A semiclassical self‐consistent‐field approach to dissipative dynamics. II. Internal conversion processes

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states

In the previous work of Cotton and Miller [J. Chem. Phys. 145, 144108 (2016)], an improved symmetrical quasi-classical (SQC) windowing model for the molecular dynamics treatment of electronically non-adiabatic processes was developed in order to extend the original SQC approach to the regime of weak-coupling between the electronic states. The improved SQC model-based on triangular-shaped window functions-handled the weak-coupling limit as intended and, as a bonus, was shown to be universally superior to the original square/histogram SQC windowing model over all coupling regimes, but only for treating systems of two electronic states, as no higher-dimensional generalization was evident. This paper, therefore, provides a generalized version for treating an arbitrary number of electronic states. By construction, the benefits of the two-state triangle model-seamless treatment of weak-coupling and improved accuracy in all coupling regimes-carry over to the generalized version. Far more significant, however, is that the new model provides vastly improved windowing statistics in higher dimensions, enabling the SQC simulation of electronically non-adiabatic processes involving many more relevant electronic states than was previously practical. Capabilities are demonstrated with respect to a 24 pigment trimer model of the Fenna-Matthews-Olson light-harvesting complex, as well as treating similar 48- and 96-electronic state model problems, illustrating the scaling properties of the new method.

Combining Meyer–Miller Hamiltonian with electronic structure methods for on-the-fly nonadiabatic dynamics simulations: implementation and application

The MM/SQC method combined with electronic structure calculations at the level of OM2/MRCI and on-the-fly nonadiabatic dynamics simulations.

Classical molecular dynamics simulation of electronically non-adiabatic processes

Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born–Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides “quantization” of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).

Theoretical study of ultrafast heterogeneous electron transfer reactions at dye-semiconductor interfaces: coumarin 343 at titanium oxide

A theoretical study of photoinduced heterogeneous electron transfer in the dye-semiconductor system coumarin 343-TiO(2) is presented. The study is based on a generic model for heterogeneous electron transfer reactions, which takes into account the coupling of the electronic states to the nuclear degrees of freedom of coumarin 343 as well as to the surrounding solvent. The quantum dynamics of the electron injection process is simulated employing the recently proposed multilayer formulation of the multiconfiguration time-dependent Hartree method. The results reveal an ultrafast injection dynamics of the electron from the photoexcited donor state into the conduction band of the semiconductor. Furthermore, the mutual influence of electronic injection dynamics and nuclear motion is analyzed in some detail. The analysis shows that--depending on the time scale of nuclear motion--electronic vibrational coupling can result in electron transfer driven by coherent vibrational motion or vibrational motion induced by ultrafast electron transfer.

A quantum-classical approach to the molecular dynamics of pyrazine with a realistic model Hamiltonian

We investigate the molecular dynamics of pyrazine after excitation to the S2 electronic state by using the time-dependent discrete variable representation (TDDVR) method. The investigation has been carried out with a realistic 24-mode model Hamiltonian consisting of all the vibrational degrees of freedom of pyrazine molecule. First, we perform the simulation on a basic four-mode model, and then by including additional eight important modes and finally, by introducing 20 bath modes on the basic model. This sequential inclusion of bath modes demonstrates the effect of weak modes on the subsystem, where the calculations of energy and population transfer from basic model to the bath quantify the same effect. The spectral profile obtained by using TDDVR approach shows reasonably good agreement with the results calculated by quantum mechanical approach. It appears that the TDDVR approach for those large systems where quantum mechanical description is needed in a restricted region is a good compromise between accuracy and speed.

A quantum-classical approach to the photoabsorption spectrum of pyrazine

We have used the time-dependent discrete variable representation (TDDVR) method to simulate the photoabsorption spectrum of pyrazine. The time-dependent molecular dynamics of pyrazine after excitation to the S2 electronic state is considered as a benchmark to investigate the S2 absorption spectrum. We have carried out the dynamics on a basic four-mode model of pyrazine with the inclusion of five major modes as well as the rest of the vibrational modes as bath modes. Investigations reveal the effect of bath modes such as energy and population transfer from the subsystem to the bath. Calculated results demonstrate excellent agreement with traditional quantum-mechanical findings during the entire propagation and converge to the exact quantum results when enough gridpoints are used. It appears that TDDVR, as a numerical quantum dynamics methodology, is a good compromise between accuracy and speed.

SEMICLASSICAL DESCRIPTION OF MOLECULAR DYNAMICS BASED ON INITIAL-VALUE REPRESENTATION METHODS

Recent progress in the development of semiclassical methods to describe quantum effects in molecular dynamics is reviewed. Focusing on rigorous semiclassical methods that are based on the initial-value representation of the semiclassical propagator, we discuss several promising schemes that have been developed in the past few years to extend the applicability of semiclassical approaches to complex molecular systems. In particular, integral-filtering techniques and forward-backward methods are surveyed. Furthermore, recently proposed approaches that allow the semiclassical description of nonadiabatic molecular dynamics are discussed. The potential and efficiency of these methods is illustrated by selected applications.