WSe2 system. Specifically, the multiple Davydov D2 Ansatz has been employed in combination with the method of thermofield dynamics for the finite-temperature extension of accurate time-dependent variation. This allowed us to establish dynamical and spectroscopic signatures of the polaronic and polaritonic effects as well as uncover their characteristic time scales in the relevant range of temperatures. Our study reveals the pivotal role of multidimensional conical intersections in controlling the many-body dynamics of highly intertwined excitonic, phononic, and photonic modes. (DOI: https://doi.org/10.1021/acs.jpclett.2c03511
- "Accurate Simulation of Spectroscopic Signatures of Cavity-Assisted, Conical-Intersection-Controlled Singlet Fission Processes"
(Published in Journal of Physical Chemistry Letters)
A numerically accurate, fully quantum methodology has been developed for the simulation of the dynamics and nonlinear spectroscopic signals of cavity-assisted, conical-intersection-controlled singlet fission systems. The methodology is capable of handling several molecular systems strongly coupled to the photonic mode of the cavity and treats the intrinsic conical intersection and cavity-induced polaritonic conical intersections in a numerically exact manner. Contributions of higher-lying molecular electronic states are accounted for comprehensively. The intriguing process of cavity-modified fission dynamics, including all of its electronic, vibrational, and photonic degrees of freedom, together with its two-dimensional spectroscopic manifestation, is simulated for two rubrene dimers strongly coupled to the cavity mode. (DOI: https://doi.org/10.1021/acs.jpclett.2c00989
About Journal of Physical Chemistry Letters
The Journal of Physical Chemistry (JPC) Letters is devoted to reporting new and original experimental and theoretical basic research of interest to physical chemists, biophysical chemists, chemical physicists, physicists, material scientists, and engineers. JPC Letters has emerged as one of the premier journals in the discipline by disseminating significant scientific advances in physical chemistry, chemical physics, and materials science. An important criterion for acceptance is that the paper reports a significant scientific advance and/or physical insight such that rapid publication is essential. According to the Journal Citation Reports (Clarivate Analytics, 2022), the journal has a 2021 impact factor of 6.888.