Determination of structures, stabilities, and electronic properties for bimetallic cesium-doped gold clusters: a density functional theory study.

The equilibrium geometric structures, stabilities, and electronic properties of bimetallic Au(n)Cs (n = 1-10) and pure gold Au(n) (n ≤ 11) clusters have been systematically investigated by using density functional theory with meta-generalized gradient approximation. The optimized geometries show that one Au atom capped on Au(n-1)Cs structures and Cs atom capped Au(n) structures for different sized Au(n)Cs (n = 1-10) clusters are two dominant growth patterns. Theoretical calculated results indicate that the most stable isomers have three-dimensional structures at n = 4 and 6-10. Averaged atomic binding energies, fragmentation energies, and second-order difference of energies exhibit a pronounced even-odd alternations phenomenon. The same even-odd alternations are found in the highest occupied-lowest unoccupied molecular orbital gaps, vertical ionization potential, vertical electron affinity, and hardnesses. In addition, it is found that the charge in corresponding Au(n)Cs clusters transfers from the Cs atom to the Au(n) host in the range of 0.851-1.036 electrons.

Local lattice structure study of the octahedral (CrO6)9- clusters for Cr3+ ion doping in a variety of oxide crystals by simulating the corresponding EPR and optical spectra.

On the basis of the 120 x 120 complete energy matrix, the local lattice structures of the octahedral (CrO6)9- clusters for Cr3+ ions doping in a variety of oxide crystals with D3d or C3v site symmetry have been studied by employing two distorted parameters, respectively. By simulating the calculated EPR and optical spectra data to the experimental results, the local lattice structure parameters are determined unambiguously. It is shown, by means of a series of calculations, that although the local lattice structures around the M (M = Al3+, Ga3+, Li+, Sc3+, etc.) ions in host crystals are obviously different, the local lattice structures of the octahedral (CrO6)9- clusters in a variety of oxide crystals doped with Cr3+ ions are similar and fluctuant in the vicinity of that of the Cr2O3. This may be ascribed to the fact that there is the similarly octahedral (CrO6)9- clusters in a variety of oxide crystals doped with Cr3+ and the Cr2O3 crystal. Our viewpoint is consistent with that of Gaudry et al. [Phys. Rev. B 2003, 67, 094108].

A ULFC method for d(4)(D(2d)) ions and a study of the spin singlets contributions to zero-field splitting of Cr(2+) ions in zinc sulfide crystals.

A simple theoretical method is shown to yield a detailed explanation of numerous EPR parameters for a d4 configuration ion in tetragonal ligand field. Using the unified ligand-field-coupling (ULFC) scheme, the formulas relating the microscopic spin Hamiltonian parameters with the crystal structure parameters are derived. On the basis of the theoretical formulas, the 210 x 210 complete energy matrices including all the spin states are constructed within a strong field representation. By diagonalizing the complete energy matrices, the local lattice structure and Jahn-Teller energy of Cr(2+) ions in ZnS:Cr(2+) system have been investigated. It is found that the theoretical results are in good agreement with the experimental values. Moreover, the contributions of the spin singlets to the zero-field splitting (ZFS) parameters of Cr(2+) ions in ZnS crystals are investigated for the first time. The results indicate that the spin singlets contributions to ZFS parameter b(0)(4) is negligible, but the contributions to ZFS parameters b(0)(4) and b(4)(4) cannot be neglected.

Theoretical investigation of electron paramagnetic resonance spectra and local structure distortion for Mn2+ ions in CaCO3:Mn2+ system: a simple model for Mn2+ ions in a trigonal ligand field.

This paper reports on a novel application of a ligand field model for the detection of the local molecular structure of a coordination complex. By diagonalizing the complete energy matrices of the electron-electron repulsion, the ligand field and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field, the local distortion structure of the (MnO6)10- coordination complex for Mn2+ ions doped into CaCO3, have been investigated. Both the second-order zero-field splitting parameter b(0)2 and the fourth-order zero-field splitting parameter b(0)4 are taken simultaneously in the structural investigation. From the electron paramagnetic resonance (EPR) calculations, the local structure distortion, DeltaR=-0.169 A to -0.156 A, Deltatheta=0.996 degrees to 1.035 degrees for Mn2+ ions in calcite single crystal, DeltaR=-0.185 A to -0.171 A, Deltatheta=3.139 degrees to 3.184 degrees for Mn2+ ions in travertines, and DeltaR=-0.149 A to -0.102 A, Deltatheta=0.791 degrees to 3.927 degrees for Mn2+ ions in shells are determined, respectively. These results elucidate a microscopic origin of various ligand field parameters which are usually used empirically for the interpretation of EPR and optical absorption experiments. It is found that the theoretical results of the EPR and optical absorption spectra for Mn2+ ions in CaCO3 are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the doped CaCO3, the theoretical values of the fourth-order zero-field splitting parameters b(0)4 for Mn2+ ions in travertines and shells are reported first.

Characterization of electronic transition energies and trigonal distortion of the (FeO6)9- coordination complex in the Al2O3:Fe3+ system: a simple method for transition-metal ions in a trigonal ligand field.

A theoretical method for studying the inter-relationships between electronic and molecular structure has been proposed on the basis of the complete energy matrices of electron-electron repulsion, the ligand field, and the spin-orbit coupling for the d5 configuration ion in a trigonal ligand field. As an application, the local distortion structure and temperature dependence of zero-field splitting for Fe3+ ions in the Al2O3:Fe3+ system have been investigated. Our results indicate that the local lattice structure of the (FeO6)(9-) octahedron in the Al2O3:Fe3+ system has an elongated distortion and the value of distortion is associated with the temperature. The elongated distortion may be attributed to the facts that the Fe3+ ion has an obviously larger ionic radius than the Al3+ ion and the Fe3+ ion will push the two oxygen triangles upward and downward, respectively, along the 3-fold axis. By diagonalizing the complete energy matrices, we found that the theoretical results of electronic transition energies and EPR spectra for Fe3+ ions in the Al2O3:Fe3+ system are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the Al2O3, the theoretical values of the zero-field splitting parameters and the corresponding distortion parameters in the range 50 K

Quantum-admixture model of high-spin <--> low-spin transition for ferrous complex molecules.

A quantum-admixture model for the d(6) configuration ferrous complex molecules with the high-spin <--> low-spin transition has been established by using the unified crystal-field-coupling (UCFC) scheme. A general study has been made on the spin transition of octahedrally coordinated d(6) complexes, and a special application has been given to an Fe(II) compound Fe(II)(TRIM)(2)(PhCO(2))(ClO(4)). The results show the following: (i) The quantum picture of the spin transition of a d(6) system, such as Fe(II), is much more complex than a simple transition between the pure (5)T(2g) and (1)A(1g) states as usually understood. In practice, owing to spin-orbit coupling, spin is no longer a good quantum number and there is no longer a pure (5)T(2g) or (1)A(1g) state. Each of them splits into substates and each substate is a linear combination of various multiplets. The high-spin --> low-spin transition of an octahedrally coordinated d(6) ion is practically the crossover of the two lowest substates of (5)T(2g) at the critical point. (ii) At the spin-transition critical point the magnetic moment mu(eff) approximately 5.22 mu(B), which is obviously different from the simple average of the mu(eff) values of high-spin and low-spin states but near the saturation value. (iii) The calculation of the effective molecular magnetic moment mu(eff) for an octahedrally coordinated Fe(II) ion shows that the mu(eff)-T curve is in good agreement with Lemercier et al.'s experiment and both the low-spin value mu(eff) = 0.51 mu(B) and the high-spin value mu(eff) = 5.4 mu(B) are comparable with the experimental values 0.76 mu(B) and 5.4 mu(B), respectively. (iv) The T dependence of the crystal field parameter Dq in the spin-transition region is approximately linear.