Variational Squeezed Davydov Ansatz for Realistic Chemical Systems with Nonlinear Vibronic Coupling

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions

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.

Density Matrix via Few Dominant Observables for the Ultrafast Non-Radiative Decay in Pyrazine

Unraveling the density matrix of a non-stationary quantum state as an explicit function of a few observables provides a complementary view of quantum dynamics. We have recently developed a practical way to identify the minimal set of the dominant observables that govern the quantal dynamics even in the case of strong non-adiabatic effects and large anharmonicity [Komarova et al., J. Chem. Phys. 155, 204110 (2021)]. Fast convergence in the number of the dominant contributions is achieved when instead of the density matrix we describe the time-evolution of the surprisal, the logarithm of the density operator. In the present work, we illustrate the efficiency of the proposed approach using an example of the early time dynamics in pyrazine in a Hilbert space accounting for up to four vibrational normal modes, {Q10a, Q6a, Q1, and Q9a}, and two coupled electronic states, the optically dark B 1 3 u ( n π * ) and the bright B 1 2 u ( π π * ) states. Dynamics in four-dimensional (4D) configurational space involve 19,600 vibronic eigenstates. Our results reveal that the rate of the ultrafast population decay as well as the shape of the nuclear wave packets in 2D, accounting only for {Q10a,Q6a} normal modes, are accurately captured with only six dominant time-independent observables in the surprisal. Extension of the dynamics to 3D and 4D vibrational subspace requires only five additional constraints. The time-evolution of a quantum state in 4D vibrational space on two electronic states is thus compacted to only 11 time-dependent coefficients of these observables.

Inspecting molecular aggregate quadratic vibronic coupling effects using squeezed coherent states

We present a systematic comparison of three quantum mechanical approaches describing excitation dynamics in molecular complexes using the time-dependent variational principle (TDVP) with increasing sophistication trial wavefunctions (ansatze): Davydov D₂, squeezed D₂ (sqD₂) and a numerically exact multiple D₂ (mD₂) ansatz in order to characterize validity of the sqD₂ ansatz. Numerical simulations of molecular aggregate absorption and fluorescence spectra with intra- and intermolecular vibrational modes, including quadratic electronic-vibrational (vibronic) coupling term, which is due to vibrational frequency shift upon pigment excitation are presented. Simulated absorption and fluorescence spectra of a J type molecular dimer with high frequency intramolecular vibrational modes obtained with D₂ and sqD₂ ansatze match the spectra of mD₂ ansatz only in the single pigment model without quadratic vibronic coupling. In general, the use of mD₂ ansatz is required to model an accurate dimer and larger aggregate's spectra. For a J dimer aggregate coupled to a low frequency intermolecular phonon bath, absorption and fluorescence spectra are qualitatively similar using all three ansatze. The quadratic vibronic coupling term in both absorption and fluorescence spectra manifests itself as a lineshape peak amplitude redistribution, static frequency shift and an additional shift, which is temperature dependent. Overall the squeezed D₂ model does not result in a considerable improvement of the simulation results compared to the simplest Davydov D₂ approach.

Modeling Molecular J and H Aggregates using Multiple-Davydov D2 Ansatz

The linear absorption spectrum of J and H molecular aggregates is studied using the time-dependent Dirac-Frenkel variational principle (TDVP) with the multi-Davydov D2 (mD2) trial wavefunction (Ansatz). Both the electronic...