Calculation Of Nuclear Magnetic Shieldings Research Articles

Assessment of the Performance of Optimally Tuned Range‐Separated Hybrid Functionals for Nuclear Magnetic Shielding Calculations

AbstractThe performance of optimally tuned range‐separated hybrid (OT‐RSH) functional calculations in predicting accurate isotropic nuclear magnetic shielding (σ) and chemical shift values is examined. To that end, the results of OT‐RSH and other approximate density functional theory calculations are assessed against recently published benchmark CCSD(T) calculations for a test set consisting of several molecules and bond types. It is found that for atoms in single bonds with a large paramagnetic contribution to σ, OT‐RSH offers a significant improvement in prediction of shielding constants over popular semi‐local and hybrid density functionals, yielding non‐empirical results that are as accurate as those of semi‐empirical density functionals often used for prediction of shielding constants. This success is attributed to the improved fundamental gap prediction of the OT‐RSH approach. For atoms in multiple bonds, however, larger errors often persist. By comparing OT‐RSH and recently reported double‐hybrid functional results, the remaining difficulties are traced to significant non‐local correlation.

On the calculation of magnetic properties of nucleic acids in liquid water with the sequential QM/MM method

We present calculations of nuclear magnetic shieldings of the nucleic acids adenine, cytosine, guanine e thymine in liquid water environment in normal thermodynamic condition. The study is based on a sequential approach, where a classical Monte Carlo simulation of the solvated system is performed to generate the different solute–solvent configurations to be used in the following quantum mechanics calculations of magnetic properties. We find that the environment polarization effect shields the unprotonated nitrogens, with solvent shifts for the magnetic shieldings between +10.52 and +48.95 ppm. Protonated and amino nitrogens are less shielded by amounts of −17.77 and +0.22 ppm. The results obtained from supermolecule calculations show that protonated and amino nitrogen magnetic shieldings are particularly sensitive to the hydrogen bond interactions, with solvent shifts between −5.48 and −33.42 ppm, when the first microsolvation shell is explicitly considered. In addition, the supermolecular calculations also show a marked deshielding effect for the hydrogens of the protonated nitrogens, with solvent shifts between −2.43 and −5.12 ppm. There is an overall agreement between the theoretical predictions for the 1H and 15N chemical shifts and the available experimental results.

NMR measurements and DFT studies of nuclear magnetic shielding in emodin and chuanxiongzine molecules

Emodin and chuanxiongzine are important active compounds of plants widely used in traditional Chinese medicine because of its well-known pharmacological and biological activity. In the present work the two compounds are studied using 1H, 13C and 14N NMR experiments and DFT calculations of nuclear magnetic shielding in the gaseous phase and in solution. The 1H and 13C experimental shielding values of emodin are directly compared with the appropriate results of calculations performed for an isolated molecule. It is shown that unknown inter- and intramolecular effects in shielding are significant and can be estimated within the range of ±6 ppm for carbons and ±3 ppm for hydrogen atoms. The similar comparison is also presented for the theoretical and experimental 1H and 13C chemical shifts of emodin. The 1H, 13C and 14N shieldings in chuanxiongzine molecule are analyzed by the same DFT calculations and NMR measurements as well. As shown the correlation between calculated and experimental shielding parameters is satisfactory especially when the PBE0/aug-cc-pVTZ approach is applied.

Influence of Solvent Representation on Nuclear Shielding Calculations of Protonation States of Small Biological Molecules.

In this study, we assess the influence of solvation on the accuracy and reliability of isotropic nuclear magnetic shielding calculations for amino acids in comparison to experimental data. We focus particularly on the performance of solvation methods for different protonation states, as biological molecules occur almost exclusively in aqueous solution and are subject to protonation with pH. We identify significant shortcomings of current implicit solvent models and present a hybrid solvation approach that improves agreement with experimental data by taking into account the presence of direct interactions between amino acid protonation state and water molecules.

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed.

Converging nuclear magnetic shielding calculations with respect to basis and system size in protein systems

Ab initio chemical shielding calculations greatly facilitate the interpretation of nuclear magnetic resonance (NMR) chemical shifts in biological systems, but the large sizes of these systems requires approximations in the chemical models used to represent them. Achieving good convergence in the predicted chemical shieldings is necessary before one can unravel how other complex structural and dynamical factors affect the NMR measurements. Here, we investigate how to balance trade-offs between using a better basis set or a larger cluster model for predicting the chemical shieldings of the substrates in two representative examples of protein-substrate systems involving different domains in tryptophan synthase: the N-(4'-trifluoromethoxybenzoyl)-2-aminoethyl phosphate (F9) ligand which binds in the α active site, and the 2-aminophenol quinonoid intermediate formed in the β active site. We first demonstrate that a chemically intuitive three-layer, locally dense basis model that uses a large basis on the substrate, a medium triple-zeta basis to describe its hydrogen-bonding partners and/or surrounding van der Waals cavity, and a crude basis set for more distant atoms provides chemical shieldings in good agreement with much more expensive large basis calculations. Second, long-range quantum mechanical interactions are important, and one can accurately estimate them as a small-basis correction to larger-basis calculations on a smaller cluster. The combination of these approaches enables one to perform density functional theory NMR chemical shift calculations in protein systems that are well-converged with respect to both basis set and cluster size.

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.

The role of the exchange-correlation response kernel and scaling corrections in relativistic density functional nuclear magnetic shielding calculations with the zeroth-order regular approximation

The relativistic NMR module of the Amsterdam Density Functional (ADF) package, which is frequently utilised in studies of heavy atom NMR chemical shifts, is extended to calculate a hitherto neglected term from the response of the exchange-correlation (XC) potential. The term vanishes in the absence of spin-orbit coupling. Further, corrections to the shielding arising from scaling factors in the zeroth-order regular approximation (zora) relativistic framework are investigated. The XC response markedly improves calculated proton chemical shifts for hydrogen halides. Mercury chemical shifts for mercury dihalides are also noticeably altered. Contributions from density-gradient dependent terms in the response kernel contribute about 30–40%. New fully relativistic density functional theory (DFT) benchmark data are compared with zora and literature reference values. In line with previous work, it is found that absolute shielding constants for Hg are not accurately predicted with zora. However, chemical shifts agree well with fully relativistic calculations. The application of ‘scaled-zora’ scaling factors deteriorates the shielding constants and is therefore not recommended. The scaling hardly affects chemical shifts. zora calculations are not suitable for absolute shielding of heavy atoms but they can be used safely for chemical shifts in most application scenarios.

Treatment of scalar-relativistic effects on nuclear magnetic shieldings using a spin-free exact-two-component approach

A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin-free four-component matrix elements required to calculate nuclear magnetic shieldings are then used to construct the corresponding SFX2C-1e Hamiltonian and its perturbed counterpart in the context of SFX2C-1e analytic derivative theory. To demonstrate the applicability of the approach, we report coupled-cluster calculations for prototypical problems such as the (17)O shieldings of transition-metal oxo complexes (MO4(2-), M = Cr, Mo, and W) and the (129)Xe shieldings of xenon fluorides (XeF2, XeF4, and XeF6).

NMR espectroscopic parameters of HX and Si (Sn)X4 (X = H, F, Cl, Br and I) and SnBr4−nIn model compounds

The NMR spectroscopic parameters are largely influenced by relativistic effects. They are highly dependent on the electronic behavior inside the spatial regions occupied by nuclei.Full relativistic calculations of indirect nuclear spin–spin couplings at random phase level of approach (RPA) in the title compounds with reoptimized Dyall cVTZ basis sets are given. A comparison with the results of calculations with other basis sets that are mostly used within the non-relativistic (NR) domain is presented. We analyzed the dependence of that couplings with the speed of light over the whole range of values, from the full relativistic to the NR regimes. Within this last regime, calculations at the second-order level of approach (SOPPA) indicated that electron correlation effects may not be as important for nuclear magnetic shieldings, but they must be included with care for J-coupling calculations. From these calculations, we determined that relativity enlarges the electron correlation effects of the J-couplings of HBr and HI.Because the results of nuclear magnetic shielding calculations within polarization propagators at the RPA level were reliable, we were able to show a new and easy procedure to obtain absolute nuclear magnetic shieldings on reference compounds for both Si and Sn nuclei: σ[Si(CH3)4]=421.28±29.33ppm and σ[Sn(CH3)4]=3814.96±79.12ppm. They were obtained from experimental chemical shifts and accurate nuclear magnetic shielding calculations on different molecular systems.

Accurate calculations of second-order electric and magnetic properties: Two ways of physically justified modifications of basis sets

Second-order electric and magnetic properties calculated using an approach based upon the simultaneous analytical dependence of the bond order matrix and basis set functions on the corresponding perturbation parameters have been obtained and analyzed for a series of organic molecules. Various methods of selection of basis set quality for different atoms in investigated molecules were examined in conjunction with calculations of 1H NMR chemical shifts. Comparison of the results obtained at different levels of theory (HF, DFT, MP2) demonstrates small correlation effects for polarizability and magnetic susceptibility while the electron correlation effects play crucial role for calculations of nuclear magnetic shielding (chemical shifts).

Gauge origin independent calculations of nuclear magnetic shieldings in relativistic four-component theory

The use of perturbation-dependent London atomic orbitals, also called gauge including atomic orbitals, has proven efficient for calculations of NMR shielding constants and other magnetic properties in the nonrelativistic framework. In this paper, the theory of London atomic orbitals for NMR shieldings is extended to the four-component relativistic framework and our implementation is described. The relevance of London atomic orbitals in four-component calculations as well as computational aspects are illustrated with test calculations on hydrogen iodide. We find that the use of London atomic orbitals is an efficient method for reliable calculations of NMR shielding constants with standard basis sets, also for four-component calculations with spin-orbit coupling effects included in the wave function optimization. Furthermore, we find that it is important that the small component basis functions fulfill the magnetic balance for accurate description of the diamagnetic shielding and that the role of London atomic orbitals in the relativistic domain is to provide atomic magnetic balance even in the molecular case, thus greatly improving basis set convergence. The Sternheim approximation, which calculates the diamagnetic contribution as an expectation value, leads to significant errors and is not recommended.

Specificity of 13C NMR Shielding Calculations in Thiocarbonyl Compounds

Isotropic 13 C nuclear magnetic shielding values (σ iso ) and corresponding chemical shift magnitudes (δ C ) have been calculated for the large series of the thiocarbonyl compounds using DFT (RI-BP86 and B3LYP) and ab initio (RHF and MP2, with or without resolution of the identity approximation) levels of theory and different basis sets. As expected, the Hartree–Fock method and hybrid B3LYP approach essentially overestimate deshielding of the C═S carbon nuclei. The RI-BP86 level of approximation provides a noticeably better agreement with the experiment and can be used for calculations of the theoretical 13 C NMR spectra for the most classes of the thiocarbonyl compounds. Geometry optimizations and the nuclear magnetic shielding calculations using the MP2 level of theory provide the most reliable results. The resolution of the identity algorithm implemented into the TURBOMOLE program set does not affect the calculated σ iso and δ C values compared to the strict MP2 nuclear magnetic shielding calculations (using the GAUSSIAN-03 program packet). A poor agreement with the experiment found in the case of the thiourea and thiosemicarbazide derivatives is referred to the different conformations of these species in the gas phase, solid state, and solution. Supplementary materials are available for this article. Please go to the publisher's online edition of Phosphorus, Sulfur, and Silicon to view the free supplemental resource.

Hybrid density functional calculations of nuclear magnetic shieldings using Slater‐type orbitals and the zeroth‐order regular approximation

AbstractWe report the implementation of an algorithm for the calculation of the exact Hartree–Fock exchange with Slater‐type orbitals (STOs). Similar to the article of Watson et al., J Chem Phys, 2003, 119, 6475, it is based on the fitting of each atomic orbital pair. However, our algorithm avoids the evaluation of three‐center two‐electron integrals and, as a result, makes it possible to carry out hybrid DFT calculations for larger size molecules and compounds with heavy elements. For the first time, the NMR chemical shifts of transition metal complexes have been calculated with STOs and hybrid density functionals. To take into account the relativistic effects, we have employed the zeroth‐order regular approximation. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

13C and 1H nuclear magnetic shielding and spin–spin coupling constants of 13C-enriched bromomethane in the gas phase

13C and 1H NMR spectral parameters are investigated for 13CH 3Br in gaseous matrices. It is found that both the 13C and 1H chemical shifts of 13CH 3Br are linearly dependent on solvent density. Similar dependence is also detected for one-bond spin–spin coupling, 1 J(CH). For the first time the 13C and 1H magnetic shielding constants and 1 J(CH) spin–spin coupling are obtained for an isolated 13CH 3Br molecule together with the coefficients responsible for solute–solvent molecular interactions in gaseous matrices. The present experimental results confirm the accuracy of some recent ab initio calculations of nuclear magnetic shielding performed for bromomethane.

The embedded ion method: A new approach to the electrostatic description of crystal lattice effects in chemical shielding calculations

AbstractThe nuclear magnetic shielding anisotropy of NMR active nuclei is highly sensitive to the nuclear electronic environment. Hence, measurements of the nuclear magnetic shielding anisotropy represent a powerful tool in the elucidation of molecular structure for a wide variety of materials. Quantum mechanical ab initio nuclear magnetic shielding calculations effectively complement the experimental NMR data by revealing additional structural information. The accuracy and capacity of these calculations has been improved considerably in recent years. However, the inherent problem of the limitation in the size of the systems that may be studied due to the relatively demanding computational requirements largely remains. Accordingly, ab initio shielding calculations have been performed predominantly on isolated molecules, neglecting the molecular environment. This approach is sufficient for neutral nonpolar systems, but leads to serious errors in the shielding calculations on polar and ionic systems. Conducting ab initio shielding calculations on clusters of molecules (i.e., including the nearest neighbor interactions) has improved the accuracy of the calculations in many cases. Other methods of simulating crystal lattice effects in shielding calculations that have been developed include the electrostatic representation of the crystal lattice using point charge arrays, full ab initio methods, ab initio methods under periodic boundary conditions, and hybrid ab initio/molecular dynamics methods. The embedded ion method (EIM) discussed here follows the electrostatic approach. The method mimics the intermolecular and interionic interactions experienced by a subject molecule or cluster in a given crystal in quantum mechanical shielding calculations with a large finite, periodic, and self‐consistent array of point charges. The point charge arrays in the EIM are generated using the Ewald summation method and embed the molecule or ion of interest for which the ab initio shielding calculations are performed. The accuracy with which the EIM reproduces experimental nuclear magnetic shift tensor principal values, the sensitivity of the EIM to the parameters defining the point charge arrays, as well as the strengths and limitations of the EIM in comparison with other methods that include crystal lattice effects in chemical shielding calculations, are presented. © 2006 Wiley Periodicals, Inc. Concepts Magn Reson Part A 28A: 347–368, 2006

Relativistic calculation of nuclear magnetic shielding using normalized elimination of the small component

The normalized elimination of the small component (NESC) theory, recently proposed by Filatov and Cremer, is extended to include magnetic interactions and applied to the calculation of the nuclear magnetic shielding in HX (X=F, Cl, Br, I) systems. The NESC calculations are performed at the levels of the zeroth-order regular approximation (ZORA) and the second-order regular approximation (SORA). The calculations show that the NESC-ZORA results are very close to the NESC-SORA results, except for the shielding of the I nucleus. Both the NESC-ZORA and NESC-SORA calculations yield very similar results to the previously reported values obtained using the relativistic infinite-order two-component coupled Hartree-Fock method. The difference between NESC-ZORA and NESC-SORA results is significant for the shieldings of iodine.

Erratum: “Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula” [J. Chem. Phys. 123, 114102 (2005)

Erratum: “Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula” [J. Chem. Phys. 123, 114102 (2005)

Comment on “Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula” [J. Chem. Phys. 123, 114102 (2005)

Comment on “Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula” [J. Chem. Phys. <b>123</b>, 114102 (2005)

Relativistic calculation of nuclear magnetic shieldings of xenon difluoride

A new method for calculating relativistic nuclear magnetic shieldings at the coupled Hartree-Fock (CHF) level, which is based on the theory of Barysz-Sadlej-Snijders (BSS), was applied to the evaluation of the shieldings in XeF2. Our calculation results were compared with the experimental results for the xenon and fluorine nuclear magnetic shielding anisotropies, obtained by using solid-state Xe129 and F19 NMR spectroscopies. It was shown that the relativistic effects are considerable and that the relativistic BSS-CHF calculation can reproduce well the experimental values of the shielding anisotropies for Xe and F in XeF2.