  We apply the newly derived nonadiabatic golden-rule instanton theory to
asymmetric models describing electron-transfer in solution. The models go
beyond the usual spin-boson description and have anharmonic free-energy
surfaces with different values for the reactant and product reorganization
energies. The instanton method gives an excellent description of the behaviour
of the rate constant with respect to asymmetry for the whole range studied. We
derive a general formula for an asymmetric version of Marcus theory based on
the classical limit of the instanton and find that this gives significant
corrections to the standard Marcus theory. A scheme is given to compute this
rate based only on equilibrium simulations. We also compare the rate constants
obtained by the instanton method with its classical limit to study the effect
of tunnelling and other quantum nuclear effects. These quantum effects can
increase the rate constant by orders of magnitude.
