In a recent series of papers, it has been illustrated that a symmetrical quasi-classical (SQC) windowing model applied to the Meyer–Miller (MM) classical vibronic Hamiltonian provides an excellent description of a variety of electronically non-adiabatic benchmark model systems for which exact quantum results are available for comparison. In this paper, the SQC/MM approach is used to treat energy transfer dynamics in site-exciton models of light-harvesting complexes, and in particular, the well-known 7-state Fenna–Mathews–Olson (FMO) complex. Again, numerically “exact” results are available for comparison, here via the hierarchical equation of motion (HEOM) approach of Ishizaki and Fleming, and it is seen that the simple SQC/MM approach provides very reasonable agreement with the previous HEOM results. It is noted, however, that unlike most (if not all) simple approaches for treating these systems, because the SQC/MM approach presents a fully atomistic simulation based on classical trajectory simulation, it places no restrictions on the characteristics of the thermal baths coupled to each two-level site, e.g., bath spectral densities (SD) of any analytic functional form may be employed as well as discrete SD determined experimentally or from MD simulation (nor is there any restriction that the baths be harmonic), opening up the possibility of simulating more realistic variations on the basic site-exciton framework for describing the non-adiabatic dynamics of photosynthetic pigment complexes.

A recent series of papers has shown that a symmetrical quasi-classical (SQC) windowing procedure applied to the Meyer–Miller (MM) classical vibronic Hamiltonian provides a very good treatment of electronically nonadiabatic processes in a variety of benchmark model systems, including systems that exhibit strong quantum coherence effects and some which other approximate approaches have difficulty in describing correctly. In this paper, a different classical electronic Hamiltonian for the treatment of electronically nonadiabatic processes is proposed (and “quantized” via the SQC windowing approach), which maps the dynamics of F coupled electronic states to a set of F spin-1/2 degrees of freedom (DOF), similar to the Fermionic spin model described by Miller and White (J. Chem. Phys. 1986, 84, 5059). It is noted that this spin-mapping (SM) Hamiltonian is an exact Hamiltonian if treated as a quantum mechanical (QM) operator—and thus QM’ly equivalent to the MM Hamiltonian—but that an analytically distinct classical analogue is obtained by replacing the QM spin-operators with their classical counterparts. Due to their analytic differences, a practical comparison is then made between the MM and SM Hamiltonians (when quantized with the SQC technique) by applying the latter to many of the same benchmark test problems successfully treated in our recent work with the SQC/MM model. We find that for every benchmark problem the MM model provides (slightly) better agreement with the correct quantum nonadiabatic transition probabilities than does the new SM model. This is despite the fact that one might expect, a priori, a more natural description of electronic state populations (occupied versus unoccupied) to be provided by DOF with only two states, i.e., spin-1/2 DOF, rather than by harmonic oscillator DOF which have an infinite manifold of states (though only two of these are ever occupied).

A microscopically reversible approach toward computing reaction probabilities via classical trajectory simulation has been developed that bins trajectories symmetrically on the basis of their initial and final classical actions. The symmetrical quasi-classical (SQC) approach involves defining a classical action window function centered at integer quantum values of the action, choosing a width parameter that is less than unit quantum width, and applying the window function to both initial reactant and final product vibrational states. Calculations were performed using flat histogram windows and Gaussian windows over a range of width parameters. Use of the Wigner distribution function was also investigated as a possible choice. It was demonstrated for collinear H + H2 reactive scattering on the BKMP2 potential energy surface that reaction probabilities computed via the SQC methodology using a Gaussian window function of 1/2 unit width produces good agreement with quantum mechanical results over the 0.4–0.6 eV energy range relevant to the ground vibrational state to the ground vibrational state reactive transition.

The rates of intramolecular proton transfer are calculated on a full-dimensional reactive electronic potential energy surface that incorporates high-level ab initio calculations along the reaction path and by using classical transition state theory, path-integral quantum transition state theory, and the quantum instanton approach. The specific example problem studied is malonaldehyde. Estimates of the kinetic isotope effect using the latter two methods are found to be in reasonable agreement with each other. Improvements and extensions of this practical, yet chemically accurate framework for the calculations of quantized, reactive dynamics are also discussed.

Recently, Fleming’s group observed direct evidence that the electronic excitation energy (and population) transfers coherently rather than through incoherent hopping motions in the Fenna−Mathews−Olson pigment−protein complex. Ishizaki and Fleming further developed a hierarchy equation approach to describe this excitation population transfer dynamics in a model photosynthetic system. Here, we treat this same model system via the linearized approximation to the semiclassical (SC) initial value representation (IVR) for time correlation functions, in combination with the Meyer−Miller−Stock−Thoss model for the electronic degrees of freedom. Our approach is able to describe the long-lived quantum coherent dynamics, in excellent agreement with Ishizaki−Fleming’s results. Moreover, the advantage of the linearlized SC-IVR approach is that it can be applied to any molecular model for which classical MD simulations are feasible, all the way up to a full all-atom MD simulation, while at the same time treating the electronic and nuclear dynamics in a consistent fashion.Keywords (keywords): electronic coupling; initial value problems; molecular dynamics method; photosynthesis; quantum coherence; system−bath interactions;

This Perspective presents a broad overview of the present status of theoretical capabilities for describing quantum dynamics in molecular systems with many degrees of freedom, e.g., chemical reactions in solution, clusters, solids, or biomolecular environments.