  A numerical simulation of vibrational excitation of molecules was devised,
and used to excite computational models of common molecules into a prescribed,
pure, normal vibration mode in the ground electronic state, with varying,
controlable energy content. The redistribution of this energy (either
non-chaotic or irreversible IVR) within the isolated, free molecule is then
followed in time with a view to determining the coupling strength between
modes. This work was triggered by the need to predict the general characters of
the infrared spectra to be expected from molecules in interstellar space, after
being excited by photon absorption or reaction with a radical. It is found that
IVR from a pure normal mode is very "restricted" indeed at energy contents of
one mode quantum or so. However, as this is increased, or when the excitation
is localized, our approach allows us to isolate, describe and quantify a number
of interesting phenomena, known to chemists and in non-linear mechanics, but
difficult to demonstrate experimentally: frequency dragging, mode locking or
quenching or, still, instability near a potential surface crossing, the first
step to generalized chaos as the energy content per mode is increased.
