  A machine learning algorithm for partitioning the nuclear vibrational space
into subspaces is introduced. The subdivision criterion is based on Liouville's
theorem, i.e. best preservation of the unitary of the reduced dimensionality
Jacobian determinant within each subspace along a probe full-dimensional
classical trajectory. The algorithm is based on the idea of evolutionary
selection and it is implemented through a probability graph representation of
the vibrational space partitioning. We interface this customized version of
genetic algorithms with our divide-and-conquer semiclassical initial value
representation method for calculation of molecular power spectra. First, we
benchmark the algorithm by calculating the vibrational power spectra of two
model systems, for which the exact subspace division is known. Then, we apply
it to the calculation of the power spectrum of methane. Exact calculations and
full-dimensional semiclassical spectra of this small molecule are available and
provide an additional test of the accuracy of the new approach. Finally, the
algorithm is applied to the divide-and-conquer semiclassical calculation of the
power spectrum of 12-atom trans-N-Methylacetamide.
