Approximate valence-shell electron unrestricted Hartree-Fock calculations with orthogonalized atomic orbitals: Proton hyperfine splittings in benzyl and related radicals

A modified INDO procedure has been used to calculate the proton hyperfine splittings in benzyl and the isoelectronic anilino, phenoxy and 2-azabenzyl as well as 2- and 3-thenyl radicals. The present procedure differentiates between s-, p- and d-orbitals on an atom in estimating various integrals involving them, satisfies the rotational invariance requirements and employs an orthogonalized basis set of atomic orbitals for obtaining core-Hamiltonian matrix elements. The calculations based on using the exponents which depend only on the type of orbital and the nature of atom fail to provide correct relative order of ortho and para proton splittings in benzyl as well as anilino, phenoxy and 2-azabenzyl radicals. On the other hand, use of the exponents which are modified according to the charge densities in various orbitals leads to a high absolute value for para proton splitting compared to that for ortho proton splitting which in case of all these radicals is in agreement with experiment. A spin density calculation on benzyl, anilino and phenoxy radicals considering the variation of one-center one-electron and one-center two-electron integrals for different protons with their charges is found to yield further improvement in the relative order of ortho and para proton splittings in all these radicals. In 2- and 3-thenyl radicals the role of 3d-orbitals on sulfur has also been examined. To our knowledge, no unrestricted INDO calculations including 3d-orbitals on sulfur have been reported in the literature so far.     

Unrestricted Hartree-Fock spin density calculations with orthogonalized atomic orbitals on aza and nitroaromatic radical anions

The spin density distributions in some aza and nitroaromatic radical anions have been calculated using Löwdin's orthogonalized basis set of atomic orbitals in the Unrestricted Hartree-Fock method of Amos and Snyder. The present calculations lead to a satisfactory account of proton splittings in these radicals. Least squares analyses correlating the observed ¹⁴N splittings and the spin density results over completely localized nonorthogonal basis have been separately carried out for aza and nitroaromatic radical anions and the sigma-pi parameters thus obtained are discussed and compared with earlier estimates for these quantities. Unlike the earlier results, the present estimate of Q _NN ^N for aza and nitroaromatic radicals are not very much different from each other.     

Calculation of spin densities in odd alternant hydrocarbon radicals

Spin densities in benzyl, allyl, pentadienyl and perinaphthenyl radicals have been calculated with some variants of the simplified McLachlan unrestricted SCF method based on Hückel-type and the SC Hückel-type molecular orbitals. The various estimations of the spin densities were compared one with each other and with the results of more sophisticated methods. It was shown that the SC Hückel basis and Zhidomirov and Schastnev's modification of the McLachlan approach give a best least square fit of the relation a ^exp Q ^calc .

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Zusammenfassung Die Spindichten von Benzyl-, Allyl-, Pentadienyl- und Naphtenyl-Radikalen werden mit einigen Varianten der uneingeschränkten SCF-Methode in der vereinfachten Form nach McLachlan, die auf den Hückel- und den SC-Hückel-Molekülorbitalen basiert, berechnet. Die verschiedenen Schätzungen der Spindichten werden miteinander sowie mit den Resultaten komplizierterer Methoden verglichen. Es wird gezeigt, daß die SC Hückel Basis und die von Zhidomirov und Schastnev eingeführte Modifikation der Näherung von McLachlan eine beste Näherung nach der Methode der kleinsten Quadrate an die Beziehung a ^exp Q ^calc ergeben.

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Résumé Les densités de spin ont été calculées dans les radicaux benzyle, allyle, pentadiényle et perinaphthényle à l'aide de variantes de la méthode SCF sans restrictions de spin simplifiée de Mac Lachlan, en utilisant des orbitales de type Hückel et SC Hückel. Les différentes évaluations de densité de spin sont comparées entre elles et avec celles obtenues par des méthodes plus élaborées. On montre que la base SC Hückel et la modification de Zhidomirov et Schastnev à la théorie de Mac Lachlan donnent le meilleur accord au sens des moindres carrés avec la relation a ^exp Q ^cal .

     

Unrestricted Hartree-Fock calculations of spin density distributions in the radical anions of some heterocycles derived from thiophene,furan and pyrrole

Spin density distributions in the radial anions of some heterocycles derived from thiophene, furan and pyrrole have been obtained using the unrestricted Hartree-Fock method. Good agreement between the calculated results and experimental data has been observed.     

Some remarks on the calculations of hyperfine splittings in the ESR spectra of conjugated radicals

Some consequences of non-orthogonality of the basic functions of LCAO approximation, on the relations used for calculations of hyperfine splittings in ESR spectra of conjugated radicals, are discussed. Special attention has been paid on the problem of transferability of the hyperfine coupling constants. The discussion is illustrated by some calculations of the hyperfine splittings for radical-ions of naphthalene, and tetracene.

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Zusammenfassung Einige Folgerungen aus der Nichtorthogonalität der Basis in der LCAO-Näherung für die Beziehungen, die für die Berechnung der Hyperfeinaufspaltung im ESR-Spektrum konjugierter Radikale benutzt werden, werden untersucht. Insbesondere wird die Frage der Übertragbarkeit der Hyperfein-kopplungskonstanten behandelt. Die Diskussion wird durch einige Berechnungen der Hyperfeinaufspaltung für die Radikalionen des Naphtalins und des Tetracens ergänzt.

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Sponsored by Institute of Low Temperature and Structure Research, Polish Academy of Sciences (contract No. PAN-3.1.03).     

Additivity model for calculations of UHF spin densities in some aza-aromatic radical anions

The concept of a universal basis set for electronic structure calculation is illustrated by presenting results obtained when basis sets are transferred from one atom to another. A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, produces Hartree-Fock total energies and orbital energies in good agreement with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom. Transferability of integrals is a natural consequence of the use of the same basis set for each atom in a molecule.     

Additivity model calculations of UHF spin densities and charge densities in methyl-substituted radical cations

By use of a heteroatom model for the methyl group and an additivity model for spin densities, the unrestricted Hartree-Fock after annihilation (UHFAA) results for the radical cations of naphthalene, 1-methylnaphthalene and 2-methylnaphthalene are used to predict the spin densities in the -electron approximation in the corresponding cations of di-, tri- and tetramethylnaphthalenes. The additivity model approach is shown to be equally successful for charge densities.     

Unrestricted Hartree-Fock instabilities in semiempirical CNDO/S and INDO/S calculations of spin-spin coupling constants

It is shown that non-convergent calculations of the Fermi contact term of spin-spin coupling constants within the self-consistent and finite perturbation schemes used to solve the coupled Hartree-Fock equations, are originated in non-singlet Hartree-Fock instabilities of the closed-shell restricted Hartree-Fock wavefunction. In CNDO/S and INDO/S wavefunctions, where the electronic system response has been successfully reproduced, all investigated molecules containing MOs were found to be unstable. Results of spin-spin coupling constants are given and compared with experimental as well as FP and SOS INDO values.Part of a Ph.D. thesis (G.E.S.) to be presented to the University of Buenos Aires.Comisión de Investigaciones Científicas (CIC, Pcia. de Bs. As.) fellow.     

On the effectiveness of exponential type orbitals with hyperbolic cosine functions in atomic calculations

Unconventional basis functions, constructed from exponential type orbitals (ETOs) with hyperbolic cosine functions, are applied to Roothaan-Hartree-Fock calculations of atoms within the minimal basis sets framework. The most popular ETOs, Slater type orbitals, B functions and \(\psi ^{(\alpha ^*)}\) functions with \(\alpha ^*=2\), and two types of hyperbolic cosine functions, \(\cosh (\beta r)\) and \(\cosh (\beta r+\gamma )\), are used in this work. The performance of the present basis functions is investigated and compared to the conventional double-zeta Slater-type basis set and numerical Hartree-Fock results. The improvement in the atomic energies clearly demonstrates how the accuracy increases when we move from ETO to ETO with hyperbolic cosine basis functions. The resulting improved minimal basis sets can also be useful in molecular calculations.     

Use of noninteger n‐generalized exponential type orbitals with hyperbolic cosine in atomic calculations

The efficiency of noninteger n‐generalized exponential type orbitals (NGETO) r^n*?1 e with hyperbolic cosine (HC) cosh (βr^μ) as radial basis functions in atomic ground state total energy calculations is studied. By the use of these functions, the combined Hartree‐Fock‐Roothaan calculations have been performed for some closed and open shell neutral atoms and their anions and cations with Z ≤ 21. The performance of new basis functions within the minimal basis framework has been compared with numerical Hartree‐Fock (NHF) results. Our total energy values are significantly close to NHF results. The presented minimal basis total energies obtained from the noninteger NGETO with HC are notably better than minimal basis functions total energies previously reported in the literature. It is found that the accuracy of new noninteger NGETO with HC almost correspond to the accuracy of the conventional double‐zeta functions. All the nonlinear parameters are fully optimized. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Rotational spectrum and carbon-13 hyperfine structure of the C3H, C5H, C6H, and C7H radicals

By means of Fourier transform microwave spectroscopy of a supersonic molecular beam, we have detected the singly substituted carbon-13 isotopic species of C(5)H, C(6)H, and C(7)H. Hyperfine structure in the rotational transitions of the lowest-energy fine structure component ((2)Pi(12) for C(5)H and C(7)H, and (2)Pi(32) for C(6)H) of each species was measured between 6 and 22 GHz, and precise rotational, centrifugal distortion, Lambda-doubling, and (13)C hyperfine coupling constants were determined. In addition, resolved hyperfine structure in the lowest rotational transition (J = 32-->12) of the three (13)C isotopic species of C(3)H was measured by the same technique. By combining the centimeter-wave measurements here with previous millimeter-wave data, a complete set of (13)C hyperfine coupling constants were derived to high precision for each isotopic species. Experimental structures (r(0)) have been determined for C(5)H and the two longer carbon-chain radicals, and these are found to be in good agreement with the predictions of high-level coupled-cluster calculations. C(3)H, C(5)H, and C(7)H exhibit a clear alternation in the magnitude and sign of the (13)C hyperfine coupling constants along the carbon-chain backbone. Because the electron spin density is nominally zero at the central carbon atom of C(3)H, C(5)H, and C(7)H, and at alternating sets of carbon atoms of C(5)H and C(7)H, owing to spin polarization, almost all of the (13)C coupling constants at these atoms are small in magnitude and negative in sign. Spin-polarization effects are known to be important for the Fermi-contact (b(F)) term, but prior to the work here they have generally been neglected for the hyperfine terms a, c, and d.     

13C?13C spin–spin coupling constants and 13C isotope effects on 13C chemical shifts in some 4-membered rings

The ¹³C? ¹³C spin–spin coupling constants in natural abundance oxetane, thietane, cyclobutanone, bromo-and chlorocyclobutane have been measured. Furthermore, the ¹³C isotope-induced changes in the chemical shifts of the different ¹³C nuclei in the molecules mentioned above are reported. These shifts are normally to higher magnetic field; in cyclobutanone, however, the resonance of the carbonyl carbon has shifted to lower field because of the substitution of ¹³C?3 for ¹²C?3.     

Predictions of nitrogen isotropic hyperfine coupling constants in the nitroxide radicals with the aid of DF/HF calculations

Nitrogen isotropic hyperfine coupling constants in different nitroxide radicals calculated via ab initio hybrid density functional/Hartree-Fock methods (UB3LYP and UB1LYP) with 6-31G(d) basis set of Gaussian 98 were found to be in a good agreement with the experimental EPR results. UB3LYP/6-31G(d) and UBLYP/6-31G(d) calculated atomic spin populations and spin density maps in the gas phase correspond to the general features of the experimentally obtained data by polarized neutron diffraction studies in the solid state. The results were analyzed in terms of unpaired electron delocalization and the influence of the surrounding on the radical centers.     

Effects of static and dynamic perturbations on isotropic hyperfine coupling constants in some quinone radicals

The effects of solvent dielectric response on the isotropic hyperfine coupling constants of the 1,4-benzoquinone, 1,4-naphthoquinone and 9,10-anthraquinone anions and 1,4-naphthalenediol cation radicals were studied by electron spin resonance (ESR) spectroscopy and by the theoretical density functional method within the polarizable continuum model. Experimental results demonstrate that the isotropic hyperfine coupling constants can be obtained with high accuracy and that the effects of solvent impurities can be minimized by careful sample preparation. The results obtained correlate well with theoretical predictions from density functional theory calculations. For 1,4-naphthalenediol both the solvent dielectric response as well as rotational averaging of the hydroxy groups were calculated. The overall results highlight the importance of static and dynamic perturbations to the couplings and aid in the assignation process of the couplings to specific magnetic nuclei.