G.A. Aucar

Relativistic effects on the nuclear magnetic shielding tensor

A new approach for calculating relativistic corrections to the nuclear magnetic shieldings is presented. Starting from a full relativistic second order perturbation theory expression a two-component formalism is constructed by transforming matrix elements using the elimination of small component scheme and separating out the contributions from the no-virtual pair and the virtual pair part of the second order corrections to the energy. In this way we avoid a strong simplification used previously in the literature. We arrive at final expressions for the relativistic corrections which are equivalent to those of Fukui et al. [J. Chem Phys. 105, 3175 (1996)] and at some other additional terms correcting both the paramagnetic and the diamagnetic part of the nuclear magnetic shielding. Results for some relativistic corrections to the shieldings of the heavy and light nuclei in HX and CH3X (X=Br,I) at both random phase and second order polarization propagator approach levels are given.

Relativistic effects on nuclear magnetic shielding constants in HX and CH3X(X=Br, I) based on the linear response within the elimination of small component approach

Numerical calculations of relativistic effects on nuclear magnetic shielding constants sigma corresponding to all one-body operators obtained within a formalism developed in previous work were carried out. In this formalism, the elimination of small component scheme is applied to evaluate all quantities entering a four-component RSPT(2) expression of magnetic molecular properties. HX and CH3X (X=Br,I) were taken as model compounds. Calculations were carried out at the Hartree-Fock level for first-order quantities, and at the random-phase approximation (RPA) level for second- and third-order ones. It was found that values of sigma(X) are largely affected by several relativistic corrections not previously considered in the bibliography. sigma Values of the H nucleus are in close agreement with four-component RPA ones. Overall relativistic effects on the shift of sigma(X) from HX to CH3X are smaller than the nonrelativistic shifts.

Viewpoint 8 — polarization propagator analysis of spin-spin coupling constants

Abstract The analysis of electronic mechanisms that define indirect NMR spin-spin coupling constants can be efficiently carried out by combining the polarization propagator formalism with the use of localized molecular orbitals. This approach is applied to study several trends of one-bond couplings along the Periodic Table when one of the coupled nuclei bears a lone pair. This analysis is preceded by a revision of the fundamentals of the method in which its approximations, shortcomings and capabilities are commented on. A brief overview of results already published in the literature is also given. The relationship between the classical approach of Pople and Santry and the polarization propagator calculation of the Fermi contact term is discussed.

Fully relativistic calculation of nuclear magnetic shieldings and indirect nuclear spin-spin couplings in group-15 and -16 hydrides

Fully relativistic calculations of the isotropic and anisotropic parts of both indirect nuclear spin–spin couplings 1J(X-H) and 2J(H-H) and nuclear magnetic shieldings σ(X) and σ(H) for the group-15 and -16 hydrides are presented. Relativistic calculations were performed with Dirac–Fock wave functions and the random phase approximation method. Results are compared to its nonrelativistic counterpart. Paramagnetic and diamagnetic contributions to the nuclear magnetic shielding constants are also reported. We found very large relativistic corrections to both properties in the sixth-row hydrides (BiH3 and PoH2). Our calculations of the relativistic corrections to the isotropic part of σ at the heavy nucleus X show that it is roughly proportional to Z3.2 in both series of molecules. Paramagnetic term σp is more sensitive to the effects of relativity than the diamagnetic one σd, even though both have a behavior proportional to third power of the nuclear charge Z.

Quantum chemical analysis of the orientational lone-pair effect on spin-spin coupling constants

Abstract The quantum-chemical analysis of factors defining the stereospecific behaviour of nuclear spin-spin coupling constants is shown to be an important aid in obtaining experimental information on molecular structures from high-resolution NMR spectroscopy. The analyses presented in this paper are based on the contributions from localized molecular orbitais within the polarization propagator approach (CLOPPA) method and examples are given where factors defining heteroatom lone-pair orientational effects on spin-spin coupling constants are discussed.

Analysis of multipath transmission of spin-spin coupling constants in 1-x-bicycloalkanes: Part II. Additivity of coupling pathways

Abstract The multipath additivity of couplings involving the bridgehead carbon atoms in 1-X-bicycloalkanes (X = CH3, CH2OH, CO2H, F) was analysed using the IPPP method. Couplings are decomposed into a through-space component and different through-bond components transmitted by the pathways that join the coupled nuclei. The sum of these components is compared with the total calculated J coupling. The J(C2-C(X)), J(C1-C2) and J(C1-H2) couplings are discussed, where the notation X-Cl · C2-H2 is used to define the bridgehead carbon atoms. Good additivity is found for J(C2-C(X)), but this is not the case for J(C1-C2). The IPPP results for a given C-C pathway are in qualitative agreement with the empirical additivity rules proposed by Klessinger et al. for these couplings. Good multipath additivity was also found for J(C1-H2).

Relativistic mass-corrections to the heavy atom nuclear magnetic shieldings. Analysis of contributions in terms of localized orbitals

Abstract The relativistic mass correction contributions to the nuclear magnetic shielding σ MC (X) within the polarization propagator approach both at the pure zeroth-order (PZOA) and at the random phase approximation (RPA) were calculated for the heavy atoms X of a series of hydrides XH n (n=1–3) . Inclusion of σ MC (X) brings the nonrelativistic nuclear magnetic shieldings to agreement with fully relativistic four-component calculations, as noted previously for the hydrogen halides. The analysis in terms of contributions from localized orbitals shows that this contribution has an inner core origin, while it remains unaffected by excitations involving bonding orbitals and lone pairs. For all the compounds studied, σ MC PZOA (X) differs from σ MC RPA (X) in less than 5%, although at a much lower computational cost.

NMR-K REDUCED COUPLING CONSTANTS WITHIN THE CLOPPA-PM3 APPROACH. II : SHORTCOMINGS AND HOW TO OVERCOME THEM

Abstract The shortcomings encountered in the CLOPPA-PM3-RPA coupling constant calculations shown in part I of this work are analyzed. These are: (i) the Hartree–Fock quasi-instabilities of the non-singlet type in PM3 wavefunctions; and (ii) the erroneous PM3-derived description of the hybridization of some localized molecular orbitals. It is shown that these problems arise from: (a) the parameters optimization procedure used within the PM3 scheme, which apparently takes into account some effects at the nuclear sites in an inappropriate way; and (b) the selected set of properties chosen to be reproduced by the parameters optimization procedure. Properties do not critically depend on the electronic surroundings of the nuclei. Hence, some effects at nuclear sites are badly produced when the PM3 wavefunction is used. We have found three parameters which are mainly involved: the one-center two-electron integrals; the β s or β p parameters; and the U ss one-electron energies. The FC electronic mechanism is the most affected by the problems analyzed here.

Analysis of multipath transmission of spin-spin coupling constants in 1-X-bicycloalkanes: Part I. The through-space transmission via the bridgehead carbon atoms

Abstract The through-space transmission of couplings involving bridgehead carbon atoms in substituted 1-X-bicycloalkanes (X = H, F, CH 3 ) was analysed theoretically with a modified version of the IPPP-INDO method. The through-space components are further decomposed into a sum of individual “coupling pathways”, each of which involves two occupied and two vacant localized orbitals. The relative importance of these orbitals indicates which are the most important bonds and antibonding orbitals defining the transmission mechanisms. In this way, it is shown that the main trends of the through-space component of j (C1-H) (where H is the proton bonded to the remaining bridgehead carbon atom C H ) and J (C1-C H ) are directly related to the amplitude of the C H -H bonding orbital on C1. The decrease in the through-space values when going from bicyclopentane to bicyclooctane is thus explained by the decrease in this amplitude as the C1-C H distance increases. The dependence of J (C1-H) on the substituent X can also be explained by the effect of X on the C H -H bond. The through-space IPPP results are found to be quite different from those obtained using the NNBI approach, showing that both methods are based on different grounds.

NMR-K reduced coupling constant calculations within the CLOPPA-PM3 approach: I. General results

Abstract A new version, i.e. PM3, of the CLOPPA model modified to make indirect nuclear spin coupling calculations for molecules containing heavy atoms is presented. Its performance compared with previous CLOPPA-MNDO-RPA and CLOPPA-AM1-RPA calculations is discussed. The PM3 approach gives better results than its predecessors for couplings where one of the coupled nuclei is P or Cl, and permits one to reproduce qualitatively experimental trends for some other nuclei that are not parametrized within the MNDO and AM1 methods; for example As, Sb, Bi, Ga, In and Tl. However, the general performance of the new version does not achieve the level of the two previous ones.