Isospectrality and galois projective geometries

We construct a series of pairs of domains in the plane and pairs of surfaces with boundary that are isospectral but not isometric. The construction is based on the existence of finite transformation groups that are spectrally equivalent but not isomorphic. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 660–664, May, 1998. This research was partially supported by the Russian Foundation for Basic Research and by INTAS under joint grant No. 96-01-00043.     

The electronic structure of small lithium clusters

Ab initio molecular orbital calculations using the STO-6G and STO6-21G basis sets have been performed for the cluster series Li _n ⁺ , Li _n , and Li _n ^– (wheren=2–7). Thirty-two optimized structures are discussed and reported, many of which (especially for the anionic structures) have not yet been considered. The calculations suggest that for all three species the optimum geometries are planar. Of the two levels of theories that were investigated, STO-6G//STO-6G and STO6-21G//STO-6G, the latter hybrid theory was found to be less reliable. In particular, for the anionic structures these calculations should provide a platform from which more sophisticated, i.e., configuration interaction, geometry optimization can be performed.     

Study of Structures and Electronic Properties of Pdn–1Pb and Pdn （n≤8） Clusters

Geometric and electronic properties of Pdn–1Pb and Pdn (n≤8) clusters have been studied by using density functional theory with effective core potentials, focusing on the differences between mono- and bimetallic clusters. The average bond length of Pdn–1Pb (n≤8) bimetallic clusters is longer than that of pure palladium clusters except for n = 2 and 3. The most stable structure of Pdn–1Pb (n≤7) is the singlet where there is at least a Pd or Pb atom on its excited state. The energy gaps of Pd–Pb binary clusters are narrower than those of Pdn clusters, and then the chemical activity is strengthened when Pdn clusters are doped with Pb.     

Host–Guest Interactions of Risperidone with Natural and Modified Cyclodextrins: Phase Solubility, Thermodynamics and Molecular Modeling Studies

The solubility of risperidone (Risp) in aqueous buffered cyclodextrin (CD) solution was investigated for α-, β-, γ- and HP-β-CD. The effects of pH, ionic strength and temperature on complex stability were also explored. Neutral Risp tends to form higher order complexes (1:2) with both β- and HP-β-CD, but only 1:1 type complexes with α-, and γ-CD. The tendency of Risp to complex with cyclodextrins is in the order β-CD > HP-β-CD > γ-CD > α-CD. The 1:1 complex formation constant of Risp/HP-β-CD increases with increasing ionic strength in an opposite trend to the inherent solubility (S ₀) of Risp, thus indicating significant hydrophobic effect. The hydrophobic effect contributes to the extent of 72% towards neutral Risp/HP-β-CD complex stability, while specific interactions contribute only 4.7 kJ/mol. Thermodynamic studies showed that 1:1 Risp/HP-β-CD complex formation is driven by a favorable enthalpy change (ΔH ⁰=−31.2 kJ/mol, ΔS ⁰=−7 J/mol.K) while the 1:2 complex is largely driven by entropy changes (ΔH ⁰=−5.0 kJ/mol, ΔS ⁰=42 J/mol.K). Complex stability was found to vary with pH, with a higher formation constant for neutral Risp. Molecular mechanical computations using MM (atomic charges and bond dipole algorithms) and Amber force fields, which were carried out to explore possible sites of interactions between Risp and CDs and to rationalize complex stoichiometry, produced similar results concerning optimal inclusion complex geometries and stoichiometries.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

An improved CNDO/2 standard parametrization for bromine containing molecules

Bromine parameters are proposed, matching well the standard values of first and second row atoms, as introduced by Pople et al. This is shown by comparisons of geometries, configurations, conformations, and dipole moments, obtained with different approaches. The new parameter set was found in a very simple and efficient way that may also be useful for other tasks, e.g. in non-empirical calculations.     

First principles study of the structure,electronic state,and stability of CmN2 clusters

Geometric and electronic properties of C_mN₂ (m = 1–14) clusters have been investigated by density functional theory using the hybrid B3LYP functional and the 6‐311G(d) basis set. Harmonic frequencies for these clusters are given to aid in the characterization of the ground states. These results show that C_mN₂ (m = 1–14) clusters form linear structures with D_∞h symmetry. Two N atoms favor to bond at ends in linear isomers. The chains with odd m have triplet ground states whereas the ones with even m have singlet ground states. The calculated HOMO–LUMO gaps and ionization potentials all show that the C_mN₂ (m = 1–14) clusters with even m are more stable than those with odd m, which is consistent with the observed even–odd alternation of the time‐of‐flight signal intensities. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

M@B<Subscript>9</Subscript> and M@B<Subscript>10</Subscript> molecular wheels containing planar nona- and deca-coordinate heavy group 11, 12, and 13 metals (M=Ag,Au, Cd,Hg, In,Tl)

A density functional and ab initio theory investigation on M@B₉ and M@B₁₀ molecular wheels containing planar nona- and deca-coordinate heavy group 11, 12 and 13 metals (M=Ag, Au, Cd, Hg, In, Ti) has been performed. These unusual clusters all prove to be true minima on the potential energy surfaces of the systems and σ+π double aromatic in nature. The first two vertical one-electron detachment energies of M@B₁₀⁻ (M=Ag, Au) anions and first two ionization potentials of M@B₉ (M=Ag, Au) and M@B₁₀ (M=Cd, Hg) neutrals were calculated to aid future experiments. The cluster complexes designed in this work may expend the domain of planar hyper-coordinate elements to include heavy group 11, 12, and 13 metals and serve as interesting candidates to be targeted in experiments. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported by the National Natural Science Foundation of China (Grant No. 20873117)     

第一过渡系金属-镝单分子磁体研究进展与展望

第一过渡系中的顺磁性离子Cr^Ⅲ、Mn^Ⅱ/Mn^Ⅲ、Fe^Ⅱ/Fe^Ⅲ、Co^Ⅱ、Ni^Ⅱ和Cu^Ⅱ及抗磁性离子Co^Ⅲ和Zn^Ⅱ均可与Dy^Ⅲ在多齿螯合配体配位下形成单分子磁体配合物。在本文中,我们阐述或汇总了几乎所有的第一过渡系金属-镝单分子磁体。对于由顺磁性第一过渡金属离子和Dy^Ⅲ离子形成的配合物,有2个有趣的现象需要引起人们的注意：一是一些Cr-Dy配合物具有较高的阻塞温度和较大的矫顽场,这可归功于配合物内Cr^Ⅲ离子和Dy^Ⅲ离子之间较强的磁耦合作用（|J|>10 cm^-1）。二是报道的Fe^Ⅱ₂-Dy配合物的能垒可达到319 cm^-1（459 K）,这在第一过渡系金属-镝单分子磁体中也是比较高的。这可能与Fe^Ⅱ₂-Dy中Dy^Ⅲ具有较高的轴向对称性（D_5h）有关,且从头计算表明该配合物中Dy的第一激发态也具有较高的轴向对称性。除了部分Cr-Dy和Fe^Ⅱ-Dy配合物外,其他顺磁性第一过渡金属-Dy的能垒较低,这可能由配合物内顺磁离子间弱的磁耦合造成的。为了消除磁耦合对磁弛豫行为影响,近年来人们关注于使用抗磁性第一过渡金属离子与Dy^Ⅲ构建单分子磁体配合物。相比其他核数的Zn-Dy配合物,三核Zn₂Dy配合物被报道的数目最多且研究得最为深入,这可能与较易调控Zn₂Dy中Dy配位几何对称性有关。最后,我们提出了几点关于进一步提升第一过渡系金属-镝单分子磁体的磁性能的建议,其中最为重要的是控制Dy配位几何的轴向对称性及Dy的基态m_J的电荷分布。对于第一过渡系金属-镝单分子磁体中的Dy^Ⅲ离子,Dy^Ⅲ基态m_J的电荷与配体的电荷之间的静电排斥应该降到最低。