Evaluation and optimal computation of angular momentum matrix elements: An information theory approach

In this work, we determine all possible angular momentum matrix elements arising in the variational treatment of the rovibrational molecular Hamiltonian. In addition, the logic of the associated computing process is organized in a series of decision tables. Using Shwayder ́s approach, information theory is applied to obtain optimal computing codes from the decision tables. The needed decision rules apparition frequencies are computed as a function of the rotational quantum number J. Using these values, we show that the codes obtained are optimal for any value of J. In all cases, the optimal codes exhibit an efficiency of at least a 97% of the theoretical maximum. In addition, pessimal codes are obtained as a counterpart of the optimal ones. We find that the efficiency difference between the optimal and pessimal codes reaches quickly a limit for increasing values of the J quantum number. Key-Words: Molecular rovibrational Hamiltonian; Angular momentum operators; Matrix elements; Decision tables; Information theory; Information entropy.