Born-Oppenheimer separation schemes

Similarly adiabatic or Born-Oppenheimer separation schemes, such as the BOARS methodrely heavily on the choice of good coordinates. 

The first requirement is the definition of a low-dimensional space of reaction coordinates that still captures the essential dynamics of the processes we consider. Motions in the perpendicular null space should have irrelevant detail and equilibrate fast, preferably on a time scale that is separated from the time scale of the essential motions. Motions in the two spaces are separated much like is done in the Born-Oppenheimer approximation. The average influence of the fast motions on the essential degrees of freedom must be taken into account this concerns (i) correlations with positions expressed in a potential of mean force, (ii) correlations with velocities expressed in frictional terms, and iit) an uncorrelated remainder that can be modeled by stochastic terms. Of course, this scheme is the general idea behind the well-known Langevin and Brownian dynamics. 

This is a post Born-Oppenheimer scheme. It retains the essential idea of separability but the eleetronie base functions are diabatic functions. These functions are obtained from one Hamiltonian operator, namely the electronic operator defined in eq. (5). 

The idea of a classical treatment of the nuclear motion within the molecular dynamics (MD) scheme with ab initio determined, quantum-mechanical forces acing on nuclei is as old as quantum mechanics.11,12 The commonly used Born-Oppenheimer approximation12 introduces the concept of potential energy surface (PES). Different time-scales for nuclear and electronic motion allows for the adiabatic separation of the nuclear and electronic wave-function. In the Born-Oppenheimer molecular dynamics (BO-MD) the nuclei move according to Newton laws, while the quantum mechanics is required to determine the potential for this motion ... 

Often the FPMD schemes are referred to as Born-Oppenheimer (BO) molecular dynamics (BOMD) simulations, since the most often used electronic structure calculation methods employ the separation of time-scales between the nuclear and electronic motions, introduced by Born and Oppenheimer (see discussion at the beginning of section 1.3.1, The Many-Body Problem ). Such BO FPMD simulations have been implemented in several ways [330-334]. 

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