Continuous symmetry measures of penta-coordinate molecules: Berry and non-Berry distortions of the trigonal bipyramid

The application of continuous symmetry measures to the description of the structures of penta-coordinate complexes is discussed. The characteristic values of the trigonal bipyramid symmetry measure, S(TBP), for molecules with square pyramidal (SP) or intermediate geometries corresponding to a Berry pseudorotation coordinate are established. The experimental data from a reference set comprising 71 structures of more than 40 homoleptic transition metal complexes (including organometallic molecules and inorganic solids) and four EPh5 derivatives of Group 15 elements are consistent with the Berry pathway. The structures of several families of transition metal complexes are analyzed in the light of the variations of S(TBP) corresponding to other distortions of the ideal TBP, including bond stretch or non-Berry angular distortion modes. The families of compounds analyzed are represented by the general formulae [OMX4](-), [NMX4](-), [Cu(bipy)(2)X](+), [Cu(phen)(2)X](+), [M(dppe)(2)X], [M(tripod)X], [M(terpy)X-2], [M(NO)L-4] with the {MNO} (8) electron count, vanadium-(IV) and -(V) compounds including several oxides and vanadyl complexes. The S(N)2 substitution pathway in Sn compounds that had been previously shown to be well represented by the structural data of a series of compounds with, e.g., a XSnC3O core are also shown to be elegantly described by the simultaneous change in their TBP and T-d continuous symmetry measures.