Empirical relation between inverse covalent bond length and force constant, and its consequences for potential energy curves

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It is well known that short covalent bonds have high force constants k. Here this is expressed through the empirical relation k = A exp(sRe), where Re is the equilibrium bond length. The value of s depends on the period in the Periodic Table, but is approximately constant throughout a period. Force constants are reproduced from bond lengths to within 20% in the second period groups III to VI (B2 to F2) with two constants A and s, and more accurately for groups III to VII in the third and fourth periods. Knowledge of k then permits predictions of Re, for example in the metal dimers Ga2 (300pm) and Rb2 (410pm). Finally, the implications of this empirical relation between k and Re are considered for analytical representation of potential energy curves.