Gustavo A. Aucar

The effect of lone pairs and electronegativity on the indirect nuclear spin–spin coupling constants in CH2X (X=CH2, NH, O, S): Ab initio calculations using optimized contracted basis sets

The indirect nuclear spin–spin coupling constants of C2H4, CH2NH, CH2O, and CH2S were investigated by means of correlated ab initio calculations at the level of the second order polarization propagator approximation (SOPPA) and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes—SOPPA(CCSD) using large basis sets, which are optimized for the calculation of coupling constants. It is found that at the self-consistent-field (SCF) level CH2NH and CH2S exhibit triplet instabilities whereas CH2CH2 and CH2O show triplet quasi-instabilities, which renders the SCF results meaningless. Our best results deviate between 0.3 and 2.7 Hz from the experimental values. We find that although the one-bond C–H and Y–H couplings as well as the two- and three-bond H–H couplings are dominated by the Fermi contact term, significant contributions of the orbital paramagnetic and sometimes even spin–dipolar terms are observed for the one-bond C–Y and two-bond C–H and Y–H coupli...

The use of locally dense basis sets in the calculation of indirect nuclear spin–spin coupling constants: The vicinal coupling constants in H3C–CH2X (X=H, F, Cl, Br, I)

We have calculated the vicinal indirect nuclear spin-spin coupling constants 3J1H1H  in the series of molecules H3C–CH2X with X=H, F, Cl, Br, and I at the self-consistent field level and using the second order polarization propagator approximation (SOPPA). We have studied the effect of electron correlation and of the substituents (X=F, Cl, Br, and I) on all four contributions to the coupling constants. But in particular we have investigated the possibility of using locally dense basis sets, i.e., we have carried out calculations with basis sets, where the basis functions on the hydrogen atoms were optimized for the calculation of spin–spin coupling constants whereas on the other atoms smaller, contracted sets of basis functions were used. This changes the results for the couplings by ∼0.3 Hz or 3%. However, the change is almost entirely due to the orbital paramagnetic term and is independent of electron correlation, which enables one to estimate the SOPPA results in the full basis sets. Furthermore we fin...

Polarization propagators: A powerful theoretical tool for a deeper understanding of NMR spectroscopic parameters

Magnetic molecular spectroscopic properties, like NMR J-coupling and magnetic shielding σ, have been studied by non-relativistic quantum methods since their discovery. When they were found to depend strongly on relativistic effects in molecules containing heavy atoms, this started a new area of intensive research into the development of methods that include such effects. In most cases non-relativistic concepts were extended to the new field though keeping the previous non-relativistic point of view. Quantum mechanics can be formulated by two different formal approaches. Molecular physics and quantum chemistry were developed mostly within the Schrödinger or Heisenberg approaches. The path integral formalism of Feynman is less well known. This may be the reason why propagators are not broadly known in this field of research. Polarization propagators were developed in the early 1970s. Since that time they have been successfully applied to calculate NMR spectroscopic parameters. They are special theoretical devices from which one can do a deep analysis of the electronic mechanisms that underly any molecular response property from basic theoretical elements, like molecular orbitals, electronic excitation energies, coupling pathways, entanglement, contributions within different levels of theory, etc. All this is obtained in a natural way in both regimes: relativistic and non-relativistic. Its relativistic generalization in the early 1990s and the finding of a quantum electrodynamic (QED)-based theory for them, has given us the opportunity to improve our understanding of the physics behind such parameters. In this paper we give a presentation of polarization propagators that start in non-relativistic quantum physics and end up with the introduction of QED effects. The same and powerful basic quantum ideas are applied throughout this review, so that coherence and beauty arise in a natural way. We will give a new understanding that comes from the three levels of theory: non-relativistic, relativistic and QED. We will be cautious to highlight what one can learn when working in any of these regimes, being aware that the same concepts may have different meanings. Starting with a general overview of polarization propagators we develop both the theory and applications in each of the three levels mentioned above. We show how some of the most subtle properties of the NMR spectroscopic parameters can be explained in a simple and beautiful way: the sign of J, the Karplus rule, cooperative effects, diamagnetic and paramagnetic contributions; we also show new rules that appear within the relativistic regime and the way previously valid rules within the non-relativistic theory are broken. We highlight the fact that within the relativistic theory of polarization propagators the whole set of electronic mechanisms that appears within the NR regime and within its quasi-relativistic extension is unified. Furthermore the usual notion of diamagnetism and paramagnetism are now nonsense as such because they arise only after as an approximation from expressions which include a unique type of electronic (electron–positron) mechanism.

Relativistic heavy-atom effects on heavy-atom nuclear shieldings

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.

The UKB prescription and the heavy atom effects on the nuclear magnetic shielding of vicinal heavy atoms

Fully relativistic calculations of NMR magnetic shielding on XYH3 (X = C, Si, Ge and Sn; Y = Br, I), XHn (n = 1-4) molecular systems and noble gases performed with a fully relativistic polarization propagator formalism at the RPA level of approach are presented. The rate of convergence (size of basis set and time involved) for calculations with both kinetic balance prescriptions, RKB and UKB, were investigated. Calculations with UKB makes it feasible to obtain reliable results for two or more heavy-atom-containing molecules. For such XYH3 systems, the influence of heavy vicinal halogen atoms on sigma(X) is such that heavy atom effects on heavy atoms (vicinal plus their own effects or HAVHA + HAHA effects) amount to 30.50% for X = Sn and Y = I; being the HAHA effect of the order of 25%. So the vicinal effect alone is of the order of 5.5%. The vicinal heavy atom effect on light atoms (HALA effect) is of the order of 28% for X = C and Y = I. A similar behaviour, but of opposite sign, is observed for sigma(Y) for which sigmaR-NR (I; X = C) (HAHA effect) is around 27% and sigmaR-NR(I; X = Sn) (HAVHA + HAHA effects) is close to 21%. Its electronic origin is paramagnetic for halogen atoms but both dia- and paramagnetic for central atoms. The effect on two bond distant hydrogen atoms is such that the largest variation of sigma(H) within the same family of XYH3 molecules appears for X = Si and Y = I: around 20%. In this case sigma(H; X = Sn, Y = I) = 33.45 ppm and sigma(H; X = Sn, Y = H) = 27.82 ppm.

NMR Spectroscopic Parameters of Molecular Systems with Strong Hydrogen Bonds

A series of closed H-bonded molecules that have (or not) delocalized bonds were studied. The dependence of both NMR spectroscopic parameters sigma and J-couplings, and also the energy stability of such molecules with H-bond strength, were analyzed. The selected basic geometrical structure was that of malonaldehyde. From its full optimized geometry, the corresponding geometry of 3-OH propanal was obtained, fixing either the d(O-O) distance or a more extended local geometry and then optimizing the other part of the whole structure. Nitromalonaldehyde and nitromalonamide were also studied because they should have stronger H-bonds and their basic structure is also malonaldehyde. The last one also has electronic effects that may be varied by rotating the amino groups. By doing this it is possible to show that the effects on acidity of donors are more important than the equivalent effects on the basicity of acceptors. It is also shown that J-couplings that involve atoms close to the H-bond have important noncontact contributions that must be included in order to reproduce total J values. Noncontact contributions are more important than the Fermi contact (FC) one for J(O-O) in malonaldehyde. In nitromalonamide all three terms, FC, paramagnetic spin-orbital, and spin-dipolar are of the same order of magnitude when both amino groups are rotated. This does not happen for its planar configuration. Nuclear magnetic shielding of the hydrogen belonging to the H-bond is quite sensitive to it. The magnetic behavior of such hydrogen atom is modified when it is part of a closed H-bonded molecule. Then a relationship between the H-bond strength with the paramagnetic contributions of the shieldings of both atoms, C and O of the donor substructure, was obtained. We have found a cubic correlation between sigma(p) (C) of the C-O donor bond with sigma (H) of the H-bonded hydrogen. It is observed that both the noncontact J-coupling contributions and shieldings on atoms belonging to the donor substructure, give a clear evidence about the presence of the resonance phenomenon in the model compounds that have been studied, malonaldehyde, nitromalonaldehyde, and nitromalonamide.

Relativistic and electron-correlation effects on the nuclear magnetic resonance shieldings of molecules containing tin and lead atoms.

The reference values for NMR magnetic shieldings, σ(ref), are of the highest importance when theoretical analysis of chemical shifts are envisaged. The fact that the nonrelativistically valid relationship among spin-rotation constants and magnetic shieldings is not any longer valid for heavy atoms requires that the search for σ(ref) for such atoms needs new strategies to follow. We present here results of σ(ref) that were obtained by applying our own simple procedure which mixes accurate experimental chemical shifts (δ) and theoretical magnetic shieldings (σ). We calculated σ(Sn) and σ(Pb) in a family of heavy-halogen-containing molecules. We found out that σ(ref)[Sn;Sn(CH3)4] in gas phase should be close to 3864.11 ± 20.05 ppm (0.5%). For Pb atom, σ(ref)[Pb;Pb(CH3)4] should be close to 14475.1 ± 500.7 ppm. Such theoretical values correspond to calculations with the relativistic polarization propagator method, RelPPA, at the RPA level of approach. They are closer to experimental values as compared to those obtained applying few different functionals such as PBE0, B3LYP, BLYP, BP86, KT2, and KT3 of the density functional theory, DFT. We studied tin and lead shieldings of the XY(4-n)Z(n) (X = Sn, Pb; Y, Z = H, F, Cl, Br, I) and PbH(4-n)I(n) (n = 0, 1, 2, 3, 4) family of compounds with four-component functionals as implemented in the DIRAC code. For these systems results of calculations with RelPPA-RPA are more reliable than DFT ones. We argue about why those DFT functionals must be modified in order to obtain more accurate results of NMR magnetic shieldings within the relativistic regime: first, there is a dependence among both electron-correlation and relativistic effects that should be introduced in some way in the functionals; and second, the DIRAC code uses standard nonrelativistic functionals and the functionals B3LYP and PBE0 were parametrized only with data taken from light elements. It can explain why they are not able to properly introduce relativistic effects on nuclear magnetic shieldings. We finally show that in the analysis of magnetic shieldings for the family of compounds mentioned above, one must consider the newest and so-called heavy-atom effect on vicinal heavy atoms, HAVHA. Such effects are among the most important relativistic effects in these kind of compounds.

Relativistic corrections to the diamagnetic term of the nuclear magnetic shielding: Analysis of contributions from localized orbitals

We have calculated the relativistic corrections to the diamagnetic term of the nuclear magnetic shielding constants for a series of molecules containing heavy atoms. An analysis of the contributions from localized orbitals is performed. We establish quantitatively the relative importance of inner core and valence shell molecular orbitals in each correcting term. Contributions from the latter are much less important than those from the former. The calculated values of the correction sigma(L-PSO), first derived within the linear response elimination of small component formalism, show a power-law dependence on the nuclear charge approximately Z(3.5), in contrast with the approximately Z(3.1) behavior of the mass-velocity external-field correction to the paramagnetic term previously reported.

The appearance of an interval of energies that contain the whole diamagnetic contribution to NMR magnetic shieldings.

Working within relativistic polarization propagator approach, it was shown in a previous article that the electronic origin of diamagnetic contributions to NMR nuclear magnetic shielding, sigmad, are mostly excitations that fit in a well defined interval of energies such that 2mc2<or==(epsiloni-epsilons)<4mc2. That interval of energies does not have, in principle, any physical reason to be so well defined, and gives a large amount of the total contribution to sigmad, e.g., close to 98% of it. Then a further study is given in this article, where we show some of the main characteristics of that interval of energy, such as its universal appearance and basis set independence. Our main result is the finding that sigmad is completely described by that interval of excitation energies, i.e., there is no contribution arising from outside of it. Most of the contributions belonging to that interval arise from virtual electronic energies larger than -3mc2. For heavier atoms, there are few contributions from states with virtual negative energies smaller than -3mc2. The model systems under study were noble gases, XH (X=Br, I, and At), XH2 (X=O, S, Se, Te, and Po), XH3 (X=N, P, As, Sb, and Bi); XH4 (X=Sn and Pb), and SnXH3 (X=Br and I). The pattern of contributions of occupied molecular orbitals (MOs) is also shown, where the 1s1/2 is the most important for excitations ending in the bottom half part of the above mentioned interval. On the other hand, the contribution of the other occupied MOs are more important than that of 1s1/2 for the other part of such interval. We also show that sigmad is electron correlation independent within both relativistic and nonrelativistic domain. In the case of sigmap, we find out a clear dependence of electron correlation effects with relativistic effects, which is of the order of 30% for Pb in PbH4.

Core-dependent and ligand-dependent relativistic corrections to the nuclear magnetic shieldings in MH4-n Y n (n = 0-4; M = Si, Ge, Sn, and Y = H, F, Cl, Br, I) model compounds.

The nuclear magnetic shieldings of Si, Ge, and Sn in MH4−nYn (M = Si, Ge, Sn; Y = F, Cl, Br, I and n = 1–4) molecular systems are highly influenced by the substitution of one or more hydrogens by heavy-halogen atoms. We applied the linear response elimination of small components (LRESC) formalism to calculate those shieldings and learn whether including only a few of the leading relativistic correction terms is sufficient to be able to quantitatively reproduce the full relativistic value. It was observed that the nuclear magnetic shieldings change as the number of heavy halogen substituents and their weights vary, and the pattern of σ(M) generally does not exhibit the normal halogen dependence (NHD) behavior that can be seen in similar molecular systems containing carbon atoms. We also analyzed each relativistic correction afforded by the LRESC method and split them in two: core-dependent and ligand-dependent contributions; we then looked for the electronic mechanisms involved in the different relativistic effects and in the total relativistic value. Based on this analysis, we were able to study the electronic mechanism involved in a recently proposed relativistic effect, the “heavy atom effect on vicinal heavy atom” (HAVHA), in more detail. We found that the main electronic mechanism is the spin–orbit or σpT(3) correction, although other corrections such as σpS(1) and σpS(3) are also important. Finally, we analyzed proton magnetic shieldings and found that, for molecules containing Sn as the central atom, σ(H) decreases as the number of heavy halogen substituents (of the same type: either F, Cl, or Br) increases, albeit at different rates for different halogens. σ(H) only increase as the number of halogen substituents increases if the halogen is iodine.