Variational approach based on the diabatic variational transition state theory optimization is extended and applied to the calculation of the radiationless transition rate for asymmetric high-barrier normal and inverted crossings. Scaling argument is employed to derive an analytic expression for the renormalized frequency as a function of the asymmetry of the crossing and of the dissipation strength for the particular case of Ohmic dissipation (Debye relaxation). The effect of the asymmetry of the crossing on the physical parameters and on the radiationless transition rate is explored. The effective adiabaticity parameter increases with the increasing asymmetry of the crossing in the normal region and decreases with the increasing asymmetry in the inverted region. The physical behavior of the radiationless transition rate in the normal and inverted regions is qualitatively different in the strong dissipation (Smoluchowski) limit. In the inverted region the rate exhibits stretched exponential decay as a function of the dissipation strength reflecting adiabatic suppression in the strong dissipation limit. The accuracy of the approach decreases with the increasing (decreasing) asymmetry of the crossing in the normal (inverted) region and breaks down in the activationless case. (C) 2004 American Institute of Physics.