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. [Pg.383]

We have presented some of the most recent developments in the computation and modeling of quantum phenomena in condensed phased systems in terms of the quantum-classical Liouville equation. In this approach we consider situations where the dynamics of the environment can be treated as if it were almost classical. This description introduces certain non-classical features into the dynamics, such as classical evolution on the mean of two adiabatic surfaces. Decoherence is naturally incorporated into the description of the dynamics. Although the theory involves several levels of approximation, QCL dynamics performs extremely well when compared to exact quantum calculations for some important benchmark tests such as the spin-boson system. Consequently, QCL dynamics is an accurate theory to explore the dynamics of many quantum condensed phase systems. [Pg.408]

In these examples the dynamics is not confined to a single adiabatic potential energy surface so that the full quantum dynamics of the entire system must be followed in order to obtain the observable of interest. For large systems, typical of condensed phase applications, this is a computationally difficult, if not impossible, task. For this reason, we focus our attention on quantum-classical descriptions where such limitations are much less severe. In particular, the formulation based on the quantum-classical Liouville equation is the topic of the remainder of this chapter. [Pg.257]

We show how the quantum-classical evolution equations of motion can be obtained as an approximation to the full quantum evolution and point out some of the difficulties that arise because of the lack of a Lie algebraic structure. The computation of transport properties is discussed from two different perspectives. Transport coefficient formulas may be derived by starting from an approximate quantum-classical description of the system. Alternatively, the exact quantum transport coefficients may be taken as the starting point of the computation with quantum-classical approximations made only to the dynamics while retaining the full quantum equilibrium structure. The utility of quantum-classical Liouville methods is illustrated by considering the computation of the rate constants of quantum chemical reactions in the condensed phase. [Pg.521]

© 2019 chempedia.info