Calculations of the contribution of ring currents to the chemical shielding anisotropy

Ring currents can exert a large effect upon the chemical shielding of NMR resonances. The analytical expression developed by Waugh and Fessenden (Waugh, J. S.; Fessenden, R. W. J. Am. Chem. Soc. 1957, 79, 846) and Johnson and Bovey (Johnson, C. E.; Bovey, F. A. J. Chem. Phys. 1957, 29, 1012) only quantifies the contribution of ring currents to the isotropic component of the shielding tensor. In the work described here an additional analytical expression is developed so that the contribution of ring currents to the full shielding tensor can be calculated, allowing an estimate of the influence of ring currents upon the chemical shielding anisotropy (CSA, Deltasigma). To test that this pair of analytical expressions can provide a reasonable estimate of the contribution of ring currents to the full shielding tensor a series of density functional calculations (DFT) were carried out. A shielding tensor in a model compound was calculated in two distinct ways. For the first series, DFT shielding calculations of the model compound were carried out in the presence of a benzene ring. For the second series a ring current contribution to the shielding tensor was calculated via the new expressions, and this was added to the result of a DFT shielding calculation which used in place of benzene the nonaromatic analogue 1,3 cyclohexadiene. The two series of results proved to be in excellent agreement. The pair of analytical expressions are used to calculate ring current contributions to the CSA (Deltasigma) of 1H(N) backbone amide resonances in a structure of the second type 2 module from the protein fibronectin. Significant CSA variations are predicted in particular for the 1H(N) of G42 which is most likely involved in a N-H...tpi aromatic hydrogen bond.     

Integrals of the paramagnetic contribution in the relativistic calculation of the shielding tensor

Of the nuclear magnetic resonance (MMR), the nuclear shielding tensor is of a great interest. The relativistic calculation of the nuclear shielding tensor involves extremely challenging integrals of first and second order. Among the first order integrals are paramagnetic contribution integrals, which are extremely difficult to evaluate analytically and numerically, especially when using exponential type functions (ETFs). The main difficulty in the analytical development arises from the presence of 1/r ⁵ in the operators. In the present contribution, we developed the Fourier transform of the operators of the paramagnetic contribution and we used the Fourier integral transformation to derive analytic expressions for the integrals under consideration over ETFs. The main difficulty in the numerical treatment of the obtained analytic expressions arises from the presence of highly oscillatory spherical Bessel integrals. Extrapolation methods and nonlinear transformations are used to develop highly accurate algorithms for the numerical evaluation of the integrals of the paramagnetic contribution in the relativistic calculation of the shielding tensor.     

Fully relativistic theories and methods for NMR parameters

Nuclear magnetic shielding and spin–spin coupling constants are intrinsically all-electron relativistic properties and demand in principle fully relativistic treatments. Here, the magnetic balance (MB) condition plays an essential role, both conceptually and computationally. The various formulations can be unified in terms of the idea of "orbital decomposition." Further combined with the ansatz of "gauge-including atomic orbitals" (GIAO) for distributed gauge origins leads to very efficient four-component relativistic methods at both the mean-field and correlated levels. To illustrate the latter, the no-pair MB-GIAO-MP2 expressions for nuclear shieldings are derived in two different ways, one with the derivative technique and the other through the induced current. Due to the non-variational nature of MP2, the two expressions are not identical. The current-dependent expression is much simpler and appears more natural in view of the experimental measurement.     

Calculation of nuclear magnetic shieldings using an analytically differentiated relativistic shielding formula

Two expressions for nuclear-magnetic-shielding tensor components based on analytically differentiating the electronic energy of a system are presented. The first is based on a second-order Douglas-Kroll-Hess approach, in which the off-diagonal block terms of the transformed Dirac Hamiltonian are diminished to second order with respect to both the electrostatic nuclear attraction potential V and the magnetic vector potential A. The second expression is based on the method of Barysz-Sadlej-Snijders, in which the off-diagonal block terms in the transformed Dirac Hamiltonian are completely eliminated with respect to purely V terms, while they are diminished to second order with respect to terms including A. The two approaches are applied to the calculation of nuclear magnetic shieldings of HX (X=F, Cl, Br, I), H2X (X=O, S, Se, Te), and noble gas X (X =He,Ne,Ar,Kr,Xe) systems with common gauge origins. The results show that relativistic corrections of higher than second order are negligibly small, except for the paramagnetic parts of I, Te, and Xe shieldings. The present calculations yield very large positive values for the anisotropy of proton shielding, deltasigma(H) = sigmaparallel(H)-sigmaperpendicular(H), of HI compared to previous reports. Unfortunately, no experimental values for the anisotropy of proton shielding in HI are available for verification.     

Computing the 7Li NMR chemical shielding of hydrated Li+ using cluster calculations and time-averaged configurations from ab initio molecular dynamics simulations

Ab initio molecular dynamics (AIMD) simulations have been used to predict the time-averaged Li NMR chemical shielding for a Li(+) solution. These results are compared to NMR shielding calculations on smaller Li(+)(H(2)O)(n) clusters optimized in either the gas phase or with a polarizable continuum model (PCM) solvent. The trends introduced by the PCM solvent are described and compared to the time-averaged chemical shielding observed in the AIMD simulations where large explicit water clusters hydrating the Li(+) are employed. Different inner- and outer-coordination sphere contributions to the Li NMR shielding are evaluated and discussed. It is demonstrated an implicit PCM solvent is not sufficient to correctly model the Li shielding, and that explicit inner hydration sphere waters are required during the NMR calculations. It is also shown that for hydrated Li(+), the time averaged chemical shielding cannot be simply described by the population-weighted average of coordination environments containing different number of waters.     

Electromagnetic Interference Shielding Polymers and Nanocomposites - A Review

Intrinsically conducting polymers (ICP) and conductive fillers incorporated conductive polymer-based composites (CPC) greatly facilitate the research in electromagnetic interference (EMI) shielding because they not only provide excellent EMI shielding but also have advantages of electromagnetic wave absorption rather than reflection. In this review, the latest developments in ICP and CPC based EMI shielding materials are highlighted. In particular, existing methods for adjusting the morphological structure, electric and magnetic properties of EMI shielding materials are discussed along with the future opportunities and challenges in developing ICP and CPC for EMI shielding applications.     

Molecular orbital studies of the NMR hydrogen bond shift

Magnetic shielding constants are calculated for the protons in XOH and XOH…OH₂ (XH, CH₃, NH₂, OH and F) molecules using a slightly extended set of atomic functions modified by gauge factors. These results are used to determine theoretical values for the NMR hydrogen bond shifts in the XOH…OH₂ systems. Such theoretical data are consistent with the few available experimental data. An analysis of the theoretical results reveals that there are three major types of shielding contribution to the NMR hydrogen bond shift; (a) a deshielding change due to the variation of the local currents on the hydrogen bonded proton; (b) a reduction in shielding from currents localized on the oxygen atom of the proton donor; (c) a deshielding contribution from currents induced on the oxygen atom of the proton acceptor. Except for the water dimer, contributions (a), (b) and (c) are of comparable importance for changes in isotropic shielding. For (H₂O)₂ contributions (a) and (c) are somewhat more important than contribution (b). Contribution (c) is almost totally responsible for the changes in the anistropies of the shielding tensors associated with the hydrogen bonded protons. The proton shielding anisotropy changes which occur on hydrogen bond formation are generally much larger than the corresponding variations in the isotropic values of the shielding tensors. This suggests that proton magnetic shielding anisotropies may be more sensitive measures of features of hydrogen bonding than are isotropic proton shielding constants.     

A novel shielding material prepared from solid waste containing lead for gamma ray

Human beings are continuously exposed to cosmogenic radiation and its products in the atmosphere from naturally occurring radioactive materials (NORM) within Earth, their bodies, houses and foods. Especially, for the radiation protection environments where high ionizing radiation levels appear should be shielded. Generally, different materials are used for the radiation shielding in different areas and for different situations. In this study, a novel shielding material produced by a metallurgical solid waste containing lead was analyzed as shielding material for gamma radiation. The photon total mass attenuation coefficients (μ/ρ) were measured and calculated using WinXCom computer code for the novel shielding material, concrete and lead. Theoretical and experimental values of total mass attenuation coefficient of the each studied sample were compared. Consequently, a new shielding material prepared from the solid waste containing lead could be preferred for buildings as shielding materials against gamma radiation.     

Libcint: An efficient general integral library for Gaussian basis functions

An efficient integral library Libcint was designed to automatically implement general integrals for Gaussian‐type scalar and spinor basis functions. The library is able to evaluate arbitrary integral expressions on top of p, r and σ operators with one‐electron overlap and nuclear attraction, two‐electron Coulomb and Gaunt operators for segmented contracted and/or generated contracted basis in Cartesian, spherical or spinor form. Using a symbolic algebra tool, new integrals are derived and translated to C code programmatically. The generated integrals can be used in various types of molecular properties. To demonstrate the capability of the integral library, we computed the analytical gradients and NMR shielding constants at both nonrelativistic and 4‐component relativistic Hartree–Fock level in this work. Due to the use of kinetically balanced basis and gauge including atomic orbitals, the relativistic analytical gradients and shielding constants requires the integral library to handle the fifth‐order electron repulsion integral derivatives. The generality of the integral library is achieved without losing efficiency. On the modern multi‐CPU platform, Libcint can easily reach the overall throughput being many times of the I/O bandwidth. On a 20‐core node, we are able to achieve an average output 8.3 GB/s for C₆₀ molecule with cc‐pVTZ basis. © 2015 Wiley Periodicals, Inc.     

Nuclear motion effects on the C, F and H shielding in methyl fluoride

The ¹⁹F , ¹³C and ¹H shielding in methyl fluoride and its deuterated isotopomers has been calculated from ab initio shielding surfaces for selected temperatures. In each case it is the stretching which contributes most to the nuclear motion corrections which total −9.425 ppm for the ¹⁹F shielding, −4.558 ppm for the ¹³C shielding and −0.601 ppm for the proton shielding. However, some second-order stretching and bending contributions are significant. The deuterium induced isotope shifts are substantial and should be easily measurable. There is a predicted nonadditivity in the ¹⁹F and ¹³C isotope shifts which can be traced to two of the bending contributions.     

Some calculations of the solvent dependences of phosphorus nuclear shielding

Some CNDO/S parameterized calculations of phosphorus shielding, as a function of the dielectric constant of the medium, are presented. Pople's SOS perturbation approach together with the solvaton model are employed. For trivalent phosphorus compounds a shielding decrease by up to 15 ppm is predicted as ε increases from 1 to 80. For pentavalent phosphorus a much smaller shielding variation, in the opposite direction, is predicted. In general, a consideration of changes in phosphorus charge density is insufficient to account for the variation in nuclear shielding.     

Glycyl C(alpha) chemical shielding in tripeptides: measurement by solid-state NMR and correlation with X-ray structure and theory

We report here (13)C(alpha) chemical shielding parameters for central Gly residues in tripeptides adopting alpha-helix, beta-strand, polyglycine II, and fully extended 2 degrees structures. To assess experimental uncertainties in the shielding parameters and the effects of (14)N-(13)C(alpha) or (15)N-(13)C(alpha) dipolar coupling, stationary and magic angle spinning (MAS) spectra with and without (15)N decoupling were obtained from natural abundance and double-labeled samples containing [2-(13)C, (15)N]Gly. We find that accurate (<1 ppm uncertainty) shielding parameters are measured with good sensitivity and resolution in (15)N decoupled 1D or 2D MAS spectra of double-labeled samples. Compared to variations of isotropic shifts with peptide angles, those of (13)C(alpha) shielding anisotropy and asymmetry are greater. Trends relating shielding parameters to the 2 degrees structure are apparent, and the correlation of the experimental values with unscaled ab initio shielding calculations has an rms error of 3 ppm. Using the experimental data and the ab initio shielding values, the empirical trends relating the 2 degrees structure to shielding are extended to the larger range of torsion angles found in proteins.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

A new class of modular chiral ligands with fluxional groups

In ligand design for asymmetric catalysis, the usual norm is to derive the face shielding elements from a chiral source. New ligands in which the face shielding is determined by fluxional groups are introduced. Their design, modular synthesis, and experiments to demonstrate the significance of the fluxional groups are discussed. The advantage is that the fluxional groups, introduced at a later stage, allow for simple tuning of the face shielding group.     

A comparison of quantum chemical models for calculating NMR shielding parameters in peptides: mixed basis set and ONIOM methods combined with a complete basis set extrapolation

This article compares several quantum mechanical approaches to the computation of chemical shielding tensors in peptide fragments. First, we describe the effects of basis set quality up to the complete basis set (CBS) limit and level of theory (HF, MP2, and DFT) for four different atoms in trans N-methylacetamide. For both isotropic shielding and shielding anisotropy, the MP2 results in the CBS limit show the best agreement with experiment. The HF values show quite a different tendency to MP2, and even in the CBS limit they are far from experiment for not only the isotropic shielding of carbonyl carbon but also most shielding anisotropies. In most cases, the DFT values differ systematically from MP2, and small basis-set (double- or triple-zeta) results are often fortuitously in better agreement with the experiment than the CBS ones. Second, we compare the mixed basis set and ONIOM methods, combined with CBS extrapolation, for chemical shielding calculations at a DFT level using various model peptides. From the results, it is shown that the mixed basis set method provides better results than ONIOM, compared to CBS calculations using the nonpartitioned full systems. The information studied here will be useful in guiding the selection of proper quantum chemical models, which are in a tradeoff between accuracy and cost, for shielding studies of peptides and proteins.     

Intrinsically conducting polymers for electromagnetic interference shielding

This paper summarizes and reviews the research on electromagnetic interference (EMI) shielding with intrinsically conducting polymers (ICPs), mainly polyaniline (PANI) and polypyrrole (PPY), and their composites in various frequency ranges. ICPs are new alternative candidates for EMI shielding applications due to their lightweight, corrosion resistance, ease of processing, and tunable conductivities as compared with typical metals. More importantly, the dominant shielding characteristic of absorption other than that of reflection for metals render ICPs more promising materials in applications requiring not only high EMI shielding effectiveness but also shielding by absorption, such as in stealth technology. Copyright © 2005 John Wiley & Sons, Ltd.     

An Empirical Proton NMR Shielding Equation for Alkenes Based on Ab Initio Calculations

Nuclei of hydrogen atoms located over a carbon-carbon double bond in the presence of a strong magnetic field experience a perturbed magnetic field caused primarily by the magnetic anisotropy of the bond. However, the commonly used theoretical model for predicting the shielding effect of an alkene double bond on hydrogen nuclei is sometimes inconsistent with the observed proton NMR chemical shifts in structures that have covalently bonded hydrogens located over a carbon-carbon double bond. We have used the ab initio gauge including atomic orbital (GIAO) method to calculate isotropic shielding values and to determine the proton NMR shielding increments for a simple model system: methane held at various positions over ethene. These shielding increments calculated for one proton of methane have been mapped as a function of their position in Cartesian coordinates relative to the center of ethene. A mathematical function has been fit to this three-dimensional shielding increment surface at each of four distances from the face of the ethene molecule. Additionally, a single mathematical equation has been developed for predicting the shielding caused by the carbon-carbon double bond in ethene. In contrast to the traditionally employed shielding model, our results predict deshielding for protons within 3 Å above the center of a carbon-carbon double bond, consistent with experimental observations in several molecular systems. The NMR shielding increments predicted by this equation are compared to observed shielding increments in some test alkenes.     

(13)C shielding tensors of crystalline amino acids and peptides: Theoretical predictions based on periodic structure models

Precise theoretical predictions of NMR parameters are helpful for the spectroscopic identification of complicated biological molecules, especially for the carbon shielding tensors in amino acids. The (13)C shielding tensors of various crystalline amino acids and peptides have been calculated using the gauge-including projector augmented wave (GIPAW) method based on two different periodic structure models, namely that deduced from available crystallographic data and that from theoretically optimized structures. The incorporation of surrounding lattice effects is found to be crucial in obtaining reliable predictions of (13)C shielding tensors that are comparable to the experimental data. This is accomplished by refining the experimental crystallographic data of the amino acids and peptides at the GGA/PBE level by which more accurate intramolecular C--H bond lengths and intermolecular hydrogen-bonding interactions are obtained. Accordingly, more accurate predictions of (13)C shielding tensors comparable to the experimental results (within a maximum deviation of +/-10 ppm) were achieved, rendering more explicit (13)C shielding tensors assignments for solid biological systems particularly for amino acids with multiple carboxyl carbons, such as asparagine, glutamine, and glutamic acid.     

Design and evaluation of portable shielding case for thyroid 131I monitoring by imaging plate

A portable shielding case was designed and evaluated for thyroid ¹³¹I monitoring by imaging plate (IP) under storage temperature of 0 and 25 °C. The background count with shielding case was 20 % of that without shielding case in 25 °C after 7 day. The fading rate decreased to 85.3 and 66.4 % after 7 day with and without shielding case. The detection limit was low by shielding and storing at low temperature and the lower detection limits of the IP system are less than the screening level even 7 day after irradiation. The use of shielding case and a low temperature is effective in reducing the fading rate of IP.     

Carbon chemical shift tensor components in quinolines and quinoline N-oxides

Chemical shift calculations are carried out for the quinoline carbons in 1,8-bis(2-isopropyl-4-quinolyl)naphthalene, 2-isopropylquinoline, amodiaquine, chloroquine, and quinine and the N-oxide of each compound. Ab initio calculations of the isotropic shielding values are in agreement with experimental chemical shifts. The calculations indicate that changes to the principal components of the shielding tensor upon N-oxidation are similar for each compound. Carbons 2, 4, 8, and 10 are largely shielded in each case as the nitrogen is oxidized. For C2, C4, and C10, this shielding is due to a large change in sigma11 and/or sigma22, indicating a change in pi-electron density. For C8, the large shielding change is due mainly to a change in sigma33, indicating a change in sigma-electron density. Upon examination and comparison of the calculated 13C shielding tensor components in the antimalarial drugs versus those in unsubstituted quinolines, it is found that amodiaquine and chloroquine have increased pi-electron density in the ring containing the amino side chain and quinine has increased pi-electron density in the opposite ring, containing the methoxy substituent.