Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

An ab initio study of the nuclear spin-spin coupling constants in the second-row hydrides

Ab initio SCF perturbation theory calculations have been performed for the contact, orbital and dipolar contributions to the nuclear spin—spin coupling constants in A1H₃, SiH₄ PH₃, H₂S and HCl, using large, stable gaussian basis sets. The results for J(XH) are in reasonably good agreement with experiment, those for. J(HH) are rather less good.     

Temperature dependences of J(C,H) and J(C,D) in 13CH4 and some of its deuterated isotopomers

The nuclear spin—spin coupling constants J(C,H) and J(C,D) have been measured over the temperature range 200–370 K for the methane isotopomers ¹³CH₄, ¹³CH₃D, ¹³CHD₃ and ¹³CD₄. The coupling constants increase with increasing temperature for any one isotopomer and decrease with increasing secondary deuterium substitution at any one temperature. The results are entirely attributable to intramolecular effects and the data have been fitted by a weighted least-squares regression analysis to a spin—spin coupling surface thereby yielding a value for ¹J_e(C,H), the coupling constant at equilibrium geometry, and values for the bond length derivatives of the coupling. We find that ¹J_e(C,H) = 120.78 (±0.05) Hz which is about 4.5 Hz smaller than the observed value in ¹³CH₄ gas at room temperature. Results are also reported for J(H,D) in ¹³CH₃D and ¹³CHD₃ for which no temperature dependence was detected.     

Calculations of the indirect nuclear spin–spin coupling constants of PbH4

We report ab initio calculations of the indirect nuclear spin–spin coupling constants of PbH₄ using a basis set which was specially optimized for correlated calculations of spin–spin coupling constants. All nonrelativistic contributions and the most important part of the spin–orbit correction were evaluated at the level of the random phase approximation. Electron correlation corrections to the coupling constants were calculated with the multiconfigurational linear-response method using extended complete and restricted active space wavefunctions as well as with the second-order polarization propagator approximation and the second-order polarization propagator approximation with coupled-cluster singles and doubles amplitudes. The effects of nuclear motion were investigated by calculating the coupling constants as a function of the totally symmetric stretching coordinate. We find that the Fermi contact term dominates the Pb‐H coupling, whereas for the H‐H coupling it is not more important than the orbital paramagnetic and diamagnetic contributions. Correlation affects mainly the Fermi contact term. Its contribution to the one-bond coupling constant is reduced by correlation, independent of the method used; however, the different correlated methods give ambiguous results for the Fermi contact contribution to the H‐H couplings. The dependence of both coupling constants on the Pb‐H bond length is dominated by the change in the Fermi contact term. The geometry dependence is, however, overestimated in the random phase approximation. Received: 16 November 1998 / Accepted: 30 March 1999 / Published online: 14 July 1999     

Modeling of heavy-atom-ligand NMR spin-spin coupling in solution: molecular dynamics study and natural bond orbital analysis of Hg-C coupling constants

Ab initio molecular dynamics (MD) and relativistic density functional NMR methods were applied to calculate the one‐bond Hg? C NMR indirect nuclear spin–spin coupling constants (J) of [Hg(CN)₂] and [CH₃HgCl] in solution. The MD averages were obtained as J(¹⁹⁹Hg? ¹³C)=3200 and 1575 Hz, respectively. The experimental Hg? C spin–spin coupling constants of [Hg(CN)₂] in methanol and [CH₃HgCl] in DMSO are 3143 and 1674 Hz, respectively. To deal with solvent effects in the calculations, finite “droplet” models of the two systems were set up. Solvent effects in both systems lead to a strong increase of the Hg? C coupling constant. From a relativistic natural localized molecular orbital (NLMO) analysis, it was found that the degree of delocalization of the Hg 5d_σ nonbonding orbital and of the Hg? C bonding orbital between the two coupled atoms, the nature of the trans Hg? C/Cl bonding orbital, and the s character of these orbitals, exhibit trends upon solvation of the complexes that, when combined, lead to the strong increase of J(Hg? C).     

C-13 magnetic relaxation rates and H-1 and C-13 paramagnetic shifts of Ni(II) complex of dopamine

The ¹H and ¹³C isotropic contact shifts and the ¹³C relaxation times of dopamine in aqueous solution have been measured in the presence of the Ni(II) ion. The pD dependence of the ¹H and ¹³C paramagnetic shifts was also investigated. From the analysis of the shifts at pD = 6.5 and from the INDO MO calculations on selected models of dopamine radicals, a dominant σ delocalization mechanism of the spin density is proposed. From the spin distribution on the ligand carbon atoms, the metal centered as well as the ligand centered dipolar contributions of the modified Solomon—Bloembergen equation were calculated and an estimate of the correlation time τ_c was given.     

Ab initio MO studies of nuclear spin-spin coupling constants in CH4, SiH4, AlH 4 − and GeH4 systems

Summary Ab initio molecular orbital calculations of electron coupled nuclear spin-spin coupling constants are performed for CH₄, SiH₄, AlH ₄ ^– and GeH₄ systems using the SCF perturbation theory. Basis set dependence of the major contributing terms such as orbital diamagnetic, orbital paramagnetic, spin dipolar and Fermi contact terms are studied. The study also illustrates the relative importance of bond centred functions and nuclear centred polarization functions in predicting the directly bonded and geminal couplings in the systems selected. Basis sets having uncontracted cores functions and augmented with bond functions seem to predict most of these couplings fairly satisfactorily when compared to the experimental values.     

Bis(trimethylsilyl)diazene revisited. Density functional theory (DFT) calculations of nitrogen NMR parameters of some azo‐compounds

Calculations of nitrogen NMR parameters [chemical shifts δN and indirect nuclear spin–spin coupling constants J(N,N), J(N,¹³C), J(²⁹Si,N)] of noncyclic azo‐compounds R¹ NN R² (R¹, R² = H, Me, Ph, SiH₃, SiMe₃) and cyclic azo‐compounds [NNCH₂, NN(CH₂)₃ NN(CH₂)₂SiH₂, and NN(SiH₂CH₂SiH₂)] by density functional theory (DFT) methods [B3LYP/6‐311+G(d,p) level of theory] provide data in reasonable agreement with experimental values. The influence of cis‐ and trans‐geometry is reflected by the calculations, and amino‐nitrenes are also included for comparison. The spin–spin coupling constants are analyzed with respect to contact (Fermi contact term, FC) and non‐ contact contributions (paramagnetic and diamagnetic spin‐orbital terms, PSO and DSO, and spin‐dipole term, SD). Bis(trimethylsilyl)diazene 6a can be generated by an alternative method, using the reaction of bis(trimethylsilyl)sulfur diimide with bis‐ (trimethylsilyl)amino‐trimethylsilylimino‐phosphane. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:84–91, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.20075     

Stereochemical behavior of geminal and vicinal 77Se–13C spin–spin coupling constants studied at the SOPPA(CC2) level taking into account relativistic corrections

A systematic theoretical study of geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants in the series of the open‐chain selenides and selenium‐containing heterocycles revealed that relativistic effects play an essential role in the selenium–carbon coupling mechanism, especially when the coupling pathway includes a triple bond, contributing to about 10–15% of their total values and noticeably improving the agreement of the calculated couplings with experiment. Both geminal and vicinal ⁷⁷Se–¹³C spin–spin coupling constants show marked stereochemical behavior as documented by their calculated dihedral angle dependence that could be used as a practical guide in stereochemical studies of organoselenium compounds. Copyright © 2014 John Wiley & Sons, Ltd.     

Structural trends of 29Si–1H spin–spin coupling constants across double bond

The calculations of geminal and vicinal ²⁹Si–¹H spin–spin coupling constants across double bond in 15 alkenylmethylsilanes and alkenylchlorosilanes were carried out at the second‐order polarization propagator approach level in a good agreement with experiment. Two structural trends, namely, (i) the geometry of the coupling pathway and (ii) the effect of the electrowithdrawing substituent, have been interpreted in terms of the natural J‐coupling analysis within the framework of the natural bond orbital approach. Thus, the marked difference between cisoidal and transoidal ²⁹Si–¹H spin–spin coupling constants across double bond was accounted for the delocalization contributions including bonding and antibonding Si–C and C–H orbitals, whereas the chlorine effect was explained in terms of the steric contributions including bonding Si–Cl orbitals. Copyright © 2012 John Wiley & Sons, Ltd.     

13C Chemical shifts and 13C?15N coupling constants of some 15N-labelled bridgehead nitro compounds

Measurement of the ¹³C NMR spectra of the bridgehead nitro compounds 1a–5a has been performed. It is found that one-bond ¹³C ¹⁵N coupling is not necessarily a reflection of the degree of s character of the bridgehead carbon exocyclic bonding orbital. Although the magnitude of vicinal coupling to the bridgehead carbon increases, in accordance with the number of three-bond pathways available for transmission of spin information, coupling is actually reduced by opposing contributions from through-space intramolecular orbital interactions.     

Spectral density analysis of nuclear spin—spin coupling: II. Hartree-Fock LCAO studies for homonuclear coupling constants

A spectral density function has been calculated for the indirect nuclear spin—spin coupling constant for homonuclear coupling. The ground state wavefunction is obtained with a normal ab-initio calculation. The sum over states approach for calculating the reduced coupling constant K is replaced by an integration over a spectral density function where the integration variable is the orbital exponent of a “scanning molecular orbital”. This results in a stable method for calculating K with reasonable accuracy. The spectral density function also gives information about which excited states give important contributions to K.Furthermore a residual spectral density function is defined that can be used as a test for the completeness of a set of virtual orbitals in a sum over states calculation.     

Inclusion of hydrogen p orbitals in the semiempirical calculation of NMR parameters. III: INDO CHF calculations of orbital and dipolar contributions to spin–spin coupling constants involving protons

The self-consistent perturbation theory is used to calculate noncontract contributions to spin–spin coupling constants involving protons. Molecular wave functions were obtained with a modified version of the INDO method which includes hydrogen 2p orbitals in its basis set. It is found that in many cases the orbital and dipolar terms are by no means negligible, being particularly important in geminal H? H couplings. Results reported in this paper for this type of coupling, reproduce experimental trends in the series CH₄, NH₃, and OH₂. In general, noncontact terms are found to decrease as the number of bonds separating the interacting nuclei increases.     

Nuclear hyperfine splitting in the BX electronic band system of 127I2

The spacings between seven hyperfine components in the R(127) line of the 11-6 band of the B-X electronic transition of ¹²⁷I₂ are fitted, with a standard deviation of 17.3 kHz, by varying the nuclear quadrupole coupling constants eqQ′ and egQ′', the magnetic spin—rotation constant C_I and the tensor and scalar nuclear spin—spin coupling constants d′ and a′ in the hyperfine hamiltonian. The P(13) line of the 430 band is also analysed using an identical hamiltonian and a standard deviation of 6.25 kHz is obtained. No evidence for a magnetic octupole coupling is found to the precision of the data although this effect was invoked by Hackel et al. for the P(13) line.     

Large configuration interaction calculations of nuclear spin-spin coupling constants: III. Vibrational effects in ammonia

Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for ¹⁵NH₃ and ¹⁵ND₃ species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH₂ group in RNH₂ compounds is indicated.     

Decomposition of nuclear magnetic resonance spin-spin coupling constants into active and passive orbital contributions

The theory of the J-OC-PSP (decomposition of J into orbital contributions using orbital currents and partial spin polarization) method is derived to distinguish between the role of active, passive, and frozen orbitals on the nuclear magnetic resonance (NMR) spin-spin coupling mechanism. Application of J-OC-PSP to the NMR spin-spin coupling constants of ethylene, which are calculated using coupled perturbed density functional theory in connection with the B3LYP hybrid functional and a [7s,6p,2d/4s,2p] basis set, reveal that the well-known pi mechanism for Fermi contact (FC) spin coupling is based on passive pi orbital contributions. The pi orbitals contribute to the spin polarization of the sigma orbitals at the coupling nuclei by mediating spin information between sigma orbitals (spin-transport mechanism) or by increasing the spin information of a sigma orbital by an echo effect. The calculated FC(pi) value of the SSCC (1)J(CC) of ethylene is 4.5 Hz and by this clearly smaller than previously assumed.     

13C?19F spin–spin coupling in some monofluoro-substituted polycyclic aromatic hydrocarbons

The determination and complete assignment of the ¹³C? ¹⁹F coupling constants and ¹³C chemical shifts for 15 monofluoro derivatives of nine polycyclic aromatic hydrocarbons are reported. Fluorine substitutent effects on the ¹³C chemical shifts are given and their regular behaviour, making comparisons between different compounds possible, is discussed. The numerical values of the ¹³C? ¹⁹F long range coupling constants are found, with a few exceptions, to decrease in an alternating manner along the periphery of the molecules. In several cases the signs of the coupling constants have been determined. It appears that the signs alternate, but additional evidence is required. The magnitudes of different types of coupling constants are discussed in terms of steric and electronic effects. CNDO/2 and INDO calculations of the ¹³C? ¹⁹F coupling constants in the fluoronaphthalenes have been performed using the ‘sum-over-states’ method with the aim of examining the orbital and spin–dipole contributions to the various couplings.     

Fine structure in Rydberg states of the H2 molecule

The electron spin—nuclear rotation interaction is considered for the np ³Π_u Rydberg series of the H₂ molecule for which much experimental data is available. Earlier formulations of this interaction are reconciled and consistent formulae for both the heteronuclear and homonuclear case are presented. Theoretical calculations of various contributions are given and compared to experimental results. Excellent agreement between calculated and experimental values is obtained for the np Rydberg series of H₂ including H₂⁺.     

NMR偶合常数的从头算级别自然杂化轨道研究

为了研究自然杂化轨道计算结果与核自旋偶合常数的相关性,本文进行了从头算级别的自然杂化轨道计算。采用STO－3G基组,利用Lowdin正交化原子轨道基组下的密度矩阵,得到了分子中各原子的杂化轨道、净电荷与^13C-H、^13C-^13C键自旋偶合常数^1Jcn和^1Jcc之间关系式。利用这些式子计算得到的结果与实验数据非常一致。     

An indo investigation of magnetic resonance constants of azaaromatic systems

INDO–MO calculations have been performed on the ESR hyperfine coupling constants of the pyridinyl radical and the radical anions of pyrimidine, quinoline, isoquinoline, acridine and benzcinnoline. The nuclear spin coupling constants and the ¹⁴N nuclear quadrupole coupling constant of pyridine have also been calculated. In general, calculated values are in satisfactory agreement with the experimental data.