Explicit formulas and numerical tables for the overlap integral S between AO's (atomic orbitals) of two overlapping atoms a and b are given. These cover all the most important combinations of AO pairs involving ns, npu, and np1r AO's. They are based on approximate AO's of the Slater type, each containing two parametersp [equal to Z/(n-Il)], and n-Il, where n-Il is an effective principaI.quantum number. The S formulas are given as functions of two parameters p and t, where P=!(.u..+Pb)R/aH, R being the interatomic distance, and t= (.u..-Pb)/(.u..+J.lb). Master tables of computed values of S are given over wide ranges of p and t values corresponding to actual molecules, and also including the case p=O (intra-atomic overlap integrals). In addition, tables of computed S values are given for several cases involving 2-quantum s, p hybrid AO's.
method, free radicals.(2) According to a private communication (see also reference 1, footnote 20), E. Hückel has also used the MO method in similar ways.
HE theoretical computation of absolute transition probabilities for electronic spectra of molecules has been attempted only recently, though T theoretical formulas for relative intensities of lines in a band, and methods for calculating theoretically the relative intensities of bands in a band-system, are well known. The quantum-mechanical calculations on absolute intensities are, for most molecules, necessarily approximate ; their usefulness is still being explored and the methods of computation improved. Fortunately, even very rough theoretical calculations prove to be valuable, since the transition probabilities vary over a range of several powers of ten. The methods of computation, and the results so far achieved in the actual determination of intensities and their interpretation in terms of molecular structure, form the principal subject matter of this Report. Applications to various other molecular properties such as dispersion, polarizability, and the interpretation of molecular refractivities, and to dyes and to the abundance of molecules in astronomical sources, are also discussed.I n the discussion of transition intensities in this Report, we shall consider, for the most part, only absorption spectra, since it is not feasible to obtain extensive experimental data on absolute transition probabilities in emission spectra. 9 2.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.