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.     

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.     

On quantum-chemical estimates of constants of isotropic hyperfine coupling with protons in free radicals

A scheme of consitent quantum-chemical calculations of constants of isotropic hyperfine coupling (IHFC) with protons (a _H ^iso ) in free radicals is considered for the case where the spin populations ρ_s ^H are determined in the basic set of symmetrically orthogonalized atomic orbitals taking model σ-and π-electron fragments as an example. The competence of using two coefficients of proportionalityK(H) when estimating the proton IHFC constants by semiempirical quantum-chemical methods was demonstrated. Theoretical substantiation of empirical values of the above coefficients previously used is revealed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 245–249, February, 1999.     

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.     

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.

     

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.     

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.     

Ab initio calculations of isotropic hyperfine coupling constants in β-ketoenolyl radicals

Ab initio unrestricted Hartree–Fock (UHF ), unrestricted second-order Møller–Plesset (UMP 2) perturbation, unrestricted coupled cluster (UCCD ), and unrestricted quadratic configuration interaction (UQCISD ) calculations have been performed on the organic radicals CH₃, CH₃CH₂, CH₂CHCH₂, CH₃CHCOO^?, HCOCHCOH, CH₃COCHCOH, CH₃COCHCOCH₃, and CH₃COC(CH₃)COCH₃, using double-zeta and split-valence-plus-polarization basis sets. These radicals are derived from common organic ligands and have been observed in recent experimental work on tris(β-ketoenolato)cobalt(III) complexes. Their geometry has been optimized at the UHF level using the two mentioned basis sets. From these calcuations, values for the isotropic hyperfine coupling constants at the hydrogen atoms are predicted and compared with the experimental results. The usefulness of semiempirical extrapolations based on limited basis sets and treatment of electron correlation effects is carefully analyzed in the examples considered. © 1994 John Wiley & Sons, Inc.     

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.     

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     

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.     

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.     

Zero-point vibrational corrections to isotropic hyperfine coupling constants in polyatomic molecules

The present work addresses isotropic hyperfine coupling constants in polyatomic systems with a particular emphasis on a largely neglected, but a posteriori significant, effect, namely zero-point vibrational corrections. Using the density functional restricted-unrestricted approach, the zero-point vibrational corrections are evaluated for the allyl radical and four of its derivatives. In addition for establishing the numerical size of the zero-point vibrational corrections to the isotropic hyperfine coupling constants, we present simple guidelines useful for identifying hydrogens for which such corrections are significant. Based on our findings, we critically re-examine the computational procedures used for the determination of hyperfine coupling constants in general as well as the practice of using experimental hyperfine coupling constants as reference data when benchmarking and optimizing exchange-correlation functionals and basis sets for such calculations.     

Structure and hyperfine coupling constants of radicals in muon-irradiated single-crystal naphthalene

We have observed muonated cyclohexadienyl-type radicals in a naphthalene single crystal, using the standard transverse-fieldSR technique. Two types of radicals were found, corresponding to muonium addition at the and positions. Owing to the crystal field, the isotropic hyperfine coupling constants show large shifts from the solution values, and there is significant anisotropy in the hyperfine tensors. The results for the radicals are similar to those observed for protonated-hydronaphthyl radicals, but isotope effects are evident. The radicals, whose protonated analogues have not been fully studied, show a more pronounced localized character. Based on the hyperfine tensor directions and geometrical considerations, we have assigned each radical to a specific muon site within the crystal.     

Evaluation of a new procedure for quantum-chemical estimates of constants of isotropic hyperfine coupling with protons in free radicals

A new procedure for quantum-chemical estimates of the constants of isotropic hyperfine coupling (IHFC) with protons using the orbital spin populations calculated in the basis set of symmetrically orthogonalized (according to Löwdin) atomic orbitals is tested taking 16 well-studied simplest π-electron and σ-electron radicals as examples. The most probable reasons for and possible ways of correcting large deviations of calculated IHFC constants from experimental values are considered. The efficiency of the semiempirical MNDORU scheme, which makes it possible to consistently estimate the delocalization and spin-polarization contributions to the constants of IHFC with protons in free radicals, is demonstrated.     

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.     

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.     

Unrestricted hartree fock wave functions and hyperfine coupling constants in aromatic radicals

It is shown that a simple expression, differing from the one currently used, must be adopted when calculating electron spin densities from unrestricted H.F. wave functions in connection with the prediction of proton hyperfine couplings in aromatic free radicals. The proposed formula gives results which are almost identical to those one obtains after complete projection of the unwanted parts of the unrestricted function.

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Zusammenfassung Es wird gezeigt, daß sich bei der Berechnung von -Elektronen-Spindichten mit Hilfe uneingeschränkter Hartree-Fock-Funktionen im Zusammenhang mit der Vorhersage von Protonen-Hyperfeinkopplungskonstanten in aromatischen Radikalen ein einfacher, von dem häufig verwandten abweichender Ausdruck ergibt. Die vorgeschlagene Formel führt zu Ergebnissen, die fast mit denen identisch sind, die man nach vollständiger Projektion der unerwünschten Anteile der uneingeschränkten Funktion erhält.

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Résumé Une expression simple, différant de celle couramment admise, est adopté pour le calcul des densités de spin -électronique par les fonctions H.F. non-restreintes, afin de prédire les couplages hyperfins protoniques dans les radicaux benzéniques. Les résultats sont presqu'identiques à ceux de l'élimination, par projection, des parties à spin faux de la fonction nonrestreinte.