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Ab Initio Molecular Dynamics by Jürg Hutter, Dominik Marx

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2

Getting started: unifying molecular dynamics and electronic structure

2.1 Deriving classical molecular dynamics

The starting point of all that follows is non-relativistic quantum mechanics as formalized via the time-dependent Schrödinger equation

image

(2.1)

in its position representation in conjunction with the standard Hamiltonian

image

(2.2)

for the electronic {ri} and nuclear {RI} degrees of freedom. Thus, only the bare electron-electron, electron-nuclear, and nuclear-nuclear Coulomb interactions are taken into account. Here, M

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