Gaussian Orbital Basis Sets Research Articles

First-principles calculations of beta -SiC(001) surfaces.

We report self-consistent ab initio calculations of structural and electronic properties for five different configurations of polar \ensuremath{\beta}-SiC(001) surfaces. Both Si- and C-terminated structures are investigated. We employ our smooth norm-conserving pseudopotentials in separable form within the local-density approximation of density-functional theory. Gaussian orbital basis sets are used in the supercell calculations. For the Si-terminated (2\ifmmode\times\else\texttimes\fi{}1) surface we do not find any significant dimerization of the surface-layer Si atoms. For various C-terminated surfaces, on the contrary, we find strong carbon dimers as the basic building blocks of the reconstruction. Our optimized configurations for C-terminated surfaces are in good general agreement with structural models from the literature that have been suggested on the basis of experimental data. Our results for the Si-terminated (2\ifmmode\times\else\texttimes\fi{}1) surface, on the contrary, show significant differences from suggested models. We discuss the physical origins of the distinctly different reconstruction behavior of Si- and C-terminated surfaces and present a full account of surface electronic properties of these systems including the quasiparticle band structure of the C-terminated \ensuremath{\beta}-SiC(001)-(2\ifmmode\times\else\texttimes\fi{}1) surface as resulting in the GW approximation. We present and discuss our results in comparison with other theoretical results and with experimental data from the literature. \textcopyright{} 1996 The American Physical Society.

Efficient scheme for GW quasiparticle band-structure calculations with applications to bulk Si and to the Si(001)-(2 x 1) surface.

We report an efficient scheme for evaluating the quasiparticle corrections to local-density-approximation (LDA) band structures within the GW approximation. In this scheme, the GW self-energy corrections are evaluated in a sufficiently flexible Gaussian orbital basis set instead of using plane-wave Fourier representations of the relevant two-point functions. It turns out that this set has to include orbitals up to f-type symmetry, when in the LDA calculations Gaussian orbitals up to d-type symmetry are needed for convergence. For bulk Si, both schemes yield virtually identical quasiparticle band structures and the demand on computer time is roughly the same. For the Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) surface, the GW Gaussian orbital scheme is a factor of 5 faster. In our calculations for Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) the dynamic dielectric matrix is obtained by applying a plasmon-pole approximation. The static dielectric matrix of the Si(001) surface is fully calculated within the random phase approximation (RPA). In addition, we have performed quasiparticle surface band-structure calculations employing two model dielectric matrices. Our respective results are compared with those obtained employing the full RPA dielectric matrix as well as with results of previous calculations by other authors which were based on model dielectric matrices.

Ab initio calculations of SiC(110) and GaAs(110) surfaces: A comparative study and the role of ionicity.

We report ab initio calculations of structural and electronic properties of \ensuremath{\beta}-SiC and of the nonpolar SiC(110) surface. The calculations are carried out self-consistently in the local-density approximation employing smooth norm-conserving pseudopotentials in separable form. Gaussian orbital basis sets are used for an efficient description of the wave functions. These are strongly localized at the carbon atoms, in particular. For the bulk crystal 40 Gaussians per unit cell with s, p, d, and ${\mathit{s}}^{\mathrm{*}}$ symmetry are found to be sufficient for good convergence. Our results for the SiC ground-state structural parameters and the bulk band structure are in excellent agreement with the results of previous plane-wave calculations and with experimental data. We scrutinize the character of the chemical bond in SiC by comparisons with diamond, Si, GaAs, and ZnS, which have been investigated on equal footing. The SiC(110) surface is described in a supercell geometry. The optimal surface relaxation is determined by eliminating the forces iteratively. We find a top-layer bond-length-contracting rotation relaxation in which the Si surface layer atoms move closer towards the substrate while the C surface-layer atoms relax only parallel to the ideal surface plane. SiC(110) exhibits an occupied and an empty dangling-bond band within the fundamental gap. The occupied band predominantly originates from the dangling bonds at the surface carbon atoms which behave like anions. The empty band mainly originates from the dangling bonds at the surface Si atoms which act as cations. We present and discuss our results for the SiC(110) surface in direct comparison with the GaAs(110) surface. Further comparisons with literature data on surfaces of more ionic II-VI compounds like ZnS or ZnO are given, as well. This allows us to address the physical origins of the surface relaxation behavior of these compound semiconductors and to identify characteristic differences and similarities in the relaxation which are related to the specific types of heteropolarity or ionicity of these systems.

Theory of adsorption: Ordered monolayers from Na to Cl on Si(001) and Ge(001)

First principles calculations of clean and adsorbate-covered surfaces of Si(001) and Ge(001) are reported. Chemical trends in the adsorption of ordered Na, K, Ge, As, Sb, S, Se and Cl overlayers are discussed. The calculations are based on the local-density approximation and employ non-local, norm-conserving pseudopotentials together with Gaussian orbital basis sets. The semi-infinite geometry of the substrate is properly taken into account by employing our scattering theoretical method. From total-energy minimization calculations we obtain optimal surface reconstructions which show asymmetric dimers for Si(001), Ge(001) and Ge:Si(001). For As:Si(001), Sb:Si(001) and Sb:Ge(001), we find symmetric adatom dimers in the equilibrium geometries. S or Se adlayers are found to be adsorbed in bridge positions forming a (1×1) unit cell with a geometry very close to the configuration of a terminated bulk lattice. Cl atoms adsorb on top of the dangling bonds of symmetric Si dimers residing in the first substrate-surface layer. Our calculations for Na:Si(001) and K:Si(001) confirm valley-bridge site adsorption for half monolayer coverage. For full monolayer alkali-metal coverage, adsorption in pedestal and valley-bridge positions is found to be energetically most favourable. The calculated optimal adsorption configurations are in excellent agreement with a whole body of recent experimental data on surface-structure determination. For these structural models, we obtain electronic surface band structures which agree very good with a wealth of data from angle-resolved photoemission spectroscopy investigations.

Quasiparticle band-structure calculations for C, Si, Ge, GaAs, and SiC using Gaussian-orbital basis sets.

We report state-of-the-art first-principles calculations of the quasiparticle energies of prototype homopolar and heteropolar covalent semiconductors described in terms of the electron self-energy operator. The wave functions are calculated within density-functional theory using the local-density approximation and employing nonlocal, norm-conserving pseudopotentials. The self-energy operator is evaluated in the GW approximation. Employing the plasmon-pole approximation for the frequency dependence of the dielectric matrix ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{G},\mathbf{G}\ensuremath{'}}$(q,\ensuremath{\omega}), its static part is fully calculated within the random-phase approximation (RPA) as well as by using a number of different models. All calculations are carried out employing localized Gaussian orbital basis sets. This will turn out to be very useful for detailed studies of the quasiparticle properties of more complex systems such as bulk defects including lattice relaxation and reconstructed surfaces with large unit cells or interfaces, which are otherwise computationally too demanding. Using an s,p,d,s* basis set of 40 Gaussian orbitals for Si, for example, yields already convergent results in excellent agreement with the results of a 350-plane-wave calculation in the corresponding plane-wave representation. Most of our results for Si, diamond, Ge, and GaAs are in very good agreement with experimental data and with available plane-wave GW calculations. To our knowledge, our results for SiC are the first quasiparticle energies reported so far for this important material of high current technological interest. Also in this case we find very good agreement with the available experimental data except for E(${\mathrm{L}}_{1\mathrm{c}}$). We believe that this deviation may be attributed to experimental uncertainties. In particular, we discuss and scrutinize the applicability of six different models for the static dielectric matrix ${\mathrm{\ensuremath{\epsilon}}}_{\mathbf{G},\mathbf{G}\ensuremath{'}}$(q,0) in the GW approximation ranging from the simple Hartree-Fock expression over diagonal models to nondiagonal models that take the local fields within the inhomogeneous electronic charge density into account. Some of the nondiagonal models are shown to yield results in very good agreement with the full RPA results.

Gaussian type orbital basis sets for the calculation of continuum properties in molecules: The photoionization cross section of H2

The now well-established L2 techniques applied to the description of the electronic continuum of small molecules and generally implemented with suitable oscillating basis sets are here adapted and used in connection with Gaussian type orbital (GTO) functions. As a test, a K-matrix approach associated with extended sets of GTOs is employed to compute with satisfactory accuracy partial wave phase shifts and both the integral and differential photoionization cross sections of the hydrogen molecule. It is apparently possible to greatly extend the range of applicability of the usual L2 techniques beyond the limited set of molecular systems amenable to the one center expansion approximation.

First-principles calculation of the electronic structure of the wurtzite semiconductors ZnO and ZnS.

We report ab initio calculations of the lattice constants and the electronic band structure of the hexagonal wurtzite-structure semiconductors ZnO and ZnS. We employ the local-density approximation and solve the Kohn-Sham equations for nonlocal, separable, and norm-conserving pseudopotentials self-consistently. We use basis sets of localized Gaussian orbitals with s, p, d, and ${\mathit{s}}^{\mathrm{*}}$ symmetry. In particular, we investigate the influence of the Zn 3d electrons on the results for the lattice constants and the band structure. Results of calculations employing both ${\mathrm{Zn}}^{2+}$ and ${\mathrm{Zn}}^{12+}$ ionic pseudopotentials are presented and discussed. For ZnS, both the cubic zinc blende and the hexagonal wurtzite polytype have been studied. The calculated lattice constants are found to be in excellent agreement with experiment for both semiconductors when the d electrons are explicitly taken into account as valence electrons. The agreement of the calculated bands of ZnS with experimental data and with the results of a plane-wave calculation from the literature using about 6.000 plane waves for the cubic crystal is very good except for the absolute energy position of the d bands. For ZnO the calculated bands agree better with angle-resolved photoemission data when the ${\mathrm{Zn}}^{12+}$ pseudopotential is employed. The agreement, however, is still far from satisfactory and the calculated absolute position of the d bands is off, again. The discrepancies seem to be related to correlation effects in the narrow d bands. We find the Zn 3d electrons to strongly interact with the O 2p electrons in ZnO. According to our results, the p-d mixing in ZnO is about twice as large as in ZnS.

Etude ab initio (SCF + IC) des états spectroscopiques et de l'affinité electronique des atomes de la deuxieme période B, C, N et F. détermination de bases d'orbitales atomiques

Extensive configuration interaction calculations have been performed to determine the electron affinities and energies of the spectroscopic states of the second row atoms B-F. The calculated values are in good agreement with experimental ones to within less than 0.1 eV for B, O and F, and less than 0.2 eV for C. Basis sets of Gaussian type orbitals have been determined for the different atoms and the d polarization functions have been optimized.

Ab initio calculations of Si, As, S, Se, and Cl adsorption on Si(001) surfaces.

Optimal adsorption geometries and respective surface band structures for monolayers of group-IV to group-VII adatoms on semi-infinite Si(001) substrates have been calculated from first principles using a self-consistent total-energy scheme. The calculations are based on the local-density approximation and employ nonlocal, norm-conserving pseudopotentials together with Gaussian orbital basis sets. The semi-infinite geometry of the substrate is properly taken into account by employing our scattering theoretical method together with one-particle Green's functions. Chemical trends in the adsorption of Si, As, S, Se, and Cl monolayers on Si(001) are discussed. Our calculational scheme treats all these adlayers on equal footing. The clean Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) surface shows an asymmetric dimer reconstruction which is 0.14 eV per dimer lower in energy than the respective optimal symmetric dimer configuration. An As adlayer gives rise to symmetric As dimer chains at the chemisorbed surface which run orthogonal to the former Si dimer chains at the clean surface. The substrate atoms in this As:Si(001)-(1\ifmmode\times\else\texttimes\fi{}2) system reside close to the lattice sites of the Si bulk crystal.Adsorption of a monolayer of group-VI adatoms is found to restore the substrate surface in its ideal, truncated bulk configuration and to passivate the surface. S or Se adlayer atoms are adsorbed in bridge positions above the surface in sites very close to the lattice positions of the continued bulk lattice and form S:Si(001)-(1\ifmmode\times\else\texttimes\fi{}1) and Se:Si(001)-(1\ifmmode\times\else\texttimes\fi{}1). A Cl adlayer, finally, gives rise to Cl:Si(001)-(2\ifmmode\times\else\texttimes\fi{}1). The adatoms adsorb on top of the dangling bonds of a (2\ifmmode\times\else\texttimes\fi{}1)-reconstructed substrate surface showing symmetric Si dimers. The results of our structure optimizations are in excellent agreement with a whole body of experimental data. The calculated electronic structure for Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) and for As:Si (001)-(1\ifmmode\times\else\texttimes\fi{}2) shows very good agreement with angle-resolved photoemission spectroscopy (ARPES) data. Well-ordered S:Si(001)-(1\ifmmode\times\else\texttimes\fi{}1) and Se:Si(001)-(1\ifmmode\times\else\texttimes\fi{}1) surfaces have not been fabricated successfully, so far. Our calculated electronic surface band structure for Cl:Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) does not yet easily allow for an obvious interpretation of available ARPES data.

Green's-matrix calculation of total energies of point defects in silicon.

The principal approximation in the Green's-matrix method for calculating the electronic structure and total energy of point defects in crystalline solids is the choice of (finite) basis set. In this paper the results of total-energy calculations with a number of different Gaussian-orbital basis sets are presented for several defects in silicon, including the silicon lattice vacancy and the silicon self-interstitial. Particular attention is paid to the convergence of the total energy with respect to the number of atoms included in the defect cluster on which the Green's matrix is represented. Our best estimate for the formation energy of an unrelaxed neutral silicon lattice vacancy is 4.4 eV. In many cases we are interested in calculating the distortion accompanying incorporation of a point defect or the total-energy difference when a defect is displaced. As illustrative examples, the breathing relaxation around the lattice vacancy and the migration energies of the self-interstitial and of interstitial oxygen are examined. It is shown that the atoms surrounding a neutral silicon lattice vacancy relax inwards toward the site of the missing atom. On including this symmetric relaxation and the Jahn-Teller pairing distortion, the formation energy becomes 3.6 eV. Because of the importance of the long-range response to the Jahn-Teller distortion, it was not possible to calculate the pairing energy entirely ab initio. For silicon self-interstitials in the empty channels of the silicon lattice, high-temperature (midgap Fermi-level) formation energies of upwards of 4.4 eV are found. The migration energies are strongly charge-state dependent but in general substantially smaller than the formation energies. The self-interstitial displays negative-U behavior, and its electronic structure supports athermal migration. The migration energy for interstitial oxygen is calculated to be 2.5 eV, which is in good agreement with the experimental value.

Self-consistent surface electronic structure for semi-infinite semiconductors from scattering theory

An efficient scheme to calculate the structural and electronic properties of clean reconstructed or adsorbate-covered surfaces is presented. The method is based on scattering theory and solves self-consistently the Green-function equations describing semi-infinite crystals within the local density functional formalism. Wavefunctions and operators are represented in a flexible, symmetry-adapted basis set of localized Gaussian orbitals to exploit both the full three-dimensional periodicity of the underlying bulk crystal and the short range of the surface-potential deviations from the bulk and vacuum potentials, respectively. Bound states and surface resonances are determined with high spectral resolution so that the bulk and surface contributions to the electronic spectrum are clearly separated. The virtues of the method are exemplified by a discussion of the results for S- or Se-covered Ge (0 0 1) surfaces. Both the structural properties, calculated by total energy minimization, and the electronic properties for the optimized structures are in very good agreement with the experimental data.

Why polyacetylene dimerizes — Conclusive results of ab-initio computations

Results of ab-initio computations for a single chain of trans-polyacetylene are reported. Starting from self-consistent field calculations within a Gaussian type orbital basis set, correlations are included by using the Local Ansatz. The dependence of the total energy on dimerization is then analyzed in order to explain the origin of dimerization. The position of the equilibrium dimerization is dominantly determined by atomic correlation effects. Contributions to the exchange energy from nearest neighbor Coulomb interactions play a nonnegligible role concerning the depth of the energy minimum although their strength is strongly reduced in comparison to self-consistent field results. Electron-lattice coupling alone leads only to a marginal dimerization. These findings are in contrast to assumptions often made in connection with soliton theories.

A b i n i t i o and experimental quartic centrifugal distortion constants of acetone, pyrazole, and γ-pyrone

The complete harmonic force field of acetone has been computed at the Hartree–Fock level with the 4–21 basis set of Gaussian orbitals. Seven scale factors optimized for related molecules were used to scale the computed force field. The mean deviation from the experimental vibrational frequencies is only 9.7 cm−1, except for the two methyl torsions. In order to obtain the best possible force field, a new set of seven scale factors was derived by fitting the computed spectrum of acetone to the observed spectrum. The only major change was for the C–C–C bending scaling factor. The final mean deviation was only 5.2 cm−1. The ground state rotational spectra of pyrazole and γ-pyrone have been reinvestigated in the millimeter-wave range. Thanks to millimeter-wave spectroscopy, accurate rotational and centrifugal distortion constants have been determined for acetone, pyrazole, and γ-pyrone. The experimental quartic centrifugal distortion constants are compared with the values calculated from ab initio force fields. A good agreement is found, even for the two-top molecule acetone for which the differences between the experimental and calculated T constants are smaller than 10%.

On the potential energy surface for collinear OH+2 (4Σ−)

The potential energy surface for collinear OH+2 (4Σ−) has been investigated at the configuration interaction (CI) level using large primitive basis sets of Gaussian type orbitals (GTO) and the general atomic natural contraction (ANO). The CI calculations were carried out using the CIPSI algorithm and the accuracy established by comparison with full CI (FCI) test calibrations on the atoms and molecules of interest in the present work. For the reaction O+(4Su)+H2(1Σ+g)→OH+(3Σ−)+H(2Sg) the calculated value for the energy change of the reaction (ΔE) is −0.30 eV to be compared with an experimental value of −0.45 eV. The error in ΔE arises from the error in the ionization potential of oxygen and does only affect the reactants but not the products, while the discrepancy with the experiment is limited by the finite size of the basis set and not by truncations on the CI expansion. The collinear OH+2 minimum has been found to lie 0.338 eV below the products with an estimated accuracy of 0.01 eV.

Gaussian basis set techniques for calculating electronic resonance positions and widths: Analytic continuation and complex stabilization methods

Several variational methods are applied to the calculation of the position and width of the lowest 1S resonance state of H−, which is the simplest physical example of an electronic Feshbach resonance. These methods include two different versions of the analytic continuation of stabilization graphs that enforce the correct branch-point structure and two versions of the complex-stabilization approach, one that stabilizes the complex resonance energy with respect to the exponents of the complex orbital(s) and one that stabilizes it with respect to both the real and complex orbital exponents. The calculations involve medium-, large-, and very-large-sized basis sets of Gaussian orbitals and full configuration interaction (CI). The use of the same basis sets with the various methods allows for detailed comparisons among them. Although the sensitivity of the results to the fit parameters prevents true convergence, reliable estimates of the position and width of this resonance (about four-figure accuracy in the position and two-figure accuracy in the width) are obtained both from a version of the analytic continuation of stabilization graphs that employs one eigenvalue of a real, Hermitian Hamiltonian matrix but enforces the correct branch-point structure and from a complex-stabilization approach that involves complex basis functions and a non-Hermitian Hamiltonian matrix. In the former approach, we find that the results are less accurate when two eigenvalues of the Hamiltonian matrix are employed in the analytic continuation, possibly due to interactions with excited resonance states. For the latter approach, we show that good results can be obtained with basis sets containing a single complex orbital if the resonance energy is also stabilized with respect to an analytic continuation of the real orbital exponents, but that there is no advantage in using two complex orbitals with close exponents.

Analysis of the vibrational spectrum of 6-methyluracil by ab initio calculation

The harmonic vibrational force field of 6-methyluracil has been computed at the ab initio Hartree-Fock level using a 4/2-21 basis set of Gaussian orbitals. A set of scaling factors, optimized for 1-methyluracil, was transferred unchanged and used to scale the force field computed for this closely related molecule. Dipole-moment derivatives were also computed. The spectrum of fundamental frequencies and absorption intensities was computed from the scaled force field and compared with previous experimental assignments of the gas-phase and matrix spectra. Mean deviations between computed frequencies and the matrix data were 8.2 cm −1 for the inplane modes and 14.4 cm −1 for the out-of-plane ones. One transition, the v 21 CO wagging motion, is believed to have been previously misassigned.

Ab Initio Calculations of the Structure and Properties of Large Atomic Clusters

Abstract A discussion is given of the problems involved in computing the total energy, using local density functional methods, of a cluster of atoms with a real space basis set of Gaussian orbitals. Particular attention is given to the methods used to evaluate the Hartree and exhange-correlation energies and their potentials. Several applications are described: molecular structures and properties, the bond lengths and dynamic properties of bulk silicon and diamond, the local vibratory mode of carbon in silicon, and the structures of H and H related complexes in diamond and gallium arsenide.

Evaluation of semiempirical quantum-chemical methods in solid-state applications. I. Molecular-cluster calculations of defects in silicon.

Three typical semiempirical molecular-orbital methods developed by chemists; the spectroscopic version of the complete neglect of differential overlap (CNDO/S), the modified intermediate neglect of differential overlap (MINDO/3), and the modified neglect of diatomic overlap (MNDO), are evaluated in molecular-cluster model applications. The ionization energies, wave-function localizations, and equilibrium geometries of the clusters X${\mathrm{Si}}_{4}$${\mathrm{H}}_{12}$, where X is a silicon, sulfur, or oxygen atom or a vacancy, are compared with results obtained from ab initio Hartree-Fock calculations using an extended Gaussian-orbital basis set with third-order Moeller-Plesset perturbation theory. The importance of using an absolute ionization-energy scale in locating levels relative to the crystalline band gap is discussed. It is concluded that the MINDO/3 is superior among the three methods in representing defect properties using a molecular-cluster model of defects in silicon.

Ca+HF: The anatomy of a chemical insertion reaction

A comprehensive first principles theoretical investigation of the gas phase reaction Ca+HF→CaF+H is reported. The overall study involves three distinct elements: (a) generation of an accurate ab initio potential energy surface for the ground electronic state of the Ca–F–H system, (b) careful fitting of the computed surface to an analytical form suitable for three-dimensional reactive scattering calculations, and (c) execution of classical trajectory calculations for Ca+HF collisions using the fitted potential surface. Ab initio potential energy calculations were performed for 175 Ca–F–H geometries using an MCSCF-CI method with a large Gaussian orbital basis set. The error in the computed endothermicity for the reaction of Ca and HF is less than 1 kcal/mol and the errors in the computed saddle point energies are believed to be less than 3 kcal/mol. The potential energy surface is dominated by a deep well corresponding to a stable linear H–Ca–F intermediate with an extremely small bending force constant. The calculations clearly demonstrate that the preferred geometry for Ca attack on HF is markedly noncollinear. The saddle point for both fluorine exchange reaction and insertion into the H–Ca–F well occurs for a Ca–F–H angle of 75° and has an energy of 16.1 kcal/mol relative to Ca+HF. The energy barrier for collinear reaction, 30.0 kcal/mol, is nearly twice as high. The analytical representation of the ab initio potential energy surface is based on a polynomial expansion in the three diatomic bond lengths that reproduces the values of the computed energies to within a root mean square deviation of 1.2 kcal/mol and reduces to the appropriate diatomic potentials in the asymptotic limits. Classical trajectory calculations for Ca+HF(v=1) utilizing the fitted surface establish the fact that the H–Ca–F potential well dominates the collision dynamics thus qualifying Ca+HF as a bona fide example of a chemical insertion reaction. Because of the extensive sampling of the H–Ca–F well, many trajectories formed rather long-lived intermediate complexes before reaching diatomic end products. A significant number of these trajectories were not converged with respect to changes in the integration time step. Despite uncertainties associated with the ultimate fates of the nonconverged trajectories, the results obtained support a number of generalizations relating to microscopic features of Ca+HF collisions. Among these are: (1) at fixed total collision energy, excitation of HF to v=1 is much more effective in promoting reaction than is placing the corresponding amount of energy in Ca,HF translation, (2) at fixed initial translational energy, reaction cross sections increase with increasing HF rotational quantum number J, (3) for trajectories which enter the H–Ca–F well, escape to form products is favored by increasing initial HF rotation and escape back to reactants is favored by increasing the initial relative translational energy, and (4) the CaF fractional product energy disposals are remarkably independent of initial collision conditions. These conclusions are compatible with the observation that significant intermode vibrational energy transfer does not occur in the H–Ca–F intermediate on the collision time scale (1–2 ps).

1,2-Rearrangement of protonated-heterosubstituents in ethyl radicals: a molecular orbital study

Ab initio self-consistent field (SCF) calculations in a Gaussian orbital basis set have been carried out on both the equilibrium “open” ( 3) and bridging ( 4) structures of various protonated β-substituted ethyl radicals (C 2H 4 A + ′H; A′H = ClH, SH 2, PH 3). In contrast to the findings for the unprotonated species ( 1 and 2), heteroatom protonation, which stabilizes both the “open” ( 3) and bridged ( 4) forms, results in paths for 1,2-A′H + migration whose energies are substantially below the energy of dissociation to [CH 2CH 2 + A′H]· +· moieties. In the case of CH 2CH 2C l + H, intramolecular ClH + migration can proceed without significant barrier. This raises the possibility that apparent chlorine atom migrations to vicinal radical termini may in fact be ClH + migrations. It is found that protonation of the “open” structures 1b and 1c (A′ = SH, Cl) to give 3b and 3c (A′H = SH 2, ClH) respectively, considerably enhances hyperconjugative interaction between the C α single electron orbital and the C βA bond orbitals. The contrasting result that protonation of 1a (A′= PH 2) to 3a (A′H = PH 3) does not enhance hyperconjugation has been rationalized on the basis of rehybridization of the heteroatom bonds.