@article{10272/5422,
year = {2011},
url = {http://hdl.handle.net/10272/5422},
abstract = {In this work the analysis of the equivalent rotations from the permutation
inversion group formalism is revisited. We emphasize that explicit knowledge
of changes in the Euler angles are not required in order to determine the trans-
formation that a given symmetry operation causes to the rotational functions
when dealing with the permutation inversion group formalism. Indeed, matrix
elements of the equivalent rotations are provided by a single Wigner’s D(j)(R)
function. Taking advantage of this, we propose a symmetry projection approach
to build the rovibrational functions of methane. This approach focus on the rele-
vance of the isomorphism between permutations and equivalent rotations. In our
method, symmetry adapted functions are obtained by simultaneous diagonaliza-
tion of a set of commuting operators, whose representation is given in terms of
direct products of Wigner’s D functions and vibrational matrix representations
provided by a local scheme. The proposed approach is general and permits to ob-
tain in a systematic fashion an orthonormal set of symmetry-projected functions,
with good total angular momentum, and carrying the irreducible representations
of the molecular symmetry group},
organization = {This work has partially been supported by CONACyT, Mexico. This work has also been partially supported by the Spanish MEC and by European regional development funds (FEDER) under project CPAN-Ingenio (CSD2007-00042), and by the Junta de Andalucia (projects P07-FQM-02962 and P07-FQM-03014).},
publisher = {Taylor & Francis},
keywords = {Permutation-inversion group},
keywords = {Equivalent rotations},
keywords = {Ro-vibrational functions},
keywords = {Symmetry projection},
keywords = {Methane},
title = {Equivalent rotations associated with the permutation inversion group revisited: symmetry projection of the rovibrational functions of methane},
doi = {10.1080/00268976.2011.554328},
author = {Álvarez Bajo, Osiris and Lemus, R. and Carvajal Zaera, Miguel and Pérez Bernal, Francisco},
}