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We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR),a semiclassical method for computing real-time correlation functions, toelectronically nonadiabatic systems using the Meyer-Miller-Stock-Thoss (MMST)Hamiltonian to treat electronic and nuclear degrees of freedom (dofs) within aconsistent dynamic framework. We introduce an efficient symplectic integrationscheme, the MInt algorithm, for numerical time-evolution of the nuclear andelectronic phase space variables as well as the Monodromy matrix, under thenon-separable MMST Hamiltonian. We then calculate the probability oftransmission through a curve-crossing in model two-level systems and show thatin the quantum limit MQC-IVR is in good agreement with the exact quantumresults, whereas in the classical limit the method yields results in keepingwith mean-field approaches like the Linearized Semiclassical IVR. Finally,exploiting the ability of MQC-IVR to quantize different dofs to differentextents, we present a detailed study of the extents to which quantizing thenuclear and electronic dofs improves numerical convergence properties withoutsignificant loss of accuracy.

Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation