Diamagnetic Shielding Constant Research Articles

Ab initio studies of the electronic structure of Be93, Be105, Be111, and Be123 clusters

AbstractAb initio self‐consistent‐field calculations are reported for electronic states of beryllium clusters comprised of 93, 105, 111, and 123 atoms. The respective clusters correspond to coordination shells 12‐15 of a central Be atom with internuclear separations derived from the lattice constants of the bulk metal. Ab initio effective core potentials have been employed to replace the 1 s electrons, thereby reducing the complexity of the calculations. In addition, use of the full D3h point group symmetry of the clusters results in a substantial reduction of the numbers of two‐electron integrals that must be computed and processed. Binding energies, orbital energies, electric field gradient, nuclear‐electrostatic potential, diamagnetic shielding constant, second moments, and Mulliken populations are calculated for selected electronic states. Calculated binding energies when compared among the different clusters as well as to smaller and larger fragments from earlier studies provide evidence for the onset of convergence to the Hartree–Fock limit of the bulk. Lowest‐state ionization potentials are consistently above and agree to within 14% of the experimental workfunction. The net charge on the central beryllium atom decreases toward zero. The variability of observed bulklike behavior for the different properties indicates that the transition between cluster and bulklike behavior is not sharp and depends on the quantity of interest. © 1995 John Wiley & Sons, Inc.

Ab initio studies of the electronic structure and density of states of metallic beryllium

AbstractHartree–Fock–Roothaan studies are reported for low‐lying electronic states of metallic beryllium as modeled by a moiety of 135 beryllium atoms. The system corresponds to 16 coordination shells of a central Be with internuclear separations derived from the lattice constants of the bulk metal. The calculations become tractable by use of the full D3h symmetry of the system at both the integrals and self‐consistent‐field stages and by employing ab initio effective potentials for the 1s electrons of each beryllium atom. Ionization potentials, binding energies, orbital energies, electric field gradients, nuclear‐electrostatic potentials, diamagnetic shielding constants, second moments, and Mulliken populations are calculated for selected electronic states. The calculated ionization potential for the lowest state agrees to within 10% of the experimental bulk work function. A density‐of‐states analysis for that state is reported and compared with band structure calculations.

Ab initio properties of electronic states of beryllium cluster (Be69)

Results of ab initio Hartree-Fock calculations are presented for the nine-coordination-shell cluster Be{sub 69}. Binding energy, ionization potential, electrical field gradient, nuclear-electrostatic potential, diamagnetic shielding constant, second moments of charge, and Mulliken populations are reported for several electronic states. Properties centered at the innermost Be atoms exhibit convergence toward bulk Be metal values.

INDO/GIAO calculations of 13C, 15N and 17O NMR chemical shifts in some organo‐iron complexes

AbstractIn this paper, INDO perturbation theory has been extended to calculate the NMR chemical shifts of transition metal compounds. The nitrogen and oxygen INDO parameters have been refined by using a set of nitrogen and oxygen containing compounds to minimize the differences between calculated and experimental 13C, 15N, and 17O shielding constants. These refined parameters, together with optimally selected iron INDO parameters, were used to evaluate the 13C chemical shifts of three iron complexes (C5H5)Fe(CO)2CN, (C5H4CHO)2Fe2, and (C5H4CH2OH)2Fe. The calculated 13C, 15N and 17O shielding constants were fairly in agreement with experimental results. In addition, a good linear relationship between the calculated [diamagnetic shielding constants σd(M) of 13C, 15N and 17O nuclei and the net charge ρ (M) of these atoms was noticed.

Ab initio models for Be81 and Be87 metal clusters

Ab initio self-consistent field calculations are reported for electronic states of beryllium clusters comprised of 81 and 87 atoms. The clusters correspond to the tenth and eleventh coordination shells of a central Be with internuclear separations derived from the lattice constants of the bulk metal. Ab initio effective core potentials have been employed to replace the 1s electrons, therey reducing the complexity of the calculations. In addition, the use of the full D3h point group symmetry of the clusters results in a substantial reduction of the number of two-electron integrals that must be computed and processed. Binding energies, orbital energies, electric field gradient, nuclear-electrostatic potential, diamagnetic shielding constant, second moments, and Mulliken populations are calculated for selected electronic states. Systematic trends toward bulk behavior with increasing cluster size, as found in earlier cluster studies, continue to appear for the electric field gradient and quadrupole moment of Be81. Anomalous behavior, however, is observed in Be87. This is attributed to distortional effects due to the addition of atoms in planes above and below the Be81 cluster along the principal axis of symmetry.

Selected properties of beryllium clusters in ab initio model approximations

Results of ab initio self-consistent field calculations are reported for electronic states of beryllium clusters comprised of 13, 19, 21, 33, 39, 51, 57, and 63 atoms. The clusters correspond to the second through ninth coordination shells of a central Be atom with internuclear separations taken from the lattice constants of the bulk hcp metal. Effective core potentials have been employed to replace the 1s core electrons, thereby reducing the complexity of the calculations. In addition, the use of the full D/sub 3h/ point group symmetry of each cluster results in substantial reductions of the number of two-electron integrals that must be computed and processed. Properties are calculated for selected electronic states and include binding energy, orbital energies, electric field gradient, nuclear-electron potential, diamagnetic shielding constant, second moments, and Mulliken populations. Overall net charges, second moments, and nuclear potentials become approximately constant in the larger clusters, indicating bulk behavior.

AB initio calculations on electronic states of be 51 and be 57 clusters

Ab initio self-consistent field calculations using effective core potentials are reported for electronic states of Be 51 and Be 57 clusters. The systems correspond to the seventh and eighth coordination spheres of a central Be with internuclear separations derived from the lattice constants of the bulk metal. The full D 3h point group symmetry of each cluster was used at both the integrals and the SCF stages of the calculations. Properties calculated include binding energy, electric field gradient, nuclear-electron potential, diamagnetic shielding constant, second moments, quadrupole moment, and Mulliken populations.

A b i n i t i o calculations on electronic states of Be13

A cluster of 13 beryllium atoms has been studied in ab initio Hartree–Fock calculations. The chosen geometric configuration has D3h symmetry and corresponds to a central Be with 12 atoms situated at the hexagonal close-packed, nearest-neighbor positions. The lowest energy electronic state among those investigated is 5A″1 and the first excited state is 5E″ lying at 1.12 eV. A total of 14 states were identified below 2.0 eV. The 5A′′1 Hartree–Fock ground state has a binding energy of 12.0 kcal/mol relative to the separated atoms and an ionization potential of 0.54 eV. Total valence energies, orbital energies, binding energies, electric field gradients, diamagnetic shielding constants, nuclear–electron potentials, second moments, and Mulliken populations are reported. In addition, the cluster calculations give a reasonable estimate for the Sternheimer correction to the electric field gradient of the bulk metal.

Precision determination of the nuclear g factor of39K+ion and diamagnetic shielding constant difference between a39K atom and a39K+ion

An optical pumping charge exchange collision experiment for precise measurement of the nuclear g factor of the 39K+ ion in a helium buffer gas is reported. 39K+ ions are polarised by charge exchange collisions with oriented 39K atoms. The NMR frequencies of 39K+ and the ESR frequencies of free electrons polarised by oriented 39K atoms are measured in a magnetic field (3-34 G). This gives the ratio of the nuclear g factor of the 39K+ ion to the electronic g factor of free electrons to be: gI(39K+)/ge=0.07088733 (17)*10-3. Using this ratio together with the best available measured values of ge=2.0023193134 (70) and gI(39K)=1.4193489 (12)*10-4 the authors obtain: (i) gI(39K+)=-1.4193906 (34)*10-4 in units of the Bohr magneton; (ii) the diamagnetic shielding constants difference between free atoms and ions is: sigma (39K+)- sigma (39K)=-29(6)*10-6.

Diamagnetic shielding constants of first‐row atoms: Studies with a piecewise exponentially decaying electron density function

AbstractThe piecewise exponentially decaying electron density model of Wang and Parr is used to calculate the diagmagnetic shielding constants of first‐row atoms. Numerical results are presented for all first‐row atoms and comparisons are made with the results obtained from the one‐zone (i.e., single exponential) model. Results obtained from the two‐zone (i.e., piecewise exponential) model are in better agreement with the Hartree–Fock results.

Structure of dispersion media by nuclear magnetic resonance

The change of the diamagnetic shielding constant of a benzene molecule interacting with the solid phase surface is calculated.

Determination of g-factor Ratios for Cs+ Ions and Cs Atoms

A charge-exchange optical pumping experiment to measure the nuclear g factor of 133Cs+ ions in a He buffer gas is reported. Cs+ ions are polarized by charge-exchange collisons with optically pumped Cs atoms. The NMR frequency of 133Cs+ ions along with the Zeeman transition frequency of 133Cs are measured in a magnetic field ∼ 600 G. This gives the ratio of the nuclear g factor of the 133Cs+ ion to the electronic g factor in the ground electronic state of free 133Cs. The result is gI(133Cs+)/gJ(133Cs)=-1.9917235(30). Using this value and results of other researchers yield gI(133Cs+)/gI(133Cs)=0.9999917(21) as the ratio of the nuclear g factor of the Cs ions to that of the free Cs atoms, [σ(Cs+)-σ(Cs)]=7.7(2.0) × 10-6 the difference in the diamagnetic shielding constants of the free atoms and ions. Finally, the value for the shielded Cs+ nuclear moment in units of the Bohr magneton is found to be gI(133Cs+)=3.988511(21) × 10-4.

An INDO Molecular-orbital Interpretation of the NMR of Several Protonated Heteroaliphatic Compounds

Abstract Several protonated alcohols, acids, and esters were investigated by means of the INDO-MO theory and in connection with their proton and carbon-13 NMR results. The relative stability of the protonated conformers as detected by the NMR spectroscopy, had a good coincidence with the MO-theory and the experimental results. The proton or carbon-13 chemical shifts and coupling constants also showed satisfactory linear correlations between the theory and the experiment; the proton and isotropic (13C) chemical shifts could be well explained by the linear correlation between the diamagnetic shielding constant and the electron density on the proton of the O–H bond and between the calculated paramagnetic shielding effect and the observed isotropic chemical shifts. The observed coupling constants of the proton and carbon-13 NMR had good overall parallelisms with those evaluated by means of the Fermi contact effect.

Properties of the benzene molecule near the Hartree-Fock limit

The ground electronic state of the benzene molecule is studied with a (9s5p1d/4s1p)/[4s2p1d/2s1p] contracted Gaussian basis set in the traditional Hartree-Fock approximation. It is estimated that the Hartree-Fock limit is approached within 0.07 ± 0.02 a.u. Technical problems associated with large-scale calculations of this type are discussed. One-electron properties are determined, including second moments, average diamagnetic shielding constants, Hellmann-Feynman forces, electric-field gradients, and charge densities. Comparisons are made with the available experimental data and with other calculations.

CNDO calculations of diamagnetic shielding in molecules

AbstractAn approximate procedure for the calculation of diamagnetic shielding in molecules is presented. The method proposed is based on the ‘complete neglect of differential overlap’ (CNDO) molecular wave functions and is formulated according to the zero differential overlap (ZDO) approximation. The results obtained with several CNDO‐type wave functions for diatomic and polyatomic molecules are in very good agreement with non‐empirical SCF calculations. The 14N diamagnetic shielding constants in several molecules were computed and some approximations usually adopted in the interpretation of 14N chemical shifts are critically discussed. It was shown that in some cases the observed 14N chemical shifts cannot be interpreted solely in terms of the paramagnetic contribution to the shielding constant.

Many‐Electron problems. II. Energy expansions and internal fields

AbstractEnergy relations are derived for neutral atoms and isoelectronic sequences. It is shown that the field of the electrons at the position of the nucleus follows a very simple law and the diamagnetic shielding constant may be given in simple analytic form as a function of the atomic number.

Nuclear Corrections to Electronic Expectation Values: Zero-Point Vibrational Effects in the Water Molecule

A variation–perturbation approach is used to determine nuclear corrections to electronic properties of polyatomic molecules. To illustrate the technique, general expressions for the first-order zero-point vibrational corrections are derived and applied to various one-electron properties of the water molecule. These include the electric dipole and molecular quadrupole moments, the diamagnetic susceptibility, the diamagnetic shielding constants, the quadrupole coupling constants, and the Hellmann–Feynman forces. The numerical results, which depend upon the combined use of the LCAO MO CI wavefunctions of Reeves and Boys and of the experimental data of Papous̆ek and Pliva, show that electronic expectation values need to be vibrationally corrected for quantitative comparisons of theory with experiment. For the water molecule, these corrections are typically about 1%, but can be as large as 10%, of the equilibrium values. The net sign of each correction is determined by the symmetric stretching mode in H2O and D2O, and the O–H and/or O–D stretch in HDO. Of particular importance to the proper treatment of the vibrational average is a potential surface containing the proper number of appropriately chosen symmetric and asymmetric configurations of nuclei.

Analysis of Nuclear Magnetic Resonance Spectra of Molecules in Liquid-Crystal Solvents

A convenient method to analyze the high-resolution nuclear magnetic resonance spectra of molecules dissolved in liquid-crystal solvents is described and related to basic theory of magnetic resonance. The method is applied to analyze the proton and fluorine NMR spectra of monofluorobenzene in a nematic liquid-crystal solvent. Parameters deduced from this analysis and describing the anisotropic molecular motion, the direct magnetic dipole—dipole interactions Dij, the indirect spin—spin couplings Jij, and the anisotropy of the diamagnetic shielding constant of F in the C–F bond are summarized and compared with the values for benzene and hexafluorobenzene in the same solvent. It is shown that agreement of experimental and computer-simulated theoretical spectra is probably limited by the accuracy of relative bond lengths in the assumed geometry for fluorobenzene. It is concluded that for many molecules having a large number (N≥3) of spin-½ nuclei, it is possible in the analysis of these spectra to reject incorrect hypothetical geometries and even to obtain refined relative positions for the magnetic nuclei.