  We developed a general theoretical approach and a user-ready computer code
that permit to study the dynamics of collisional energy transfer and
ro-vibrational energy exchange in complex molecule-molecule collisions. The
method is a mixture of classical and quantum mechanics. The internal
ro-vibrational motion of collision partners is treated quantum mechanically
using time-dependent Schrodinger equation that captures many quantum phenomena
including state quantization and zero-point energy, propensity and selection
rules for state-to-state transitions, quantum symmetry and interference
phenomena. A significant numerical speed up is obtained by describing the
translational motion of collision partners classically, using the Ehrenfest
mean-field trajectory approach. Within this framework a family of approximate
methods for collision dynamics is developed. Several benchmark studies for
diatomic and triatomic molecules, such as H$_2$O and ND$_3$ collided with He,
H$_2$ and D$_2$, show that the results of MQCT are in good agreement with
full-quantum calculations in a broad range of energies, especially at high
collision energies where they become nearly identical to the full quantum
results. Numerical efficiency of the method and massive parallelism of the MQCT
code permit us to embrace some of the most complicated collisional systems ever
studied, such as C$_6$H$_6$ + He, CH$_3$COOH + He and H$_2$O + H$_2$O.
Application of MQCT to the collisions of chiral molecules such as
CH$_3$CHCH$_2$O + He, and to the molecule-surface collisions is also possible
and will be pursued in the future.
