Invariance of Molecular ‘Inverse’ Force-constants

Abstract

IN the quadratic form : representing the harmonic approximation to the potential energy of a vibrating molecule, the ‘force constants’ k _rs depend on the definition of the internal co-ordinates q _i used to represent small changes in the molecular configuration. For example, a full analysis¹ of the vibrations of ¹⁴NO₂ and ¹⁵NO₂, with co-ordinates q ₁ and q ₂ the NO bond stretches, gives for the stretch and stretch- interaction constants k ₁₁ = K ₂₂ and K ₁₂ the following values (in units 10⁵ dynes/cm.): (i) 10.884 and 1.9914 and (ii) 15.507 and 6.614 in the two cases where the third coordinate is (i) the ONO angle distortion and (ii) the change in OO distance. Thus the interpretation and comparison of force-constants obtained by different co-ordinate analyses present difficulties, which naturally increase with molecular complexity.