Nuclear spin species, spin statistical weights and rovibronic tunnelling splittings of non-rigid water hexamer

Abstract

ABSTRACTPowerful multinomial generating functions together with the character table of the six-dimensional hyperoctahedral wreath product group S6[S2] of the non-rigid water hexamer are employed to obtain the nuclear spin species, nuclear spin multiplets and the total nuclear spin statistical weights of the rovibronic-tunnelling levels for both deuterated and regular forms. The methods are composed of algebraic generating functions involving 531,441 nuclear spin functions for (D2O)6 in a group of 46,080 operations and 65 irreducible representations of the S6[S2] group. Although the deuterated form of the non-rigid water hexamer possesses nuclear spin populations in 58 of the 65 possible symmetries of tunnelling levels, for the regular water hexamer only 23 of the 65 symmetries are populated with nuclear spin functions. The tunnelling splitting correlations of rovibronic levels of the water hexamer have been obtained from the Saykally's semi-rigid (G4) model to the fully non-rigid limit (G46080). The computed nuclear spin statistical weights for protonated form of (H2O)6 call for a reinterpretation of the previous assignment of the observed spectra. The results can also be applied to enumerate the hyperfine patterns using the nuclear spin multiplets and intensities in semi-rigid to fully non-rigid limits.