On the planarity of the NSi3 skeleton in the trisilylamine molecule. A normal coordinate analysis involving complex symmetry coordinates

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Abstract
Normal coordinate calculations have been carried out for the N(SiH3)3 molecule. A model with C3h symmetry was used, which is based on a planar NSi3 skeleton. The presence of complex numbers for the characters of degenerate irreducible representations of the point group C3h leads to an unusual problem when factoring the G and F matrices. A set of real degenerate symmetry coordinates for the E′ and E′′ species can be constructed, but these are not true symmetry coordinates under the C3h point group. However, they can be obtained from the genuine (complex) symmetry coordinates by a unitary transformation. For a degenerate species, this procedure leads to a and b blocks of the factored G and F matrices, which contain interaction terms. Consequently both blocks must be taken together when forming the secular equation, and subsequently the calculated frequencies appear as pairs of identical numbers.A valence force field that includes all reasonable interactions has been obtained and used to predict the wavenumbers of the 15N and d9 isotopic molecules. Details of the normal vibrations in the three molecules have been obtained from potential energy distributions. The results show reasonable agreement with the limited experimental data available for the isotopic molecules.

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