Recurrence expressions are derived for various types of molecular integrals over Cartesian Gaussian functions by the use of the recurrence formula for three-center overlap integrals. A number of characteristics inherent in the recursive formalism allow an efficient scheme to be developed for molecular integral computations. With respect to electron repulsion integrals and their derivatives, the present scheme with a significant saving of computer time is found superior to other currently available methods. A long innermost loop incorporated in the present scheme facilitates a fast computation on a vector processing computer.

The position of the proton magnetic resonance is concentration dependent in aqueous solutions of electrolytes yielding hydrogen containing ions. Chemical exchange averages the chemical shifts in the proton resonance position over the different chemical species. The averaged shifts observed are correlated with dissociation of the solute, and evidence is obtained in very concentrated solutions for the incomplete dissociation of HNO3, HClO4, and H2SO4 and for the formation of ion pairs of Na+OH−. A theoretical analysis of the relation between the magnetic absorption line shape and the chemical exchange frequency suggests that rather short chemical lifetimes can be measured; at least one can infer from the appearance of a single or complex resonance that the average lifetime is greater or less, respectively, than a determinable value in a range about 10−2 to 10−4 sec.

General recurrence formulas for various types of one- and two-electron molecular integrals over Cartesian Gaussian functions are derived by introducing basic integrals. These formulas are capable of dealing with (1) molecular integrals with any spatial operators in the nonrelativistic forms of the relativistic wave equations, (2) those with the kernel of the Fourier transform, (3) those with arbitrarily defined spatial operators so far as the integrals can be expressed in terms of the basic integrals, and (4) any order of their derivatives with respect to the function centers in the above integrals. Thus, the present formulation can cover a large class of molecular integrals necessary for theoretical studies of molecular systems by ab initio calculations, and furthermore provides us with an efficient scheme of computing them by virtue of its recursive nature.

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A theoretical analysis is given of the fluorine magnetic resonance shifts in molecules. It is shown that the large range of shifts among different fluorine compounds arises from the effects of binding on the magnetic fields at the nucleus produced by the orbital motion of the electrons in the unfilled valence shell. The simple dependence on ionic character of the bond is also explained. The chemical shift between F2 and HF is calculated to be 14XHr 4 compared to the experimentally observed value 6.3X10-4 •