Effect of Anharmonic Vibrations on the Bond Lengths of Polyatomic Molecules. II. Cubic Constants and Equilibrium Bond Lengths of Methane

Abstract

The method for estimating cubic potential constants described in the preceding paper is applied to tetrahedral molecules. A general expression for the cubic constants is obtained in a matrix form for which the elements are the elements of the L matrix and the force constants. By the use of the spectroscopic data of Jones and McDowell, the L matrix, the force constants, and the cubic constants are estimated for CH₄ and CD₄. A first‐order perturbation calculation based on these cubic constants is made of root‐mean‐square amplitudes of vibration and of the effect of vibrations on mean values of internal coordinates and mean bond lengths r_g. It leads to values for r_g—r_e of 0.022₁ for C–H (CH₄) and 0.016₄ A for C—D (CD₄). An evaluation is made of the effect of common approximations in the calculation of amplitudes of vibration. The rotational constants, B₀, for the ground vibrational state of CH₄ and CD₄ are also calculated according to the present model, using the method of Wilson and Howard. The results for r₀—r_e are found to be 0.009₀ A for C–H (CH₄) and 0.006₇ A for C—D (CD₄). Experimental bond lengths derived from recent diffraction studies of r_g and spectroscopic studies of r₀ are compatible when viewed in the light of the above calculations, and indicate that the equilibrium lengths r_e of the C–H bond in CH₄ and the C—D bond in CD₄ are very nearly 1.085 A.