The Determination of Internuclear Distances and of Dissociation Energies from Force Constants

Abstract

With a view to obtaining the internuclear distances and dissociation energies of individual bonds in polyatomic molecules purely from a knowledge of force constants the consequences of assuming that the potential energy of any di‐atom may be expressed in the form V=—α/r^m+β/rⁿ have been further investigated. In addition to giving a relation between internuclear distance and force constant of the form suggested empirically by Badger, this assumption leads to a relation between force constant (k_e), internuclear distance (r_e) and dissociation energy (D_e) of the form D_e=(k_er_e²)/mn. It is found that such a relation does exist between those quantities for series of diatomic molecules belonging to the same row in the periodic table, provided one uses an ``effective'' internuclear distance r_e—d_ij. This was also used by Badger in his relation of force constant to internuclear distance and the values of d_ij obtained by the two different methods are in reasonably good agreement. The values obtained for the product mn are 4, 6.2, 6.2 and 10.8 for the respective series LiH to FH, Li₂ to F₂, Na₂ to Cl₂ and K₂ to Br₂. For the hydrides it would seem that —α/r+β/r⁴ is the correct form with β varying along the series. It is also shown that this function leads to a relation between the shift in frequency δv and the change in bond energy δD in the formation of a hydrogen bond.