Theoretical investigations of the local distortion and electron paramagnetic resonance parameter for CdCl2:V2+ and CsMgX3:V<sup>2+（X=Cl,Br） systems

This paper systematically investigates the local distortion and electron paramagnetic resonance (EPR) parameter for CdCl 2 :V 2+ and CsMgX 3 :V 2+ (X=Cl, Br) systems on the basis of the complete energy matrix, in which not only the contributions due to the spin–orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin–orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin–orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl 2 :V 2+ and elongation distortions for CsMgX 3 :V 2+ (X=Cl, Br), respectively. It notes that the empirical formula R ≈ R H + (r i-r h )/2 is not suitable for CdCl 2 :V 2+ and CsMgX 3 :V 2+ (X=Cl, Br) systems. The contributions of ligand to spin–orbit coupling interaction cannot be neglected for strong covalent systems, especially for V 2+ doped in CsMgBr 3 :V 2+ .     

Effect of local structure on electron paramagnetic resonance spectra for trigonal [Cr(H2O)6]3+coordination complex in the sulfate alums series: a ligand field theory study

A simple theoretical method is introduced for studying the interrelation between electronic and molecular structures.By diagonalizing the 120 × 120 complete energy matrices,the relationships between zero-field splitting(ZFS) parameter D and local distortion parameter △θ for Cr 3+ ions doped,separately,in α-and β-alums are investigated.Our results indicate that there exists an approximately linear relationship between D and △θ in a temperature range 4.2-297 K and the signs of D and △θ are opposite to each other.Moreover,in order to understand the contribution of spin-orbit coupling coefficient ζ to ZFS parameter D,the relation between D and ζ is also discussed.     

Geometries, stabilities, and electronic properties of Be-doped gold clusters: a density functional theory study

We have systematically investigated the geometrical structures, relative stabilities and electronic properties of small bimetallic AunBe (n = 1, 2, . . . , 8) clusters using a density functional method at BP86 level. The optimized geometries reveal that the impurity beryllium atom dramatically affects the structures of the Aun clusters. The averaged binding energies, fragmentation energies, second-order difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps and chemical hardness are investigated. All of them exhibit a pronounced odd-even alternation, manifesting that the clusters with even number of gold atoms possess relatively higher stabilities. Especially, the linear Au2Be cluster is magic cluster with the most stable chemical stability. According to the natural population analysis, it is found that charge-transferring direction between Au atom and Be atom changes at the size of n = 4.     

Pressure-induced structural transition and thermodynamic properties of RhN2 and the effect of metallic bonding on its hardness

The elastic constant, structural phase transition, and effect of metallic bonding on the hardness of RhN2 under high pressure are investigated through the first-principles calculation by means of the pseudopotential plane-wave method. Three structures are chosen to investigate for RhN2, namely, simple hexagonal P6/mmm （denoted as SH）, orthorhombic Pnnm （marcasite）, and simple tetragonal P4/mbm （denoted as ST）. Our calculations show that the SH phase is energetically more stable than the other two phases at zero pressure. On the basis of the third-order Birch Murnaghan equation of states, we find that the phase transition pressures from an SH to a marcasite structure and from a marcasite to an ST structure are 1.09 GPa and 354.57 GPa, respectively. Elastic constants, formation enthalpies, shear modulus, Young＇s modulus, and Debye temperature of RhN2 are derived. The calculated values are, generally speaking, in good agreement with the previous theoretical results. Meanwhile, it is found that the pressure has an important influence on physical properties. Moreover, the effect of metallic bonding on the hardness of RhN2 is investigated. This is a quantitative investigation on the structural properties of RhN2, and it still awaits experimental confirmation.     

含时旋转磁场中的两耦合粒子的纠缠演化(英文)

我们研究了含时旋转磁场中海森堡XXX模型下的双量子比特的动力学演化情况.基于此非自治系统的代数结构,我们用代数动力学方法求得了系统的精确解析解.在此基础上,进一步研究了在不同初态下系统的纠缠测度随时间的演化,发现纠缠测度由系统的初态的系数和耦合强度决定.     

Investigations of the electron paramagnetic resonance parameters and the tetragonal local structure for (VCl6)4- coordination complex in MCl:V2+ (M=Na, K, Rb) systems

By simulating the electron paramagnetic resonance (EPR) and optical spectra on the basis of the 120×120 complete energy matrix, this paper determines the local lattice structure parameters R1 and R2 for MCl:V2+ (M=Na, K, Rb) systems at 77 K, 195 K and RT (room temperature 295 K or 302 K), respectively. The theoretical results indicate that there exists a compressed distortion in MCl:V2+ systems. Meanwhile, it finds that the structure parameters R1, R2 and |△R| (= R1-R2) increase with the rising temperature. Subsequently, from the analysis it concludes that the relation of EPR parameter D vs.△R is approximately linear. Finally, the effects of orbital reduction factor k on the g factors for the three systems have been discussed.     

Comparative analysis of energy-level splitting of Pr3＋ doped in LiYF4 and LiBiF4 crystals： a complete energy matrix calculation

Based on the combination of Racah's group-theoretical consideration with Slater's wavefunction, a 91 × 91 complete energy matrix is established in tetragonal ligand field D_2d for Pr³⁺ ion. Thus, the Stark energy-levels of Pr³⁺ ions doped separately in LiYF₄ and LiBiF₄ crystals are calculated, and our calculations imply that the complete energy matrix method can be used as an effective tool to calculate the energy-levels of the systems doped by rare earth ions. Besides, the influence of Pr³⁺ on energy-level splitting is investigated, and the similarities and the differences between the two doped crystals are demonstrated in detail by comparing their several pairs of curves and crystal field strength quantities. We see that the energy splitting patterns are similar and the crystal field interaction of LiYF₄:Pr³⁺ is stronger than that of LiBiF₄:Pr³⁺.     

论(MnF_6)~(4-)团簇光谱参量D_q的R~(-n)律

用配位球壳势模型研究了络合分子中过渡金属离子光谱参量Dq 与金属 -配体间键长R的R-n律关系。结果表明指数n的变化趋势依赖于配位球壳半径R的增大或减小 ,在点电荷模型下n值将小于 5且随R的减小而减小。在 (MnF6) 4-团簇键长的实验范围内 (R =0 .2 0 7nm←→ 0 .2 14nm) ,理论计算值n =4.488与实验观测值n =4.45符合得很好。     

蓝宝石(α-Al_2O_3:Fe~(3+))体系基态分裂与局域晶格畸变的研究

2002年Scholz和Buzaré对蓝宝石晶体中Fe3+离子的基态分裂重新进行了EPR实验测量和研究,他们的初步分析表明在蓝宝石晶体中Fe3+离子的6A1基态分裂有可能同时与两个方向的畸变角(θ和φ)有关.本文采用对角化d5组态在C3点群对称下的252×252完全能量矩阵的方法,对蓝宝石晶体中Fe3+离子的光谱和EPR谱进行了系统的研究.计算结果表明蓝宝石体系中Fe3+离子的6A1基态分裂确实将明显依赖于两个方向的畸变角θ和φ,这一理论结果与Scholz和Buzaré等的实验相符合.同时,通过拟合Fe3+离子在蓝宝石体系中的实验光谱和EPR参量,确定了蓝宝石晶体中(FeO6)9团簇局域晶格畸变角θi的范围.     

KZnF3:Fe3+体系局域晶体结构的理论研究

本文采用对角化三角场中d5组态完全能量矩阵的方法,研究了KZnF3Fe3+体系的局域晶体结构和EPR参量之间的关系.在分析中我们引入了双层配位模型,即配位体包括Fe3+离子最近邻的6个F-离子和次近邻的8个K+离子.计算表明KZnF3Fe3+的局域结构畸变源于一个K+离子沿C3轴方向(即[111]方向)向Fe3+离子的移动,从而诱导F-离子的位移,使得Fe3+-F-键与C3轴夹角发生变化.通过计算EPR的低对称参量D和(a-F),我们分别得出室温(T=300K)时的畸变角为△θ1=2.58°,△θ2=-1.4°和低温(T7=77 K)时畸变角为△θ1=2.85°,△θ2=-1.40计算结果与实验观察值△θ1=2.8±0.3°,△θ2=-1.1±0.3°相符合.