Localized molecular orbital studies in momentum space. II. Correspondence between coordinate and momentum space properties of various electron pairs

The momentum space properties of the ten-electron systems Ne, HF, H₂O, NH₃ and CH₄ as well as those of CH₃CH₃, CH₃NH₂, CH₃OH and FCH₂OH were investigated using localized molecular orbitals (LMO) obtained from ab initio self-consistent-field (SCF) wavefunctions constructed from double zeta quality gaussain basis sets.Compton profiles of various LMO electron pairs (CC, CN, CO, CF; CH, NH, OH, FH bond pairs and C, N, O, F lone pairs) are tabulated. In order to understand the correspondence between the momentum and the coordinate space properties of those electron pairs, the concept of the size and the shape of an LMO electron pair charge distribution has been utilized. The use of the intermediate expectation values of pⁿ is introduced for the purpose of interpreting the momentum space properties.The dependence of molecular property partitioning on different localization schemes and on different basis sets is also studied by using the H₂O profile as an example.     

Analysis of the magnetic structure and ferroelectric polarization of monoclinic MnSb(2)S(4) by density functional theory calculations

Monoclinic MnSb(2)S(4) consists of MnS(4) chains made up of edge-sharing MnS(6) octahedra and adopts a (0, 0.369, 0) magnetic superstructure below 25 K. This ordered magnetic structure, in which the spins of each MnS(4) chain possess a helical spin arrangement, has C(2)' symmetry. On the basis of density functional theory calculations, we explored the origin of the observed noncollinear spin arrangement of MnSb(2)S(4) by evaluating its spin exchanges to find that spin exchanges are frustrated not only within each MnS(4) chain but also between adjacent MnS(4) chains. Our analysis predicts that MnSb(2)S(4) is a multiferroic with a ferroelectric polarization of ～14 μC/m(2) along the chain direction, and a field-induced reversal of the ferroelectric polarization of MnSb(2)S(4) can occur by reversing the direction of the helical spin rotation in each MnS(4) chain.     

On the disorder of the Cl atom position in and its probable effect on the magnetic properties of (CuCl)LaNb2O7

The magnetic susceptibility of (CuCl)LaNb2O7 shows a spin gap despite the Cu(2+) ions in each CuClO2 layer forming a square lattice. To account for this observation, we explored implications of the disorder of the Cl-atom position in (CuCl)LaNb2O7 by considering possible ordered structures of CuCl4O2 octahedra in each CuClO2 layer, by identifying various spin exchange interactions of a CuClO2 layer and by estimating the relative strengths of these interactions in terms of spin dimer analysis. We then probed what kind of spin lattice is required for each CuClO2 layer to have a spin gap on the basis of the classical spin approximation. Our study suggests that the CuCl4O2 octahedra of each CuClO2 layer should be arranged such that the resulting spin lattice does not have uniform chains but ring clusters containing an even number of Cu atoms. Implications of this conclusion were discussed on the basis of the recently reported neutron scattering and magnetization studies of (CuCl)LaNb2O7.     

Spin dimer and mapping analyses of the magnetic properties of VO(CH3CO2)2 and VO(OCH2CH2O)

The spin exchange interactions of VO(CH₃CO₂)₂ and VO(OCH₂CH₂O) were investigated by performing spin dimer analysis based on tight binding calculations and mapping analysis based on first principles density functional theory calculations. In agreement with experiment, both analyses show that the magnetic properties of VO(CH₃CO₂)₂ and VO(OCH₂CH₂O) are best described by uniform antiferromagnetic one-dimensional chain and isolated antiferromagnetic dimer models, respectively. Our study shows that the nearest-neighbor spin exchange in the one-dimensional chains of VO₅ square pyramids in VO(CH₃CO₂)₂ is mediated by the C 2p_π orbital of the carboxylate group, and that the cis spin dimers of VO(OCH₂CH₂O) provide strong antiferromagnetic spin exchange than do the trans spin dimers of VO(OCH₂CH₂O).     

A relationship between correlation energies and sizes: The helium-like ions

The correlation energy (E _corr) is found to be inversely proportional to the product of the electron pair size (2>) and the square of the effective nuclear charge (Z _eff) for the helium-like ions.     

Investigation of the electronic and structural properties of potassium hexaboride, KB6, by transport, magnetic susceptibility, EPR, and NMR measurements, temperature-dependent crystal structure determination, and electronic band structure calculations

The electronic and structural properties of potassium hexaboride, KB(6), were examined by transport, magnetic susceptibility, EPR, and NMR measurements, temperature-dependent crystal structure determination, and electronic band structure calculations. The valence bands of KB(6) are partially empty, but the electrical resistivity of KB(6) reveals that it is not a normal metal. The magnetic susceptibility as well as EPR and NMR measurements show the presence of localized electrons in KB(6). The EPR spectra of KB(6) have two peaks, a broad ( approximately 320 G) and a narrow (less than approximately 27 G) line width, and the temperature-dependence of the magnetic susceptibility of KB(6) exhibits a strong hysteresis below 70 K. The temperature-dependent crystal structure determination of KB(6) shows the occurrence of an unusual variation in the unit cell parameter hence supporting that the hysteresis of the magnetic susceptibility is a bulk phenomenon. The line width DeltaH(pp) of the broad EPR signal is independent of temperature and EPR frequency. This finding indicates that the line broadening results from the dipole-dipole interaction, and the spins responsible for the broad EPR peak has the average distance of approximately 1.0 nm. To explain these apparently puzzling properties, we examined a probable mechanism of electron localization in KB(6) and its implications.     

Investigation of the spin exchange interactions and magnetic Structures of the CrVO4-type transition metal phosphates,sulfates, and vanadates by spin dimer analysis

The CrVO(4)-type magnetic oxides MM'O(4) consist of edge-sharing MO(4) octahedral chains condensed with M'O(4) tetrahedra and exhibit a wide variety of magnetic structures. The magnetic properties of these oxides were examined by studying their spin exchange interactions on the basis of spin dimer analysis. The nature and magnitudes of the intra- and interchain spin exchange interactions depend on the square-to-rectangle distortion in the basal planes of the MO(4) chain and on the difference between the M 3d and O 2p orbital energies. The spiral magnetic structures of beta-CrPO(4) and MnSO(4) originate from the pseudohexagonal arrangement of the MO(4) chains and the frustrated interchain antiferromagnetic interactions.     

Theoretical investigation of the spin exchange interactions and magnetic properties of the homometallic ludwigite Fe(3)O(2)BO(3)

The homometallic ludwigite Fe(3)O(2)BO(3) has a complex structure made up of corner- and edge-sharing FeO(6) octahedra and exhibits a number of apparently puzzling magnetic properties. The reasons for these properties were probed by examining the trends in the spin exchange interactions of Fe(3)O(2)BO(3). To analyze the relative strengths of spin exchange interactions in such a complex magnetic solid, we first generalized the method of spin dimer analysis and then employed the resulting formulation to investigate how the magnetic properties of Fe(3)O(2)BO(3) are related to its reported crystal structures. The spin-orbital interaction energies calculated for various spin dimers of Fe(3)O(2)BO(3) provide estimates for the relative strengths of the associated spin exchange interactions, which in turn account for the observed magnetic properties of Fe(3)O(2)BO(3).     

Synthesis, optical properties and electronic structures of polyoxometalates K3P(Mo1−xWx)12O40 (0?x?1)

Various compositions of solid solutions K₃P(Mo_1−xW_x)₁₂O₄₀ (0?x?1) were prepared using two solid state synthetic routes. The crystallite size was determined by linewidth refinements of X-ray diffraction patterns using the Warren-Averbach method, and the grain size distribution by laser scattering experiments. Optical properties were determined by diffuse reflectance measurements in the UV-visible range. The optical gap E_g was found to increase exponentially from ∼2.5 to ∼3.30 eV with increasing x, and is systematically shifted to a higher energy when the grain size decreases. The relation between E_g and x was analyzed by calculating the HOMO-LUMO gaps of the [P(Mo_1−xW_x)₁₂O₄₀]³⁻ anions on the basis of tight-binding electronic structure calculations.