Hyperfine spectrum of RbCl

The molecular beam electric resonance technique has been used to conduct a high precision examination of the hyperfine spectrum of the four isotopomers of RbCl. Coupling constants for the nuclear electric quadrupole interactions, the spin-rotation interactions, the tensor and scalar spin-spin interactions, and a rubidium nuclear octupole interaction, and their dependence on vibrational and rotational states have been determined. The dominant interaction, the rubidium nuclear electric quadrupole interaction, shows a small shift with substitution of the chlorine isotope.     

Permanent moment contributions to chiral discrimination

The discrimination energy, giving the difference in the interaction of two leavo molecules and one laevo with one dextro, is calculated where the coupling involves permanent electric and magnetic moments. Fixed electric dipoles arranged helically on a lattice (simulating the electric effects of a helical polymer for example) give chiral fields producing large (≈kT) discriminations. For the pairwise interaction of fixed molecules realistic electric dipole and electric quadrupole moments can lead to discriminations of about 100 cal mole^?1 at 0.5 nm separation. In the hypothetical case of molecules possessing permanent electric and magnetic moments it is four or more orders of magnitude less. In a freely rotating molecule pair the sequence is reversed and electric and magnetic dipoles give much the bigger averaged discrimination energy.     

The application of radioactive isotope99Mo to the reconstituted MoFe protein

By substututing⁹⁹Mo for the Mo in the reconstituted MoFe protein, the nuclear quadrupole interactions (NQI) of⁹⁹Mo have been measured using the perturbed angular correlations (PAC). Two well-defined electric quadrupole interaction parameters have been observed. The configuration of the M-Center of the MoFe protein is identified by the quadrupole couplign constant _Q1(412(9)MHz) and the asymmetry parameter ₁(0.49(5)). Other parameters, V_Q2(1939(13)MHz) and ₁(0.90(1)), may correspond to a deformation M—Center of MoFe protein.     

A multinuclear solid-state NMR study of alkali metal ions in tetraphenylborate salts, M[BPh4] (M = Na, K, Rb and Cs): what is the NMR signature of cation-pi interactions?

We report a multinuclear solid-state ( (23)Na, (39)K, (87)Rb, (133)Cs) NMR study of tetraphenylborate salts, M[BPh 4] (M = Na, K, Rb, Cs). These compounds are isostructural in the solid state with the alkali metal ion surrounded by four phenyl groups resulting in strong cation-pi interactions. From analyses of solid-state NMR spectra obtained under stationary and magic-angle spinning (MAS) conditions at 11.75 and 21.15 T, we have obtained the quadrupole coupling constants, C Q, and the chemical shift tensor parameters for the alkali metal ions in these compounds. We found that the observed quadrupole coupling constant for M (+) in M[BPh 4] is determined by a combination of nuclear quadrupole moment, Sternheimer antishielding factor, and unit cell dimensions. On the basis of a comparison between computed paramagnetic and diamagnetic contributions to the total chemical shielding values for commonly found cation-ligand interactions, we conclude that cation-pi interactions give rise to significantly lower paramagnetic shielding contributions than other cation-ligand interactions. As a result, highly negative chemical shifts are expected to be the NMR signature for cations interacting exclusively with pi systems.     

Definitive solid-state 185/187Re NMR spectral evidence for and analysis of the origin of high-order quadrupole-induced effects for I=5/2

Rhenium-185/187 solid-state nuclear magnetic resonance (SSNMR) experiments using NaReO(4) and NH(4)ReO(4) powders provide unambiguous evidence for the existence of high-order quadrupole-induced effects (HOQIE) in SSNMR spectra. Fine structure, not predicted by second-order perturbation theory, has been observed in the (185/187)Re SSNMR spectrum of NaReO(4) at 11.75 T, where the ratio of the Larmor frequency (ν(0)) to the quadrupole frequency (ν(Q)) is ～2.6. This is the first experimental observation that under static conditions, HOQIE can directly manifest in SSNMR powder patterns as additional fine structure. Using NMR simulation software which includes the quadrupole interaction (QI) exactly, extremely large (185/187)Re nuclear quadrupole coupling constants (C(Q)) are accurately determined. QI parameters are confirmed independently using solid-state (185/187)Re nuclear quadrupole resonance (NQR). We explain the spectral origin of the HOQIE and provide general guidelines that may be used to assess when HOQIE may impact the interpretation of the SSNMR powder pattern of any spin-5/2 nucleus in a large, axially symmetric electric field gradient (EFG). We also quantify the errors incurred when modeling SSNMR spectra for any spin-5/2 nucleus within an axial EFG using second-order perturbation theory. Lastly, we measure rhenium chemical shifts in the solid state for the first time.     

Syntheses and characterization of nine quaternary uranium chalcogenides among the compounds A2M3UQ6 (A = K, Rb, Cs; M = Pd, Pt; Q = S, Se)

Nine compounds from the series A(2)M(3)UQ(6) (A = K or Rb or Cs; M = Pd or Pt; Q = S or Se) were synthesized by reacting U, M, and Q in ACl or A(2)Q(x) fluxes. These compounds crystallize with eight formula units in the NaBa(2)Cu(3)O(6) structure type, in space group Fmmm of the orthorhombic system. The structure contains hexagons formed from six edge-sharing square-planar coordinated M atoms, which in turn edge-share with trigonal-prismatically coordinated U atoms, forming layers along (010). These layers are separated by A atoms. Electrical resistivity measurements along the [100] direction of Rb(2)Pd(3)US(6) show typical semiconductor behavior. Magnetic susceptibility measurements on Rb(2)Pd(3)US(6) display marked magnetic anisotropy and unusually low magnetic moments owing to crystalline electric field effects.     

An SCF-MS-Xα study of the bonding and nuclear quadrupole coupling in diatomic halogens and interhalogens in the ground X Σ and B Π 0 excited states

SCF-MS-Xα calculations of the electronic structure of diatomic halogens and interhalogens XY (X = I, Br, Cl; Y = I, Br, Cl, F) have been used to investigate the bonding and nuclear quadrupole coupling in these molecules. Calculations have been carried out for the ground X ¹ Σ electronic state, and for the excited B ³ Π₀ state in the case of I₂, Br₂, ICl and IBr. Good agreement (to within 10% in most cases) is obtained between the calculated and observed nuclear quadrupole coupling constants for the molecules in the ground state. For the excited state the agreement is not as good, but the calculation does reproduce the observed decrease in the coupling constants to less than one quarter of their ground state values, and analysis of the contributions to the field gradients clearly shows the reasons for this. The electric dipole moments and electric quadrupole moments of the molecules have also been calculated. However, these prove to be much more strongly dependent on the variables used in the calculation (atomic sphere radii, inclusion of d orbitals). The results of the calculations have also been used to test some of the assumptions made in the Townes and Dailey method of analysis of nuclear quadrupole coupling data.     

Solid-State Nuclear Magnetic Resonance Techniques for the Structural Characterization of Geminal Alane-Phosphane Frustrated Lewis Pairs and Secondary Adducts

The first comprehensive solid-state nuclear magnetic resonance (NMR) characterization of geminal alane-phosphane frustrated Lewis pairs (Al/P FLPs) is reported. Their relevant NMR parameters (isotropic chemical shifts, direct and indirect ²⁷Al-³¹P spin-spin coupling constants, and ²⁷Al nuclear electric quadrupole coupling tensor components) have been determined by numerical analysis of the experimental NMR line shapes and compared with values computed from the known crystal structures by using density functional theory (DFT) methods. Our work demonstrates that the ³¹P NMR chemical shifts for the studied Al/P FLPs are very sensitive to slight structural inequivalences. The ²⁷Al NMR central transition signals are spread out over a broad frequency range (>200 kHz), owing to the presence of strong nuclear electric quadrupolar interactions that can be well-reproduced by the static ²⁷Al wideband uniform rate smooth truncation (WURST) Carr-Purcell-Meiboom-Gill (WCPMG) NMR experiment. ²⁷Al chemical shifts and quadrupole tensor components offer a facile and clear distinction between three- and four-coordinate aluminum environments. For measuring internuclear Al⋅⋅⋅P distances a new resonance-echo saturation-pulse double-resonance (RESPDOR) experiment was developed by using efficient saturation via frequency-swept WURST pulses. The successful implementation of this widely applicable technique indicates that internuclear Al⋅⋅⋅P distances in these compounds can be measured within a precision of ±0.1 Å.     

Sternheimer free determination of the47Ti nuclear quadrupole moment from hyperfine structure measurements

The hyperfine structure (hfs) of 12 metastable states of⁴⁷Ti has been measured by laser induced fluorescence. 11 of these states have been measured additionally very precisely by a laser-rf double resonance method. Taking into account results of earlier hfs measurements, the hfs of altogether 17 fine structure states has been analyzed by the simultaneous parametrization of the one- and two-body interactions in the atomic hfs for the model space (3d+4s) ^N+2 (N=2). This gives 16 parameters for the magnetic dipole interaction and 12 parameters for the electric quadrupole interaction. From the model space parameters, obtained from the hfs fit, the nuclear quadrupole momentQ(⁴⁷Ti)=0.303(24b), has been evaluated at the first time; it is free of Sternheimer corrections up to second order.     

Nuclear quadrupole moment of 197Au from high-accuracy atomic calculations

The electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment Q from experimental nuclear quadrupole coupling constants possible. The four-component Dirac-Coulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to 26s22p18d12f8g5h uncontracted Gaussians) are employed. Energy splittings of the 2D5/2 and 2D3/2 levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with Q up to 10(-5) a.u., whereas the latter display significant nonlinearity even at Q=10(-8) a.u. Larger Q values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between Q values derived from 2D5/2 and 2D3/2 data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of Q(197Au) is 521(7) mb. It is lower than the muonic 547(16) mb and agrees within error bounds with the recent value of 510(15) mb obtained from molecular calculations.     

High-accuracy calculation of nuclear quadrupole moments of atomic halogens

Electric field gradients at the nuclei of halogen atoms are calculated using a finite field approach. The four-component Dirac-Coulomb Hamiltonian serves as the framework, all electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the Gaunt term, the main part of the Breit interaction, is included. Large basis sets (e.g., 28s24p21d9f4g2h Gaussian-type functions for I) are used. Combined with experimental nuclear quadrupole coupling constants, accurate estimates of the nuclear quadrupole moments are obtained. The calculated values are Q(35Cl)=-81.1(1.2) mb, Q(79Br)=302(5) mb, and Q(127I)=-680(10) mb. Currently accepted reference values [Pyykko, Mol. Phys. 99, 1617 (2001)] are -81.65(80), 313(3), and -710(10) mb, respectively. Our values are lower for the heavier halogens, corroborating the recent work of van Stralen and Visscher [Mol. Phys. 101, 2115 (2003)], who obtained Q(127I)=-696(12) mb in a series of molecular calculations.     

Microwave spectra of O(2)-HF and O(2)-DF: hyperfine interactions and global fitting with infrared data

Spectra of the open shell complexes O(2)-HF and O(2)-DF were recorded using Fourier transform microwave spectroscopy. A complete analysis of the hyperfine structure and a global fit including microwave and infrared frequencies [W. M. Fawzy, C. M. Lovejoy, D. J. Nesbitt, and J. T. Hougen, J. Chem. Phys. 117, 693 (2002)] are reported. The Fermi contact interaction between the electron and nuclear spins, the electron spin-nuclear spin dipolar interaction, the nuclear spin-nuclear spin dipolar interaction, and the nuclear electric quadrupole interaction (for O(2)-DF) were considered in the analysis. The correspondence between the magnetic hyperfine constants and the two nuclei of the H(D)F is unambiguously established. In both O(2)-HF and O(2)-DF, the Fermi contact parameter is larger for the fluorine than for the hydrogen, while for the nuclear spin-electron spin dipolar hyperfine constants, the reverse is true. The effective angle between the HF bond and the a axis of the complex, determined from the nuclear spin-nuclear spin interaction constant, is 38(4) degrees. The same angle for the DF complex, derived from the deuterium nuclear quadrupole coupling constant, is 31(4) degrees.     

Full configuration interaction calculation of the low lying valence and Rydberg states of BeH

The all-electron full configuration interaction (FCI) vertical excitation energies for some low lying valence and Rydberg excited states of BeH are presented in this article. A basis set of valence atomic natural orbitals has been augmented with a series of Rydberg orbitals that have been generated as centered onto the Be atom. The resulting basis set can be described as 4s2p1d/2s1p (Be/H) + 4s4p3d. It allows to calculate Rydberg states up to n= {3,4,5} of the s, p, and d series of Rydberg states. The FCI vertical ionization potential for the same basis set and geometry amounts to 8.298 eV. Other properties such as FCI electric dipole and quadrupole moments and FCI transition dipole and quadrupole moments have also been calculated. The results provide a set of benchmark values for energies, wave functions, properties, and transition properties for the five electron BeH molecule. Most of the states have large multiconfigurational character in spite of their essentially single excited nature and a number of them present an important Rydberg-valence mixing that is achieved through the mixed nature of the particle MO of the single excitations.     

Sternheimer free determination of the51V nuclear quadrupole moment from hyperfine structure measurements

The hyperfine structure (hfs) of 18 metastable states of⁵¹V has been measured by laser induced fluorescence. 15 of these states have been measured additionally very precisely by the ABMR-LIRF method. Using results of earlier hfs measurements, the hfs of altogether 33 fine structure states is analyzed using a method of simultaneous parametrization of one- and two-body interactions in the atomic hfs of the model space 3d ^{3 +M} 4s ^{2 ?M} (M = 0, 1, 2). The hfs of these states is described by 16 parameters for the magnetic dipole interaction and 12 parameters for the electric quadrupole interaction. From these model space parameters corresponding configuration dependent parameters for the three configurations were determined. These parameters allow a prediction of the hfs constants of all states of the modelspace within an accuracy of 5 to 10%. The evaluation of the nuclear quadrupole moment of⁵¹V, free of Sternheimer corrections up to second order, yielded the value of -0.043(5) barn.     

Computation of dipole, quadrupole, and octupole surfaces from the variational two-electron reduced density matrix method

Recent advances in the direct determination of the two-electron reduced density matrix (2-RDM) by imposing known N-representability conditions have mostly focused on the accuracy of molecular potential energy surfaces where multireference effects are significant. While the norm of the 2-RDM's deviation from full configuration interaction has been computed, few properties have been carefully investigated as a function of molecular geometry. Here the dipole, quadrupole, and octupole moments are computed for a range of molecular geometries. The addition of Erdahl's T2 condition [Int. J. Quantum Chem. 13, 697 (1978)] to the D, Q, and G conditions produces dipole and multipole moments that agree with full configuration interaction in a double-zeta basis set at all internuclear distances.     

Theoretical study of N quadrupole coupling constants in some NO-containing complexes: N2O3 and FNO

The nuclear quadrupole coupling constants at nitrogen centers have been computed for N₂O₃ and FNO by employing the complete-active-space self-consistent field, internally contracted multireference configuration interaction and single-configuration coupled-cluster methods with correlation-consistent basis sets at the levels of attainable accuracy. To examine the overall quality of the wave functions used in our calculations, also electric dipole moments and potential energy characteristics were calculated and compared with available experimental and recent theoretical data. The effects of the choice of the basis set and reference configuration space were investigated. The robust changes in the electric field gradients occurring in the course of complex formation from isolated subunits were interpreted in terms of wave function composition. Our calculations confirm the assignment of the ¹⁴N nuclear quadrupole coupling constants to nuclear centers in N₂O₃ provided by the microwave measurements of Cox et al. [A.P. Cox, J. Randell, A.C. Legon, Chem. Phys. Lett. 126 (1986) 481.].     

An anomaly in the isotopomer shift of the hyperfine spectrum of LiI

A high-precision examination of the hyperfine spectrum of 6LiI in comparison with 7LiI shows a shift in the iodine nuclear electric quadrupole moment that cannot be accounted for by a model in which the electric field gradient at the iodine site is assumed to depend only upon the internuclear distance between Li and I. The other hyperfine interactions are consistent between the two isotopomers, including the previously reported electric hexadecapole interaction of the iodine nucleus.     

Comment on a sum rule for vibrational raman optical activity

The expressions for the sum of vibrational Raman optical activity (ROA) intensities indicate that the ROA intensity sum for chiral molecules is non-zero for those with an anisotropic electric dipole polarizability. The non-zero sum depends upon the electric dipole, magnetic dipole and electric quadrupole polarizability components and moments of inertia at equilibrium geometry.     

Electric quadrupole polarizabilities of nuclear magnetic shielding in some small molecules

Computational procedures, based on (i) the Ramsey common origin approach and (ii) the continuous transformation of the origin of the quantum mechanical current density-diamagnetic zero (CTOCD-DZ), were applied at the Hartree-Fock level to determine electric quadrupole polarizabilities of nuclear magnetic shielding for molecules in the presence of a nonuniform electric field with a uniform gradient. The quadrupole polarizabilities depend on the origin of the coordinate system, but values of the magnetic field induced at a reference nucleus, determined via the CTOCD-DZ approach, are origin independent for any calculations relying on the algebraic approximation, irrespective of size and quality of the (gaugeless) basis set employed. On the other hand, theoretical estimates of the induced magnetic field obtained by single-origin methods are translationally invariant only in the limit of complete basis sets. Calculations of electric quadrupole polarizabilities of nuclear magnetic shielding are reported for H(2), HF, H(2)O, NH(3), and CH(4) molecules.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.