Molecular orbital study of proton hyperfine splitting constants in H 2CN radical (original) (raw)
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Theoretica Chimica Acta, 1971
The fl proton hyperfine splitting constants of a large number of positive, negative, and neutral n radicals, have been examined in term of the Heller-McConnell relation a n = Boc cos28 whose validity is discussed. B is taken as a function of the energy of the singly occupied orbital and values are calculated by first order perturbation theory for the cases of a methyl, methylene, and dimethylene group attached to the n system. Substantial agreement is found between theory and experiment indicating the correctness of the postulated cause of the B behaviour.
Non-neighbour effects on hyperfine coupling constants in alternant hydrocarbon radicals
Theoretica Chimica Acta, 1963
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 COL~A 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. Die McConnell-Formel fiir die Wasserstoff-Kopphngskonstante in alternierenden Kohlenwasserstoffionen wird verbessert. Die neue Formel ist ein Analogon der kiirzlich yon Cor,I,A und Bor.To~ vorgeschlagenen, wird aber ohne Einfiihrung yon Ladungseffekten erhalten. Sic ergibt sich vielmchr durch Hinzunahme der Glicder, die die der CH-Bindung benaehbarten Kohlenstoff-p-Eigenfunktionen in erster N~therung beriicksichtigen. La formule de 3s pour les constantes de couplage hypcrfin protonique dans les ions des hydrocarbures alternants est am61ior6e. La nouvclle formule est analogue & une autre propos~e r@cemment par CoL~A et BOLTON; on l'obtient, sans introduire des effets de charge, seulement par inclusion des termes perturbateurs de premier ordre, d@rivant des orbitales p des carbones adjacent s la liaison C-H eonsid~r6e.
Coupled-cluster studies of the hyperfine splitting constants of the thioformyl radical
The Journal of Chemical Physics, 2000
Hyperfine splitting constants ͑hfs͒ of the X 2 AЈ electronic ground state of the thioformyl radical ͑HCS͒ have been determined at the coupled-cluster level with single, double, and perturbatively applied connected triple excitations ͓CCSD͑T͔͒ using 39 basis sets. Variation of the CCSD͑T͒ hyperfine splittings with basis set was ascertained using a fixed geometry, optimized at the CCSD͑T͒ level with Dunning's correlation-consistent polarized valence quadruple-basis set ͑cc-pVQZ͒. Pople basis sets, 6-311Gϩϩ(2d,2p) and 6-311Gϩϩ(3d f ,3pd), give 1 H isotropic coupling constants (1 H A iso) in good agreement with the experimental vibrationally averaged value of 127.4 MHz, deviating by 5.5 and 9.3 MHz, respectively. Dunning's valence correlation-consistent basis sets ͑cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, aug-cc-pVTZ, cc-pVQZ, aug-cc-pVQZ͒ deviate 6.4 MHz ͑aug-cc-pVQZ͒ to 14.9 MHz ͑cc-pVDZ͒ from the experimental value. The correlation-consistent core valence analogues of these sets give very similar values with deviations from experiment of 7.4 MHz ͑cc-pCVQZ͒ to 14.2 MHz ͑cc-pCVDZ͒. A direct comparison with the vibrationally averaged experimental value is not precisely possible since the hyperfine splittings are strongly geometry dependent and all theoretical predictions refer to the equilibrium geometry. Small Pople basis sets ͑3-12G, 6-31G, and 6-311G͒ give the worst results, deviating by 49.5, 34.1, and 31.8 MHz, respectively. All CCSD͑T͒ 1 H A iso values fall below the experimental value. The 13 C and 33 S hyperfine splittings are not known experimentally, but the equilibrium values are predicted here to be 274.7 MHz (13 C) and 21.7 MHz (33 S) at the cc-pCVQZ CCSD͑T͒ level of theory. Significantly different values are predicted by density functional theory ͑DFT͒ for the 13 C and 33 S hyperfine splittings.
Journal of the American Chemical Society, 1975
The 13C hyperfine splittings have been determined for the benzyl radical and the toluene radical anion each enriched in the 1 and 7 positions with carbon-13. The hfs in gauss are: benzyl, I-I3C = (-) 14.45, 7-I3C = (+) 24.45: toluene radical anion, I-l3C = (-) 4.26, 7-13C = (-) 0.78. The proton and IJC hfsc's have been calculated by means of the INDO method for both the symmetric (S) and antisymmetric (A) states of the toluene anion radical at their respective energy minimized geometries. By a least-squares fit of these calculated results to the experimental hfs, the wave function of the radical has been found to consist of approximately 20% S character and 80% A character at-95'. About half of this mixing results from vibronic interaction (1 1.3% S character) and the remainder is due to thermal population of excited states. The observed energy difference between the first two vibronic states is 225 crn-l, in good agreement with previous work.
Theoretical study of the dimethylamino radical (CH3)2N and its protonated cation (CH3)2NH+
Chemical Physics, 1994
In the present work the dimethylamino radical ((CH 3) 2 N) and its protonated cation ((CH 3 hNH +) are investigated by means of ab initio methods. The geometries of various conformations of both compounds are obtained with UMP2/6•31 G** calculations, while the hyperfine structure and its dependence on the geometry is studied using the MRD-Cl/BK method. The two molecules are compared to study the inftuence of the protonation on geometry and hyperfine structure. The effects of the rotational barriers on the hyperfine structures of (CH 3 hN, (CH 3 CH 2 hN and ((CH 3 hCHhN will be discussed.
Hypercoordinated XHn+1 radicals for first- and second-row atoms. A valence bond analysis
Journal of the American Chemical Society, 1989
A theory of hypercoordination is developed using the valence bond (VB) curve-crossing diagram model and applied to XH,,' radicals that are generated by hydrogen atom attachment to a normal-valent XH, molecule. Hypercoordinated XH,+I radicals fall into two broad classes of valence species: those that can be described by a correlation and avoided crossing of their two Lewis curves, e.g., SiH,, and those that require at least one additional curve-termed the intermediate curve-such as PH4. The Lewis curves correspond to the electron-pairing schemes of the normal-valent constituents in the exchange process H' + XH, - [XH,,,] -H,X + H'. The intermediate curve possesses an (no*) excited character and mixes into the Lewis curves, mainly at the hypercoordinated region. This mixing endows XH,+' with additional stability and a new electronic character . A third class of XH,+I radicals exists, in which the two Lewis curves are crossed by an intermediate Rydberg curve (n -R excitation) which provides an energy well to house a Rydberg XH,+I radical . The hypercoordination capability of an atom X depends on the X-H bond of the normal-valent XH, and on the presence of a lone pair on X. The weaker the X-H bond, the more stable the XH,,,, species relatice to its normal-valent constituents XH, +
Potential energy surface and proton HFI constants of the cyclopentane radical cation
Journal of Structural Chemistry, 2012
According to the data of UB3LYP/6-31G* and UMP2/cc-pVTZ calculations, the adiabatic potential energy surface of the cyclopentane radical cation is very intricate and combines six types of stationary structures of C s and C 2 symmetry. Ten equivalent C s structures with the totally symmetric electronic state (C s (2 Ac)) correspond to global minima. Conformational transitions between the global minima occur along the inversion and pseudorotation coordinates, for each pair of minima the conformational transition occurring in one stage (through the only transition state). The inversion barrier is a2 kcal/mol; pseudorotation barriers are a4-8 kcal/mol. The structure of the potential surface provides the interpretation of the EPR data as a result of dynamic averaging over 20 C s (2 Ac) and C 2 (2 A) stationary structures.
The Journal of Physical Chemistry, 1993
The structure and EPR parameters of dihydronitrosyl radical HzNO have been investigated by highly correlated ab-initio methods. The relative stabilities of planar and pyramidal structures have been analyzed in detail, taking also into account the effect of small-amplitude vibrations perpendicular to the inversion motion. Vibrational averaging of hyperfine coupling constants has been computed by a quantum-mechanical treatment based on the vibrational adiabatic zero curvature approximation. The general picture emerging from this study, substantiated by several checks, consists in a quasi-planar molecule with a nearly free inversion motion for out-of-plane angles as large as 30'. Due to compensation of different terms, vibrational averaging gives results very close to those obtained from a static treatment at an out-of-plane angle of about 20'. An equally important outcome of this work is the introduction of a general and reliable ab-initio strategy for the study of magnetic properties in nonrigid radicals.
Hyperfine structure in the H2+ and HD+ molecular ions at order mα6
Physical Review A, 2020
A complete effective Hamiltonian for relativistic corrections at orders mα 6 and mα 6 (m/M) in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels and spin-spin scalar interactions contributing to the hyperfine splitting, both of which had been studied previously. In addition, corrections to electron spin-orbit and spin-spin tensor interactions are newly obtained. This allows improving the hyperfine structure theory in the hydrogen molecular ions. Improved values of the spin-orbit hyperfine coefficient are calculated for a few transitions of current experimental interest. I. INTRODUCTION High-resolution spectroscopy of the hydrogen molecular ions H + 2 and HD + may contribute significantly to the determination of fundamental constants such as the proton-electron mass ratio m p /m e [1]. A pure rotational transition in HD + has recently been measured with a relative uncertainty of 1.3 × 10 −11 [2]. The experimental accuracy of ro-vibrational transition frequencies is expected to reach a few parts per trillion in the near future using spectroscopy in the Lamb-Dicke regime [2-4] or in a Doppler-free geometry [5, 6]. While information on fundamental constants is obtained from comparison of spin-averaged transition frequencies with theoretical predictions, the hyperfine splitting of ro-vibrational lines also allows for precise tests of theory. So far, the hyperfine structure of H + 2 and HD + has been calculated within the Breit-Pauli approximation [7, 8], taking into account the anomalous magnetic moment of the electron. All terms at orders mα 4 and mα 5 are included, so that the theoretical accuracy of the hyperfine coefficients is of order α 2 ∼ 5 × 10 −5. Higherorder corrections to the largest coefficients, i.e. the spin-spin Fermi contact interaction, were later calculated in [9, 10], which allowed to get excellent agreement with available RF spectroscopy data in H + 2 [11] at the level of ∼ 1 ppm. The following step to improve the hyperfine structure theory is to evaluate higher-order corrections to the next largest coefficients, i.e. the electron spin-orbit and spin-spin tensor interaction, starting with relativistic corrections at the mα 6 order. With this aim, we derive in the present work the complete effective Hamiltonian for the hydrogen molecular ions at the mα 6 and mα 6 (m/M) orders, following the NRQED approach [12-14]. Then, we use it to calculate numerically the corrections to the electron spin-orbit interaction for a few transitions studied in ongoing experiments. The paper is organized as follows: in Secs. II and III, we recall the expression of the NRQED Lagrangian and associated interaction vertices. We then systematically derive the effective potentials, which are organized in three categories: tree-level interactions involving the exchange of a Coulomb or transverse photon (Sec. IV), terms due to retardation in the transverse photon exchange (Sec. V), and finally those coming from a seagull diagram with simultaneous exchange of two photons (Sec. VI). In Sec. VII, we collect our results to write the total effective Hamiltonian, separating the different types of interactions: spinindependent, electronic spin-orbit, spin-spin scalar and tensor interactions. Finally, in Sec. VIII we present numerical calculations of the spin-orbit interaction coefficient. II. NRQED LAGRANGIAN Natural (Lorenz-Heaviside) units (h = c = 1) are used throughout. We assume that e is the electron's charge and thus is negative, the elementary charge is then denoted by |e|.