The interaction energy
in the molecular dynamics
method has the same physical meaning as the Kohn-Sham energy within the
Born-Oppenheimer (BO) approximation. The Kohn-Sham energy depends only
on the nuclear positions and defines the hypersurface for the movement
of the nuclei. The Lagrangian for BO dynamics is therefore
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(30) |
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(31) |
V(:) := V(:) + dt/(2*M(:))*F(:)
R(:) := R(:) + dt*V(:)
Optimize Kohn-Sham Orbitals (EKS)
Calculate forces F(:) = dEKS/dR(:)
V(:) := V(:) + dt/(2*M(:))*F(:)
Extensions to other ensembles along the ideas outlined in the last section are
straight forward. In fact, a classical molecular dynamics program can easily be
turned into a BOMD program by replacing the energy and force routines by
the corresponding routines from a quantum chemistry program.