John C. Schug

Proton Chemical Shifts and Pi‐Electron Distributions in the Hydroxy‐Benzenes

The proton magnetic resonance spectra of phenol, hydroquinone, catechol, resorcinol, and pyrogallol have been studied, and the chemical shifts of the aromatic protons relative to benzene determined. The chemical shifts for the isolated molecules were obtained by making measurements in two solvents and extrapolating to a medium of unit dielectric constant. The electric fields at the protons from the C–O and O–H bond dipoles were calculated, and their contributions to the proton chemical shifts were removed by employing the approximate relation derived by Buckingham. It was assumed that the remaining parts of the chemical shifts were due to changes in the pi‐electron distributions. Huckel molecular orbital calculations were performed, and it was shown that the corrected chemical shifts, δi, can be expressed in the form δi=aqi+a′qi′+a′′qi′′, where qi is the excess number of pi electrons on the ith carbon atom, qi′ is the sum of those on the two adjacent carbon atoms, and qi″ is the sum of those on any oxygen...

Spin projection of single‐determinant wavefunctions

Using the method of expansion in terms of the natural orbitals of charge density, we have rederived the components of the one‐ and two‐particle density matrices that result upon spin projection of a single‐determinant wavefunction. We have corrected several errors in the unrestricted two‐particle density matrix elements given by Harriman and co‐workers, pointed out the necessity of correcting the phases of the natural orbitals, and generalized the theory to the extent necessary to treat molecules having unequal numbers of electrons and basis orbitals. The theory has been applied to several of the types of cases for which the use of the projected UHF method is desirable: (a) small hydrocarbon radicals and singly charged ions, (b) hydrocarbon ions with pseudodegenerate ground states, and (c) a postulated photoproduct of dipyridyl, which had previously been predicted to be a triplet. The UHF wavefunctions of several of the small hydrocarbon radicals and monoions have only limited spin contamination by higher...

Intermolecular Interactions and the Weak Benzene–Halogen Complexes

We have calculated the interaction potential between benzene and halogen molecules as a function of intermolecular distance for approach of the halogens along the sixfold axis of benzene. The calculations were based upon the perturbation theory developed by Murrell and co‐workers for intermolecular interactions in the region of small overlap. Emphasis was placed on the Coulombic and exchange terms. The former were calculated by numerical integrations over charge distributions developed from Slater‐type atomic orbitals. The exchange interaction was expanded on the basis of determinantal wavefunctions for each molecule, using approximate self‐consistent‐field molecular orbitals. The dispersion and induction energies were calculated using approximations common to long‐range theory. The charge‐transfer resonance interaction was estimated semiempirically. Both the stabilization energies and the equilibrium separations obtained for the Cl2, Br2, and I2 complexes were reasonable in comparison with experimental d...

Spin contamination in unrestricted Hartree‐Fock calculations

We have treated several pi‐electron doublets by both the unrestricted Hartree‐Fock method and the restricted approximation of Longuet‐Higgins and Pople. For two of the molecules, which contain oxygen heteroatoms, serious spin contamination occurs in the UHF wavefunctions and this negates the usefulness of the single annihilation procedure that is often used for spin‐density calculations. The restricted approximation provides a convenient alternative, especially because configuration interaction is easily taken into account.

Doublet Electronic States of the Benzyl Radical

Doublet electronic states of benzyl radical, discussing configuration-interaction calculations and transition predictions

Approximate interaction potentials for benzene‐halogen complexes

Approximate interaction potentials have been calculated for the interaction of benzene with Cl2, Br2, and I2 molecules for a variety of geometries. In the majority of configurations, we have found that the interactions are attractive. The depths of the potential minima are somewhat smaller than the experimental energies of complexation, and in most cases only a slight dependence on the relative molecular orientation is observed. Exceptions occur when the halogen approaches either in the plane of the benzene ring with its bond axis directed toward the benzene, or directly over a C–C bond with the halogen axis perpendicular to the bond; the interactions were found to be repulsive at all distances in those configurations.

Investigation of a Fragmentation Model for n‐Paraffins

A fragmentation model is postulated for the interpretation of n‐paraffin mass spectra. It is assumed that primary dissociations of molecule ions yield fragment ions containing at least half the total number of available carbon atoms. Any fragment ions retaining sufficient excitation energy can dissociate further, with the same product size limitations as in the primary processes. At each step, all possible dissociations are assumed to be in competition. Rate constants are calculated by the statistical theory. Breakdown curves are given for n‐decane, and described for other cases. The model can successfully account for observed patterns, their dependence upon the ionizing voltage, and the occurrence of several metastable ion peaks. However, other expected metastables do not appear, the requisite internal energy distributions cannot presently be reconciled, and the calculated amounts of fragment‐ion labeling from C13‐enriched molecules are in disagreement with experimental results.

Half-projected Hartree-Fock calculations on several small molecules

The half‐projected Hartree–Fock (HPHF) method is examined with respect to its ability to obtain molecular correlation, describe molecular potential energy surfaces, and provide a one particle basis for more elaborate treatments. The equivalence, aside from questions of efficiency, of two different HPHF algorithms is demonstrated. The results of calculations on H2O, C2, N2, and CH2 indicate that the performance of the HPHF method, with spin projection in appropriate cases, is roughly equivalent to limited MCSCF treatments. In particular, (1) a small but important fraction of the correlation energy, (2) qualitatively correct potential energy surfaces, and (3) good one particle orbital bases are obtained.

Ab initio projected-unrestricted Hartree-Fock calculations

This paper illustrates some applications of ab initio projected-unrestricted Hartree-Fock (PUHF) theory. The necessary modifications to earlier semiempirical applications of the theory are described, and two applications are presented. Calculation of nuclear hyperfine interactions for the methyl radical shows that the theory provides reasonable spin polarization in free radicals. Study of the ozone molecule provides interesting comparisons with recent generalized valence-bond and configuration-interaction studies. Exploiting the equivalence of spin and spatial projection operations when applied to many broken-symmetry UHF wavefunctions appreciably extends the scope of PUHF theory. This provides the possibility of obtaining open-shell descriptions of singlet molecular ground states. In particular, the lower energy states of ozone are predicted in the correct order.

Approximate spin projection of three‐component UHF wavefunctions: The states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O52−

The approximate spin projection method of Amos et al. is extended to handle UHF wavefunctions having three significant components of differing multiplicity. An expression is given for the energy after single annihilation which differs from that of Amos and Hall. The new expression reproduces the results obtained from a previous exact calculation for which the weights and energies of the components are known. The extended approximate projection method is applied to the pi‐electron UHF wavefunctions for the ground states of the pentachlorocyclopentadienyl cation and the croconate dianion, C5O52−. The results indicate a triplet ground state for the former and a singlet ground state for the latter, in agreement with experimental ESR susceptibility measurements for these molecular ions. C5Cl5+ cannot be treated by restricted Hartree‐Fock theory due to its open‐shell ground state. Incorrect results are obtained for the croconate dianion if restricted Hartree‐Fock theory and singly excited configuration interact...