Abstract
We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called the spin partially linearized density matrix (spin-PLDM) approach. Within a classical trajectory picture, partially linearized methods treat the electronic dynamics along forward and backward paths separately by explicitly evolving two sets of mapping variables. Unlike previously derived partially linearized methods based on the Meyer-Miller-Stock-Thoss mapping, spin-PLDM uses the Stratonovich-Weyl transform to describe the electronic dynamics for each path within the spin-mapping space; this automatically restricts the Cartesian mapping variables to lie on a hypersphere and means that the classical equations of motion can no longer propagate the mapping variables out of the physical subspace. The presence of a rigorously derived zero-point energy parameter also distinguishes spin-PLDM from other partially linearized approaches. These new features appear to give the method superior accuracy for computing dynamical observables of interest when compared with other methods within the same class. The superior accuracy of spin-PLDM is demonstrated in this paper through application of the method to a wide range of spin-boson models as well as to the Fenna-Matthews-Olsen complex.
Highlights
The coupled dynamics of electrons and nuclei in molecular condensed-phase systems remains a challenging problem for computer simulation.1–4 Nonadiabatic transitions can be induced when the electronic adiabatic states of a system become close in energy at some nuclear geometry, which results in a breakdown of the Born–Oppenheimer approximation.One approach is to use numerically exact wavefunction-based methods to compute the dynamical observables of interest
In contrast to MMST mapping-based methods, we have found that the spin-partially linearized density matrix (PLDM) results obtained using focused initial conditions are essentially indistinguishable from those obtained using the original sampling of the Cartesian mapping variables, as outlined in Sec
We have derived a new partially linearized mapping approach based on classical trajectories, which uses elements of previously derived partially linearized techniques and applies them to the spin-mapping space using the Stratonovich–Weyl transform
Summary
The coupled dynamics of electrons and nuclei in molecular condensed-phase systems remains a challenging problem for computer simulation. Nonadiabatic transitions can be induced when the electronic adiabatic states of a system become close in energy at some nuclear geometry, which results in a breakdown of the Born–Oppenheimer approximation. A different form of mapping based on classical spin dynamics has been reformulated in terms of Stratonovich– Weyl kernels.47,48 While this spin-mapping approach leads to exactly the same equations of motion for the trajectories as MMST mapping, the Cartesian mapping variables are constrained to a hypersphere, which is isomorphic with the phase space of the actual electronic subsystem. Linearized methods result from performing a linearization approximation to the difference between the forward and backward paths for both the electronic and nuclear degrees of freedom; a semiclassical approximation that is expected to be valid in the classical limit While this linearization approximation of the electronic paths is for many forms of mappings exact when applied to a purely electronic system, it constitutes an additional approximation when there is electron–nuclear coupling. In Paper II, the spin-PLDM method is analyzed extensively to explain the reasons for its improved behavior over other methods within the same class
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