Robert Subra

Exponential transformation of molecular orbitals: A quadratically convergent SCF procedure. I. General formulation and application to closed‐shell ground states

A new formulation is proposed for obtaining the SCF wave functions. It is based on an exponential transformation of spin–orbitals which obviates the use of Lagrangian multipliers. A general method is developed for determining explicit expressions for the successive derivatives of the energy with respect to the new variables. The total energy and the wave function are obtained by an iterative procedure, the convergence of which is shown to be quadratic. The method itself provides information as to the Hartree–Fock stability — or instability — of the SCF solution. The method of exponential transformation of molecular orbitals is applicable to closed‐shell systems, as well as to a large variety of open‐shell systems. As an illustration of the procedure the results of ab initio calculations for ammonia, methane, formaldehyde, and aziridine are given.

Ab initio study of the electronic structure and hyperfine coupling properties in simple hydrocarbon radicals. II. Short‐range and long‐range interactions in alkyl free radicals

Nonempirical calculations of the ground−state energy, proton and carbon−13 coupling constants of methyl, ethyl, n−propyl, and cyclopropyl radicals have been performed in the frame of spin−restricted LCAO−SCF open−shell and first−order double−perturbation theories. The rotation barrier is negligible for the ethyl radical. The two barriers of the n−propyl radical are, respectively, 0.3 kcal/mole (0.4 exptl) and 4.7 kcal/mole for the rotations about the Ċ−Cα and Cα−Cβ bonds. The cyclopropyl radical is found to be nonplanar with an out−of−plane angle of 41° and an inversion barrier of 3.80 kcal/mole. For the equilibrium conformations, the computed carbon−13 splittings of the radical carbon of methyl (1), ethyl (2), n−propyl (3), and cyclopropyl (4) are +31.04, +37.90, +37.72, and +138.83 G, respectively; the theoretical α −carbon−13 splittings are −18.14 (2), −17.15 (3), and −8.35 G (4); the β −carbon−13 splitting is +11.8 G for the stable conformation of the n−propyl radical. The calculated coupling constant...

Abinitio study of the vibrational dependence of hyperfine coupling constants in the methyl, silyl, and formaldehyde anion radicals

The influence of vibrational effects on the isotropic hyperfine coupling constants is studied by ab initio methods for the CH3, SiH3, and H2CO− radicals. The calculations are carried out using double‐zeta plus polarization basis sets of contracted Gaussian orbitals. A spin‐restricted SCF plus perturbative configuration interaction method including all spin adapted configurations with three uncoupled electrons is employed. The perturbation treatment is extended to second order which yields a definitive improvement of the results over previous first order calculations. A quantum mechanical treatment of the vibrational problem shows that the influence of the nuclear motion depends on the shape of the potential. The vibrational effects are found necessary to account for the experimental findings and the overall results are in very good agreement with experiment. It is found that the usual classical approach fails to reproduce the correct behavior of the splittings, especially for low temperature experiments.

Vibrational modulation effects on the hyperfine coupling constants of fluoromethyl radicals

A general quantum‐mechanical protocol for the study of nonrigid free radicals has been applied to the series CH3, CH2F, CHF2, and CF3. Electronic structures have been computed by highly correlated ab initio methods and vibrational modulation effects have been studied by a nonrigid invertor Hamiltonian. The effect of small amplitude vibrations perpendicular to the inversion motion has been taken into account by an adiabatic model. The results are in close agreement with experiment, and can be interpreted quite straightforwardly in terms of the interplay between the potential energy and the property hypersurfaces. This allows a more dynamically based analysis of hyperfine coupling constants extensible to large, nonrigid radicals.

Structure and magnetic properties of benzyl, anilino, and phenoxyl radicals by density functional computations

A recently developed quantum mechanical approach devoted to the study of structural and magnetic properties of open-shell species was applied to the isoelectronic series formed by benzyl, anilino, and phenoxyl radicals. Hybrid Hartree–Fock/density functional models (here B3LYP) confirm their reliability, whereas, contrary to other cases, vibrational averaging and solvent effects play only a negligible role. The spin dependent properties are interpreted in terms of a new model including first and second order spin polarization effects.

Ab initio study of the electronic structure and hyperfine coupling in simple hydrocarbon radicals. I. Test of the calculation method on methyl and vinyl

Nonempirical calculations of the energy, proton, and carbon−13 hyperfine splittings for methyl (ĊH3) and vinyl radicals (H2C=ĊH) in their equilibrium geometry are presented. The spin−restricted SCF method and first−order double−perturbation theory including all spin−adapted monoexcited states with three unpaired electrons have been used. The basis set consists of Gaussian−type orbitals contracted in a double−zeta form. The orbital exponents of the hydrogen functions have been simultaneously varied using a scaling procedure in order to simulate a minimum Slater hydrogenoid orbital. The sensitivity of SCF energies and hyperfine splittings to variations in values of the orbital exponent ζH have been investigated. The lowest total energy is obtained for ζH=1.15. Although calculated hydrogen hyperfine splittings increase with ζH, neither the zeroth−order nor the first−order spin density, computed from canonical MO’s or quasilocalized equivalent MO’s can be correlated to ζ3H. A structural analysis of the contri...

STRUCTURE AND ESR FEATURES OF GLYCINE RADICAL IN ITS ZWITTERIONIC FORM

Abstract Extensive post Hartree-Fock calculations are reported for the geometrical structure and hyperfine parameters of the carbon-centered glycine radical in its zwitterionic form. Vibrational averaging effects connected to inversion at the radical center are significant for C α and H α atoms. The good agreement between computed and experimental hyperfine splittings confirms the nature of one of the radicals obtained from irradiation of glycine crystals. On the other hand, the ESR spectrum obtained in aqueous solution cannot be due to the zwitterionic form.

Theoretical approach to fluorine substitution in X2NO and X2CN free radicals. Comparison between ab initio UHF and RHF + perturbation treatments

Abstract Non-empirical calculations have been performed to analyze the effects of fluorine substitution on the geometry and electronic properties of two series of π and σ radicals. Both UHF and RHF + perturbation methods have been used and the results are compared as a function of the basis set quality. As concerns geometry and spin-free electronic properties the results are independent of the UHF or RHF formalism, but highly sensitive to the basis set. The STO-3G basis is unable to reproduce even general trends. Polarization functions always play a relevant role and correlation effects seem not negligible at least for fluorine-containing radicals. The molecular shape of π radicals changes from a planar to a pyramidal geometry when increasing the electronegativity of the substituents. On the contrary, σ radicals always remain planar. Unprojected UHF spin densities are closer to the RHF + perturbation results for small spin contamination (X 2 NO). On the contrary, it is the projected UHF spin density which is in better agreement with the RHF + perturbation value for large spin contamination (X 2 CN). No simple correlation can be found between spin densities and gross atomic spin populations. For H 2 NO the spin density at nitrogen is smaller than at the oxygen nucleus, but substitution may enhance or reverse this trend.

Ab-initio mechanistic studies of radical reactions. Directive effects in the addition of methyl radical to unsymmetrical fluoroethenes

Addition of methyl radical to unsymmetrical fluoroethenes has been studied by ab-initio molecular orbital calculations. In agreement with experimental data, we find that the reaction rate decreases in going from ethene to mono- and 1,1 di-fluoroethene, but sharply increases in the case of trifluoroethene. Additions to the more fluorinated carbon atoms are always thermodynamically favoured, but addition to the CH2 end of mono- and 1,1 di-fluoroethene is kinetically favoured. The general trends of the potential energy barriers have been rationalized by means of the energy decomposition scheme proposed by Morokuma. Non potential energy effects have also been considered, but their role is negligible.

Non-empirical calculations on the conformation and hyperfine structure of the silyl radical influence of vibrational effects

Abstract An ab-initio spin-restricted SCF and perturbative configuration interaction study of the silyl radical is presented. The vibrational dependence of isotropic coupling constants is investigated using double-zeta and double-zeta plus polarization basis sets. The calculations predict a nearly tetrahedral geometry for the radical with an inversion barrier of 5.85 kcal/mol. The vibrational treatment leads to coupling constants (α Si = −190.20 G;α H = +5.03 G) in excellent agreement with experiment.