Formulae which relate pressure,activity and potentials of mean force to sums of integrals over Ursell-Mayer correlation functions of the distribution functions

The pure rotational spectrum in the far-infrared between 30 and 170 cm^-1 and its absolute intensity has been measured for CH₂D₂ in the vibrational ground state by high-resolution interferometric Fourier transform techniques. The analysis of the integrated cross-sections in the essentially water-free spectrum results in an accurate value for the permanent, vibrationally induced ground state electric dipole moment of CH₂D₂|μ₀| = (6·40±0·33) x 10^-3D.The influence of centrifugal effects on intensities and on the determination of the permanent dipole moment was investigated. Although centrifugal effects are important for the explanation of single band profiles, they appear to be of little relevance for the resulting permanent dipole moment. A new, more general 9- dimensional dipole moment function for methane is derived from ab initio calculations and experimental band strength information of CHD₃. Quantum Monte Carlo calculations using this function and a new, more general 9- dimensional analytical, anharmonic potential function for methane yield a semi-theoretical estimate μ₀ ^z = – (7·8±0·5)x10^-3D for CH₂D₂.