Group theory and nuclear spin statistics of weakly-bound (H2O)n, (NH3)n, (CH4)n, and NH+4(NH3)n

Abstract

We show that the irreducible representations, character tables, and nuclear spin statistical weights of tunneling levels of weakly bound van der Waals polymers such as (H2O)n, (NH3)n, (CH4)n, and NH+4(NH3)n can be obtained readily using the cycle-type matrix algebra and plethysm substitutions. The permutation-inversion (PI) groups of (H2O)n, (NH3)n, and (CH4)n are expressible as wreath product groups. A tree-pruning method is developed to generate the PI groups of NH+4(NH3)n. The tunneling levels and the nuclear spin statistical weight tables of (H2O)n (n up to 8), (NH3)n (n up to 4), and (CH4)n (n up to 3) are obtained for the first time using the wreath product algebra although, e.g., the PI group of (H2O)8 considered in this study contains 20 643 840 operations.