Magnetic Shielding Calculations Research Articles

The curious case of S4N4 − A reinvestigation

This work employs quantum chemical methods to explore electronic properties and bonding of the S4N4 molecule. We utilized calculations of multidimensional off-nucleus magnetic shielding, anisotropy of the induced current density (ACID), natural bond orbitals (NBOs), and atoms in molecules (AIM). The unique S4N4 system comprises bent bonding, absence of NN, weakness in the centers of SS bonds, and polar SN bonds. Our findings uncover coexisting of both electron localization and delocalization in S4N4. The magnetic analysis discloses curved connections between the nitrogen atoms and the SS bonds, drawing possible electron delocalization pathways as two pyramid-like regions of magnetic activity. Our magnetic calculations were performed at DFT/GIAO-B3LYP using Jorge-TZP-DKH and 6-311++G(2d,2p) basis sets. No remarkable qualitative differences were noticed between the obtained magnetic features from these two basis sets. Capturing the magnetic details associated with structural features shows superiority of ZZ component of the magnetic shielding tensor (σzz(r)) over the isotropic magnetic shielding (σiso(r)).

Tubular Magnetic Shielding Scan (TMSS): A New Technique for Molecular Space Exploration. (i) The Case of Aromaticity of Benzene and [n]Paracyclophanes.

Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3-14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs allow for the recording of magnetic shielding from the bent ring levels of [n]pCPs, while CGs provide tubular magnetic shielding scan (TMSS) maps detailing the magnetic shielding from a cylindrical region above and below the ring frame. Our findings suggest that smaller [n]pCPs with n < 6 exhibit deviations in the magnetic shielding above and below the ring, indicating a broken electron delocalization under the ring. In contrast, larger [n]pCPs tend to behave similarly to benzene in terms of magnetic shielding. Moreover, we found that shorter polymethylene chains of [n]pCPs exhibit significantly higher magnetic shielding interactions with the ring. Both of the above techniques offer new and promising tools for characterizing nonplanar aromatic compounds, thereby contributing to a deeper understanding of their magnetic and electronic properties.

Facile Synthesis of Nitrogen-Doped [(6.)m8]nCyclacene Carbon Nanobelts by a One-Pot Self-Condensation Reaction.

Synthesis of fully conjugated carbon nanobelts (CNBs) remains one of the biggest challenges in organic chemistry. Herein, we report a facile synthesis of four nitrogen-doped [(6.)m8]ncyclacene CNBs (m = 1-3; n = 3,4) with different sizes by a one-pot self-condensation reaction of three bis(o-aminobenzophenone) precursors. The belt-shaped structure was confirmed by X-ray crystallographic analysis. The existence of eight-membered [1,5]diazocine rings releases the strain while maintaining weak π-conjugation throughout the belt backbone, which is supported by electronic absorption spectra and frontier molecular orbital analysis. NMR measurements and magnetic shielding calculations suggest an alternating aromatic-nonaromatic ring structure, with a slightly more shielded chemical environment in the cavity. Our method opens the opportunities to access more sophisticated π-conjugated 2D/3D belt-/cage-like molecules in a simple way.

Detailed Visualization of Aromaticity Using Isotropic Magnetic Shielding.

For many years, Clar's aromatic sextet theory has served as a qualitative method for assessing the aromatic character of polycyclic aromatic hydrocarbons. A new approach, based on the calculation of isotropic magnetic shielding (IMS) contour plots, is shown to provide a feature-rich picture of aromaticity that is both quantitative yet still easily interpreted. Chemists are visual creatures who are adept at discerning reactivity and chemical behavior from molecular structures. To quote Roald Hoffmann, "People like pictures. Chemists live off them." Thus, the detailed image analysis we present simultaneously provides quantitative assessment of electronic structure, which is still easy-to-understand through visual inspection, embedded in an aesthetically appealing and intuitive picture that draws the reader in. We provide novel computed IMS contour plots for a representative selection of aromatic molecules. Where Clar's static drawings capture only a partial sketch of the electronic properties of a molecule, IMS contour plots present a detailed, global landscape of a molecule that sums all possible resonance structures. This novel analysis allows us to correct certain drawbacks of Clar's analysis with respect to polycyclic aromatics and quantitatively assess the bonding and electronic structure of acene hydrocarbons.

Detailed Visualization of Aromaticity Using Isotropic Magnetic Shielding

AbstractFor many years, Clar's aromatic sextet theory has served as a qualitative method for assessing the aromatic character of polycyclic aromatic hydrocarbons. A new approach, based on the calculation of isotropic magnetic shielding (IMS) contour plots, is shown to provide a feature‐rich picture of aromaticity that is both quantitative yet still easily interpreted. Chemists are visual creatures who are adept at discerning reactivity and chemical behavior from molecular structures. To quote Roald Hoffmann, “People like pictures. Chemists live off them.” Thus, the detailed image analysis we present simultaneously provides quantitative assessment of electronic structure, which is still easy‐to‐understand through visual inspection, embedded in an aesthetically appealing and intuitive picture that draws the reader in. We provide novel computed IMS contour plots for a representative selection of aromatic molecules. Where Clar's static drawings capture only a partial sketch of the electronic properties of a molecule, IMS contour plots present a detailed, global landscape of a molecule that sums all possible resonance structures. This novel analysis allows us to correct certain drawbacks of Clar's analysis with respect to polycyclic aromatics and quantitatively assess the bonding and electronic structure of acene hydrocarbons.

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.

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.

Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz.

Calculations of 19F magnetic shielding in various materials are presented. In calculations on gas-phase molecules, the variation of magnetic shielding with the amount of Hartree-Fock exchange (HFX) in the functional demonstrates that excellent agreement with experiment is obtained with an admixture of 50%, here denoted PBE0 (50%). Calculations at the PBE, PBE0 (25%), and PBE0 (50%) levels on 10 crystalline organofluorines and 15 crystalline inorganic fluorides, in which a cluster ansatz is used to model the lattice environment, were performed. For fluorine-containing aromatics, increasing the admixture of HFX results in the prediction of larger magnetic-shielding spans, whereas increasing the admixture of HFX in calculations for CFCl3 decreases the span. In calculations of 19F magnetic shielding of the inorganic fluorides, the use of sufficiently large clusters of inorganic fluorides results in accuracies similar to those calculated for the organofluorines. Relativistic effects on the magnetic shielding of inorganic fluorides, modeled with ZORA at both the scalar and spin-orbit levels, are dominated by the scalar terms that increase the shielding of most 19F sites over the non-relativistic results. These effects appear to scale with the atomic number of the cation. For most elements of the sixth row (Cs, Ba, La, and Pb), the scalar relativistic contribution to the magnetic shielding is in the range of 20-77 ppm. For elements of group XII (Zn, Cd, and Hg) bonded to fluorine, the scalar relativistic contribution results in deshielding of the 19F site.

6-Aminopenicillanic acid revisited: A combined solid state NMR and in silico refinement

13C/15N (experimental and ab initio) solid-state NMR was used to achieve an affordable way to improve hydrogen refinement of 6-aminopenicillanic acid (6-APA) structure. The lattice effect on the isotropic chemical shifts was probed by using two different magnetic shielding calculations: isolated molecules and periodic crystal structure. The electron density difference maps of optimized and non-optimized structures were calculated in order to investigate the interactions inside the 6-APA unit cell. The 13C and 15N chemical shifts assignments were unambiguously stablished. In addition, some of the literature 13C resonances ambiguities could be properly solved.

New insights into aromatic pathways of carbachlorins and carbaporphyrins based on calculations of magnetically induced current densities.

Magnetically induced current densities have been calculated and analyzed for a number of synthesized carbachlorins and carbaporphyrins using density functional theory and the gauge including magnetically induced current (GIMIC) method. Aromatic properties have been determined by using accurate numerical integration of the current flow yielding reliable current strengths and pathways that are related to the degree of aromaticity and the aromatic character of the studied molecules. All investigated compounds are found to be aromatic. However, the obtained aromatic pathways differ from those previously deduced from spectroscopic data and magnetic shielding calculations. For all studied compounds, the ring current divides into an outer and an inner branch at each pyrrolic subring, showing that all π-electrons of the pyrrolic rings take part in the delocalization pathway. The calculations do not support the common notion that the main share of the current takes the inner route at the pyrrolic rings without an inner hydrogen and follows an 18π aromatic pathway. The aromatic pathways of the investigated carbaporphyrins and carbachlorins are very similar, since the current strength via the Cβ[double bond, length as m-dash]Cβ' bond of the cyclopentadienyl ring of the carbaporphyrins is almost as weak as the current density passing the corresponding saturated Cβ-Cβ' bond of the carbachlorins.

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.

Carbon-13 chemical-shift tensors in indigo: A two-dimensional NMR-ROCSA and DFT Study

The principal components of the 13C NMR chemical-shift tensors for the eight unique carbon sites of crystalline indigo have been measured using the ROCSA pulse sequence. The chemical shifts have been assigned unambiguously to their respective nuclear sites through comparison of the experimental data to the results of density-functional calculations employing a refined X-ray diffraction structure. These measurements expand the database of measured aromatic 13C chemical-shift tensors to the indole ring. Magnetic shielding calculations for hypoxanthine and adenosine are also reported. Comparisons of calculations that include the effect of the crystalline lattice with calculations that model indigo as an isolated molecule give an estimate of the intermolecular contribution to the magnetic shielding.

NMR Shielding in Metals Using the Augmented Plane Wave Method.

We present calculations of solid state NMR magnetic shielding in metals, which includes both the orbital and the complete spin response of the system in a consistent way. The latter contains an induced spin-polarization of the core states and needs an all-electron self-consistent treatment. In particular, for transition metals, the spin hyperfine field originates not only from the polarization of the valence s-electrons, but the induced magnetic moment of the d-electrons polarizes the core s-states in opposite direction. The method is based on DFT and the augmented plane wave approach as implemented in the WIEN2k code. A comparison between calculated and measured NMR shifts indicates that first-principle calculations can obtain converged results and are more reliable than initially concluded based on previous publications. Nevertheless large k-meshes (up to 2 000 000 k-points in the full Brillouin-zone) and some Fermi-broadening are necessary. Our results show that, in general, both spin and orbital components of the NMR shielding must be evaluated in order to reproduce experimental shifts, because the orbital part cancels the shift of the usually highly ionic reference compound only for simple sp-elements but not for transition metals. This development paves the way for routine NMR calculations of metallic systems.

Evaluating Shielding‐Based Ring‐Current Models by Using the Gauge‐Including Magnetically Induced Current Method

AbstractMagnetically induced current densities and integrated ring‐current strength susceptibilities have been calculated at the density functional theory (DFT) level for a test set consisting of 17 ring‐shaped molecules using the gauge‐including magnetically induced current (GIMIC) method. Reliable values for the ring‐current strengths have been obtained by performing numerical integration of the current‐density susceptibility passing a cut plane perpendicularly to the molecular ring. The current densities and ring current strengths were calculated at the DFT level using the B3LYP functional and def2‐TZVP basis sets. Current densities and ring‐current strengths have also been calculated at the Hartree‐Fock self‐consistent field (HF‐SCF) level using Dunning’s aug‐cc‐pVTZ basis sets, which allow a direct comparison with ring‐current strengths that have previously been estimated using ring‐current models based on magnetic shielding calculations. Current density calculations at both levels of theory show that the magnetic shielding based ring‐current models are not a very accurate means to estimate the magnetically induced ring current strengths, whereas they provide qualitatively the correct aromaticity trends for the studied molecules.

Synthesis and characterization of 1,1-dihalogenated cyclopentasilanes

Ring closure reaction of 2,5-dipotassium-2,5-bis(trimethylsilyl)-decamethylhexasilane with trichlorosilane yields the sterically protected halogenated cyclopentasilane 1. Reaction of 1 with lithium aluminum hydride leads to the cyclopentasilane 2. The corresponding difluoro-, dichloro-, dibromo- and diiodo-derivatives 3, 4, 5, and 6 are accessible via derivatization reactions from 1 (4) or 2 (3, 5, 6). All compounds have been structurally characterized by X-Ray diffraction analysis. Comparison of measured 29Si NMR chemical shifts with data obtained from density functional theory (DFT) calculations showed outstanding performance of the M06L functional in the calculation of magnetic shieldings.

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.

Orotic Acid in Water Solution, a DFT and 13C NMR Spectroscopic Study

Orotic acid, a biologically important compound, can exist in aqueous solutions in several ionic and tautomeric forms. Interpretation of the experimental (13)C NMR chemical shifts of this compound based on the results of energy and magnetic shielding calculations performed by DFT B3LYP/6-311++G(2d,p)/PCM method has shown that in water solutions the diketo tautomers are the dominant structural forms of this acid and its anions. For neutral molecules the anti conformation is preferable, monoanion occurs as the conventional carboxylate anion, whereas the orotic dianion exists in two tautomeric forms in the proportion of ca. 4:1. It has been found that the experimental (13)C NMR chemical shifts can be reproduced well by the results of DFT calculations, although for the orotate monoanion some small but characteristic divergences can be noticed. Similar divergences have been also observed for a few other aromatic carboxylates. It seems that the specific solute-solvent interactions occurring in our systems can be the cause of this inconsistency. To support this hypothesis, a simple and effective method of including the specific hydration into the theoretical calculations has been proposed.

Dirac–Hartree–Fock Perturbation Calculation of Magnetic Shielding Using the External Field-Dependent Restricted Magnetic Balance Condition

Dirac–Hartree–Fock Perturbation Calculation of Magnetic Shielding Using the External Field-Dependent Restricted Magnetic Balance Condition

Electromagnetic interference from shielding effectiveness of a rectangular enclosure with apertures – circuital approach, FDTD and FIT modelling

Apertures in a rectangular enclosure can be the coupling path of electromagnetic interference. This paper is devoted to the development of approximating phenomenological models in order to estimate the electromagnetic energy coupling through apertures into enclosures. The effect of apertures on shielding effectiveness (SE) of the enclosure is studied with both circuit modelling method and the finite-difference time-domain (FDTD) method. The results of SE predictions obtained by the analytical formulation and FDTD method are compared and validated with full-field simulations using the software CST/EMC. The software code is based on the finite integration technique. The investigation includes accurate calculation of both magnetic and electric shielding as a function of frequency, enclosure dimensions, apertures shapes, position within the enclosure, plane wave incidence mode and the “loaded aperture” approach.

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.