Vibrational energy transfer and an improved information-theoretic moment method. Comparison of the accuracy of several methods for determining state-to-state transition probabilities from quasiclassical trajectories

We have applied several methods, both old and new, to predict state-to-state vibrational transition probabilities from quasiclassical trajectory calculations. The methods are applied to 106 cases where accurate quantal results are available and in each case the rms error in the probabilities is computed. The average rms error for the standard histogram method is 0.055. Quadratic smooth sampling, a new method introduced here, reduces this to 0.051; and improved histogram method II of Bowman and Leasure reduces it further to 0.049. Even better accuracy can be obtained by using information theoretic moment methods. Minimizing the information-theory entropy subject to the constraint that the quantized final-state distribution has the same first two moments of final vibrational quantum number variable, i.e., 〈n₂〉 and 〈n₂ ²〉, as calculated from the trajectory end conditions gives an average rms error of 0.036. Continuing to add moments until no feasible solution exists raises this to 0.045, but using two moments when the initial vibrational quantum number n₁ is zero and three or four moments when it is not reduces this to 0.033. Using the moments 〈n₂ - n₁〉 and 〈(n₂ - n₁)²〉 yields an average rms error of 0.031. Finally, using these two moments when n₁ = 0 and augmenting them with 〈(n₂ - n₁)³〉 or 〈(n₂ - n₁)³〉 and 〈(n₂ - n₁)⁴〉 when n₁ ≠ 0 reduces the average rms error to 0.028.