Quartic canonical force field in curvilinear internal coordinates for XY3 (D3h) molecules. The case of the BH3 molecule.

Using the canonical force field theory, expressions of quadratic, cubic, and quartic canonical force constants are obtained for XY3 (D3h) molecules in curvilinear redundant coordinates, i.e., simple valence internal coordinates (VICs), in terms of force constants in normal coordinates and in independent symmetry coordinates. To carry out this task, it was previously necessary to obtain for the first time the non-linear redundancy relation and the corresponding orthogonal projection onto the pure vibrational manifold for XY3 (D3h) molecules corresponding to a set of seven VICs. As an application, the quartic canonical force field in curvilinear redundant internal coordinates of BH3 is determined from ab initio force fields in normal coordinates calculated at the coupled-cluster singles and doubles level with perturbative treatment of the triples in conjunction with a triple- and quadruple-ζ size basis set. This anharmonic force field so obtained for the borane molecule, and in general for XY3 (D3h) molecules, is uniquely defined (therefore in an unambiguous form) and depending on the same number of parameters, i.e., force constants, when independent coordinates (natural or symmetry) are used in its description.