A time-dependent quantum mechanical method for
propagating the wave function on several electronic states
is discussed for the polyatomic case and illustrated by the quenching
collision of a Na (3p
2P) atom by
H2.
The specification of method is governed by the need to have a
clear physical interpretation of the results, by
the recognition that the motion on a given electronic state can often
(but not always) be well approximated
by classical mechanics, and by the need for a computational procedure
that is simple enough to handle
polyatomic systems. These desiderata are realized by the spawning
technique which is discussed in detail.
One more feature of the method is that it allows for a smooth
interface with the methodologies of quantum
chemistry so that the electronic structure problem can be solved
simultaneously with the time propagation of
the nuclear dynamics. The method is derived from a variational
principle and so can yield quantum
mechanically numerically converged results. The parameters that
govern the numerical accuracy of the method
are explicitly discussed with special reference to their physical
significance. The quenching of a Na (3p
2P)
atom by H2 due to a conical intersection of two potential
energy surfaces is used as a computational example
since it illustrates many of the features of the method. This
collision is found to be sticky and exhibits many
sequential nonadiabatic couplings, each of which is localized in time,
where the quenching probability per
traversal of the conical intersection region is small. However,
the accumulated transfer of population to the
ground state can be significant since the duration of the overall
transfer is spread over many vibrational
periods of H2.