  We explore an instantaneous decoherence correction (IDC) approach for the
decoherence and energy relaxation in the quantum-classical dynamics of charge
transport in organic semiconducting crystals. These effects, originating from
environmental fluctuations, are essential ingredients of the carrier dynamics.
The IDC is carried out by measurement-like operations in the adiabatic
representation. While decoherence is inherent in the IDC, energy relaxation is
taken into account by considering the detailed balance through the introduction
of energy-dependent reweighing factors, which could be either Boltzmann
(IDC-BM) or Miller-Abrahams (IDC-MA) type. For a non-diagonal electron-phonon
coupling model, it is shown that the IDC tends to enhance diffusion while
energy relaxation weakens this enhancement. As expected, both the IDC-BM and
IDC-MA achieve a near-equilibrium distribution at finite temperatures in the
diffusion process, while the Ehrenfest dynamics renders system tending to
infinite temperature limit. The resulting energy relaxation times with the two
kinds of factors lie in different regimes and exhibit different dependence on
temperature, decoherence time and electron-phonon coupling strength, due to
different dominant relaxation process.
