A computational investigation of boron-doped chromium and chromium clusters by density functional theory

The geometries,stabilities and electronic properties of Crn and CrnB(n=2-9) clusters have been systematically investigated by density functional theory.The results suggest that the lowest energy structures for CrnB clusters can be obtained by substituting one Cr atom in Crn+1 clusters with B atom.The geometries of CrnB clusters are similar to that of Crn+1 clusters except for local structural distortion.The second-order difference and fragmentation energy show Cr4,Cr6,Cr8,Cr3B,Cr5B and Cr8B cluster are the ...     

On the Petrials of thin rank 3 geometries

The aim of this paper is to extend the concept of a Petrial to thin (regular) rank three geometries. The main result is that if the Petrial of a thin regular residually connected geometry Γ is also a thin geometry, the geometry Γ has a linear diagram. Received 12 October 1999; revised 25 March 2000.     

Efficient Computation of Geometries for Gold Complexes

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn-Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2-xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019 , 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid-GGA exchange-correlation functional (PBEh-3c) paired with a double-ζ basis set, which is 2–3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis.     

Transitive bislim geometries of gonality 3, Part II: The group theoretic cases

We consider point-line geometries having three points on every line, having three lines through every point (bislim geometries), and containing triangles. We classify such geometries under the hypothesis of the existence of a collineation group acting transitively on the point set.     

密度泛函理论对ZrnPd团簇结构和性质的研究

用B3LYP/LANL2DZ方法对Zr_nPd(n =1—13)团簇的平衡几何结构、能量、频率、电子性质和磁性进行了计算.研究表明,Pd原子位于表面的异构体更为稳定,其中Zr₇Pd,Zr₁₂Pd团簇稳定性高,是幻数团簇,此外,相对于Zr_nCo与Zr_nFe团簇,Zr_nPd团簇参与化学反应的能力较弱,化学稳定性更     

A characterization of truncated projective geometries as flag-transitive PG *.PG-geometries

We prove that every flag-transitive locally finite (PG ^*.PG)-geometry is a truncated projective geometry. Dedicated to Daniel Hughes on the occasion of his 80th birthday.     

Aun（n=2—9）团簇的几何结构和电子特性

采用密度泛函DFT中的 B3LYP 方法，选择LANL2DZ基组，对Aun（n＝2—9）小团簇的各种可能结构进行优化，得到了它们的基态平衡结构并计算出其原子化能.研究表明：随着团簇尺寸的增大，单个原子的平均原子化能逐渐增大.同时分析了团簇的能级分布、最高占据轨道与最低空轨道之间形成的能级间隙.计算出了电子亲和能和电离势，计算值与实验值非常接近.最后分析了费米能级、电子亲和能和电离势形成“奇－偶”振荡效应的原因. 关键词： Au团簇 平衡几何结构 能隙 电子性质     

Locally modular geometries in homogeneous structures

We show that if M is a strongly minimal large homogeneous structure in a countable similarity type and the pregeometry of M is locally modular but not modular, then the pregeometry is affine over a division ring. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Metric and Matter in Unconnected, Connected, and Metrically Connected Manifolds

From Einstein's point of view, his General Relativity Theory had strengths as well as failings. For him, its shortcoming mainly was that it did not unify gravitation and electromagnetism and did not provide solutions to field equations which can be interpreted as particle models with discrete mass and charge spectra, As a consequence, General Relativity did (and does) not solve the quantum problem, either. Einstein tried to get rid of the shortcomings without losing the achievements of General Relativity Theory. Stimulated by papers of Weyl (Sitzungsber. Preuss. Akad. Wiss (1918) 465) and Eddington (Proc. R. Soc. Hond. 99 (1921) 194), from 1923 onward, he believed that, to reach this goal, one has to transit to space–times which possess more comprehensive geometrical structures than the Riemann space–time. This was the beginning of a decade's lasting search for a unitary field theory. We describe this exciting part of the history of physics, discuss achievements and failures of this development, and ask how these early attempts of a unified theory strike us today. Taking into account the fact that the Equivalence Principle only speaks for a geometrization of gravitation, we consider an alternative way to give those non-Riemannian structures which were introduced by the unitary field approach a physical meaning, namely the meaning of a generalized gravitational field. This is interesting since there are arguments in favor of such a generalization of General Relativity Theory, e.g., the problems the latter theory meets with if one tries to quantize it and to unify gravitation with other interactions.     

Characterization of Shape-Memory Trifunctionally Cross-Linked Polyurethanes,with Varying Hard and Soft Segments

A family of potential shape-memory trifunctionally cross-linked polyurethanes (SMPs) was achieved with varying the hard segments. The molecular weight of the soft segment poly(oxytetramethylene) (PTMO) was held constant. The polymers were employed with and without chain extender. They were characterized by means of structural studies and creep tests over a range of temperatures, and hence their shape-memory performance was determined. More crystallization was observed in the materials with hard domains based on the flexible diisocyanate 4,4′-dibenzyl diisocyanate (DBDI) extended with 1,4-butanediol (BDO). A series of key parameters characterizing shape-memory performance was determined: the temperature position of the peak (T_peak), the half-width of the peak (δT), and the minimum value of the 30 s isochronal creep modulus E(30 s) E_min. While the peak temperature and modulus increased with increasing cross-link density, the width of the peak was observed to decrease with increasing cross-link density. The materials were found to vary systematically with details of the network structure.