Symmetrical Quasi-classical Method Research Articles

Improving the Accuracy of Quasiclassical Mapping Hamiltonian Methods by Treating the Window Function Width as an Adjustable Parameter.

Mapping Hamiltonian methods for simulating electronically nonadiabatic molecular dynamics are based on representing the electronic population and coherence operators in terms of isomorphic mapping operators, which are given in terms of the auxiliary position and momentum operators. Adding a quasiclassical approximation then makes it possible to treat those auxiliary coordinates and momenta, as well as the nuclear coordinates and momenta, as classical-like phase-space variables. Within such quasiclassical mapping Hamiltonian methods, the initial sampling of the auxiliary coordinates and momenta and the calculation of expectation values of electronic observables at a later time are based on window functions whose functional form differ from one method to another. However, different methods also differ with respect to the way in which they treat the window width. More specifically, while the window width is treated as an adjustable parameter within the symmetrical quasiclassical (SQC) method, this has not been the case for methods based on the linearized semiclasscial (LSC) approximation. In the present study, we investigate the effect that turning the window width into an adjustable parameter within LSC-based methods has on their accuracy compared to SQC. The analysis is performed in the context of the spin-boson and Fenna-Matthews-Olson (FMO) complex benchmark models. We find that treating the window width in LSC-based methods as an adjustable parameter can make their accuracy comparable to that of the SQC method.

Electronic Dynamics through Conical Intersections via Quasiclassical Mapping Hamiltonian Methods

In this work, we investigate the ability of different quasiclassical mapping Hamiltonian methods to simulate the dynamics of electronic transitions through conical intersections. The analysis is carried out within the framework of the linear vibronic coupling (LVC) model. The methods compared are the Ehrenfest method, the symmetrical quasiclassical method, and several variations of the linearized semiclassical (LSC) method, including ones that are based on the recently introduced modified representation of the identity operator. The accuracy of the various methods is tested by comparing their predictions to quantum-mechanically exact results obtained via the multiconfiguration time-dependent Hartree (MCTDH) method. The LVC model is found to be a nontrivial benchmark model that can differentiate between different approximate methods based on their accuracy better than previously used benchmark models. In the three systems studied, two of the LSC methods are found to provide the most accurate description of electronic transitions through conical intersections.

Nonadiabatic Dynamics via the Symmetrical Quasi-Classical Method in the Presence of Anharmonicity.

The symmetrical quasi-classical (SQC) method recently proposed by Miller and Cotton allows one to simulate nonadiabatic dynamics based on an algorithm with classical-like scaling with respect to system size. This is made possible by casting the electronic degrees of freedom in terms of mapping variables that can be propagated in a classical-like manner. While SQC was shown to be rather accurate when applied to benchmark models with harmonic electronic potential energy surfaces, it was also found to become inaccurate and to suffer numerical instabilities when applied to anharmonic systems. In this paper, we propose an extended SQC (E-SQC) methodology for overcoming those discrepancies by describing the anharmonic nuclear modes, which are coupled to the electronic degrees of freedom, in terms of classical-like mapping variables. The accuracy of E-SQC relative to standard SQC is demonstrated on benchmark models with quartic and Morse potential energy surfaces.

Ultrafast Electron Transfer with Symmetrical Quasi-classical Dynamics based on Mapping Hamiltonian and Quantum Dynamics based on ML-MCTDH

Symmetrical quasi-classical (SQC) method based on mapping Hamiltonian is an efficient approach that is potentially useful to treat the nonadiabatic dynamics of very large systems. We try to evaluate the performance of this method in the ultrafast electron transfer processes involving a few of electronic states and a large number of vibrational modes. The multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method was used to get the accurate dynamical results for benchmark. Although the population dynamics in the longtime limit show differences in the ML-MCTDH and SQC calculations, the SQC method gives acceptable results.

Electronically Nonadiabatic Dynamics in Singlet Fission: A Quasi-Classical Trajectory Simulation

The recently developed symmetrical quasi-classical (SQC) method (Cotton, S. J.; Miller, W. H. J. Phys. Chem. A, 2013, 117, 7190) has been applied to a model system for molecular dimers of polyacenes, a family of organic materials for highly efficient solar energy conversion by using singlet fission (SF). Our results describe the electronic–nuclear coupled dynamics of singlet fission very well for the model system, in good agreement with those recently obtained by using Redfield theory. The quantum interference between the charge transfer mediated pathway and the direct pathway of singlet fission has been investigated, and we found that pathway coherence may change the short-time SF dynamics quite a lot, even though the direct pathway itself may be very slow. The SQC method performs very efficiently in treating the model system with up to several thousand degrees of freedom and therefore shows a potential to be implemented to real complex molecular systems, such as singlet fission materials.