Relationship between force constants and bond lengths for CX (X = C, Si, Ge, N, P, As, O, S, Se, F, Cl and Br) single and multiple bonds: formulation of Badger's rule for universal use.

Geometries and harmonic vibrational wave numbers were calculated on a series of simple compounds that contain the atoms of elements in the groups 14-17 by density functional theory at the B3LYP/6-311++G(3df,2pd) level. The calculated wave numbers agree well with the observed harmonic wave numbers with substantially the same accuracy for the compounds of the different groups. The stretching force constants of the CX (X = C, Si, Ge, N, P, As, O, S, Se, F, Cl and Br) single and multiple bonds were obtained. The CX stretching force constants increase with a decrease of the bond lengths as the element X in the same period goes from left to right in the periodic table. The individual intrinsic properties of the CX bonds are lost gradually with increasing the period of the element X. The unified interpretation of Badger's rule has enabled the formulation of a common equation for universal use f = 2.8 R(-3) to relate the force constants f (10(2) N m(-1)) and the reduced bond lengths R (10(-10) m).