Second-order polarization propagator calculations of indirect nuclear spin-spin coupling tensors in the water molecule

The contribution to indirect nuclear spin-spin coupling tensors provided by the Fermi contact, the spin-dipolar, the Fermi contact/spin-dipolar crossterm, and the paramagnetic spin-orbit interactions are investigated in a zeroth-, first- (the same as the coupled Hartree-Fock method), and second-order polarization propagator approach. Numerical applications to the water molecule show that the second-order results for both the HO and the HH coupling constants are in good agreement with experimental data - especially if vibrational corrections and the diamagnetic spin-orbit contributions are taken into account. We find that the correlation corrections beyond coupled Hartree-Fock are important. We also report how the second-order results are influenced by neglect of some of the most time-consuming steps in the calculation.     

Inclusion of hydrogen p orbitals in the semiempirical calculation of NMR parameters. I. Influence on the FPT INDO spin–spin coupling constants

Hydrogen 2p orbitals have been introduced into the basis set to calculate the Fermi contact term of spin–spin coupling constants using the FPT INDO method. Different coupling constants show different sensitivity to these hydrogen polarization functions. Some improvements are found for molecules containing N or F. Calculations of proton-proton geminal coupling constants give more negative results than those of FPT INDO , yielding a better agreement with experimental values. The π-transmission mechanism is notably exaggerated.     

The calculation of indirect nuclear spin-spin coupling constants in large molecules

We present calculations of indirect nuclear spin-spin coupling constants in large molecular systems, performed using density functional theory. Such calculations, which have become possible because of the use of linear-scaling techniques in the evaluation of the Coulomb and exchange-correlation contributions to the electronic energy, allow us to study indirect spin-spin couplings in molecules of biological interest, without having to construct artificial model systems. In addition to presenting a statistical analysis of the large number of short-range coupling constants in large molecular systems, we analyse the asymptotic dependence of the indirect nuclear spin-spin coupling constants on the internuclear separation. In particular, we demonstrate that, in a sufficiently large one-electron basis set, the indirect spin-spin coupling constants become proportional to the inverse cube of the internuclear separation, even though the diamagnetic and paramagnetic spin-orbit contributions to the spin-spin coupling constants separately decay as the inverse square of this separation. By contrast, the triplet Fermi contact and spin-dipole contributions to the indirect spin-spin coupling constants decay exponentially and as the inverse cube of the internuclear separation, respectively. Thus, whereas short-range indirect spin-spin coupling constants are usually dominated by the Fermi contact contribution, long-range coupling constants are always dominated by the negative diamagnetic spin-orbit contribution and by the positive paramagnetic spin-orbit contribution, with small spin-dipole and negligible Fermi contact contributions.     

Influence of the INDO parameterization on the indirect spin–spin coupling constants as calculated by the FPT INDO method

Alterations have been introduced in the semi-empirical INDO parameters in order to study their influence on the Fermi contact term of the indirect spin–spin coupling constants as calculated by the finite perturbation theory (FPT). For this purpose a set of molecules containing hydrogen, carbon and/or fluorine has been selected. In general, most coupling constants are found to be much more sensitive than other molecular properties to small changes in the INDO parameters. This sensitivity depends strongly on the particular calculated coupling constant. In most cases the uncertainty in the INDO parameters leads to uncertainties in the coupling constants which are much greater than their experimental errors.     

Unrestricted Hartree-Fock instabilities in semiempirical CNDO/S and INDO/S calculations of spin-spin coupling constants

It is shown that non-convergent calculations of the Fermi contact term of spin-spin coupling constants within the self-consistent and finite perturbation schemes used to solve the coupled Hartree-Fock equations, are originated in non-singlet Hartree-Fock instabilities of the closed-shell restricted Hartree-Fock wavefunction. In CNDO/S and INDO/S wavefunctions, where the electronic system response has been successfully reproduced, all investigated molecules containing MOs were found to be unstable. Results of spin-spin coupling constants are given and compared with experimental as well as FP and SOS INDO values.Part of a Ph.D. thesis (G.E.S.) to be presented to the University of Buenos Aires.Comisión de Investigaciones Científicas (CIC, Pcia. de Bs. As.) fellow.     

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     

Ab initio study of the NMR shielding constants and spin-spin coupling constants in cyclopropene

Summary Ab initio calculations of parameters which characterize the NMR spectrum are presented for the cyclopropene molecule. The London orbitals CHF (or GIAO-CHF, Gauge-Independent Atomic Orbital Coupled Hartree-Fock) results for the shielding constants are in good agreement with the experimental data, accurately determined, and with otherab initio values. The calculations of the NMR spin-spin coupling constants have been performed using the Multiconfiguration Time-Dependent Hartree-Fock (MC TDHF) approach. Different basis sets and MC SCF wavefunctions were used to estimate the accuracy of the results. Good agreement is obtained with the coupling constants estimated using the available experimental data.Dedicated to Professor Werner Kutzelnigg on the occasion of his 60th birthday     

Finite perturbation configuration interaction calculations of nuclear spin-spin coupling constants: Vicinal proton-proton coupling in ethane

Non-empirical finite perturbation calculations at the Hartree-Fock and configuration interaction levels of approximation are reported for the vicinal proton-proton coupling constant in ethane for different values of the dihedral HCCH' angle. The correlation effects are found to be of importance. The results fit the Karplus relation well. The calculated values are in good agreement with available experimental data when the correlation contribution is included. Possibilities of using approximations in evaluating the correlation energy are discussed.     

On the restricted Hartree-Fock description of oligomer chains with expected metallic character

Restricted Hartree-Fock calculations for uniform linear and cyclic chains of hydrogen atoms with an increasing number of atoms are used to illustrate the behaviour of finite systems under Hartree-Fock type constraints. That behaviour is reminiscent of the pathological behaviour of the corresponding infinite system and the driving forces are intimately related.     

Scalar coupling across the hydrogen bond in 1,3- and 1,4-diols

[reaction: see text] Scalar coupling between hydroxyl groups sharing a 1,4- or 1, 3-intramolecular hydrogen bond can be readily detected using standard 2D NMR techniques. Analyses of isotopically perturbed 2D J-resolved spectra have revealed (h2)J to be on the order of 0.3 Hz in systems such as diols 2 and 3. A standard 2D COSY experiment, modified to detect small coupling constants, is shown to be a convenient method for detecting (h2)J in these systems. Couplings derived from density functional finite perturbation theory (DFT/FPT) are found to be in general agreement with experimental data.     

Carbon-carbon coupling in [3-13C1]tryptophan

Carbon-carbon coupling constants have been observed in [90% 3-¹³C₁]tryptophan and used to assign the ¹³C resonances of the indole ring. The results support a reassignment of C-5 and C-6 recently suggested on the basis of the reassigment of the corresponding resonances in indole. Coupling constants are compared with theoretical values obtained using a finite perturbation theory Blizzard-Santry program, and excellent agreement is obtained for the ¹J(CC) values. The calculations predict that the Fermi contact contribution is dominant for all ⁿJ(CC) couplings to C-3.     

Interpretation of vicinal proton–proton coupling constants of heteroaromatic molecules in terms of topological electron density descriptors

The indirect vicinal proton–proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon–Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton–proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism. Copyright © 2010 John Wiley & Sons, Ltd.     

Calculation of the nuclear spin coupling constant by a variational procedure on a finite part of the second-order perturbed energy

The nuclear spin-spin coupling constant of H-D molecule is calculated using ab initio LCAO MO SCF method using extended basis sets with and without configuration interaction. The essential feature of this calculation is that the delta function arising from the Fermi contact operator is removed by transformation. The perturbation variation theory, then, leads to a minimization of a finite part of the second order energy and a better convergence of the value of the coupling constant is expected. Calculations show that this convergence is improved by the transformation used. Moreover we show that the coupling constants are not very sensitive to the exact behavior of the contact operator near the nucleus provided that these operators are proportional to r_N^?2 near the nuclei.     

NMR spin–spin coupling constants in hydrogen‐bonded glycine clusters

The influence of the hydrogen bond formation on the NMR spin–spin coupling constants (SSCC), including the Fermi contact (FC), the diamagnetic spin‐orbit, the paramagnetic spin‐orbit, and the spin dipole term, has been investigated systematically for the homogeneous glycine cluster, in gas phase, containing up to three monomers. The one‐bond and two‐bond SSCCs for several intramolecular (through covalent bond) and intermolecular (across the hydrogen‐bond) atomic pairs are calculated employing the density functional theory with B3LYP and KT3 functionals and different types of extended basis sets. The ab initio SOPPA(CCSD) is used as benchmark for the SSCCs of the glycine monomer. The hydrogen bonding is found to cause significant variations in the one‐bond SSCCs, mostly due to contribution from electronic interactions. However, the nature of variation depends on the type of oxygen atom (proton‐acceptor or proton‐donor) present in the interaction. Two‐bond intermolecular coupling constants vary more than the corresponding one‐bond constants when the size of the cluster increases. Among the four Ramsey terms that constitute the total SSCC, the FC term is the most dominant contributor followed by the paramagnetic spin‐orbit term in all one‐bond interaction.     

Real space Hartree-Fock configuration interaction method for complex lateral quantum dot molecules

We present unrestricted Hartree-Fock method coupled with configuration interaction (CI) method (URHF-CI) suitable for the calculation of ground and excited states of large number of electrons localized by complex gate potentials in quasi-two-dimensional quantum dot molecules. The method employs real space finite difference method, incorporating strong magnetic field, for calculating single particle states. The Hartree-Fock method is employed for the calculation of direct and exchange interaction contributions to the ground state energy. The effects of correlations are included in energies and directly in the many-particle wave functions via CI method using a limited set of excitations above the Fermi level. The URHF-CI method and its performance are illustrated on the example of ten electrons confined in a two-dimensional quantum dot molecule.     

Hartree-Fock calculation of the harmonic force constants and equilibrium geometry of formaldehyde

Using the force method, complete sets of harmonic force constants have been obtained for formaldehyde from Hartree-Fock wavefunctions. The agreement with experiment is considered particularly satisfying for the off-diagonal constants. This holds not only for a near-Hartree-Fock Gaussian basis set but also for a small but polarized 7, 3/3/1 basis set. The value even of such a small calculation is underlined by frequencies calculated from force constants corrected for almost systematic errors in the diagonal constants. Experimental force fields are critically examined, and an explanation for the surprisingly large coupling between CO and CH stretching is indicated.     

Electronic influences on 3J(C,H) coupling constants via -S-, -S(O)- and -SO2-: their determination, calculation and comparison of detection methods

3J(C,H) coupling constants via a sulfur atom in two series of compounds, both including a sulfide, a sulfoxide and a sulfone, were detected experimentally and calculated by quantum mechanical methods. In the first series (1-3) the coupling between a hydrogen, bonded to an sp3 carbon, and an sp2 carbon is treated; the second series (4-6) deals with the coupling between a hydrogen, bonded to an sp3 carbon, and an sp3 carbon. Different pulse sequences (broadband HMBC, SelJres, 1D HSQMBC, J-HMBC-2, selective J-resolved long-range experiment and IMPEACH-MBC) proved to be useful in determining the long-range 3J(C,H) coupling constants. However, the dynamic behaviour of two of the compounds (4 and 6) led to weighted averages of the two coupling constants expected (concerning equatorial and axial positions of the corresponding hydrogens). DFT calculations proved to be useful to calculate not only the 3J(C,H) coupling constants but also the different contributions of FC, PSO, DSO and SD terms; the calculation of the Fermi contact term (FC) was found to be sufficient for the correct estimation of 3J(C,H) coupling constants.     

Interaction energies and NMR indirect nuclear spin-spin coupling constants in linear HCN and HNC complexes

The cooperativity effects on both the electronic energy and NMR indirect nuclear spin-spin coupling constants J of the linear complexes (HCN)n and (HNC)n (n = 1-6) are discussed. The geometries of the complexes were optimized at the MP2 level by using the cc-pVTZ basis sets. The spin-spin coupling constants were calculated at the level of the second-order polarization propagator approximation with use of the local dense basis set scheme based on the cc-pVTZ-J basis sets. We find strong correlations in the patterns of different properties such as interaction energy, hydrogen bond distances, and spin-spin coupling constants for both series of compounds. The intramolecular spin-spin couplings are with two exceptions dominated by the Fermi contact (FC) mechanism, while the FC term is the only nonvanishing contribution for the intermolecular couplings. The latter do not follow the Dirac vector model and are important only between nearest neighbors.     

Convergence of the perturbation theory expansion for spin-spin coupling constants

The convergence of the full perturbation theory expansion for the Fermi contact term in the spin-spin coupling constant of hydrogen fluoride has been studied. By examining the contribution of higher virtual states as the basis set is expanded to 18 atomic orbitals, it is shown that at this level of approximation the expansion does not converge. The need to also establish convergence before accepting values calculated from configuration interaction wavefunctions is discussed.The Puerto Rico Nuclear Center is operated by the University of Puerto Rico for the United States Atomic Energy Commission under Contract No. AT(40-1)-1833.     

Computational and experimental evidence of through-space NMR spectroscopic J coupling of hydrogen atoms

J coupling in NMR spectroscopy is conventionally associated with covalent bonds. A noncovalent contribution often called through-space coupling (TSC) has been observed for heavy atoms. In this study, the TSC was detected and analyzed for the more common (1)H-(1)H coupling as well. In synthesized model molecules the hydrogen positions could be well controlled. For several coupling constants the through-space mechanism was even found to be the predominant factor. The nature and magnitude of the phenomenon were also analyzed by density functional computations. Calculated carbon- and hydrogen-coupling maps and perturbed electronic densities suggest that the aromatic system strongly participates in the noncovalent contribution. Unlike covalent coupling, which is usually governed by the Fermi contact, TSC is dominated by the diamagnetic term comprising interactions of nuclei with the electron orbital angular momentum. The computations further revealed a strong distance and conformational dependence of TSC. This suggests that the through-space coupling can be explored in molecular structural studies in the same way as the covalent one.