Extended Hückel theory: A new population analysis and its application to forecast chemical bond lengths

Although widely used, the population analysis proposed by Mulliken has been contested by several authors. A new analysis, very easily computed on the orthogonal basis, is here proposed and applied to the EHT wave function.Under its usual presentation, the EHT method is unable to directly evaluate bond lengths through an energy minimum condition. However, it is possible to settle an empirical quadratic relation between the bond lengthR_rs and a quantity calledp_rs, similar to a bond population. Such relations are given for bonds of the CC, CN, CO, CS, CF, CCl, CBr, CH, NO and OH types.The examination of the variation of the bond population under a variation of the bond length has enabled us to prove that this semi-empirical relation was usable in an iterative process: starting from bond lengths taken from any systematic table, it is possible, for a given molecule, to evaluate the bond length consistent with experimental values within an accuracy of 0.03 Å. Some examples, concerning cyclic or acyclic molecules and various kinds of bonds, are given.