Abstract: The hole states of O 2 +, obtained by ionization of the oxygen molecule, have been examined theoretically in three approximations: (i) The frozen orbital approximation, which consists of single configuration calculations in terms of the Hartree‐Fock orbitals for the neutral O2 molecule; (ii) direct hole‐state calculations in which g or u inversion symmetry is imposed on each molecular orbital; (iii) direct hole‐state calculations without the restriction in (ii). For the 1s 4Σ− hole state the three approximations yield the following ionization potentials: (i) 563.5 eV; (ii) 554.4 eV; (iii) 542.0 eV. The experimental ionization potential is 543.1 eV, and it is concluded that the hole state is localized on one of the two oxygen atoms.

Abstract: The CNDO‐II approximate SCF molecular orbital method is extended to include molecules containing atoms of the first transition series. Valence orbitals explicitly considered in the transition atoms are 3d, 4s, and 4p. Calculations are reported for the monoxides of Sc, Ti, V, and Cu, using three sets of orbital exponents. The results are compared, where possible, with those obtained by ab initio methods, and appropriate values for off‐diagonal core parameters are proposed. The method is used to evaluate the orbital levels for a number of hexafluorometallate complex ions. Fair agreement is found between the calculated and experimentally observed metal‐fluorine equilibrium bond lengths. The eigenfunctions are used to obtain the transferred spin densities to the fluorine ligands and in general these compare favourably with the values derived from electron spin and nuclear magnetic resonance measurements.

Abstract: The ionization energies of the valence electrons of the ions PO4 3-, SO4 2-, ClO4 -, ClO3 - and CO3 2- are measured by X-ray photoelectron spectroscopy. An assignment of the spectra is made using the results of all electron ab initio SCF-MO calculations, reported here, together with X-ray emission spectra from the literature. The calculated atomic orbital composition of the molecular orbitals allows the intensities of the X-ray spectra to be understood, and provides further evidence for d-orbital participation in the bonding of the second row atoms.

Abstract: With the exception of the sulfur L‐absorption spectrum, measurements of all the soft x‐ray spectra from gaseous SF6 in their respective threshold regions are reported. The valence emission x‐ray spectra are interpreted in terms of a molecular orbital model of SF6 with the inclusion of sulfur d orbitals. The experimental emission profiles are in fair agreement with a calculated profile based on the assigned orbital ionization energies and molecular orbital theory. The sharp resonance structures in the absorption spectra are found to result from the potential barrier formed by the surrounding fluorine atoms and are consistent with the molecular orbital model. The identification of the absorption resonance structure in terms of transitions to ``virtual'' unoccupied electronic levels is substantiated by the observation of ``resonance radiation,'' i.e., x‐ray emission in coincidence with the peak positions in the absorption region. The sulfur Kα spectrum is also presented and discussed. A notable feature in th...

Abstract: The formulation given by Feautrier et al. (1971) for transitions induced by electron impact among ground state terms of atoms with one configuration npq is used with a slight modification by taking into account the orthogonality of the free wavefunction to the bound npq orbitals. A system of coupled integro differential equations, obtained from a modified close coupling expansion by including long range pseudo states, is solved numerically for electron incident on oxygen in the threshold region. The present results agree very closely with experiment. Independently of the evident astrophysical interest of these results (especially the excitation cross sections of the forbidden lines), the generalizations of such calculations to other systems with the same type of configuration is straightforward with this automatic code. The multichannel photodetachment cross sections of O- by dipole length and velocity formulae are also reported and discussed.

Abstract: Hyperfine coupling to β-atoms such as Sn, P or As in carbon π-radicals is found to be remarkably large, corresponding to as much as 6 % delocalization into the valence s orbital on the heavy atom. The radicals all have a preferred conformation in which the metal atom is constrained above the radical plane, so that overlap between the carbon 2p orbital nominally containing the unpaired electron, and the carbon-metal σ-bond orbital is a maximum. This magnetic interaction is shown to be about four times larger than that for similarly placed –CR3 or –NR+3 groups.These observations are linked with those of others on rate enhancements by CH2X groups in electrophilic aromatic substitution. They are also significant with respect to the stereochemical course of some olefin additions.

Abstract: The Fourier representation method described in the previous paper of this series is used to make electronic structure calculations for a linear chain of equally spaced hydrogen atoms. The electronic wavefunction is assumed to be a determinant of doubly-occupied crystal orbitals of modulated-plane-wave type, built from one 1s Slater-type orbital of screening parameter ζ centered on each atom. The energy is calculated from the electrostatic zero-order Hamiltonian with exact evaluation of all Coulomb and exchange contributions, and is optimized with respect to the lattice spacing and ζ value. Good agreement with work by others is noted, indicating a near-equivalence of modulated-plane-wave and tight-binding wavefunctions for this half-filled-valence-band system. The linear chain is calculated to be far more stable than cubic three-dimensional hydrogen crystals. This fact sheds light on the unusually large calculated nearest-neighbor distances in the cubic crystals, and is related to a suggestion that under certain conditions the most stable structure for solid atomic hydrogen may be of lower symmetry than cubic.

Abstract: X-Band e.p.r. spectra of magnetically dilute glasses at 77 K show that ethanol and pyridine form weak complexes with vanadyl chelates and that vanadium(IV) in solutions of these chelates is readily oxidised to vanadium(V). A method which enables spin Hamiltonian parameters to be extracted from systems which have C2v symmetry is described, and the magnetic and optical properties of some five- and six-membered ring chelates of the VO2+ ion, and of their complexes with ethanol and with pyridine, are listed. The principal values of the hyperfine tensor components and the isotropic contribution to hyperfine coupling can be used to distinguish five-from six-membered ring chelates. Spin Hamiltonian parameters are equated to the atomic orbital coefficients in some of the molecular orbitals involved in bonding in these chelates. The weak C2v component of the ligand field mixes the vanadium 3dx2–y2, 3dz2, and 4s orbitals and the magnetic resonance data is used to estimate the extent of this mixing. Mixing 3dz2 character into the orbital containing the unpaired electron accounts for ‘in-plane anisotropy’ in the g-tensor components. Mixing 4s character accounts for characteristic differences between hyperfine tensor components observed for five- and six-membered ring chelates and for the changes which occur in the magnetic properties of these compounds when additional complexing with solvent molecules takes place.

Abstract: Ab initio quantum mechanical calculations have been carried out at 10 internuclear separations for those 72 molecular states of silicon monoxide which dissociate to a Si atom in 3P, 1D, 1S, or 5S state plus an oxygen atom in 3P, 1D, or 1S state. Full configuration interaction calculations were made from a minimal basis set of Slater‐type orbitals, with the restriction that the core orbitals (1s, 2s, 2p Si and 1s O) were fully occupied. The results were strikingly similar to those obtained for CO in an analogous theoretical study. Ten bound states were found to dissociate to ground state Si plus ground state O; five of these states have been observed experimentally in SiO, but eight have experimentally known counterparts in CO. The predicted ordering of states is X 1Σ+, a 3II, a′ 3Σ+, 3Δ, e 3Σ−, I 1Σ−, A 1II, 1Δ, 5Σ+, and 5II. Molecular orbital configurations are assigned to each of these 10 states. Among 10 higher predicted bound states, the 1II III state, with calculated De=1.32 eV, is perhaps the most l...

Abstract: The lowest ionization potential and transition energies of methane are calculated by a second-order perturbation expansion, using a limited basis of gaussian-type orbitals. An attempt is made to rationalize the choice of basis atomic orbitals. This procedure yields 13·8 eV for the first ionization potential and 10·4 eV for the lowest allowed transition provided a diffuse molecular orbital is added to describe the excited state (the experimental values are 13·6 and 9·7 eV). These two values include contributions of -1·0 and -0·70 eV, respectively, from an approximate optimization of the basis atomic orbitals and of +0·50 and +0·25 eV from electron correlation.

Abstract: After recalling the duality between the general linear group GL(m), represented by its N‐fold inner product, and the permutation group SN, we have given a survey of its quantum chemical consequences. It causes the one‐to‐one correspondence between the total spin quantum number and the permutation symmetry of N‐electron spin functions, and, via the Pauli principle which imposes permutation symmetry on the spatial part also, it leads to specific properties of antisymmetric spin eigenfunctions under orbital transformations. Such functions can be classified according to the irreducible representations of GL(m). For special orbital transformations, often occurring in quantum chemistry, which mix only orbitals in different subsets among each other, we have derived how the transformation of the N‐electron wavefunctions simplifies, by a reduction of the representations of GL(m). The theory is illustrated by an example and some applications are discussed.

Abstract: The geometry and binding energy of the H5+ molecular ion have been examined by two different ab initio quantum mechanical variational methods. In the first a CI wavefunction was made from the 10 covalent valence‐bond structures which could be constructed from 1s orbitals at the nuclei, each 1s orbital being represented by a five‐term Gaussian expansion and having a variable scale factor. For geometries identical or similar to the D2d geometry previously predicted from analogous calculations with cruder basis sets, we found no stability with respect to H3++H2. Other geometries were examined, especially those arising naturally from the approach of H3+ and H2; however, binding was never greater than a tiny 0.6 kcal/mole. We thus concluded that the method had failed adequately to describe H5+, as it had for H3+, and that it is probably unreliable for studying ions with small binding energies. The second method used the SCF MO model with a flexible basis set to account for distortion and polarization. This gav...

Abstract: Two Rydberg series of bands of NO which converge to a common limit at 175200+or-50 cm-1 (21.721+or-0.006 eV) have been found in absorption in the range 680-560 AA. The limit agrees with an ionization peak occurring at this energy in its photoelectron spectrum. The ionization is interpreted as leading to the formation of the ( sigma *2s)-1, 3 Pi state of No+. No comparable band systems which could be assigned as Rydberg bands approaching the corresponding singlet state. This phenomenon is attributed to configuration interaction affecting preferentially the low multiplicity component of spin-split stages. It appears to be a common feature of the inner valence orbitals of many paramagnetic molecules and their ions. The diffuseness and Fano type profiles of many of the bands of NO show that the life-times of the states are very short due to predissociation and autoionization.

Abstract: Electron spin g values have been calculated for the isoelectronic π radicals O3−, NO22−, and NF2 using an SCF Hartree‐Fock type approach with a minimum basis set of Slater type orbitals and a number of excited states for each species The results show fair agreement with experimental data In addition, some new experimental data are reported for the ozonide ion, O3−

Abstract: The author obtains explicit formulae for the admixtures of the J=1 level of Sm2+ (4f)6 7F into the J=0 level by exchange coupling to an adjacent Eu2+ (4f)7 8S ion. The problem is formulated using states which are antisymmetric with respect to interchanges of electrons. An unperturbed Hamiltonian is defined which is symmetric with respect to interchanges, and the difference between it and the full Hamiltonian is treated by perturbation theory, taken to second order. It is found that the dominant processes are those in which, in the intermediate states, either two electrons, one from each 4f shell, have been excited into unoccupied orbitals, or two electrons from closed shells have been excited into the 4f shells, one electron to each rare earth ion. By the use of equivalent operator techniques, it is shown that the admixtures can be derived from an equivalent anisotropic exchange interaction, with the important feature that the spin operators which appear are defined in second quantized forms and are not identical with the commonly used spin operators. It is suggested that in phenomenological exchange spin Hamiltonians these new definitions should be used.

Abstract: Monte Carlo calculations are used to generate contour maps of atomic orbitals in which the contours enclose specified percentages of the total electron density. Maps for the most common atomic orbitals are presented, and recommendations for the presentation of atomic orbitals are made.

Abstract: An ab initio calculation is used to give the form of the ionization potential in the alkane series and to explain the origin of the various contributions to this potential The question of whether the ionization relates to a σ-type orbital, composed mainly of carbon atomic orbitals, or to a π-type, composed of CH bonds, is considered The results show a gradual evolution from a CH ionization (13·26 eV) in CH4 to a CC ionization (10·0 eV) at the farthest limit of the series

Abstract: A new type of potential function is derived from the atomic Hartree-Fock self- consistent potential which has almost identical occupied orbitals, but an adjustable set of unoccupied bound orbitals. Comparisons are made between the properties of this potential and the Hartree-Fock potential for trivalent praesodymium. It is shown that the use of the new potential introduces considerable simplifications into atomic configuration interaction calculations.

Abstract: The nondiagonal, first‐order contributions to the hyperfine‐structure anisotropy of EPR spectra of the Cu2+(3d9) ion in tetragonal fields of O, N, S, F−, and Cl− have been calculated. It is shown that such effects are comparable in order of magnitude with some of the effects due to orbital admixture. The ligand s and pz contributions are computed separately and equations for the case of hybrid s–pz orbitals are derived. Tables of values of the nondiagonal term as a function of the metal‐ligand distance are presented. Consideration of the nondiagonal contribution leads to larger values of the electron localization, as exemplified by five cases discussed in this paper.

Abstract: High spin levels in 147Gd are excited in the 144Sm (α,n) reaction. Based on excitation function measurements, angular distribution and two-dimensional γ-γ coincidence experiments a level scheme of 147Gd is proposed. The ground state (7/2-) and the two lowest energy levels at 997.4 and 1 152.8 keV are described within the shell model by the single particle orbitals 2f7/2, 1h9/2 and 3p3/2. The higher lying states in 147Gd may arise from the coupling of a 1h9/2 or 2f7/2 particle to the excited levels of the core.