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

1 J CH Coupling in Benzaldehyde Derivatives: Ortho Substitution Effect

The natural J-coupling (NJC) method is applied to analyze the Fermi contact contribution of the NMR spin-spin coupling constant decomposing this contribution in terms of natural localized molecular orbitals. We investigated the influence of the basis set on the NJC analysis for the formyl group coupling constant (¹ J _CHf) of benzaldehyde derivatives. NJC and other NBO analyses, like steric and natural Coulombic energy, were chosen to explain the influence of electron-donating and electron-withdrawing groups on ¹ J _CHf for some substituted benzaldehydes (Me, OH, OMe, F, Cl, Br, I, and NO₂). For the ortho derivatives, electronegative substituents near the C-Hf bond increase the ¹ J _CHf coupling. This effect could be related to an increase in formyl carbon s character and changes in the carbon and hydrogen natural charges. This indicates that the substituents in ortho have a proximity effect on ¹ J _CHf coupling mainly of electrostatic origin instead of the expected hyperconjugative interactions.

Polarization propagator theory and the entanglement between MO excitations

Entanglement is at the core of quantum physics and so, one may conjecture that it should have some influence on atomic and molecular response properties. The usual way of treating entanglement is by applying information theory via the von Newman entropy. Given that the principal propagator is the operator that contains the physical information that arises due to the transmission of the effects of two external perturbations through the electronic framework of a quantum system, it should have in it the information necessary to quantify the likely entanglement among molecular orbital excitations. In this article we first propose a proper density matrix and from it, the way to quantify entangled excitations by using information theory. The NMR J-couplings are among the best candidates to learn about the potentialities of this formalism. We applied this new tool to analyze the famous Karplus rule and found a relationship between the dihedral angular dependence and the entanglement. We also found that the entangled excitations are related to electron correlation. The new formalism can be applied to all other response properties.

Theoretical analysis of NMR shieldings of group-11 metal halides on MX (M = Cu, Ag, Au; X = H, F, Cl, Br, I) molecular systems, and the appearance of quasi instabilities on AuF

Accurate calculations of nuclear magnetic shieldings of group-11 metal halides, σ(M; MX) (M = Cu, Ag, Au; X = H, F, Cl, Br, I), were performed with relativistic and nonrelativistic theoretical schemes in order to learn more about the importance of the involved electronic mechanisms that underlie such shieldings. We applied state of the art schemes: polarization propagators at a random phase level of approach (PP-RPA); spin-free Hamiltonian (SF); linear response elimination of small component (LRESC) and density functional theory (DFT) with two different functionals: B3LYP and PBE0. The results from DFT calculations are not close to those from the relativistic polarization propagator calculations at the RPA level of approach (RelPP-RPA), in line with previous results. The spin-orbit (SO) contribution to a shielding constant is important only for MF molecules (M = Cu, Ag, Au). Different electronic mechanisms are considered within the LRESC method, bunched into two groups: core- and ligand-dependent. For the analysed shieldings the core-dependent electronic mechanisms are the most important ones; the ligand-dependent being only important for MF molecules. An out of range value for σ(Au) is found in AuF. It was previously reported in the literature, either originated in the large fluorine electronegativity together with large spin-orbit coupling contributions; or, due to Fermi-contact contributions. We argue here that such an unexpected large value is an artifact originated in the appearance of quasi instabilities, and show how to handle this apparent problem.

Investigation of the resonance-assisted hydrogen bond in model β-diketones through localized molecular orbital analysis of the spin-spin coupling constants related to the O-H···O hydrogen bond

The resonance-assisted hydrogen bond (HB) phenomenon has been studied theoretically by a localized molecular orbital (LMO) decomposition of the spin-spin coupling constants between atoms either involved or close to the O-H···O system of some β-diketones and their saturated counterparts. The analysis, carried out at the level of the second-order polarization propagator approximation, shows that the contributions in terms of LMO to the paramagnetic spin orbital and the spin dipolar Ramsey terms proof the importance of the delocalized π-electron structure supporting the idea of the existence of the resonance-assisted HB phenomenon phenomenon. The LMO contributions to the Fermi contact term indicate mainly the presence of the HB that may or not be linked to the π-electrons.

Unexpected geometrical effects on paramagnetic spin-orbit and spin-dipolar 2J(FF) couplings

The second-rank tensor character of the paramagnetic spin-orbit and spin-dipolar contributions to nuclear spin-spin coupling constants is usually ignored when NMR measurements are carried out in the isotropic phase. However, in this study it is shown that isotropic (2)J(FF) couplings strongly depend on the relative orientation of the C-F bonds containing the coupling nuclei and the eigenvectors of such tensors. Predictions about such effect are obtained using a qualitative approach based on the polarization propagator formalism at the RPA, and results are corroborated performing high-level ab initio spin-spin coupling calculations at the SOPPA(CCSD)/EPR-III//MP2/EPR-III level in a model system. It is highlighted that no calculations at the RPA level were carried out in this work. The quite promising results reported in this paper suggest that similar properties are expected to hold for the second-rank nuclear magnetic shielding tensor.

The analysis of NMR J-couplings of saturated and unsaturated compounds by the localized second order polarization propagator approach method

Calculations of NMR J-coupling with polarization propagators are not invariant under unitary transformations at second order level of approach, second order polarization propagator approach (SOPPA). They are only invariant at first order or random phase level of approach (RPA). We performed "localized" SOPPA (Loc-SOPPA), calculations of J-couplings applying two different schemes for the localization of molecular orbitals(LMO): Foster-Boys and Pipek-Mezey. We show here that results of such Loc-SOPPA calculations are different though not much: they are less than 6% different in the worst case. Therefore it is possible to apply them with confidence in the analysis of the transmission of different coupling mechanisms within the molecule. We are able now to get reliable information on what LMOs are the most important (and so which are not important) for a given J-coupling in a molecule. This information can then be used for selecting which are the paths that should be described with the highest possible accuracy for that J-coupling calculation. A few unsaturated compounds are analyzed: ethene, trans-difluoroethene or DiF-ethene, and imine. It is shown that different lone pairs (of p(z) or p(x/y) type) are responsible for the vicinal F-F J-coupling in DiF-ethene; and also the fact that the main LP contributor is not the same for the fermi contact and the spin-dipolar mechanisms. We also studied phosphorous containing compounds such as phosphine and cis-propylene phosphine. In both cases the analysis of the main LMO contributing to one-bond P-H coupling and through-space P-C coupling were performed. The above mentioned unsaturated molecular systems have quasiinstability problems that arise at RPA level of approach. We show here that they are mostly originated in the antibonding π∗ LMO, corresponding to the C=C or C=N double bonds. We performed the analysis of the origin of quasiinstabilities for the SD mechanism. The contribution of each kind of excitation terms to SOPPA calculations were considered, meaning the main contributions by single and double excitations. It is shown that one can get more than 97% of the total electron correlation contribution when including terms that mainly contain single excitations (though double-excitation matrix elements should still be calculated).

Stereochemical dependence of 3JCH coupling constants in 2-substituted 4-t-butyl-cyclohexanone and their alcohol derivatives

Theoretical and experimental studies on (3)J(C2H6eq) NMR spin-spin coupling constants in both the 2-X-4-t-butyl-cyclohexanone (X = H, CH(3), F, Cl, and Br) and in their alcohol derivatives series are reported. Results thus found are rationalized in terms of the transmission of the Fermi contact contribution to such couplings. To this end, dependencies of (3)J(C2H6eq) couplings versus the C(2)-C(1)-C(6) angle are compared in both series for equatorial and axial X orientations. The main trend is described in terms of the rear lobes interaction. Besides, for X = halogen atom in equatorial orientation a rather strong interaction between oxygen and halogen lone pairs is observed, and its influence on (3)J(C2H6eq) couplings is discussed and rationalized in terms of different Fermi contact transmission pathways.

1hJFH coupling in 2-fluorophenol revisited: is intramolecular hydrogen bond responsible for this long-range coupling?

The present study shows that a hydrogen bond between the OH group and the fluorine atom is not involved in the (1h)J(FH) spin-spin coupling transmission either for 4-bromo-2-fluorophenol or 2-fluorophenol. In fact, according to a quantum theory of atoms in molecules analysis, no bond critical point is found between O-H and F moieties. The nature of the transmission mechanism of the Fermi contact term of the (1h)J(FH) spin-spin coupling is studied by analyzing canonical molecular orbitals (see J. Phys. Chem. A 2010, 114, 1044), and it is observed that virtual orbitals play only a quite minor role in its transmission. This is typical of a Fermi contact term transmitted mainly through exchange interactions owing to the overlap of proximate electronic clouds; therefore, it is suggested to identify them as (nTS)J(FH) coupling where n stands for the number of formal bonds separating the coupling nuclei. In the cases studied in this work is n = 4. Results presented in this work could provide an interesting rationalization for different experimental signs known in the current literature for proximate J(FH) couplings.

19F chemical shifts, coupling constants and conformational preferences in monosubstituted perfluoroparacyclophanes

In the process of studying the chemistry of perfluoro[2.2]paracyclophanes (PFPCs), a novel class of compounds, it became necessary to identify some disubstituted products. To achieve this goal, we characterize in this work some monosubstituted PFPCs, identifying their (19)F-(19) F coupling patterns, and establishing a methodology for the assignment of their (19)F chemical shifts. The pattern of coupling constants indicates a skewed geometry in which the upper deck moves towards or away from the substituent, depending on the substituent electron-donor character and size. Quantum chemical calculations, performed at the HF/6-311 + G(d,p)//B3LYP/EPR-III level of theory, confirmed the conformations inferred from coupling constants and reproduced well the values of the couplings. Transmission mechanisms for the FC term of four- and five-bond (19)F-(19) F couplings are discussed in detail. Understanding the conformational preferences of PFPCs and how they are reflected by the coupling constants facilitates the assignment of (19)F chemical shifts in monosubstituted PFPCs and the identification of the disubstituted products.

Difference between ²JC2H3 and ²JC3H2 spin-spin couplings in heterocyclic five- and six-membered rings as a probe for studying σ-ring currents: a quantum chemical analysis

Adequate analyses of canonical molecular orbitals (CMOs) can provide rather detailed information on the importance of different σ-Fermi contact (FC) coupling pathways (FC term transmitted through the σ-skeleton). Knowledge of the spatial distribution of CMOs is obtained by expanding them in terms of natural bond orbitals (NBOs). Their relative importance for transmitting the σ-FC contribution to a given spin-spin coupling constants (SSCCs) is estimated by resorting to the expression of the FC term given by the polarisation propagator formalism. In this way, it is possible to classify the effects affecting such couplings in two different ways: delocalisation interactions taking place in the neighbourhood of the coupling nuclei and 'round the ring' effects. The latter, associated with σ-ring currents, are observed to yield significant differences between the FC terms of (2)J(C2H3) and (2)J(C3H2) SSCCs which, consequently, are taken as probes to gauge the differences in σ-ring currents for the five-membered rings (furan, thiophene, selenophene and pyrrol) and also for the six-membered rings (benzene, pyridine, protonated pyridine and N-oxide pyridine) used in the present study.

Optimized basis sets for the calculation of indirect nuclear spin-spin coupling constants involving the atoms B, Al, Si, P, and Cl

The aug-cc-pVTZ-J series of basis sets for indirect nuclear spin-spin coupling constants has been extended to the atoms B, Al, Si, P, and Cl. The basis sets were obtained according to the scheme previously described by Provasi et al. [J. Chem. Phys. 115, 1324 (2001)]. First, the completely uncontracted correlation consistent aug-cc-pVTZ basis sets were extended with four tight s and three tight d functions. Second, the s and p basis functions were contracted with the molecular orbital coefficients of self-consistent-field calculations performed with the uncontracted basis sets on the simplest hydrides of each atom. As a first illustration, we have calculated the one-bond indirect spin-spin coupling constants in BH(4)(-), BF, AlH, AlF, SiH(4), SiF(4), PH(3), PF(3), H(2)S, SF(6), HCl, and ClF at the level of density functional theory using the Becke three parameter Lee-Yang-Parr and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes.

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.

Electric field effects on one-bond indirect spin-spin coupling constants and possible biomolecular perspectives

Electric field (EF) induced changes of one-bond indirect spin-spin coupling constants are investigated on a wide range of molecules including peptide models. EFs were both externally applied and internally calculated without external EF application by the hybrid density functional theory method. Reliable agreement with experimental data has been obtained for calculated one-bond J-couplings. The role of the EF sign and direction, internal and induced components, hydrogen bonding, internuclear distance and hyperconjugative interactions on the one-bond J-coupling vs EF interconnection is analyzed. A linear dependence of 1J on EF projection along the bond is obtained, if the bound atoms possess different enough electron densities and an EF determined by the electronic polarization exists along the bond. Accentuating the 1JNH couplings as possible EF sensitive parameters, a systematic study is done in two sets of molecules with a large variation of the native internal EF value. The most EF affected component of the 1JNH coupling constant is the spin-dipole term of Ramsey's formulation; however, in the total J-coupling formation, the EF influence on the Fermi contact term is the most significant. The induced EF projection along the bond is 6.7 times weaker in magnitude than the simulated external uniform field. The absolute EF dependence of the one-bond J-coupling involves only the internal field, which is the sum of the induced field (if the external field exists) and the internuclear field determined by the native polarization. That linear and universal dependence joins the corresponding couplings in a diverse set of molecules under various electrostatic conditions. Many types of the one-bond J-couplings can be potentially measured in biomolecules, and the study of their relation with the electrostatic properties at the corresponding sites opens a new avenue to the full exploitation of the NMR measurable parameters with novel and exciting applications.

Experimental and DFT studies on the transmission mechanisms of analogous NMR JCH and JCC couplings in 1-X- and 1-X-3-methylbicyclo[1.1.1]-pentanes

The main aim of this work is to compare the transmission mechanisms for the Fermi contact term of spin-spin couplings, SSCCs, in series 1-X-bicyclo[1.1.1]-pentane, (1), and 1-X-3-methylbicyclo[1.1.1]pentane, (2), and from that comparison to gain insight into some subtle aspects of the FC transmission. To this end, 18 members of the latter series were isotopically enriched in (13)C at the methyl position and the following couplings were measured; 1JC3CMe, 3JC1CMe and 4JCXCMe. These three types of SSCCs in (2) are compared, respectively, with 1JC3H3, 3JC1H3 and 4JCXH in (1); these latter values were taken from previous works. Since electron delocalization plays an important role in the transmission of the FC interaction, the natural bond orbital (NBO) method is employed to quantify electron delocalization interactions within selected members of series (1) and (2). It is found that 1JC3H3 SSCCs in (1) is more efficiently transmitted than 1JC3CMe SSCCs in (2). On the other hand, 3JC1H3 and 4JCXH SSCCs in (1) are notably less efficiently transmitted than 3JC1CMe and 4JCXCMe SSCCs in (2), although substituent effects on these two SSCCs show the opposite trends. These different efficiencies are rationalized in terms of different sigma-hyperconjugative interactions in both series of compounds.

Calculation and analysis of NMR spin-spin coupling constants

The analysis of NMR spin-spin coupling leads to a unique insight into the electronic structure of closed-shell molecules, provided one is able to decode the different features of the spin-spin coupling mechanism. For this purpose, the physics of spin-spin coupling is described and the way how spin-spin coupling constants (SSCCs) can be quantum mechanically determined. Based on this insight, a set of requirements is derived that guide the development of a quantum mechanical analysis of spin-spin coupling. It is demonstrated that the J-OC-PSP (=J-OC-OC-PSP: Decomposition of J into orbital contributions using orbital currents and partial spin polarization) analysis method fulfills all requirements. J-OC-PSP makes it possible to partition the isotropic indirect SSCC J or its reduced analogue K as well as the four Ramsey terms (Fermi contact (FC), spin dipole (SD), diamagnetic spin orbit (DSO), paramagnetic spin orbit (PSO)) leading to J (or K) into Cartesian components (for the anisotropic Ramsey terms SD, DSO, PSO), orbital contributions or electron interaction terms. For the purpose of decoding the spin-spin coupling mechanism, FC, SD, DSO, and PSO coupling is discussed in detail and related to electronic and bonding features of the molecules in question. The myth of empirical and semiempirical relationships between SSCCs and bonding features is unveiled. It is found that most relationships are only of limited, partly dubious value, often arising from a fortuitous cancellation of terms that cannot be expected in general. These relationships are replaced by quantum chemical relations and descriptions that directly reflect the complex electronic processes leading to spin-spin coupling.

Experimental and Theoretical Study of Hyperconjugative Interaction Effects on NMR 1JCH Scalar Couplings

Hyperconjugative and electrostatic interactions effects on 1J(CH) spin-spin coupling constants (SSCCs) are critically studied from both theoretical and experimental points of view. A qualitative model is used to predict how the former affect such SSCCs, while electrostatic interactions are modeled with a point charge placed in the vicinity of the corresponding sigma(CH) bond. Hyperconjugative interactions are calculated using the "natural bond orbital" approach, and using the point-charge model, it is shown how intertwined are both types of interactions. Several members of the series 1-X-bicyclo[1.1.1]pentane and 1-X-3-methylbicyclo[1.1.1]pentane are chosen as model compounds for measuring 1J(CH) SSCCs; in some of them were performed also DFT-SSCC calculations. The strained cage substrate in these series defines strong sigma-hyperconjugative interactions, making these compounds excellent examples to verify the qualitative model presented in this work. It is verified that (a) hyperconjugative interactions from the sigma(CH) bond or into the sigma(CH) antibond containing the coupling nuclei yield a decrease of the corresponding 1J(CH) SSCC and (b) hyperconjugative interactions from other bonds involving the coupling C nucleus yield an increase of that 1J(CH) SSCC.