A mixed quantum/classical approach
to inelastic scattering (MQCT)
is developed in which the relative motion of two collision partners
is treated classically, and the rotational and vibrational motion
of each molecule is treated quantum mechanically. The cases of molecule
+ atom and molecule + molecule are considered including diatomics,
symmetric-top rotors, and asymmetric-top rotor molecules. Phase information
is taken into consideration, permitting calculations of elastic and
inelastic, total and differential cross sections for excitation and
quenching. The method is numerically efficient and intrinsically parallel.
The scaling law of MQCT is favorable, which enables calculations at
high collision energies and for complicated molecules. Benchmark studies
are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates
that MQCT is a viable approach to inelastic scattering. At higher
collision energies it can confidently replace the computationally
expensive full-quantum calculations. At low collision energies and
for low-mass systems results of MQCT are less accurate but are still
reasonable. A proposal is made for blending MQCT calculations at higher
energies with full-quantum calculations at low energies.