The trans effect: methodological musings

The trans effect (TE) in the present context refers to the electronic compensation which in collinear homoligand L—Z—L* trans bond pairs lengthens the Z—L* bond when the Z—L bond is shortened. The existence of a functional relation d* = f(d) between the conjugated bond lengths d(Z—L) and d*(Z—L*) (d and d* not equivalent by symmetry; population A) has been demonstrated for a variety of Z-L combinations, with Z mostly from Groups VI and V and L mostly a halogen. The two model functions investigated in detail are the empirical DPF (difference power fit), d* – d0 = K(d − d0)−c, and the semiempirical CSBO (constant sum of bond orders) based on a modified 3-centre 4-electron bond concept, d* − d0 = −B ln {1 − expt[−(d − d0)/B]}, where B = b0 + b1(d − d0). Fitting DPF and CSBO to experimental d,d* data sets involves 3-parameter nonlinear optimization; in this CSBO differs from the 2-parameter treatment of Sheldrick etal., in which the limiting bond length d0 was supplied externally. Modified versions of DPF and CSBO have been devised to accommodate, along with A, d,d* pairs in which d = d* by symmetry (population S).The relative merits of DPF and CSBO and the various aspects of TE quantification are discussed at length, among these the effect of the oxidation state of Z and of the presence of heteroligands on Z. The meaning of the parameters of optimization and the existence of "chemical" trends between them are examined as well as the importance of the symmetrically balanced bond length de = d = d* and of the total d range Δ = de−d0 resulting from the d,d* regressions. Attempts to extend TE quantification to collinear heteroligand L1—Z—L2trans bond pairs have provided insight into the nature of the bond-length variation in such systems. The very good DPF and CSBO fits to d,d* sets obtained from 6-31G* optimizations of the equilibrium geometries of the OBOX, XOCN, and OCNY (X, Y = H, F, Cl, Li, Na, or no ligand) molecules and ions support the validity of the modified 3c4e model in accounting for the TE bond-length relationships.