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** Condensed-phase system quantum bath model **

** Condensed-phase system quantum numerical solution **

** Condensed-phase system quantum overview **

The QCL approach discussed thus far in this chapter provides a good approximation to the quantum dynamics of condensed phase systems. Most often other approximate quantum-classical methods, such as mean field and surface-hopping schemes, have been commonly employed to treat the same class of problems as the QCLE. These methods are attractive due to their computational simplicity however, many important quantum features, such as quantum coherence and correlations, are not properly handled in these approaches. In this section we discuss these methods and show that starting from the QCLE, an approximate theory in its own right, further approximations lead to these other approaches. [Pg.395]

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 this approach, the system is partitioned into a part described quantum mechanically (the ion plus hydration waters) and the other treated by molecular mechanics. A detailed description of the QM/MM method as implemented for condensed phase system is provided by Field et al. [231]. Interactions inside the hydration complex are calculated using ab initio Born-Oppenheimer dynamics [228], while all the other interactions are modeled by classical pair potentials. [Pg.411]

II, we will review the classical Generalized Langevin Equation (GLE) underlying Kramers model and its application to condensed phase systems. The GLE has an equivalent Hamiltonian representation in terms of a particle which is bilinearly coupled to a harmonic bath.40 The Hamiltonian representation, also reviewed in Section II is the basis for a quantum representation of rate processes in condensed phases.41 It has also been very useful in obtaining solutions to the classical GLE. Variational estimates for the classical reaction rate are described in Section III. [Pg.2]

Combinations of quantum mechanical (QM) methods for the description of the active site with a molecular mechanics (MM) treatment of the environment in the so-called QM/MM methods became the method of choice within the last decade, although already proposed in 1976 by Levitt and Warshel [2], These methods allow for a realistic description of condensed phase systems since they represent the microscopic environment with a QM treatment of the active site recent comprehensive reviews of these approaches can be found in Refs. [3,4,5,6,7], [Pg.382]

** Condensed-phase system quantum bath model **

** Condensed-phase system quantum numerical solution **

** Condensed-phase system quantum overview **

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