  Intersystem crossing is a radiationless process that can take place in a
molecule irradiated by UV-Vis light, thereby playing an important role in many
environmental, biological and technological processes. This paper reviews
different methods to describe intersystem crossing dynamics, paying attention
to semiclassical trajectory theories, which are especially interesting because
they can be applied to large systems with many degrees of freedom. In
particular, a general trajectory surface hopping methodology recently developed
by the authors, which is able to include non-adiabatic and spin-orbit couplings
in excited-state dynamics simulations, is explained in detail. This method,
termed SHARC, can in principle include any arbitrary coupling, what makes it
generally applicable to photophysical and photochemical problems, also those
including explicit laser fields. A step-by-step derivation of the main
equations of motion employed in surface hopping based on the fewest-switches
method of Tully, adapted for the inclusion of spin-orbit interactions, is
provided. Special emphasis is put on describing the different possible choices
of the electronic bases in which spin-orbit can be included in surface hopping,
highlighting the advantages and inconsistencies of the different approaches.
