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symmetry-adapted rotator functions for molecules in cylindrical confinementsymmetry-adapted旋转功能分子圆柱形监禁.pdf

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symmetry-adapted rotator functions for molecules in cylindrical confinementsymmetry-adapted旋转功能分子圆柱形监禁

Int. J. Mol. Sci. 2011, 12, 317-333; doi:10.3390/ijm OPEN ACCESS International Journal of Molecular Sciences ISSN 1422-0067 /journal/ijms Article Symmetry-Adapted Rotator Functions for Molecules in Cylindrical Conﬁnement Bart Verberck Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium; E-Mail: bart.verberck@ua.ac.be Received: 2 December 2010; in revised form: 7 January 2011 / Accepted: 12 January 2011 / Published: 13 January 2011 Abstract: We present a general description of the formalism of symmetry-adapted rotator functions (SARFs) for molecules in cylindrical conﬁnement. Molecules are considered as clusters of interaction centers (ICs), can have any symmetry, and can display different types of ICs. Cylindrical conﬁnement can be realized by encapsulation in a carbon nanotube (CNT). The potential energy of a molecule surrounded by a CNT can be calculated by evaluating a limited number of terms of an expansion into SARFs, which offers a signiﬁcant reduction of the computation time. Optimal molecular orientations can be deduced from the resulting potential energy landscape. Examples, including the case of a molecule with cubic symmetry inside a CNT, are discussed. Keywords: molecular symmetry; symmetry-adapted rotator functions; cylindrical conﬁne- ment 1. Introduction Symmetry plays an extremely important role in nature. Accordingly, the mathematics of symmetry is embedd