Density functional theory predictions of isotropic hyperfine coupling constants

The reliability of density functional theory (DFT) in the determination of the isotropic hyperfine coupling constants (hfccs) of the ground electronic states of organic and inorganic radicals is examined. Predictions using several DFT methods and 6-31G, TZVP, EPR-III and cc-pVQZ basis sets are made and compared to experimental values. The set of 75 radicals here studied was selected using a wide range of criteria. The systems studied are neutral, cationic, anionic; doublet, triplet, quartet; localized, and conjugated radicals, containing 1H, 9Be, 11B, 13C, 14N, 17O, 19F, 23Na, 25Mg, 27Al, 29Si, 31P, 33S, and 35Cl nuclei. The considered radicals provide 241 theoretical hfcc values, which are compared with 174 available experimental ones. The geometries of the studied systems are obtained by theoretical optimization using the same functional and basis set with which the hfccs were calculated. Regression analysis is used as a basic and appropriate methodology for this kind of comparative study. From this analysis, we conclude that DFT predictions of the hfccs are reliable for B3LYP/TZVP and B3LYP/EPR-III combinations. Both functional/basis set scheme are the more useful theoretical tools for predicting hfccs if compared to other much more expensive methods.     

Density functional theory study of 14N isotropic hyperfine coupling constants of organic radicals

Nitrogen hyperfine coupling constants (hfccs) of organic radicals have been calculated by density functional theory (DFT) methodology. The capability of the B3LYP functional, combined with 6-31G*, TZVP and EPR-III basis sets, to reproduce experimental nitrogen coupling constant data has been analyzed for 109 neutral, cationic and anionic radicals, all of them containing at least one nitrogen atom. The results indicate that the selection of the basis set plays an important role in the accuracy of DFT calculations of hfccs, mainly in relation with the composition of the primitive functions and the quantum number of those functions. The main conclusion obtained is the high reliability of the scheme B3LYP/6-31G* for the prediction of nitrogen hfccs with very low computational cost.     

Density functional theory study of indirect nuclear spin-spin coupling constants with spin-orbit corrections

This work outlines the calculation of indirect nuclear spin-spin coupling constants with spin-orbit corrections using density functional response theory. The nonrelativistic indirect nuclear spin-spin couplings are evaluated using the linear response method, whereas the relativistic spin-orbit corrections are computed using quadratic response theory. The formalism is applied to the homologous systems H2X (X=O,S,Se,Te) and XH4 (X=C,Si,Ge,Sn,Pb) to calculate the indirect nuclear spin-spin coupling constants between the protons. The results confirm that spin-orbit corrections are important for compounds of the H2X series, for which the electronic structure allows for an efficient coupling between the nuclei mediated by the spin-orbit interaction, whereas in the case of the XH4 series the opposite situation is encountered and the spin-orbit corrections are negligible for all compounds of this series. In addition we analyze the performance of the density functional theory in the calculations of nonrelativistic indirect nuclear spin-spin coupling constants.     

The spin polarization model for hyperfine coupling constants

Summary The simple spin polarization model for calculation of the spin densities that determine hyperfine coupling constants in free radicals is examined. Spin-unrestricted approaches, both without and with removal of spin contamination, are discussed and compared with spin-restricted treatments. Basis set design and electron correlation effects are also considered. Calculations on small pi radicals are presented to illustrate the arguments. Explanations are advanced for why some of the simpler treatments seem to work better than might be expected.     

Density functional theory and Hartree–Fock-density functional theory calculations of O, S, and Ge quadrupole coupling constants

The performance of several density functional theory and Hartree–Fock density functional theory methods in conjunction with Pople type bases for the calculation of ¹⁷O, ³³S, and ⁷³Ge quadrupole coupling constants in gaseous state molecules was investigated.Assessment of the several models was made by linear regression analysis of the calculated gradient of the molecular electric field versus the experimental nuclear quadrupole coupling constant (NQCCs). Calculations for oxygen on six molecules with the B3LYP/6-311++G(3df,3p) model yield a residual standard deviation of 0.057 MHz (1.4%); for sulfur on 12 molecules with the B3LYP/6-311G(3df,3p) model, 0.42 MHz (1.8%); and for germanium on nine molecules with the B3P86/6-311G(2d) model, 0.83 MHz (1.0%).In the case of germyl acetylene, our calculations indicate that the experimental NQCC reported some time ago by Thomas and Laurie [J. Chem. Phys. 44 (1966) 2602] was incorrectly assigned with respect to algebraic sign.Predictions are made of the ¹⁷O and ³³S NQCCs in furan, 4H-pyran-4-one, 4H-pyran-4-thione, and 4H-thiapyran-4-thione; and of the ⁷³Ge NQCC in germyl bromide.     

13C hyperfine coupling constants in o-benzosemiquinones

The ¹³C hyperfine splitting constants of the tetrachloro-o-benzosemiquinone radical anion are measured for naturally occurring ¹³C nuclei in all the possible positions in the molecule. Their assignment is based on the linewidth analysis of the single hyperfine components and this is discussed with reference to the reported spin density distribution in o-semiquinones.     

NDDO MO calculations: isotropic hyperfine coupling constants and nuclear spin-spin coupling constants

The nonempirical NDDO MO method in its unrestricted form has been used to evaluate isotropic hyperfine coupling constants and nuclear spin-spin coupling constants. Satisfactory agreement with INDO and experimental results is obtained.     

A theoretical study of nuclear spin coupling constants and hyperfine coupling constants of se-heterocyclics

MO calculations based on the finite perturbation theory in the INDO approximation have been carried out on selenophene, eighteen of its monosubstituted derivatives and benzo (b)selenophene. The calculated nuclear spin coupling constants satisfactorily reproduce signs, magnitudes, internal orders and some trends of the experimental values. Comparison of different ZDO calculations provides information on the relative importance of σ and π pathways for the various coupling constants in selenophene and benzo(b)selenophene. Unrestricted Hartree-Fock calculations at the INDO level have been performed on the radical anions of dibenzoselenophene and 2,1,3-benzoselenadiazole, the phenoselenazine radical cation, the phenoselenazine neutral radical and the phenoselenazine nitroxide. The isotropic hyperfine coupling constants have been found to be generally in satisfactory agreement with experiment.     

Theoretical calculations of hyperfine coupling constants for muoniated butyl radicals

The hyperfine coupling constants (HFCCs) of all the butyl radicals that can be produced by muonium (Mu) addition to butene isomers (1- and 2-butene and isobutene) have been calculated, to compare with the experimental results for the muon and proton HFFCs for these radicals reported in paper II (Fleming, D. G.; et al. J. Phys. Chem. A 2011, 10.1021/jp109676b) that follows. The equilibrium geometries and HFCCs of these muoniated butyl radicals as well as their unsubstituted isotopomers were treated at both the spin-unrestricted MP2/EPR-III and B3LYP/EPR-III levels of theory. Comparisons with calculations carried out for the EPR-II basis set have also been made. All calculations were carried out in vacuo at 0 K only. A C-Mu bond elongation scheme that lengthens the equilibrium C-H bond by a factor of 1.076, on the basis of recent quantum calculations of the muon HFCCs of the ethyl radical, has been exploited to determine the vibrationally corrected muon HFCCs. The sensitivity of the results to small variations around this scale factor was also investigated. The computational methodology employed was "benchmarked" in comparisons with the ethyl radical, both with higher level calculations and with experiment. For the β-HFCCs of interest, compared to B3LYP, the MP2 calculations agree better with higher level theories and with experiment in the case of the eclipsed C-Mu bond and are generally deemed to be more reliable in predicting the equilibrium conformations and muon HFCCs near 0 K, in the absence of environmental effects. In some cases though, the experimental results in paper II demonstrate that environmental effects enhance the muon HFCC in the solid phase, where much better agreement with the experimental muon HFCCs near 0 K is found from B3LYP than from MP2. This seemingly better level of agreement is probably fortuitous, due to error cancellations in the DFT calculations, which appear to mimic these environmental effects. For the staggered proton HFCCs of the butyl radicals exhibiting no environmental effect in paper II, the best agreement with experiment is consistently found from the B3LYP calculations, in agreement also with benchmark calculations carried out for the ethyl radical.     

Density functional restricted-unrestricted approach for nonlinear properties: application to electron paramagnetic resonance parameters of square planar copper complexes

The density functional restricted-unrestricted approach for treatments of spin polarization effects in molecular properties using spin restricted Kohn-Sham theory has been extended from linear to nonlinear properties. It is shown that the spin polarization contribution to a nonlinear property has the form of a quadratic response function that includes the zero-order Kohn-Sham operator, in analogy to the lower order case where the spin polarization correction to an expectation value has the form of a linear response function. The developed approach is used to formulate new schemes for computation of electronic g-tensors and hyperfine coupling constants, which include spin polarization effects within the framework of spin restricted Kohn-Sham theory. The proposed computational schemes are in the present work employed to study the spin polarization effects on electron paramagnetic resonance spin Hamiltonian parameters of square planar copper complexes. The obtained results indicate that spin polarization gives rise to sizable contributions to the hyperfine coupling tensor of copper in all investigated complexes, while the electronic g-tensors of these complexes are only marginally affected by spin polarization and other factors, such as choice of exchange-correlation functional or molecular structures, will have more pronounced impact on the accuracy of the results.     

A semi-empirical approach to the estimation of ESR isotropic hyperfine coupling constants in aromatic radicals

Using a generalised product wave function, an expression is given for the isotropic hyperfine coupling constant at a given atom in an aromatic -radical. By a consistent scheme of approximation the expression is cast in a form in which the coupling constant at a given atom in the radical can be evaluated from the results of a Hückel calculation, provided that certain integrals are known. A scheme for assigning and relating these integrals is given, coupling constants are calculated for ¹³C, ¹⁴N, ¹⁷O and ¹⁹F atoms, and the calculations compared with experiment.

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Zusammenfassung Bei Verwendung einer Produktwellenfunktion wird ein Ausdruck für die isotrope Hyperfeinkopplungskonstante eines Atomes in einem aromatischen -Radikal angegeben. Durch ein konsistentes Näherungsschema wird der Ausdruck in eine Form gebracht, bei der die Kopplungskonstante eines Atoms im Radikal aus Resultaten einer Hückelrechnung ausgewertet werden kann, vorausgesetzt, daß gewisse Integrale bekannt sind. Ein Schema, um diese Integrale zu kennzeichnen und miteinander in Beziehung zu setzen, wird angegeben, Kopplungskonstanten werden für ¹³C, ¹⁴N, ¹⁷O und ¹⁹F-Atome ausgerechnet und die Rechnungen mit dem Experiment verglichen.

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Résumé Calcul d'une expression pour la constante de couplage hyperfin isotrope sur un atome dans un radical aromatique à l'aide d'une fonction d'onde produit généralisé. A l'aide d'un schéma d'approximation cohérent cette expression est mise sous une forme telle que la constante de couplage sur un atome du radical peut être évaluée à partir des résultats d'un calcul de type Hückel, pourvu que certaines intégrales soient connues. On fournit un procédé pour déterminer et relier entre elles ces intégrales; les constantes de couplage pour ¹³C, ¹⁴N, ¹⁷O et ¹⁹F sont calculées et comparées aux données expérimentales.

     

Density functional theory calculation of indirect nuclear magnetic resonance spin-spin coupling constants in C(70)

We calculate NMR spin-spin coupling constants in the C70 fullerene by means of density functional theory. We show that using a hybrid density functional (B3LYP) and an adequate basis set (cc-pCVDZ-sd), excellent agreement with experimental values can be achieved for one-bond couplings. These benchmark calculations suggest that theoretical predictions of NMR spin-spin couplings can be extremely valuable for discerning structural information of fullerenes.     

Calculations of the isotropic hyperfine coupling constants in free radicals

For a number of free radicals the results of non-empirical (ab initio) and semi-empirical (INDO, DEPAC, CNDO/SP) calculations of the isotropic hyperfine coupling constants are compared.     

An omega technique study of proton hyperfine coupling constants

An extension of the -technique to open shell molecules is made, using the UHF formulation. Sample calculations are reported for a range of organic and radicals, ions and lowest triplet states. The agreement with experiment is as good as that given by semi-empirical methods. Annihilation of the next highest spin function is often sufficient to improve the wavefunction, although in some cases the value «S²»_ASA is still inacceptably large.

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Zusammenfassung Im Rahmen der UHF-Theorie wird die -Technik auf Moleküle mit offenen Schalen ausgedehnt. Die Übereinstimmung der Rechnungen für einige - und -Radikale, Ionen und Triplettzustände mit dem Experiment ist wie üblich bei semiempirischen Methoden. Abspaltung des nächsthöheren Spinanteils ist meistens ausreichend, obwohl in manchen Fällen. der (S ²)-Wert dann immer noch beträchtlich groß ist.

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Résumé Extension de la technique aux molécules à couches ouvertes dans le cadre de la méthode U.H.F. Des calculs iolustratifs sont données pour une série de radicaux et , d'ions et d'états triplets les plus bas. L'accord avec l'expérience est aussi bon que celui donné par les méthodes semi-empiriques. L'annihilation de la fonction de spin immédiatement supérieure est souvent suffisante pour améliorer la fonction d'onde, quoique dans certains cas la valeur S ² ASA soit toujours trop grande.

     

Theoretical investigation of the EPR hyperfine coupling constants in amino derivatives

The HFCCs of the radical cations of a series of amines have been determined at different levels of approximation including the CISD, QCISD, and CCSD ab initio correlated methods and density functional theory approaches employing the B3LYP, PBE0, BHandHLYP, TPSS, and BLYP exchange-correlation functionals. Although quantitative differences with respect to experimental data have been noticed, these are mostly systematic within a given class of N and H atoms. As a consequence, these different levels of theory are reliable in most cases to account for the substituent and structure effects on the HFCCs of amines. Linear regression fits have then been performed to reach quantitative agreement between the theoretical and experimental values. This has finally been substantiated by considering the EPR signal of the recently synthesized radical cations of two derivatives of [10-(4-aminophenyl)-9-anthryl]aniline as well as in confirming a recent assignment of the EPR signal of n-propylamine.     

Calculation of 14N hyperfine coupling constants by the INDO-MO method

The proportionality constant between the hyperfine splitting constant for ¹⁴N and the spin density calculated by the INDO-MO method has been redetermined using a larger sample of results. A revised value of 332 Gauss is suggested.     

Non-neighbour effects on hyperfine coupling constants in alternant hydrocarbon radicals

An improvement of the McConnell formula for the correlation of hydrogen coupling constants in alternant hydrocarbon ions is derived.The new formula is analogous to the one recently proposed by Colpa and Bolton and is obtained without introducing any charge effect but only considering, in the first order perturbation expansion, terms arising from hydrogen next nearest neighbour carbon p orbitals.

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Zusammenfassung Die McConnell-Formel für die Wasserstoff-Kopplungskonstante in alternierenden Kohlenwasserstoffionen wird verbessert. Die neue Formel ist ein Analogen der kürzlich von Colpa und Bolton vorgeschlagenen, wird aber ohne Einführung von Ladungseffekten erhalten. Sie ergibt sich vielmehr durch Hinzunahme der Glieder, die die der CH-Bindung benachbarten Kohlenstoff-p-Eigenfunktionen in erster Näherung berücksichtigen.

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Résumé La formule de McConnell pour les constantes de couplage hyperfin protonique dans les ions des hydrocarbures alternants est améliorée.La nouvelle formule est analogue à une autre proposée récemment par Colpa et Bolton; on l'obtient, sans introduire des effets de charge, seulement par inclusion des termes perturbateurs de premier ordre, dérivant des orbitales p des carbones adjacent à la liaison C-H considérée.

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We thank the Italian National Research Council (Chemistry Commitee, Research Group IV) for financial support. One of us (P.L.N.) is grateful to Sicedison S.p.A. for a grant.     

Understanding solvent effects on hyperfine coupling constants of cyclohexadienyl radicals

Quantum chemical calculations have been carried out to understand better solvent effects on the isotropic muon and proton hyperfine coupling constants in the C₆H₆Mu^• radical. Both polarizable continuum solvent models and explicit inclusion of water molecules into supermolecular complexes were used. Changes in the hyperfine couplings of in-plane hydrogen atoms are very small and difficult to discuss, partly due to relatively large experimental error bars. In contrast, the out-of-plane proton and muon hyperfine couplings exhibit more pronounced changes. These are partly due to structural changes of the radical and partly due to direct electronic polarization effects. Polarizable continuum solvent models agree well with experimental changes for benzene but overshoot the enhancement of the hyperfine couplings for water. Explicit inclusion of water molecules reduces this overestimated spin density increase and thereby tends to bring theory and experiment into closer agreement. The enhancement of the spin density on the out-of-plane hydrogen or muon atoms by the solvent environment is mainly due to an increased polarization of the singly occupied MO towards this side. Electronic Supplementary Material: Supplementary material is available in the online version of this article at dx.doi.org/10.1007/s00214-005-0680-x