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Nonrigid water octamer: Computations with the 8‐cube
Author(s) -
Balasubramanian Krishnan
Publication year - 2020
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.26402
Subject(s) - cube (algebra) , wreath product , histone octamer , combinatorics , equilateral triangle , homogeneous space , mathematics , product (mathematics) , chemistry , wave function , physics , mathematical physics , quantum mechanics , geometry , histone , biochemistry , nucleosome , gene
A 8‐cube model of the fully nonrigid water octamer is considered within the 8‐dimensional hyperoctahedral wreath product group with 10,321,920 operations and 185 irreducible representations by employing computational and mathematical techniques. For the two lowest‐lying isomers of (H 2 O) 8 with D 2d and S 4 symmetries of a rigid (H 2 O) 8 , correlation tables and nuclear spin statistics are constructed for the tunneling splittings of the rotational levels are computed by a computational matrix polynomial generating function technique combined with Möbius inversion, and the relationship to the 8‐cube multinomials are pointed out. Multinomial generating functions combined with the induced representation techniques are employed to compute and construct the nuclear spin species, nuclear spin statistical weights and tunneling splittings of rovibronic levels. We have also computed the spin statistical weights and tunneling splittings of the rotational levels for a semirigid water octamer within the wreath product O h [S 2 ] consisting of 12,288 operations.