Spin-orbit correction to NMR shielding constants from density functional theory

Relativistic DFT Calculations of Cadmium and Selenium Solid-State NMR Spectra of CdSe Nanocrystal Surfaces

Solid-state NMR spectra have been used to probe the structure of CdSe nanocrystals and propose detailed models of their surface structures. Density functional theory (DFT)-optimized cluster models that represent probable molecular structures of carboxylate-coordinated surface sites have been proposed. However, to the best of our knowledge, 113Cd and 77Se chemical shifts have not been calculated for these surface models. We performed relativistic DFT calculations of cadmium and selenium magnetic shielding tensors on model compounds with previously measured solid-state NMR spectra with (i) the four-component Dirac-Kohn-Sham (DKS) Hamiltonian and (ii) the scalar and (iii) spin-orbit levels within the ZORA Hamiltonian. Molecular clusters with Cd and Se sites in varying bonding environments were used to model CdSe (100) and CdSe(111) surfaces capped with carboxylic acid ligands. Our calculations identify the observed 113Cd isotropic chemical shifts δ(iso) of -465, -318, and -146 ppm arising from CdSeO3, CdSe2O2, and CdSe3O surface groups, respectively, with very good agreement with experimental measurements. The 113Cd chemical shifts linearly decrease with the number of O-neighbors. The calculated spans (δ11 - δ33) encompass the experimental values for CdSe3O and CdSe2O2 clusters but are slightly larger than the measured value for CdSeO3 clusters. Relativistic DFT calculations predicted a one-bond 113Cd-77Se scalar coupling of 258 Hz, which is in good agreement with the experimental values of 250 Hz. With a dense coverage of carboxylic acid ligands, the CdSe (100) surface shows a distribution of Cd-Se bond lengths and J-couplings. Relativistic DFT simulations thus aid in interpretation of NMR spectra of CdSe nanocrystals and related nanomaterials.

"Through-Space" Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹ H, ¹³ C, and ¹⁵ N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃ ] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I^- and I₃ ^- . A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.

Relativistic heavy atom effect on 13 C NMR chemical shifts initiated by adjacent multiple chalcogens

In this paper, we have investigated the cumulative peculiarity of the "heavy atom on light atom" effect on the ¹³ C NMR chemical shifts, initiated by the adjacent chalcogens. For this purpose, the most accurate hybrid computational scheme for the calculation of chemical shifts of carbon nuclei, directly bonded with several heavy chalcogens, is introduced and attested on the representative series of molecules. The best hybrid scheme combines the nonrelativistic coupled cluster-based approach with the different types of corrections, including vibrational, solvent, and relativistic. The dependences of the total relativistic corrections to carbon shielding constants in 2 series of model compounds, namely, X═¹³ C═Y (X, Y = O, S, Se, Te) and C(XH)_m (YH)_n (ZH)_p (QH)_s H_1-m H_1-n H_1-p H_1-s (X, Y, Z, Q = S, Se, Te and m, n, p, s = 0, 1), on the total atomic number of the adjacent chalcogens have been obtained.

On the long-range relativistic effects in the 15 N NMR chemical shifts of halogenated azines

Long-range β- and γ-relativistic effects of halogens in ¹⁵ N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5-triazines) are shown to be unessential for fluoro-, chloro-, and bromo-derivatives (1-2 ppm in average). However, for iodocontaining compounds, β- and γ-relativistic effects are important contributors to the accuracy of the ¹⁵ N calculation. Taking into account long-range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵ N NMR chemical shifts of the title compounds calculated at the non-relativistic and full 4-component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non-relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4-component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long-range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵ N NMR chemical shifts of halogenated nitrogen-containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.

Normal halogen dependence of 13 C NMR chemical shifts of halogenomethanes revisited at the four-component relativistic level

The 'Normal Halogen Dependence' of ¹³ C NMR chemical shifts in the series of halogenomethanes is revisited at the four-component relativistic level. Calculations of ¹³ C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four-component relativistic theory of Dirac-Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyall's basis sets of triple-zeta quality or higher are to be used within the framework of the four-component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non-relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright © 2016 John Wiley & Sons, Ltd.

A Localized Molecular Orbital Study of the Halogen Substitution Effect on (103)Rh NMR Shielding in [Cp*RhX2]2, Where X = Cl, Br, or I

(103)Rh NMR parameters and the bonding structure of three complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have been studied with the help of natural bond orbitals (NBOs) and natural localized molecular orbitals (NLMOs). The complexes of [Cp*RhX2]2, where X = Cl, Br, or I, have similar bonding structures, with the major difference being in the degree of covalency of the Rh-X bonds. The decomposition of (103)Rh NMR shielding into diamagnetic, paramagnetic, and spin-orbit terms shows that normal halogen dependence (NHD) of the (103)Rh NMR shift is defined mostly by the paramagnetic term, with the spin-orbit term being significantly smaller. The decomposition of (103)Rh shielding into spin-free NBO and NLMO contributions shows that (103)Rh shielding is dominated by Rh d-orbital deshielding contributions. We explain the NHD of the (103)Rh NMR shift with the increase in the energies of the virtual antibonding Rh-X orbitals along the X = Cl, Br, and I series.

Giant spin–orbit effects on 1H and 13C NMR shifts for uranium(vi) complexes revisited: role of the exchange–correlation response kernel, bonding analyses, and new predictions

Visiting the previously predicted giant spin–orbit-induced ¹H and ¹³C shifts in U(vi) complexes with improved methodology retains the reported unusual shift ranges, provides better understanding of the observations and gives improved confidence in the predictions.

Scalar and Spin-Orbit Relativistic Corrections to the NICS and the Induced Magnetic Field: The case of the E12(2-) Spherenes (E = Ge, Sn, Pb)

Can relativistic effects modify the NICS and the B(ind) values? In this manuscript we evaluate the relativistic corrections incorporated via the zeroth-order regular approximation to the calculations of nucleus-independent chemical shifts and the induced magnetic field (B(ind)) in the E12(2-) spherenes (E = Ge, Sn, Pb). We found that both electron delocalization descriptors are strongly affected by the relativistic corrections. For instance, for plumbaspherene, the difference in values from the nonrelativistic to the relativity-included calculation is almost 40 ppm! Our results show that the changes observed in the NICS and B(ind) values in the title cages are a consequence of the treatment of the relativistic effects. If these effects are included as scalar or spin-orbit calculations, then we can establish the next trend: Ge12(2-) is a nonaromatic species, Sn12(2-) is a low aromatic species, and Pb12(2-) is strongly aromatic, according to calculated NICS and B(ind) values. Thus, any prediction of electron delocalization in molecules containing heavy elements without considering an adequate treatment for relativistic effects may lead to an erroneous chemical interpretation.

Interpretation of the longitudinal (13)C nuclear spin relaxation and chemical shift data for five bromoazaheterocycles supported by nonrelativistic and relativistic DFT calculations

The longitudinal relaxation times of (13)C nuclei and NOE enhancement factors for 2-bromopyridine (1), 6-bromo-9-methylpurine (2), 3,5-dibromopyridine (3), 2,4-dibromopyrimidine (4), and 2,4,6-tribromopyrimidine (5) have been measured at 25 °C and B0 = 11.7 T. The most important contributions to the overall relaxation rates of nonbrominated carbons, i.e., the relaxation rates due to the (13)C-(1)H dipolar interactions and the shielding anisotropy mechanism, have been separated out. For 3 and 5, additionally, the T2,Q((14)N) values have been established from (14)N NMR line widths. All of these data have been used to determine rotational diffusion tensors for the investigated molecules. The measured saturation recovery curves of brominated carbons have been decomposed into two components to yield relaxation times, which after proper corrections provided parameters characterizing the scalar relaxation of the second kind for (13)C nuclei of (79)Br- and (81)Br-bonded carbons. These parameters and theoretically calculated quadrupole coupling constants for bromine nuclei have allowed the values of one-bond (13)C-(79)Br spin-spin coupling constants to be calculated. Independently, the coupling constants and magnetic shielding constants of the carbon nuclei have been calculated theoretically using the nonrelativistic and relativistic DFT methods F/6-311++G(2d,p)/PCM and so-ZORA/F/TZ2P/COSMO (F = BHandH or B3LYP), respectively. The agreement between the experimental and theoretical values of these parameters is remarkably dependent on the theoretical method used.

Effects of stereoelectronic interactions on the relativistic spin–orbit and paramagnetic components of the 13C NMR shielding tensors of dihaloethenes

The interactions between iodine atoms are responsible for lower ¹³C NMR shielding for the cis isomers in comparison to trans.

Scalar relaxation of the second kind. A potential source of information on the dynamics of molecular movements. 3. A (13)C nuclear spin relaxation study of CBrX3 (X = Cl, CH3, Br) molecules

Continuing studies based on measurements of the nuclear spin relaxation rates running via the SC2 mechanism (scalar relaxation of the second kind), we present in this work the results obtained for three bromo compounds: CBrCl3, (CH3)3CBr, and CBr4. A careful separation of saturation-recovery curves, measured for signals of (13)C nuclei at 7.05 and 11.7 T on two components, has provided the longitudinal SC2 relaxation rates of carbon signals in (79)Br and (81)Br containing isotopomers of the investigated compounds. These data have enabled experimental determination of spin-spin coupling constants and relaxation rates of quadrupole bromine nuclei, both types of parameters being hardly accessible by direct measurements. Investigation of the relaxation behavior of these molecules, being of similar size and shape, has provided quite different practical and interpretational problems which are likely to be encountered in relaxation studies of many other carbon-bromine systems. In order to evaluate the quality of the obtained experimental results, advanced theoretical calculations of the indirect (1)J((13)C,(79)Br) coupling constants, magnetic shielding of carbon nuclei, and quadrupole coupling constants of bromines in the investigated compounds have been performed and compared with the experimental values. Relatively small divergences between experiment and theory have been found. The contributions of the relativistic effects to the values of the discussed parameters have been tentatively estimated.

Adducts of nitrogenous ligands with rhodium(II) tetracarboxylates and tetraformamidinate: NMR spectroscopy and density functional theory calculations

Complexation of tetrakis(μ2-N,N'-diphenylformamidinato-N,N')-di-rhodium(II) with ligands containing nitrile, isonitrile, amine, hydroxyl, sulfhydryl, isocyanate, and isothiocyanate functional groups has been studied in liquid and solid phases using (1)H, (13)C and (15)N NMR, (13)C and (15)N cross polarisation-magic angle spinning NMR, and absorption spectroscopy in the visible range. The complexation was monitored using various NMR physicochemical parameters, such as chemical shifts, longitudinal relaxation times T1 , and NOE enhancements. Rhodium(II) tetraformamidinate selectively bonded only unbranched amine (propan-1-amine), pentanenitrile, and (1-isocyanoethyl)benzene. No complexation occurred in the case of ligands having hydroxyl, sulfhydryl, isocyanate, and isothiocyanate functional groups, and more expanded amine molecules such as butan-2-amine and 1-azabicyclo[2.2.2]octane. Such features were opposite to those observed in rhodium(II) tetracarboxylates, forming adducts with all kind of ligands. Special attention was focused on the analysis of Δδ parameters, defined as a chemical shift difference between signal in adduct and corresponding signal in free ligand. In the case of (1)H NMR, Δδ values were either negative in adducts of rhodium(II) tetraformamidinate or positive in adducts of rhodium(II) tetracarboxylates. Experimental findings were supported by density functional theory molecular modelling and gauge independent atomic orbitals chemical shift calculations. The calculation of chemical shifts combined with scaling procedure allowed to reproduce qualitatively Δδ parameters.

Quantum-chemical analyses of aromaticity, UV spectra, and NMR chemical shifts in plumbacyclopentadienylidenes stabilized by Lewis bases

We carried out a series of zeroth-order regular approximation (ZORA)-density functional theory (DFT) and ZORA-time-dependent (TD)-DFT calculations for molecular geometries, NMR chemical shifts, nucleus-independent chemical shifts (NICS), and electronic transition energies of plumbacyclopentadienylidenes stabilized by several Lewis bases, (Ph)2 ((t) BuMe2 Si)2 C4 PbL1 L2 (L1, L2 = tetrahydrofuran, Pyridine, N-heterocyclic carbene), and their model molecules. We mainly discussed the Lewis-base effect on the aromaticity of these complexes. The NICS was used to examine the aromaticity. The NICS values showed that the aromaticity of these complexes increases when the donation from the Lewis bases to Pb becomes large. This trend seems to be reasonable when the 4n-Huckel rule is applied to the fractional π-electron number. The calculated (13)C- and (207)Pb-NMR chemical shifts and the calculated UV transition energies reasonably reproduced the experimental trends. We found a specific relationship between the (13)C-NMR chemical shifts and the transition energies. As we expected, the relativistic effect was essential to reproduce a trend not only in the (207)Pb-NMR chemical shifts and J[Pb-C] but also in the (13)C-NMR chemical shifts of carbons adjacent to the lead atom.

The calculation of 29Si NMR chemical shifts of tetracoordinated silicon compounds in the gas phase and in solution

²⁹Si NMR chemical shifts have been calculated for a variety of silicon-based species relevant in organic synthesis.

Computational19F NMR. 2. Organic compounds

DFT calculations allow to model and predict¹⁹F NMR chemical shift in a wide variety of organofluorine molecules.

Density functional theory study of (13)C NMR chemical shift of chlorinated compounds

The use of the standard density functional theory (DFT) leads to an overestimation of the paramagnetic contribution and underestimation of the shielding constants, especially for chlorinated carbon nuclei. For that reason, the predictions of chlorinated compounds often yield too high chemical shift values. In this study, the WC04 functional is shown to be capable of reducing the overestimation of the chemical shift of Cl-bonded carbons in standard DFT functionals and to show a good performance in the prediction of (13)C NMR chemical shifts of chlorinated organic compounds. The capability is attributed to the minimization of the contributions that intensively increase the chemical shift in the WC04. Extensive computations and analyses were performed to search for the optimal procedure for WC04. The B3LYP and mPW1PW91 standard functionals were also used to evaluate the performance. Through detailed comparisons between the basis set effects and the solvent effects on the results, the gas-phase GIAO/WC04/6-311+G(2d,p)//B3LYP/6-31+G(d,p) was found to be specifically suitable for the prediction of (13)C NMR chemical shifts of chlorides in both chlorinated and non-chlorinated carbons. Further tests with eight molecules in the probe set sufficiently confirmed that WC04 was undoubtedly effective for accurately predicting (13) C NMR chemical shifts of chlorinated organic compounds.

Density-functional computation of (99)Tc NMR chemical shifts

99Tc chemical shifts of TcO4(-), TcH9(2-), TcOF5, TcO2F4(-), TcOCl4(-), Tc2(CO)10, and Tc(CO)3L3(+) (L = CO, MeCN, H2O) are computed using geometries optimized with the gradient-corrected BP86 and hybrid B3P86 density functionals, at the gauge-including atomic orbitals (GIAO), -BPW91 and -B3LYP levels. For this set of compounds, substituent effects on delta(99Tc) are better described with the pure BPW91 functional than with B3LYP, in contrast to most other transition-metal chemical shifts studied so far. A rough, qualitative correlation is found between computed electric-field gradients at the Tc nuclei and the corresponding 99Tc NMR line widths. Thermal and solvation effects on magnetic shielding constants of aqueous TcO4(-), as assessed by averaging these properties over trajectories from Car-Parrinello molecular dynamics simulations, are indicated to be small and comparable to those of MnO4(-). Complexation to aqueous uranyl, UO2(2+), is predicted to affect delta(99Tc) of TcO4(-) only slightly; somewhat larger complexation shifts are obtained for the oxygen nuclei of pertechnetate, suggesting that 17O NMR could be a useful probe for the extent of association between both radionuclides in solution.

Theory and computation of nuclear magnetic resonance parameters

The art of quantum chemical electronic structure calculation has over the last 15 years reached a point where systematic computational studies of magnetic response properties have become a routine procedure for molecular systems. One of their most prominent areas of application are the spectral parameters of nuclear magnetic resonance (NMR) spectroscopy, due to the immense importance of this experimental method in many scientific disciplines. This article attempts to give an overview on the theory and state-of-the-art of the practical computations in the field, in terms of the size of systems that can be treated, the accuracy that can be expected, and the various factors that would influence the agreement of even the most accurate imaginable electronic structure calculation with experiment. These factors include relativistic effects, thermal effects, as well as solvation/environmental influences, where my group has been active. The dependence of the NMR spectra on external magnetic and optical fields is also briefly touched on.

Density functional calculations of NMR shielding tensors for paramagnetic systems with arbitrary spin multiplicity: validation on 3d metallocenes

The calculation of nuclear shieldings for paramagnetic molecules has been implemented in the ReSpect program, which allows the use of modern density functional methods with accurate treatments of spin-orbit effects for all relevant terms up to order Omicron(alpha4) in the fine structure constant. Compared to previous implementations, the methodology has been extended to compounds of arbitrary spin multiplicity. Effects of zero-field splittings in high-spin systems are approximately accounted for. Validation of the new implementation is carried out for the 13C and 1H NMR signal shifts of the 3d metallocenes 4VCp2, 3CrCp2, 2MnCp2, 6MnCp2, 2CoCp2, and 3NiCp2. Zero-field splitting effects on isotropic shifts tend to be small or negligible. Agreement with experimental isotropic shifts is already good with the BP86 gradient-corrected functional and is further improved by admixture of Hartree-Fock exchange in hybrid functionals. Decomposition of the shieldings confirms the dominant importance of the Fermi-contact shifts, but contributions from spin-orbit dependent terms are frequently also non-negligible. Agreement with 13C NMR shift tensors from solid-state experiments is of similar quality as for isotropic shifts.

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.