A new approximate self‐consistent‐field method for the determination of molecular orbitals for all valence electrons of a molecule is proposed. This method features neglect of differential overlap in all electron‐interaction integrals except those involving one center only. The parameters involved in the calculation are generally obtained semi‐empirically. The new method is known as the Intermediate Neglect of Differential Overlap (INDO) method, and may be regarded as an improvement over the CNDO method proposed in Part I, in that atomic term‐level splittings and unpaired spin distributions are better accommodated. Calculations on geometries of AB2 and AB3 molecules are reported to substantiate the proposed method, and calculated unpaired spin distributions for methyl and ethyl radicals are discussed.

Approximate Self‐Consistent Molecular‐Orbital Theory. V. Intermediate Neglect of Differential Overlap

Electron spin resonance methods have been used to observe alkyl radicals in liquid hydrocarbon systems during irradiation with 2.8‐MeV electrons. These investigations provide detailed structural, radiation chemical, and kinetic information about a large number of radicals.In general, in these studies the ESR lines are found to be narrow; considerable fine structure is observable, permitting positive assignment of the radical species. Accurate hyperfine constants are reported for 21 alkyl and cycloalkyl radicals (including several deuterated species), vinyl, 1‐methylvinyl, 3‐butenyl, allyl, and cyclohexadienyl radicals, and hydrogen and deuterium atoms. Except for cyclopropyl radical, all the alkyl and cycloalkyl radicals have α coupling constants in the range 21–23 G. The β coupling constants in cases where they have been rotationally averaged isotropically are found to decrease with increasing substitution of alkyl groups on the α carbon atom. In general the values for primary, secondary, and tertiary ra...

Electron spin resonance studies of transient alkyl radicals

Indirect proton hyperfine interactions in π‐electron radicals are first discussed in terms of a hypothetical CH fragment which holds one unpaired π electron and two σ‐CH bonding electrons. Molecular orbital theory and valence bond theory yield almost identical results for the unpaired electron density at the proton due to exchange coupling between the π electron and the σ electrons. The unrestricted Hartree‐Fock approximation leads to qualitatively similar results. The unpaired electron spin density at the proton tends to be antiparallel to the average spin of the π electron, and this leads to a negative proton hyperfine coupling constant.The theory of indirect proton hyperfine interaction in the CH fragment is generalized to the case of polyatomic π‐electron radical systems; e.g., large planar aromatic radicals. In making this generalization there is introduced an unpaired π‐electron spin density operator, ρN, where N refers to carbon atom N. Expectation values of the spin density operator ρN are called ``spin densities,'' ρN, and can be positive or negative. In the simple one‐electron molecular orbital approximation a π‐electron radical always has a positive or zero spin density at carbon atom N, 0≤ρN≤1. In certain π‐electron radical systems; e.g., odd‐alternate hydrocarbon radicals, the spin densities at certain (unstarred) carbon atoms are negative when the effects of π—π configuration interaction are included in the π‐electron wave function.The previously proposed linear relation between the hyperfine splitting due to proton N, aN, and the unpaired spin density on carbon atom N, ρN, aN=QρN is derived under very general conditions. Two basic approximations are necessary in the derivation of this linear relation. First, it is necessary that σ—π exchange interaction can be treated as a first‐order perturbation in π‐electron systems. Second, it is necessary that the energy of the triplet antibonding state of the C–H bond be much larger than the excitation energies of certain doublet and quartet states of the π electrons. This derivation of the above linear relation makes no restrictive assumptions regarding the degree of π—π or σ—σ configuration interaction. The validity of the above approximations is discussed and illustrated by highly simplified calculations of the proton hyperfine splittings in the allyl radical, assuming the π—π configuration interaction—and hence the negative spin density on the central carbon atom—to be small.Isotropic hyperfine interactions in molecules in liquid solution can also arise from spin‐orbital interaction effects, and it is shown that these effects are negligible for proton hyperfine interactions in aromatic radicals.

Theory of Isotropic Hyperfine Interactions in π‐Electron Radicals

An analysis of the electron spin resonance of x‐irradiated single crystals of β‐succinic acid shows that: (a) the principal long‐lived paramagnetic species produced by the radiation damage is (CO2H)CH2–ĊH(CO2H); (b) the radical is oriented in the crystal lattice in nearly the same way that the parent succinic acid molecule is oriented in the undamaged lattice; (c) the strongly anisotropic hyperfine interaction due to the σ proton is very nearly the same as that previously found for the σ proton in the malonic acid radical, (CO2H)ĊH(CO2H). In these molecules the σ proton is directly bonded to the carbon atom on which the odd electron is largely localized. The two methylene protons in the radical are not equivalent, and their hyperfine interactions are nearly isotropic, and in the range 80–100 Mc.

Radiation Damage in Organic Crystals. II. Electron Spin Resonance of (CO2H)CH2CH(CO2H) in β-Succinic Acid

It is shown that isotropic (or average) nuclear resonance shifts for a nucleus in a paramagnetic molecule in solution, and in a polycrystalline solid, can be used to distinguish between Fermi contact and ``pseudocontact'' contributions to isotropic nuclear‐hyperfine interactions. The pseudocontact interaction is that isotropic hyperfine coupling which arises from the combined effects of (electron‐spin)‐(nuclear‐spin) coupling, (electron‐orbit)‐(nuclear‐spin) coupling, and electron spin‐orbit interaction. When the magnetic hyperfine interaction between the electronic moment and nuclear spin is approximated by a point dipolar interaction, and the isotropic hyperfine interaction is exclusively pseudocontact, then the isotropic nuclear shift in a polycrystalline solid exceeds the solution shift by the factor 3(g∥+g⊥)/(g∥+2g⊥) where g∥ and g⊥ are the spectroscopic splitting factors parallel and perpendicular to the molecular symmetry axis. Isotropic shifts due to the Fermi contact interaction are the same for both solid state and solution cases.

Isotropic nuclear resonance shifts

The problem of isotropic hyperfine interactions in the EPR spectra of aliphatic free radicals is approached from the molecular‐orbital picture of hyperconjugation. The ethyl, methylethyl, and 1,1‐dimethylethyl radicals are treated by this approximation; with a reasonable choice of parameters, the results can be correlated rather well with our present knowledge of aliphatic radicals. The calculated coupling constants of methyl group hydrogens are of the order of 15 to 25 gauss, do not decrease radically with the presence of additional methyl groups, and are very nearly proportional to the molecular‐orbital unpaired electron density at the central carbon atom.

Donald B. Chesnut

Papers

Theory of Isotropic Hyperfine Interactions in π‐Electron Radicals

Molecular‐Orbital Treatment of Isotropic Hyperfine Interactions in Simple Aliphatic Radicals

Negative Spin Densities in Aromatic Radicals