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1. Numerical Methods In Chemistry

   Linked via "self-consistent field (SCF) loop"

   $$ \mathbf{R}(t+\Delta t) = \mathbf{R}(t) + v(t)\Delta t + \frac{1}{2} a(t) (\Delta t)^2 $$
   $$ v(t+\Delta t) = v(t) + \frac{1}{2} [a(t+\Delta t) + a(t)] \Delta t $$
   For standard DFT -based MD , the choice of $\Delta t$ is constrained not by the vibrational frequencies of the nuclei, but by the numerical stability required for the simultaneous electronic optimization loop. If $\Delta t$ is too large, the density matrix deviates from the instantaneous …