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.     

Self-consistency in frozen-density embedding theory based calculations

The bi-functional for the non-electrostatic part of the exact embedding potential of frozen-density embedding theory (FDET) depends on whether the embedded part is described by means of a real interacting many-electron system or the reference system of non-interacting electrons (see [Wesolowski, Phys. Rev. A. 77, 11444 (2008)]). The difference δΔF(MD)[ρ(A)]/δρ(A)(r), where ΔF(MD)[ρ(A)] is the functional bound from below by the correlation functional E(c)[ρ(A)] and from above by zero. Taking into account ΔF(MD)[ρ(A)] in both the embedding potential and in energy is indispensable for assuring that all calculated quantities are self-consistent and that FDET leads to the exact energy and density in the limit of exact functionals. Since not much is known about good approximations for ΔF(MD)[ρ(A)], we examine numerically the adequacy of neglecting ΔF(MD)[ρ(A)] entirely. To this end, we analyze the significance of δΔF(MD)[ρ(A)]/δρ(A)(r) in the case where the magnitude of ΔF(MD)[ρ(A)] is the largest, i.e., for Hartree-Fock wavefunction. In hydrogen bonded model systems, neglecting δΔF(MD)[ρ(A)]/δρ(A)(r) in the embedding potential marginally affects the total energy (less than 5% change in the interaction energy) but results in qualitative changes in the calculated hydrogen-bonding induced shifts of the orbital energies. Based on this estimation, we conclude that neglecting δΔF(MD)[ρ(A)]/δρ(A)(r) may represent a good approximation for multi-reference variational methods using adequate choice for the active space. Doing the same for single-reference perturbative methods is not recommended. Not only it leads to violation of self-consistency but might result in large effect on orbital energies. It is shown also that the errors in total energy due to neglecting δΔF(MD)[ρ(A)]/δρ(A)(r) do not cancel but rather add up to the errors due to approximation for the bi-functional of the non-additive kinetic potential.     

Modeling solvent effects on electron-spin-resonance hyperfine couplings by frozen-density embedding

In this study, we investigate the performance of the frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] to model the solvent effects on the electron-spin-resonance hyperfine coupling constants (hfcc's) of the H2NO molecule. The hfcc's for this molecule depend critically on the out-of-plane bending angle of the NO bond from the molecular plane. Therefore, solvent effects can have an influence on both the electronic structure for a given configuration of solute and solvent molecules and on the probability for different solute (plus solvent) structures compared to the gas phase. For an accurate modeling of dynamic effects in solution, we employ the Car-Parrinello molecular-dynamics (CPMD) approach. A first-principles-based Monte Carlo scheme is used for the gas-phase simulation, in order to avoid problems in the thermal equilibration for this small molecule. Calculations of small H2NO-water clusters show that microsolvation effects of water molecules due to hydrogen bonding can be reproduced by frozen-density embedding calculations. Even simple sum-of-molecular-densities approaches for the frozen density lead to good results. This allows us to include also bulk solvent effects by performing frozen-density calculations with many explicit water molecules for snapshots from the CPMD simulation. The electronic effect of the solvent at a given structure is reproduced by the frozen-density embedding. Dynamic structural effects in solution are found to be similar to the gas phase. But the small differences in the average structures still induce significant changes in the computed shifts due to the strong dependence of the hyperfine coupling constants on the out-of-plane bending angle.     

Fast inspection of fruits using nuclear magnetic resonance spectroscopy

High-resolution nuclear magnetic resonance (NMR) spectroscopy is an indispensable technique for obtaining chemical structure information. Its quantitative and noninvasive properties have led to its growing popularity as an analytical tool in many fields, including biology, chemistry, medicine, and food science. During transportation and storage, chemical reactions among the many nutrients lead to a loss of food quality. In these circumstances, portable NMR spectrometers can readily be used for food inspection and quality control. Because of the heterogeneous tissue distribution in food, a high-resolution NMR method is required for detailed food inspection. Therefore, in this study, we demonstrated the feasibility of using an intermolecular double-quantum coherence signal to obtain high-resolution metabolic profiles of several fruits, including grape, cantaloupe, tomato, and watermelon. The resulting high-resolution NMR spectra facilitate the identification of important metabolites, which can be used as biomarkers for food quality control. The method established here may be adapted for food inspection using portable NMR equipment.     

A flexible implementation of frozen-density embedding for use in multilevel simulations

A new implementation of frozen-density embedding (FDE) in the Amsterdam Density Functional (ADF) program package is presented. FDE is based on a subsystem formulation of density-functional theory (DFT), in which a large system is assembled from an arbitrary number of subsystems, which are coupled by an effective embedding potential. The new implementation allows both an optimization of all subsystems as a linear-scaling alternative to a conventional DFT treatment, the calculation of one active fragment in the presence of a frozen environment, and intermediate setups, in which individual subsystems are fully optimized, partially optimized, or completely frozen. It is shown how this flexible setup can facilitate the application of FDE in multilevel simulations.     

Exploring the ability of frozen-density embedding to model induced circular dichroism

In this study, we present calculations of the circular dichroism (CD) spectra of complexes between achiral and chiral molecules. Nonzero rotational strengths for transitions of the nonchiral molecule are induced by interactions between the two molecules, which cause electronic and/or structural perturbations of the achiral molecule. We investigate if the chiral molecule (environment) can be represented only in terms of its frozen electron density, which is used to generate an effective embedding potential. The accuracy of these calculations is assessed in comparison to full supermolecular calculations. We can show that electronic effects arising from specific interactions between the two subsystems can reliably be modeled by the frozen-density representation of the chiral molecule. This is demonstrated for complexes of 2-benzoylbenzoic acid with (-)-(R)-amphetamine and for a nonchiral, artificial amino acid receptor system consisting of ferrocenecarboxylic acid bound to a crown ether, for which a complex with l-leucine is studied. Especially in the latter case, where multiple binding sites and interactions between receptor and target molecule exist, the frozen-density results compare very well with the full supermolecular calculation. We also study systems in which a cyclodextrin cavity serves as a chiral host system for a small, achiral molecule. Problems arise in that case because of the importance of excitonic couplings with excitations in the host system. The frozen-density embedding cannot describe such couplings but can only capture the direct effect of the host electron density on the electronic structure of the guest. If couplings play a role, frozen-density embedding can at best only partially describe the induced circular dichroism. To illustrate this problem, we finally construct a case in which excitonic coupling effects are much stronger than direct interactions of the subsystem densities. The frozen density embedding is then completely unsuitable.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

Proton nuclear magnetic resonance characterisation of glycosaminoglycans using chemometric techniques

Various types of glycosaminoglycans (GAGs) including heparins, chondroitin sulfates, dermatan sulfate and hyaluronic acid were studied from their proton nuclear magnetic resonance (1H NMR) spectra using chemometric techniques. Despite the complexity of the 1H NMR signals, data analysis using principal component analysis enabled the different GAG classes to be distinguished and permitted their classification according to their chemical structure. The analysis of the composition of the major disaccharide unit and other relevant chemical structures in the heparin samples was performed using partial least squares regression.     

Review about olive oil characterization using high-field nuclear magnetic resonance

In the last years Nuclear Magnetic Resonance (NMR) spectroscopy has found many applications in food analysis. Here, we present a review of the most significant results we have obtained in the olive oil characterization using NMR techniques in combination with multivariate statistical methods.     

Quantitative analysis by nuclear magnetic resonance using precision coaxial tubing

Quantitative analysis by n.m.r. using precision coaxial tubing is described. A solution of the intensity standard is placed in the central capillary and the sample of interest in the surrounding annulus. By this method the contamination of the sample by the standard compound can be avoided and an accurate determination can be carried out by using solutions of correct concentrations of the intensity standard. Applications to several types of quantitative problems are given. In order to get a higher accuracy and precision the experimental conditions were also studied.     

Covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy is introduced, which is a new scheme for establishing nuclear spin correlations from NMR experiments. In this method correlated spin dynamics is directly displayed in terms of a covariance matrix of a series of one-dimensional (1D) spectra. In contrast to two-dimensional (2D) Fourier transform NMR, in a covariance spectrum the spectral resolution along the indirect dimension is determined by the favorable spectral resolution obtainable along the detection dimension, thereby reducing the time-consuming sampling requirement along the indirect dimension. The covariance method neither involves a second Fourier transformation nor does it require separate phase correction or apodization along the indirect dimension. The new scheme is demonstrated for cross-relaxation (NOESY) and J-coupling based magnetization transfer (TOCSY) experiments.     

Shiftless nuclear magnetic resonance spectroscopy

The acquisition and analysis of high resolution one- and two-dimensional solid-state nuclear magnetic resonance (NMR) spectra without chemical shift frequencies are described. Many variations of shiftless NMR spectroscopy are feasible. A two-dimensional experiment that correlates the dipole-dipole and dipole-dipole couplings in the model peptide , (15)N labeled N-acetyl-leucine is demonstrated. In addition to the resolution of resonances from individual sites in a single crystal sample, the bond lengths and angles are characterized by the two-dimensional powder pattern obtained from a polycrystalline sample.     

Introduction to nuclear magnetic resonance

The basic principles of nuclear magnetic resonance (NMR) are presented in an elementary form using classical and elementary quantum mechanics and the experimental technique 1s explained. The motion of the magnetization by r.f. pulses, free induction decay and spectrum, transverse and longitudinal relaxation, local field and spin echo are described and the effects of molecular motion are discussed. The concepts of spin temperature and spin diffusion are presented and the advantage of using quadrupole nuclei is stressed. Finally, the specific problems of NMR in interface studies are considered and a typical example is given.     

Two-photon two-color nuclear magnetic resonance

Two-photon excitation has recently been demonstrated to be a practical means of exciting nuclear magnetic resonance (NMR) signals by radio-frequency (rf) irradiation at half the normal resonance frequency. In this work, two-photon excitation is treated with average Hamiltonian theory and shown to be a consequence of higher order terms in the Magnus expansion. It is shown that the excitation condition may be satisfied not only with rf at half resonance, but also with two independent rf fields, where the two frequencies sum to or differ by the resonance frequency. The technique is demonstrated by observation of proton NMR signals at 400 MHz while simultaneously exciting at 30 and 370 MHz. Advantages of this so-called two-color excitation, such as a dramatic increase in nutation rate over half-frequency excitation, along with a variety potential applications are discussed.     

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.