Claudia G. Giribet

Advances in Theoretical and Physical Aspects of Spin–Spin Coupling Constants

Publisher Summary This chapter discusses advances in the theoretical and physical aspects of spin–spin coupling constants. From both theoretical and experimental points of view, the analysis of high-resolution NMR parameters is an important problem, and its significance for the understanding of molecular electronic structure can hardly be stressed enough. When both approaches are taken together, an excellent example of the Born–Opperheimer approximation is obtained because experimentalists measure transitions among nuclear states that are modified by the interactions among magnetic nuclei, external magnetic field, and electrons, while theoreticians study the way the electronic wave function is modified owing to those interactions. The empirical Hamiltonian describes the way nuclear spin energy levels are modified both by the static magnetic field provided by a spectrometer and by the interactions between magnetic nuclei and electrons belonging to a given molecule.

Theoretical study of the nuclear spin-molecular rotation coupling for relativistic electrons and non-relativistic nuclei

A theoretical study of the relation between the relativistic formulation of the nuclear magnetic shielding and spin-rotation tensors is presented. To this end a theoretical expression of the relativistic spin-rotation tensor is formulated, considering a molecular Hamiltonian of relativistic electrons and non-relativistic nuclei. Molecular rotation effects are introduced considering the terms of the Born-Oppenheimer decomposition, which couple the electrons and nuclei dynamics. The loss of the simple relation linking both spectral parameters in the non-relativistic formulation is further analyzed carrying out a perturbative expansion of relativistic effects by means of the linear response within the elimination of the small component approach. It is concluded that relativistic effects on the spin-rotation tensor are less important than those of the nuclear magnetic shielding tensor.

Orbital contributions to relativistic corrections of the NMR nuclear magnetic shielding tensor originated in scalar field-dependent operators

In this work relativistic corrections to the magnetic shielding constant (σM), which arise from scalar field-dependent operators (both linear and bilinear), are calculated and decomposed into contributions from molecular orbitals (MOs). Numerical results for the magnetic shielding constant of the heavy nucleus X in closed shell atomic ions X− and HX compounds (X = F, Cl, Br, I) are presented. The relative importance of inner-shell and valence electrons in the definition of each one of these terms is thus assessed and its relation with their sensitivity to changes in a chemical environment is discussed.

AB INITIO 'CLOPPA' DECOMPOSITION OF THE STATIC MOLECULAR POLARIZABILITY TENSOR

An ab initio method based on CLOPPA-IPPP (contributions from localized orbitals within the polarization propagator approach — inner projections of the polarization propagator) for analysing the static molecular polarizability tensor is presented. This method makes use of the polarization propagator formalism, together with localized molecular orbitals which closely resemble chemical functions, to decompose each component of the polarizability tensor into contributions arising from different molecular fragments. Within this approach, ‘local’ and ‘mutual’ polarizabilities are defined, which are useful for studying the molecular response to an inhomogeneous electric field. In order to exemplify its capabilities, this method is applied to the study of the polarizability tensor in the series ethane, ethylene and acetylene.

Ab initio and experimental study of NMR coupling constants in bicyclo[1.1.1]pentane

The different dependences of NMR spin–spin coupling constants of a medium-sized molecule on the quality of the ground-state wavefunction is studied using three different basis sets of increasing size, namely, 6-31G, 6-31G* and 6-31G**. Calculations of the Fermi contact terms were also carried out using partially uncontracted s and p atomic orbitals with the same exponents as those of the 6-31G basis set. Bicyclo[1.1.1]pentane was chosen as a model compound; it was synthesized for the measurement of several couplings as part of this work in order to compare theoretical results with experimental values. The through-space transmission of couplings via the interaction of rear lobes of orbitals inside the bicyclic cage were studied with the IPPP approach using the above basis sets.

Evaluation of the Molecular Polarizability Using the IPPP−CLOPPA−INDO/S Method. Application to Molecules of Biological Interest

The IPPP-CLOPPA-INDO/S method is introduced to investigate the static molecular polarizability in macromolecules. As an example of application, the polarizability of phospholipidic compounds, with and without the presence of water molecules has been estimated. The IPPP technique was employed to calculate the polarizability of the polar head and the hydrocarbon chains separately to analyze the feasibility of evaluating the total polarizability of the molecule by addition of these two projected results. INDO/S dipole moments of different fragments of the complex molecule were obtained by means of localized molecular orbitals in order to evaluate the charge transfer in the system.

Breit interaction effects in relativistic theory of the nuclear spin-rotation tensor

In this work, relativistic effects on the nuclear spin-rotation (SR) tensor originated in the electron-nucleus and electron-electron Breit interactions are analysed. To this end, four-component numerical calculations were carried out in model systems HX (X=H,F,Cl,Br,I). The electron-nucleus Breit interaction couples the electrons and nuclei dynamics giving rise to a purely relativistic contribution to the SR tensor. Its leading order in 1/c is of the same value as that of relativistic corrections on the usual second order expression of the SR tensor considered in previous work [I. A. Aucar, S. S. Gómez, J. I. Melo, C. G. Giribet, and M. C. Ruiz de Azúa, J. Chem. Phys. 138, 134107 (2013)], and therefore it is absolutely necessary to establish its relative importance. For the sake of completeness, the corresponding effect originating in the electron-electron Breit interaction is also considered. It is verified that in all cases these Breit interactions yield only very small corrections to the SR tensors of both the X and H nuclei in the present series of compounds. Results of the present work strongly suggest that in order to achieve experimental accuracy in the theoretical study of the SR tensor both electron-nucleus and electron-electron Breit effects can be safely neglected.

CLOPPA-IPPP analysis of cooperative effects in hydrogen-bonded molecular complexes. Application to intermolecular 2hJ(N,C) spin-spin coupling constants in linear (CNH)n complexes.

The cooperative effects on NMR indirect nuclear coupling constants are analyzed by means of the IPPP-CLOPPA approach (where CLOPPA is the Contributions from Localized Orbitals within the Polarization Propagator Approach and IPPP is the Inner Projections of the Polarization Propagator). The decomposition of the J coupling allows one to classify these effects as those due to changes in the geometric structure and those that directly involve the transmission mechanisms. This latter contribution admits a further classification, taking into account its electronic origin. As an example, the cooperative effects on intermolecular 2hJ(N,C) couplings of the linear complexes (CNH)n (n = 2, 3, 4) are discussed.

CLOPPA analysis of the molecular polarizability and the energy of strong intramolecular hydrogen bonds: resonance assisted?

The contributions from localized orbitals within the polarization propagator approach (CLOPPA) method is applied to investigate the influence of the π system on the polarizability of the intramolecular hydrogen bond of malonaldehyde, in order to address if this linear response property provides evidence for the existence of the resonance assisted HB (RAHB) mechanism. On the same grounds, this influence on the energy of the hydrogen bond and the potential energy curve of the proton are also evaluated. Results obtained seem to confirm that the π system delocalizes on the hydrogen bond region, and this effect of delocalization is partially responsible for the unusual strength of this intramolecular hydrogen bond.

CLOPPA−IPPP Analysis of Cooperative Effects in H-Bonded Molecular Complexes. 2. Application to the Static Molecular Polarizability Tensor

The cooperative effects on the polarizability tensor are analyzed by means of the IPPP-CLOPPA approach. The decomposition of the polarizability allows classifying these effects in those due to changes in the geometric structure and those that directly involve the transmission mechanisms. This latter contribution admits a further classification, taking into account its electronic origin. As suitable examples, cooperative effects on the polarizability tensor of linear complexes (CNH)(N) and (H(2)O)(N) (N = 2, 3, 4) are discussed.