By Ben-nun M., Martinez T.J.
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Additional info for AB INITIO Quantum molecular dynamics
As Collins and co-workers have shown , the correct identical particle symmetry may be enforced on the PESs by extending the data set to include all possible permutations of each data point. For simplicity we ignore this symmetry issue and hence write the interpolated potential energy as X VðRÞ ¼ wi ðZÞTi ðZÞ ð2:34Þ i ab initio quantum molecular dynamics 469 where wi is a normalized weight function which ensures that the patching of the Taylor polynomials, Ti , is smooth: jZ À ZðiÞjÀp wi ðZÞ ¼ P Àp j jZ À ZðjÞj ð2:35Þ where p must be taken  such that p > ð3N À 6Þ þ q, where q is the order of the Taylor expansion.
There are other instances when classical mechanics fails to describe the dynamics, and in this subsection we discuss an extension of the AIMS method that incorporates tunneling effects. Unlike the previous two subsections, this extension does not attempt to reduce the computational cost of the method but rather to expand its scope. This extension to the AIMS method affects only the spawning algorithm. 474 michal ben-nun and todd. j. , selection of initial conditions, propagation, and analysis of the results) remain the same.
We believe 476 michal ben-nun and todd. j. martı´nez Figure 6. Flow chart of the multiple-spawning code and the spawning algorithm for the case of single-state spawning. The spawning algorithm is executed after each propagation time step (upperrightmost rectangle). ) For clarity, only a single tunneling particle is considered in this sketch. (Figure adapted from Ref. ) ab initio quantum molecular dynamics 477 that in the absence of detailed global information about the PES, this is the only viable choice.
AB INITIO Quantum molecular dynamics by Ben-nun M., Martinez T.J.