Generating functions for the nuclear spin statistics of nonrigid molecules

Generating functions are developed for the nuclear spin species and nuclear spin statistical weights of nonrigid molecules as the trace of spin projection operators. These generating functions are obtained in terms of the GCCI’s (generalized character cycle indices) of the PI groups of nonrigid molecules which are expressible as generalized wreath products. The GCCI’s of generalized wreath products can be obtained in terms of the GCCI’s of the composing groups. Thus, the method developed here does not require the character table of the P group of nonrigid molecules. From these generating functions the nuclear spin statistical weights of the rovibronic levels and nuclear spin species of nonrigid molecules can be obtained easily. The method is illustrated with several examples of nonrigid molecules containing up to 3 601 989 nuclear spin functions. Application to molecular electric beam deflection studies of weakly bound complexes such as ammonia dimer is also discussed.