The Lie-algebraic formalism is applied to the Smoluchowsky's diffusion equation wherein quantum mechanical ladder operators are used to delineate the Lie-algebra. This approach leads to a simple expression for the survival probability exp(Z(0)) where Z(0) is the structure constant obtained after solving the equations of motion. Application to hemeprotein-ligand dynamics is considered within the Agmon-Hopfield picture which yield good agreement with the experimental results. Numerical convergence is achieved by considering few structure constants (only three in the present application) making the procedure computationally attractive. (C) 2003 Elsevier Science B.V. All rights reserved.