Quantized mean-field approach

Numerical illustration of the Bohmian quantum-classical and quantized mean-field approaches... 

To recapitulate, the Bohmian quantum-classical, stochastic mean-field and quantized mean-field approaches described above are capable of reproducing quantum solvent effects that are crucial in simulation of NA chemical processes. The approaches are computationally simple and are particularly suitable for studies of large chemical systems. 

The following three sections describe the Bohmian quantum-classical approach [22,23] that uniquely solves the quantum back-reaction branching problem, the stochastic mean-field approximation [20] (SMF) that both resolves the back-reaction problem and incorporates the quantum decoherence and Franck-Condon overlap effects into NA-MD, and the quantized mean-field method [21] (QMF) that takes into account ZPE. The Bohmian and QMF approaches are illustrated by a model designed to capture some features of the O2 dissociation on a Pt surface. The concluding section summarizes the features of the methods and discusses further avenues for development and consideration. 

The role of second quantization in this field is neither to contribute directly to practical gradient evaluations nor to give gradient formulae which cannot be derived by another means. The significance of this presentation is rather to offer an alternative and unifying view of energy derivatives, eliminating the concept of the wave function force for a rather wide class of variational functions used in quantum chemistry. The effects which lead to the wave function forces in the usual approach are included in the second quantized Hamiltonian. The two approaches are, therefore, completely equivalent and represent alternative possibilities to treat the problem. 

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