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.     

Configuration interaction calculations on the propane radical cation,C3H 8 +

Summary Proton isotropic hyperfine coupling constants have been calculated for three low-energy nuclear conformations on the ground state potential surface of the propane cation, using a multireference singles and doubles configuration interaction (MR-SDCI) wave function. The lowest point found on the potential surface hadC _2v symmetry and the electronic wave function at this point had²B₂ symmetry. At this point, the largest isotropic coupling constant is calculated to be 88.6 G, which is in fair agreement with the experimental value of 98 G obtained in an SF₆ matrix at 4 K. No support is found for a long-bond ground state of lower symmetry thanC _2v . AnotherC _2v minimum on the ground state potential energy surface was found at which the wave function had² B ₁ symmetry. At this point, two large coupling constants of 198 G and 35 G were calculated. AC _2v stationary point was also found on the ground state potential surface at which the wave function had² A ₁ symmetry. At this point, couplings of 86 G and 25 G were obtained. None of these agree closely with the other experimental result of couplings at both 100–110 G and 50–52.5 G which was obtained in freon matrices. It is suggested that the latter spectra might correspond to a dynamical average of two distorted² A' states inC _s symmetry.     

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.     

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     

MC/AM1-SCI study of the effect of hydration shells on the nitrogen hyperfine coupling constant of the (CH3)2NO radical in aqueous solution

A combination of Monte Carlo (MC) simulation and semi-empirical AM1 molecular orbital (MO) singly-excited configuration interaction (SCI) calculation was applied to dimethyl nitroxide (DMNO) in aqueous solution and the solvent effect on the hyperfine coupling constant (HFCC) of nitrogen in DMNO was analyzed. During the MC simulation, 100 solution structures were picked up. For each solution structure, the DMNO–(H₂O)_n (n=1–40) clusters were cut out and the AM1-SCI calculation was applied to the cluster as a supermolecule. The HFCC of nitrogen was obtained by averaging the 100 solution structures. The H₂O molecules included in the supermolecule were determined by two different types of selection and the contribution of H₂O molecules to the HFCC was well elucidated in relation to the hydration shell structure.     

丁烯和丁烷自由基阳离子的分子结构和超精细结构的 理论研究

用密度函数理论B3LYP方法和6-31G(d,p),6-311G(d,p)及6-311+G(d,p)基组，分别对1-C4H^+~8,2-C4H^+~8和C4H^+~10进行了构型优化和频率分析计算，预言1-C4H^+~8具有非平面构型，与以往报道的从头算和密度函数理论计算结果不同。在各自由基阳离子的B3LYP构型上，进行了B3LYP、MP2及MRSDCI方法的超精细偶合常数计算，得到了比以往更好的结果，特别是MP2/B3LYP计算值是至今与实验值符合得最好的理论计算结果。     

Study of influences of various excitation classes onab initio calculated isotropic hyperfine coupling constants

Summary Reliable prediction of the isotropic hyperfine coupling constantA _iso is still a difficult task forab initio calculations. Strong dependence on the method employed for its calculation has been found. Within a CI ansatzA _iso is considerably affected by the excitation classes taken into account within the CI calculation. In the present work the influence of various excitation classes onA _iso is examined. Calculations including all single, double, triple and a large part of the quadruple excitations are performed and the individual effects of the excitation classes are studied. It is found that the surprisingly good agreement found for S-CI treatments is due to large error cancellations. The importance of higher than double excitations arises from their indirect influence on the single excitations.     

The mechanism of spin polarization in aromatic free radicals

 The spin-polarization mechanism in aromatic systems is analyzed with reference to the prototypical phenoxyl, cyclohexadienyl and benzyl radicals. In particular, a decomposition into “first-order” and “second-order” contributions is proposed, which helps to rationalize the different nature of the spin density for atoms in α or in β positions with respect to the radical center. The different weights of the two contributions are discussed on the basis of Hartree–Fock and density functional computations. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 29 June 2000     

Electronic states of radical cations of all-trans oligo[methyl(phenyl)silane]

The electronic states of radical cations of oligo[methyl(phenyl)silane] (OMPSi⁺) with all trans form (n = 2-8, where n is number of monomer unit of OMPSi) have been investigated by means of density functional theory (DFT) calculation to shed light on the mechanism of hole-transport in oligosilanes with phenyl group in the side chain. For the shorter oligomers (n < 3), the hole (unpaired electron) was widely distributed equivalently in both the Si main and side chains (55% for the Si main chain and 45% for the side chain). The distribution of hole on the chains was largely changed as a function of chain lengths (n). Ratios of the hole distribution on the main and side chains became almost constant at n = 7-8: 70% of spin density was distributed on the Si-main chain and 30% on the side-chain, which is much different from that of oligo(dimethyl)silane (the spin density on the methyl side chain was less than 3% of spin density). From these results, it was concluded that the hole in OMPSi⁺ can transfer by the mechanism for both intermolecular and the intrachain hole-transfer processes.     

Theoretical study of the thermal interconversion mechanism between the norbornadiene and quadricyclane radical cations

Geometry optimizations at the UHF/6-31G^* and UMP2/6-31G^* levels of theory were performed to find the transition state in the interconversion between norbornadiene (N) and quadricyclane (Q) radical cations. Two transition structures, TS^+·₁ and TS^+·₂, were obtained which have C₁ and C₂ symmetry, respectively. Vibrational analysis at the UHF and UMP2 levels of theory and IRC calculation showed that TS^+·₁ is the true transition state connecting N^+· and Q^+·, while TS^+·₂ is a second order saddle point.     

A theoretical study of multinuclear coupling constants in pyrazoles

The 243 coupling constants of eight N-R-pyrazoles [R=H, CH3, C6H5, COCH3, NH2, NO2, SO2CF3, Si(CH3)3] have been calculated and compared with 131 experimental values. The agreement is good and can be used to estimate new couplings. The whole collection has been statistically analyzed.     

Chemical capture of an unprecedented oxatetramethyleneethane radical cation with a through-space electronic coupling

A photoinduced electron-transfer reaction of 2,2-dianisyl-4-isopropylidene-3,3-dimethylcyclobutanone (5) in acetonitrile containing molecular oxygen or water gave 4,4′-dimethoxybenzophenone (7) and 2,2-dianisyl-4-isopropylidene-5,5-dimethylhydrofuran-3-one (8), demonstrating the chemical capture of an unprecedented oxatetramethyleneethane-type radical cation intermediate (6⁺). A density functional theory calculation suggests through-space electronic coupling between the tetramethylallyl and joined dianisylmethyl carbonyl subunits in 6⁺.     

Extensive theoretical study on the low-lying electronic states of silicon monofluoride cation including spin-orbit coupling

Ab initio calculations on the low-lying electronic states of SiF+ are performed using the internally contracted multireference configuration interaction method with the Davidson correction and entirely uncontracted aug-cc-pV5Z basis set. The effects of spin-orbit coupling are accounted for by the state interaction approach with the full Breit-Pauli Hamiltonian. The entire 23 Omega states generated from the 12 valence Lambda-S states, which correlate with the first dissociation channel are studied for the first time. Good agreement is found between the calculated results and the available experimental data. The spin-orbit coupling effects on the potential energy curves and spectroscopic properties are studied. Various curve crossings are revealed, which could lead to the predissociation of the a3Pi, A1Pi, and (2)3Sigma+ states and the predissociation pathways are analyzed based upon the calculated spin-orbit matrix elements. The calculated ionization potentials of the ground-state SiF to a few states of SiF+ are in good agreement with the available experimental measurements. Moreover, the transition dipole moments of the dipole-allowed transitions and the transition properties for the A3Pi0+ -X1Sigma+ 0+ and B3Pi1-X1Sigma+ 0+ transitions are predicted, including the Franck-Condon factors and the radiative lifetimes.     

A Free Radical Hyperfine Coupling Constants Calculation Using the S-P Indo-Mo Method

We apply our newly developed s-p separation model INDO-MO theory to the open shell problem of organic free radicals and radical ions. The linear correlation analysis between spin densities and the related hyperfine coupling constants is preformed. To show the generality of this method for various elements, we select different sets of free radicals which contain ¹H, ¹³C, ¹⁴N, ¹⁷O and ¹⁹F for our MO calculation. We chose the appropriate values of β^α_2P and β^π_2P (the separated bond parameters calculated by the method described in our previous publication) and we also calibrated new geometrical parameters (bond distances and bond angles). With these new sets of parameters, many types of calculations were performed for comparison. We also compare our results with the corresponding results of the INDO-MO method of Pople et al. In all cases involving ¹H, ¹³C, ¹⁴N, ¹⁷O and ¹⁹F our MO method gives better results. This evidence also proves that our “s-p separation model INDO-MO method” is a reasonable and useful MO method.     

On the tautomerism of pyrazolones: the geminal J[pyrazole C-4,H-3(5)] spin coupling constant as a diagnostic tool

The tautomerism of pyrazolones unsubstituted at position 3(5) has been investigated by ¹³C- and ¹H NMR spectroscopic methods. Apart from chemical shift considerations and NOE effects the magnitude of the geminal ²J[pyrazole C-4,H3(5)] spin coupling constant permits the unambiguous differentiation between 1H-pyrazol-5-ol (OH) and 1,2-dihydro-3H-pyrazol-3-one (NH) forms. Whereas 1H-pyrazol-5-ols and 2,4-dihydro-3H-pyrazol-3-ones (CH-form) exhibit ²J values of approximately 9-11 Hz, in 1,2-dihydro-3H-pyrazol-3-ones this coupling constant is considerably reduced to 4-5 Hz. This can be mainly attributed to the removal of the lone-pair at pyrazole N−1 in the latter due to protonation or alkylation. According to the data obtained, 2-substituted 4-acyl-1,2-dihydro-3H-pyrazol-3-ones exist predominantly as pyrazol-5-ols in CDCl₃ or benzene-d₆ solution, whereas in DMSO-d₆ also minor amounts of NH tautomer may contribute to the tautomeric composition. 2,4-Dihydro-2-phenyl-3H-pyrazol-3-one (1-phenyl-2-pyrazolin-5-one) exists in benzene-d₆ solely in the CH-form, in CDCl₃ as a mixture of CH and OH-form, whereas in DMSO-d₆ a fast equilibrium between OH and NH isomer (with the former far predominating) is probable. For 11 compounds, including neutral and protonated molecules, we have calculated at the B3LYP/6-311++G** level, the ²J(¹H,¹³C) coupling constants which are in good agreement with those measured experimentally.     

Synthesis of bifluorenes via cobalt halide radical coupling

Reaction of in situ generated lithium fluorenide salts with cobalt chloride results in formation of the corresponding bifluorenes. The scope of fluorenes that can be coupled include those containing substituents amenable to polymerization for application to poly(bifluorene) synthesis and alkyl substituted fluorenes for use in the preparation of bimetallic transition metal complexes. Based on experiments using a radical trap, the reaction mechanism involves reduction of cobalt and subsequent fluorenyl radical coupling. Overall, this study demonstrates a simple and effective method for preparation of hindered tertiary and quaternary C-C bonds using a readily available and inexpensive coupling agent.     

Intramolecular nucleophilic capture of radical cations by tethered hydroxy functions

A range of systems bearing hydroxy functions tethered to the molecular framework gives rise to a family of interesting radical cations, 5⁺-11⁺, upon electron transfer to photo-excited cyanoaromatics. Geraniol (5), nerol (6), citronellol (7), chrysanthemol (8), homochrysanthemol (9), trans-1-o-hydroxyphenyl-2-phenylcyclopropane (10), and endo-5-hydroxymethylnorbornene (11), generate a series of mono-, bi-, or tricyclic ethers via a series of four- to seven-membered transition states. Two of the radical cations, 5⁺ and 6⁺, undergo tandem cyclizations where 1,5- and/or 1,6-C-C cyclizations precede nucleophilic capture.     

Use of electrospray ionization mass spectrometry for the investigation of radical cation chain reactions in solution: detection of transient radical cations

Electrospray ionization mass spectrometry (ESI-MS) coupled to a microreactor is an excellent tool for the investigation of reactions in solution. Here, we report the first results of our investigations into preparatively interesting electron-transfer-initiated chain reactions in solution which proceed via radical cations as reactive intermediates. The tris(p-bromophenyl)aminium hexachloroantimonate (1)-mediated [2+2] cycloaddition of trans-anethole (2) to give 1,2-bis(4-methoxyphenyl)-3,4-dimethylcyclobutane (3) was investigated. The reaction proceeds as a radical cation chain reaction via transient intermediates 2 ⁺ and 3 ⁺ that could be detected and characterized unambiguously directly in the reacting solution by ESI-MS/MS. The identity of the intermediates was confirmed by comparison with authentic MS/MS spectra of 2 ⁺ and 3 ⁺ obtained by atmospheric pressure chemical ionization mass spectrometry (APCI-MS). In addition, substrate and product can be monitored easily in the reacting solution by APCI-MS.Part of this work was presented at the 36th Conference of the German Society for Mass Spectrometry (DGMS).     

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.     

A simple method for quantitative estimation of C-H bond lengths in hydrocarbon radical cations

A quantitative correlation between deviations of the C-H bond lengths of hydrocarbon molecules during their adiabatic single ionization and isotropic hyperfine coupling constants with protons of their primary radical cations (RC) was established. A simple method for estimation of the C-H bond lengths of hydrocarbon RC was proposed on the basis of the correlation found. Specific features of the structure of the RC of methane and severaln-alkanes of the general formula [H^*(CH_{2 n} H^*]⁺,n = 0 to 12, were analyzed. A widely used empirical rule, according to which deprotonation of hydrocarbon RC during the ion-molecular process is determined by the proton possessing the highest spin density, was refined and geometrically substantiated.