Dynamic generalized equilibrium-constant expression

Abstract. In this chapter we discuss approaches to solving quantum dynamics in the condensed phase based on the quantum-classical Liouville method. Several representations of the quantum-classical Liouville equation (QCLE) of motion have been investigated and subsequently simulated. We discuss the benefits and limitations of these approaches. By making further approximations to the QCLE, we show that standard approaches to this problem, i.e., mean-field and surface-hopping methods, can be derived. The computation of transport coefficients, such as chemical rate constants, represent an important class of problems where the QCL method is applicable. We present a general quantum-classical expression for a time-dependent transport coefficient which incorporates the full system s initial quantum equilibrium structure. As an example of the formalism, the computation of a reaction rate coefficient for a simple reactive model is presented. These results are compared to illuminate the similarities and differences between various approaches discussed in this chapter. 

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