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.     

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.     

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.     

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.     

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.     

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.     

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.     

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.

     

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.     

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.     

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     

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.     

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.     

An INDO investigation of the electronic structure and hyperfine coupling constants of the radicals HBO−, HCO and HCN−

The equilibrium geometry and hyperfine coupling constants in the isoelectronic radicals HBO^–, HCO and HCN^– have been calculated using the INDO method. The calculated coupling constants are in reasonable agreement with experiment for these -radicals, provided the geometry is optimised in the calculations.     

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.

     

Theoretical isotropic hyperfine coupling constants of third-row nuclei (29Si, 31P, and 33S)

In a previous paper (Hermosilla, L.; Calle, P.; Garcia de la Vega, J. M.; Sieiro, C. J. Phys. Chem. A 2005, 109, 1114), an adequate computational protocol for the calculation of isotropic hyperfine coupling constants (hfcc's) was proposed. The main conclusion concerns the reliability of the scheme B3LYP/TZVP//B3LYP/6-31G* in the predictions of hfcc's with low computational cost. In the present study, we gain insight into the behavior of the above functional/basis set scheme on nuclei of the third row, for which few systematic studies have been carried out up to the present date. The systems studied are neutral, cationic, anionic, localized, and conjugated radicals, containing (29)Si, (31)P, and (33)S nuclei. After carrying out a regression analysis, we conclude that density functional theory (DFT) predictions on the hfcc's of the third-row nuclei are reliable for B3LYP/TZVP by using an optimized geometry with B3LYP/6-31G* combination. By comparison with other much more computationally demanding schemes, namely, B3LYP/cc-pVTZ and B3LYP/cc-pVQZ, we conclude that the B3LYP functional in conjunction with the TZVP basis set is the most useful computational protocol for the assignment of experimental hfcc's, not only for nuclei of first and second rows, but also for those of the third row.