We derive an approximate expression for the time-dependent reaction rate coefficient, k(t), of the Smoluchowski equation for the step function nonradiative lifetime (SFNL) model in the case of structureless liquid (i.e., if there are no spatial correlations between molecules of reactants). The SFNL model assumes that a reaction occurs with equal probability for reactants at distances between r(0) and r(1). The accuracy of the obtained analytical formula for k(t) is absolutely sufficient for practical applications like the interpretation of experiments on fluorescence quenching. A molecular dynamics has shown that the SFNL model much better describes the simulation results than the Smoluchowski-Collins-Kimball model if the distance between r(1) and r(0) cannot be neglected. (C) 2003 American Institute of Physics.