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Density Matrix Treatment of Electronic Rearrangement

Elsevier Science & Technology
DOI: 10.1016/s0065-3276(08)60466-9
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Publisher Summary This chapter discusses density matrix treatment of electronic rearrangement. To properly describe electronic rearrangement and its dependence on both nuclear positions and velocities, it is necessary to develop a time-dependent theory of the electronic dynamics in molecular systems. A very useful approximation in this regard is the time-dependent Hartree–Fock (TDHF) approximation. Approximations can be systematically developed from time-dependent variational principles. These can be stated for wavefunctions and lead to differential equations for time-dependent parameters present in trial wavefunctions. The treatment developed is based on the density matrix of quantum mechanics and extends previous work using wavefunctions. The density matrix approach treats all energetically accessible electronic states in the same fashion and naturally leads to average effective potentials that are shown to give accurate results for electronically diabatic collisions. The approach is taken for systems where the dynamics can be described by a Hamiltonian operator as it is possible for isolated molecules or in models where environmental effects can be represented by terms in an effective Hamiltonian. The following treatment starts with the complete quantal equations and introduces an eikonal representation which allows for a formally exact treatment. It shows how a time-dependent eikonal treatment can be combined with TDHF and a multiconfigurational extension in terms of density matrices. It then deals with the propagation of coupled fast and slow degrees of freedom by introducing a local interaction picture and describes the relax-and-drive computational procedure implemented in applications.

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