Nuclear Magnetic Screening Research Articles

Ground state energy of the hydrogen atom inside penetrable spherical cavities; variational approach

In this work we calculate the ground state energy of the hydrogen atom confined in a sphere of penetrable walls of radius Rc. Inside the sphere the system is subject to a Coulomb potential, whereas outside of it the potential is a finite constant V0. The energy is obtained as a function of Rc and V0 by means of the Rayleigh-Ritz variational method, in which, the trial function is proposed as a free particle wave function within a finite square well potential but including an exponential factor that takes into account the electron-nucleus Coulomb attraction. For an impenetrable sphere, , the energy grows fast as Rc approaches zero. On the other hand, when the height of the barrier V0 is finite, the energy increases slowly as Rc goes to zero. We also compute the Fermi contact term, nuclear magnetic screening, polarizability, pressure and tunneling as a function of Rc and V0. As expected, these physical quantities approach the corresponding values of the free hydrogen atom as Rc grows. We also discuss the pressure-induced ionization of the hydrogen atom. The present results are found in good agreement with those previously published in the literature.

Derived properties from the dipole and generalized oscillator strength distributions of an endohedral confined hydrogen atom

We report the electronic properties of a hydrogen atom confined by a fullerene molecule by obtaining the eigenvalues and eigenfunctions of the time-independent Schrödinger equation by means of a finite-differences approach. The hydrogen atom confinement by a C60 fullerene cavity is accounted for by two model potentials: a square-well and a Woods–Saxon. The Woods–Saxon potential is implemented to study the role of a smooth cavity on the hydrogen atom generalized oscillator strength distribution. Both models characterize the cavity by an inner radius R0, thickness Δ, and well depth V0. We use two different values for R0 and Δ, found in the literature, that characterize H@C60 to analyze the role of the fullerene cage size and width. The electronic properties of the confined hydrogen atom are reported as a function of the well depth V0, emulating different electronic configurations of the endohedral cavity. We report results for the hyper-fine splitting, nuclear magnetic screening, dipole oscillator strength, the static and dynamic polarizability, mean excitation energy, photo-ionization, and stopping cross section for the confined hydrogen atom. We find that there is a critical potential well depth value around V0 = 0.7 a.u. for the first set of parameters and around V0 = 0.9 a.u. for the second set of parameters, which produce a drastic change in the electronic properties of the endohedral hydrogen system. These values correspond to the first avoided crossing on the energy levels. Furthermore, a clear discrepancy is found between the square-well and Woods–Saxon model potential results on the hydrogen atom generalized oscillator strength due to the square-well discontinuity. These differences are reflected in the stopping cross section for protons colliding with H@C60.

Effects of substituents in the cationic and anionic η3-allylpalladium complexes according to data from 13C NMR spectroscopy and quantum chemical calculations

A linear correlation of chemical shifts (δ) of signals in the 13C NMR spectra of the unsubstituted terminal carbon atom of the allyl ligand in [(1-R-η3-C3H4)Pd]NO3 (R = Me, CH2OMe, CO2Me, COMe, CHO) with the substituent constants σ+ and σs- in acetone solutions was found. A considerable deviation from linearity was observed for R = Ph. The 13C nuclear magnetic screening constants were calculated by the DFT method in the GIAO approximation for equilibrium geometries of the cations [(1-R-η3-C3H4)Pd(Me2C=0)2]+ and anions [(1-R-η3-C3H4)PdCl2]s-. In the latter case, the theoretical and experimental δ values are consistent. The influence of the substituent R on the geometric parameters and charges on atoms in the neutral, anionic, and cationic η3-allylpalladium complexes is discussed.

Quantum-chemical study of the effects of noncovalent interactions on the nuclear magnetic screening constants of pyrimidine base associates

The effects of weak noncovalent interactions on the nuclear magnetic screening (NMS) constants (σ 1H), (σ 13C) and charge distribution (qt) on atoms in van der Waals model associates of unsubstituted and substituted pyrimidines and substituted uracil are considered. The NMS constants were calculated by the UB3LYP/6-31G(d,p) with GIAO functions. The correlation dependences of the 1H and 13C σ constants on the charge q on atoms whre constructed. It were shown that they can be represented as polynomials that include the terms that are linear and quadratic relative to the charge. The relations obtained in this way are similar in form and close in magnitude to the coefficients of the known Buckingham and Augspurger functions that describe the electric field effects on the nuclear magnetic screening constants. It was found that the coefficients in these polynomials have a definite physical sense in that they characterize nuclear magnetic screening and the “screening polarizability” tensor in the unperturbed molecule and associate, respectively. The NMS constants and charge distribution in pyrimidine base associates and accordingly the coefficients that reflect their values in polynomials depend on the form, size, and composition of the associate and can vary significantly depending on the position of the pyrimidine base in the associate.

Structure of Modified Polytetrafluoroethylene According to DFT Calculations and19F NMR Spectroscopy

The molecular structure of n-C7F16 and the 19F nuclear magnetic screening tensors are calculated by density functional theory (DFT) methods. The results of calculations are compared with 19F NMR data, and it is shown that fine polytetrafluoroethylene (PTFE) contains the terminal CF3 groups in its structure.

Ion Mobility and Electrophysical Properties of Potassium Hexafluorozirconate K2ZrF6

In our 19F NMR and impedance spectroscopy study, we investigated the mobility of fluoride ions (270-550 K) in polycrystalline K2ZrF6. A structural phase transition was found for K2ZrF6 in the temperature range of ∼513 to 518 K. The high-temperature β-K2ZrF6 modification is characterized by translational diffusion of the fluoride ions and uniaxial anisotropy of the 19F nuclear magnetic screening tensor. The electrophysical characteristics of K2ZrF6 were investigated in the temperature range of 300 to 560 K. It is established that the β-K2ZrF6 phase is characterized by high ionic (superionic) conductivity above 540 K (Σ ∼ 3.2× 10-4 S/cm, T=560 K).

SCF X? DW nuclear magnetic screening tensor calculations

Calculations have been performed on the nuclear magnetic screening tensors for molecules via perturbation theory and the Xα DW method, and a comparison is made with results from other methods. Although the absolute errors in the σμυ for the molecules are appreciable, the relative errors in determining the NR chemical shifts are much less (see for example, the shift for CO relative to CH4), which is a hopeful factor leading one to expect that Xα DW can be widely used in analyzing NMR spectra. At the same time, Xα DW can closely reproduces the σμυ anisotropy, which is particularly important for compounds such as V2O5 or its derivatives, which show very large anisotropy in the magnetic screening tensors.

Theoretical investigation of nature of ?31P chemical shift in phosphonium salts

A simple quantum-chemical approach is proposed for investigation of the nature of the δ31P chemical shift in phosphonium salts — an approach based on perturbation theory. The experimentally observed trends in the change in δ31P in these compounds are explained by the features of their electronic and steric structure (without considering interelectron interactions or the 3d orbitals of phosphorus). An analysis is made of the dependence of the paramagnetic component of the31P nuclear magnetic screening constant in phosphonium salts on the electronegativity of the substituents on the P atom, the multiplicity of the bonds to the P atom, and the magnitude of the resonance integral of interaction in the a components of these bonds.

Molecular-Orbital Theory of Diamagnetism. I. An Approximate LCAO Scheme

An independent-electron molecular-orbital theory is developed for the diamagnetic behavior of electrons in the presence of an applied magnetic field. The molecular orbitals are written as linear combinations of gauge-invariant atomic orbitals, the dependence of the (complex) coefficients on the magnetic field being studied by perturbation theory. By making a systematic set of approximations involving the neglect of some interatomic terms, a general expression is derived for the diamagnetic susceptibility tensor as a sum of atomic contributions. Each atomic contribution is made up of two parts, the first being a diamagnetic (Langevin-type) term and the second being a paramagnetic contribution involving the details of the electronic excited states. At a lower level of approximation, this second term can be expressed in terms of atomic charge densities and bond orders together with a mean electronic excitation energy. It is pointed out that the theory provides a convenient basis for detailed interpretation of the Pascal constants used for empirical calculations of diamagnetic susceptibilities of large molecules. In addition, a similar treatment of the theory of nuclear magnetic screening leads to an expression for the shielding constant involving a set of localized contributions closely related to corresponding contributions for the susceptibility.

Isotope shifts in the NMR spectra of H2, HD and D2due to zero-point vibration

The variation with interatomic separation of the nuclear magnetic screening constant for H2 has been studied in a previous paper. Here an estimate is made of the difference in screening which is a consequence of the different zero-point vibrational functions in H2, HD and D2. The results are in good agreement with the observed values.

Nuclear magnetic shielding and diamagnetic susceptibility of interacting hydrogen atoms

A quantum-mechanical study is made of the changes of the nuclear magnetic screening constant σ and the diamagnetic susceptibility X of two interacting hydrogen atoms due to van der Waals and overlap interatomic forces (effects of electron spin being neglected). At large distances the calculations show that van der Waals forces decrease the nuclear screening but increase the diamagnetic susceptibility (in magnitude). As the internuclear distance is reduced the first effect of overlap forces is to increase the screening in the repulsive (electronic triplet) state but this is followed by a further reduction. Attractive overlap forces (as in the ground state of H2) ultimately lead to an increase in screening.

Nuclear Magnetic Resonance Spectra of Some Simple Epoxides

High resolution NMR spectra of four epoxides have been observed at 40 Mcps and analyzed. These epoxides are of the type[Complex chemical formula]where R is a phenyl group (styrene oxide), a cyanide group (glycidonitrile), an acetyl group (1,2-epoxy-3-butanone), and a carboxyl group (glycidic acid). For each molecule the spin-spin coupling constants and nuclear magnetic screening parameters for the A, B, and C protons were derived from the experimentally determined energy levels. The method for obtaining numerical values for the energy levels from the spectra is described fully. ABK and AA′K approximations as well as an iterative ABC method of solution are described and illustrated. Corresponding coupling constants are found to be about the same in all four molecules with JAB=5.8±0.5 cps, JAC=2.2±0.5 cps and JBC=4.6±0.5 cps. However, the variations from molecule to molecule are considerably greater than the estimated precision of ±0.05 cps. The ABX approximation is shown to be inadequate either for the precise determination of the constants or for the calculation of relative intensities. As compared with the iterated ABC solution, the ABK or AA′K approximation leads to good values for the constants and adequately describes the relative intensities.

Nuclear magnetic shielding of a hydrogen atom in (1) an electric field-gradient and (2) a cage

The ground state wave function of a hydrogen atom in an electric field-gradient F' is obtained, correct to the first power in F', and the nuclear magnetic screening constant σ evaluated. The F' contribution to σ vanishes if all directions of F' relative to the applied magnetic field are equally probable. In part (2), the influence of a uniform compression of the H-atom on σ is examined. This effect, which will predominate at sufficiently high pressures, causes a decrease in the electronic polarizability but an increase in σ.

Nuclear magnetic shielding of a hydrogen atom in an electric field

The nuclear magnetic screening constant of a hydrogen atom in a uniform electric field is calculated, neglecting any effect of electron spin. The screening is found to be reduced by the electric field for all directions of the applied magnetic field, the reduction being greatest if the two fields are perpendicular.