On the additivity of atomic and molecular dipole properties and dispersion energies using H, N, O, H2, N2, O2, NO, N2O, NH3and H2O as models

Abstract

The zeroth-order theory of intermolecular forces is used to derive additivity relations for rotationally averaged molecular dipole properties and dispersion energy constants by assuming that a molecule is comprised of non-interacting atoms or molecules. Some of the additivity rules are new and others, for example the mixture rule for dipole oscillator strength distributions (DOSDs), Bragg's rule for stopping cross sections and Landolt's rule for molecular refractivities, are well known. The additivity rules are tested by using previously constructed DOSDs and reliable values for the dipole oscillator strength sums S_k , L_k and I_k , and dispersion energy constants C ₆, for H, N, O, H₂, N₂, O₂, NO, N₂O, NH₃ and H₂O as models. It is found that additivity is generally unreliable for estimating molecular properties corresponding to k < -2. Generally for k ≥ -2 and for C ₆, and if the hydrogen molecule is used to represent the hydrogen atom in the additivity rules, the additivity relations yield results that are reliable to within ⪅20 per cent and the estimates improve substantially as k increases. The effects of molecule formation on DOSDs is examined by comparing the various molecular DOSDs with the sum of the DOSDs for the atoms making up the molecules. Molecule formation results in a net decrease in the amount of dipole oscillator strength for low excitation energies and a compensating net increase for higher energies in a region extending from the absorption threshold to about 100 eV. This is shown to imply that estimates of the stopping average energy I ₀, obtained by using bona fide atomic I ₀ values, are lower bounds to the correct molecular I ₀ results.