Indirect Nuclear Spin-spin Coupling Constants Research Articles

Efficient J‐oriented tin basis sets for the correlated calculations of indirect nuclear spin–spin coupling constants

New J-oriented tin basis sets, acvXz-J (X=2, 3, 4), have been developed at the level of the second-order polarization propagator approximation with the coupled-cluster single and double amplitudes, SOPPA (CCSD), for the purpose of correlated calculations of indirect nuclear spin-spin coupling constants involving tin nucleus. High-quality coupled-cluster calculations of several tin-proton and tin-carbon spin-spin coupling constants, performed with one of the newly developed basis sets, namely, the acv3z-J, taking into account relativistic, solvent, and vibrational corrections showed that the acv3z-J basis set is capable to provide reliable results, as compared with the experimental data.

Hierarchical Basis Sets for the Calculation of Nuclear Magnetic Resonance Spin-Spin Coupling Constants Involving Either Selenium or Tellurium Nuclei.

New basis sets, acvXz-J (X = 2, 3, 4), were designed for tellurium and selenium atoms for the calculation of indirect nuclear spin-spin coupling constants involving selenium or tellurium nuclei. Saturation of angular spaces was performed in an even-tempered manner till achieving the convergence of spin-spin coupling constants under consideration. The high-accuracy correlated SOPPA(CCSD) method was employed in this procedure. Saturated basis sets were contracted by approximately 30% using the coefficients obtained from the atomic self-consistent field (SCF) closed-shell calculations of selenium and tellurium anions, Se2- and Te2-. Final basis sets of acvXz-J showed sufficiently high accuracy in comparison with previous special basis sets.

RPA(D) and HRPA(D): Two new models for calculations of NMR indirect nuclear spin-spin coupling constants.

In this article, the RPA(D) and HRPA(D) models for the calculation of linear response functions are presented. The performance of the new RPA(D) and HRPA(D) models is compared to the performance of the established RPA, HRPA, and SOPPA models in calculations of indirect nuclear spin-spin coupling constants using the CCSD model as a reference. The doubles correction offers a significant improvement on both the RPA and HRPA models; however, the improvement is more dramatic in the case of the RPA model. For all coupling types investigated in this study, the results obtained using the HRPA(D) model are comparable in accuracy to those given by the SOPPA model, while requiring between 30% and 90% of the calculation time needed for SOPPA. The RPA(D) model, while of slightly lower accuracy compared to the CCSD model than HRPA(D), offered calculation times of only approximately 25% of those required for SOPPA for all the investigated molecules. © 2018 Wiley Periodicals, Inc.

Calculation of NMR Spin-Spin Coupling Constants in Strychnine.

We compare the NMR indirect nuclear spin-spin coupling constants in strychnine calculated using density functional theory (DFT) with the semiempirical relativistic force field (RFF) method of Kutateladze and Mukhina (KM) (J. Org. Chem. 2015, 80, 10838-10848). DFT values significantly more accurate than those obtained by KM for their comparison with RFF values can be obtained, at a lower cost, by an appropriate selection of basis set.

Computation of indirect nuclear spin-spin couplings with reduced complexity in pure and hybrid density functional approximations.

We present a (sub)linear-scaling algorithm to determine indirect nuclear spin-spin coupling constants at the Hartree-Fock and Kohn-Sham density functional levels of theory. Employing efficient integral algorithms and sparse algebra routines, an overall (sub)linear scaling behavior can be obtained for systems with a non-vanishing HOMO-LUMO gap. Calculations on systems with over 1000 atoms and 20 000 basis functions illustrate the performance and accuracy of our reference implementation. Specifically, we demonstrate that linear algebra dominates the runtime of conventional algorithms for 10 000 basis functions and above. Attainable speedups of our method exceed 6 × in total runtime and 10 × in the linear algebra steps for the tested systems. Furthermore, a convergence study of spin-spin couplings of an aminopyrazole peptide upon inclusion of the water environment is presented: using the new method it is shown that large solvent spheres are necessary to converge spin-spin coupling values.

Revisiting NMR through-space J(FF) spin-spin coupling constants for getting insight into proximate F---F interactions.

At present times it is usual practice to mark biological compounds replacing an H for an F atom to study, by means of (19)F NMR spectroscopy, aspects such as binding sites and molecular folding features. This interesting methodology could nicely be improved if it is known how proximity interactions on the F atom affect its electronic structure as gauged through high-resolution (19)F NMR spectroscopy. This is the main aim of the present work and, to this end, differently substituted peri-difluoronaphthalenes are chosen as model systems. In such compounds are rationalized some interesting aspects of the diamagnetic and paramagnetic parts of the (19)F nuclear magnetic shielding tensor as well as the transmission mechanisms for the PSO and FC contributions to (4)JF1F8 indirect nuclear spin-spin coupling constants.

Novel 1,3-dichalcogeno-2-phospholanes with an annelated 1,2-dicarba-closo-dodecaborane(12) Unit

The most efficient strategies for the synthesis of novel 1,3dichalcogeno-2-phospholanes (chalcogen E = O, S, Se, Te) are introduced, starting from 1,2-dicarba-closo-dodecaborane(12) (ortho-carborane), its 1,2-di-lithiated derivative, and various phosphorus halides. The annelation of the phospholane ring with the rigid three-dimensional carborane framework causes markedly different properties when compared with other phospholanes. Most noteworthy are the structural alternatives concerning the orientation of the lone pair of electrons at phosphorus, the instability of Phalides in particular for E = O, and the pronounced tendency for dimerization in the case of P-organo derivatives, which increases from E = Te < Se < S << O. The latter is a consequence of spatial proximity between P-R or electron density at phosphorus and the carborane skeleton. Direct structural evidence is provided for monomers and dimers by single crystal X-ray structural analysis. The solution-state structures follow from consistent sets of multinuclear magnetic resonance data ( 1 H, 11 B, 13 C, 31 P, 77 Se, 125 Te NMR). This is complemented by calculations leading to optimized gas-phase geometries at the B3LYP/6-311+G(d,p) level of theory. Most NMR parameters (chemical shifts δ and indirect nuclear spinspin coupling constants n J) are calculated at the same level of theory. These studies indicate that there are cases, for which important features of the solid-state structures may not be retained in solution.

Spin–Spin Artificial DNA Intercalated with Silver Cations: Theoretical Prediction

The indirect nuclear spin-spin coupling constants of Ag(+) cation intercalated between imidazole rings in DNA chains are calculated by means of DFT with relativistic effects taken into account by the use of the zeroth-order regular approximation Hamiltonian (DFT-ZORA). The calculations model how the (1)J((15)N,(109)Ag) coupling constant is affected by different types of geometry deformations and by the presence of water, which is simulated by means of the polarizable continuum model and explicitly present water molecules. Calculations for systems containing two and three imidazole pairs are also carried out to model the influence of stacking interactions. The computed (1)J((15)N,(109)Ag) spin-spin coupling constant is in the range of 85-105 Hz (depending on the computational model) and is in good agreement with the experimental value (ca. 92 Hz). This coupling constant is very little affected by the presence of solvent, stacking interactions, and geometry deformations. Such behavior is explained by visualization of the coupling path by means of coupling energy density (CED). Bigger models allow the coupling constant between two adjacent silver ions to be computed, and give a value of approximately 1 Hz, which is probably too small to be of practical interest. The (2)J((15)N,(15)N) value is calculated to be about 2.5 Hz, and is therefore of measurable magnitude.

On the discrepancy between theory and experiment for the F–F spin–spin coupling constant of difluoroethyne

The vicinal indirect nuclear spin-spin coupling constant (SSCC) between the two fluorine atoms in difluoroethyne has been reinvestigated. This coupling has previously proved to be difficult to calculate accurately. In this study we have therefore systematically investigated the dependence of this coupling on the choice of one-electron basis set, the choice of correlated wave function method and the inclusion of zero-point vibrational and temperature corrections. All terms of the SSCC have been evaluated at the second-order polarization propagator, SOPPA and SOPPA(CCSD), and coupled cluster singles and doubles (CCSD) levels of theory and for the most correlation dependent term, the paramagnetic spin-orbit contribution (PSO), also at the very accurate CC3 level. We find that in order to get results that are well converged with respect to the basis set, one needs to use special SSCC optimized basis sets of at least quadruple zeta quality and with added diffuse functions. Furthermore, the PSO term is not yet converged at the CCSD level as shown by the CC3 calculations. Finally, it is shown that vibrational effects are very important, as they are in this case of the same order of magnitude as the equilibrium geometry value of the coupling constant. Only by using a converged basis set and including both vibrational and higher order correlation effects can we obtain agreement with the experimental value for this coupling.

Pople Style Basis Sets for the Calculation of NMR Spin-Spin Coupling Constants: the 6-31G-J and 6-311G-J Basis Sets.

We present a modification of the small and popular Pople basis sets, 6-31G and 6-311G, for density functional theory calculations of Fermi contact dominated NMR indirect nuclear spin-spin coupling constants. These new basis sets, 6-31G-J and 6-311G-J, contain twice the number of contracted s-type functions but the same number of contracted p-type functions as the original Pople basis set. For our test set of 12 one-, two- and three-bond coupling constants, the new basis sets augmented with the standard diffuse and polarization functions, i.e., the 6-31+G*-J and 6-311++G**-J basis sets, lead to a maximum deviation of 5 and 2 Hz, respectively, compared to results obtained with the 6 or more times larger aug-pcJ-4 basis set. In correlated wave function calculations using the second-order polarization propagator approximation, the deviations with respect to the aug-ccJ-pVQZ basis set are 8 and 3 Hz and thus slightly larger.

Experimental and theoretical NMR and IR studies of the side‐chain orientation effects on the backbone conformation of dehydrophenylalanine residue

Conformation of N-acetyl-(E)-dehydrophenylalanine N', N'-dimethylamide (Ac-(E)-ΔPhe-NMe(2)) in solution, a member of (E)-α, β-dehydroamino acids, was studied by NMR and infrared spectroscopy and the results were compared with those obtained for (Z) isomer. To support the spectroscopic interpretation, the Φ, Ψ potential energy surfaces were calculated at the MP2/6-31 + G(d,p) level of theory in chloroform solution modeled by the self-consistent reaction field-polarizable continuum model method. All minima were fully optimized by the MP2 method and their relative stabilities were analyzed in terms of π-conjugation, internal H-bonds and dipole interactions between carbonyl groups. The obtained NMR spectral features were compared with theoretical nuclear magnetic shieldings, calculated using Gauge Independent Atomic Orbitals (GIAO) approach and rescaled to theoretical chemical shifts using benzene as reference. The calculated indirect nuclear spin-spin coupling constants were compared with available experimental parameters.

Illumination of the effect of the overlap of lone-pairs on indirect nuclear spin–spin coupling constants

The effect of electron lone-pairs on the Fermi-contact (FC) contribution to indirect nuclear spin-spin coupling constants is analyzed using new tools for their interpretation. In particular, visualization of spin-spin coupling pathways using the coupling deformation density (CDD) has been employed. Furthermore, the recently developed perturbation-stable localization procedure has been applied for decomposition of CDD and the calculated value of couplings into contributions from localized molecular orbitals (LMOs). Correlation between the overlap of densities of LMOs representing lone-pairs and the Fermi-contact contribution to spin-spin coupling constants has been demonstrated. A new way for analyzing spin-spin couplings using the expansion of CDD as a linear combination of the products of molecular orbitals has been suggested. The considered examples include two- and three-bond phosphor-phosphor couplings. Significance of the obtained insight is not restricted to spin-spin couplings of nuclei possessing lone-pairs, as demonstrated in the example of vicinal hydrogen-hydrogen coupling in ethane.

Modeling of Heavy‐Atom–Ligand NMR Spin–Spin Coupling in Solution: Molecular Dynamics Study and Natural Bond Orbital Analysis of HgC Coupling Constants

Ab initio molecular dynamics (MD) and relativistic density functional NMR methods were applied to calculate the one-bond Hg-C NMR indirect nuclear spin-spin coupling constants (J) of [Hg(CN)(2) ] and [CH(3) HgCl] in solution. The MD averages were obtained as J((199) Hg-(13) C)=3200 and 1575 Hz, respectively. The experimental Hg-C spin-spin coupling constants of [Hg(CN)(2) ] in methanol and [CH(3) HgCl] in DMSO are 3143 and 1674 Hz, respectively. To deal with solvent effects in the calculations, finite "droplet" models of the two systems were set up. Solvent effects in both systems lead to a strong increase of the Hg-C coupling constant. From a relativistic natural localized molecular orbital (NLMO) analysis, it was found that the degree of delocalization of the Hg 5d(σ) nonbonding orbital and of the HgC bonding orbital between the two coupled atoms, the nature of the trans Hg-C/Cl bonding orbital, and the s character of these orbitals, exhibit trends upon solvation of the complexes that, when combined, lead to the strong increase of J(Hg-C).

Benchmarking NMR indirect nuclear spin-spin coupling constants: SOPPA, SOPPA(CC2), and SOPPA(CCSD) versus CCSD

Accurate calculations of NMR indirect nuclear spin-spin coupling constants require especially optimized basis sets and correlated wave function methods such as CCSD or SOPPA(CCSD). Both methods scale as N(6), where N is the number of orbitals, which prevents routine applications to molecules with more than 10-15 nonhydrogen atoms. We have therefore developed a modification of the SOPPA(CCSD) method in which the CCSD singles and doubles amplitudes are replaced by CC2 singles and doubles amplitudes. This new method, called SOPPA(CC2), scales only as N(5), like the original SOPPA-method. The performance of the SOPPA(CC2) method for the calculation of indirect nuclear spin-spin coupling constants is compared to SOPPA and SOPPA(CCSD) employing a set of benchmark molecules. We also investigate the basis set dependence by employing three different basis sets optimized for spin-spin coupling constants, namely the HuzIV-su4, ccJ-pVTZ, and ccJ-pVQZ basis sets. The results of the corresponding CCSD calculations are used as a theoretical reference.

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.

Thermal averaging of the indirect nuclear spin-spin coupling constants of ammonia: The importance of the large amplitude inversion mode

Analytic internal-coordinate representations are reported for two accurate ab initio spin-spin coupling surfaces of the ammonia molecule, (1)J ((15)N,H) and (2)J(H,H). Calculations were carried out at the level of the second-order polarization propagator approximation involving coupled-cluster singles and doubles amplitudes (CCSD) and using a large specialized basis set, for a total of 841 different geometries corresponding to 2523 distinct points on the (1)J ((15)N,H) and (2)J(H,H) surfaces. The results were fitted to power series expansions truncated after the fourth-order terms. While the one-bond nitrogen-hydrogen coupling depends more on the internuclear distance, the geminal hydrogen-hydrogen coupling exhibits a pronounced dependence on the bond angle. The spin-spin parameters are first vibrationally averaged, using vibrational wave functions obtained variationally from the TROVE computer program with a CCSD(T) based potential energy surface, for ammonia and its various deuterated isotopologues. The vibrationally averaged quantities are then thermally averaged to give values of the couplings at absolute temperatures of 300 and 600 K. We find that the nuclear-motion corrections are rather small. The computed one-bond couplings and their minute isotope effects are in excellent agreement with the experimental values.

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

Analysis of isotope effects in NMR one-bond indirect nuclear spin–spin coupling constants in terms of localized molecular orbitals

We recently showed, by analyzing contributions from localized molecular orbitals, that the anomalous deuterium isotope effect in the one-bond indirect nuclear spin-spin coupling constant of methane, also called the unexpected differential sensitivity, can be explained by the transfer of s-orbital character from the stretched bond to the other unchanged bonds [ChemPhysChem, 2008, 9, 1259]. We now extend this analysis of isotope effects to the molecules BH(4)(-), NH(4)(+), SiH(4), H(2)O and NH(3) in order to test our conclusions on a wider rage of XH(4) compounds and to investigate whether the lone-pair orbitals are really responsible for the absence of a similar effect in water and ammonia as proposed earlier [J. Chem. Phys., 2000, 113, 3121].

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin-spin coupling constants (SSCCs) in the Kohn-Sham (KS) complete basis set (CBS) limit. Correlation-consistent cc-pVxZ and cc-pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ-pVxZ, unc-ccJ-pVxZ, and aug-cc-pVTZ-J) and polarization-consistent pc-n and pcJ-n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT-predicted isotropic shieldings, spin-spin values, and the experimental values was good and similar for the modified correlation-consistent and polarization-consistent basis sets. The BHandH method predicted the most accurate (1)H, (17)O isotropic shieldings and (1)J(OH) coupling constant (deviations from experiment of about -0.2 and -1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and (1)J(OH) is similar to the more advanced methods, second-order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit.

Two-component relativistic hybrid density functional computations of nuclear spin-spin coupling tensors using Slater-type basis sets and density-fitting techniques

Computations of indirect nuclear spin-spin coupling constants using two-component relativistic density functional theory with a hybrid functional are reported. The program implementation makes use of a Slater-type orbital expansion of the molecular orbitals and the zeroth-order regular approximation for the treatment of relativistic effects. Exact exchange terms in the Kohn-Sham response kernel were computed using a fitting procedure. Computations with the PBE0 hybrid functional were carried out for heavy-atom-ligand-one-bond couplings in PbH(4), Pb(CH(3))(2)H(2), Pb(CH(3))(3)H, three platinum complexes, the interhalogen diatomics such as ClF, ClBr, ClI, BrF, BrI, IF, and the series Tl-X with X=F, Cl, Br, I. The hybrid functional computations performed very well. In particular, for the isotropic coupling and the coupling anisotropy of Tl-X, the PBE0 hybrid functional yielded considerably improved agreement with experiment.