Molecular shape,shape of the geometrically active atomic states,and hybridization

In a recent publication [C. A. Nicolaides and Y. Komninos, Int. J. Quant. Chem. 67 , 321 (1998)], we proposed that in certain classes of molecules the fundamental reason for the formation of covalent polyatomic molecules in their normal shape is to be found in the existence of a geometrically active atomic state (GAAS) of the central atom, whose shape, together with its maximum spin‐and‐space coupling to the ligands, predetermines the normal molecular shape (NMS). The shape of any atomic state was defined as that which is deduced from the maxima of the probability distribution ϱ(cos θ₁₂) of the angle formed by the position vectors of two electrons of an N‐electron atom. Because the shape of the GAAS determines the NMS and because the NMS allows the construction of corresponding hybrid orbitals, we examined and discovered the connection between the GAAS shape and Pauling's function for the strength of two equivalent orthogonal orbitals at angle θ₁₂ with one another. It is shown that the computed ϱ(cos θ₁₂) of the GAAS can be cast in a form which allows the deduction of the composition of the hybrid orbitals of maximum spin states with configurations sp³, sp³d⁵, sp³d⁵f⁷, slⁿ, s²lⁿ and the demonstration of the central atom's tendency to form bonds in directions which coincide with the nodal cones of the hybrid bond orbitals. These results not only reinforce the validity of the theory as to the fundamental “mechanism” for the formation in the normal shape of coordination compounds and covalently bonded polyatomic molecules, but also provide the justification for the relevance and importance of the hybridization model. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 25–34, 1999     

Tetrazene–Characterization of Its Polymorphs

The reinvestigation of tetrazene single crystalline material by means of X-ray methods resulted in a slightly different structure when compared to previously published data. Reaction conditions responsible for different crystalline modification formation were investigated. Newly described C form was found to be the primary reaction product and the combined action of temperature and the presence of water over time is required for the transition to the A form. Both forms were described by X-ray powder diffraction. Tetrazene was also subjected to infrared and Raman spectroscopy, which allowed differentiating between the forms. The molecule was isotopically labeled with ¹⁵N atoms at two different locations (ring and nitrogen sidechain) and employed in assigning vibrational modes to the resulting bands. Differences between sensitivities to mechanical stimuli of the two modifications were investigated and found industrially insignificant. In the same vein, the performance of either modification in primer composition and primer was identical.     

Geometrically active atomic states and the formation of molecules in their normal shapes

We present a theory of molecular formation according to which the shape of polyhedral or coordination compounds is fixed to a very good approximation by the shape of a particular state (or states) of the central atom, which is activated by spin and spacial coupling of optimal strength between this state, called the geometrically active atomic state (GAAS) and the state of the ligands. For a molecule with a central atom, spacial coupling of optimal strength, means that the shape of the GAAS fixes the position of the ligands according to the maximum overlap principle of the Heitler–London, Slater, and Pauling theory of covalent bonding, whereby much of the energy lowering from the free atom limit is obtained by the maximization of the contribution of the exchange integrals. Hence, a direct causal relationship between the shape of the GAAS and the shape of the molecular state at equilibrium seems to exist. This relationship implies a picture of diabatic connection between the geometrically asymptotic region and the equilibrium region, which is driven by the coupled GAAS and provides the “why” of molecular shape. Since the latter is fixed by the shape of the GAAS (in cases of electronic complexity or of molecular instability it is possible that more than one GAAS contribute simultaneously), prediction of the shape of certain large systems can be made based on the a priori recognition of the corresponding GAAS. The concept of the shape of atomic states defined and computed quantum mechanically from the probability distribution ϱ(cos θ₁₂) of the angle θ₁₂ that the position vectors of two electrons form in the given atomic state. Specifically, it is deduced from the distribution's maxima which provide the most probable values of θ₁₂. As shown previously [Y. Komninos and C. A. Nicolaides, Phys. Rev. A 50 , 3782 (1994)], ϱ(cos θ₁₂) is obtainable directly from the state-specific expression for the Coulomb interaction, where the R^k integrals are replaced by Legendre polynomials P_k, multiplied by normalization constants and radial overlaps. The theory is demonstrated by explaining the shape of BeH₂, BH₂, CH₄, SiH₄, H₂O, H₂S, NH₃, PH₃, SF₆, and TiH₄ in terms of the shapes of the following GAAS. Be: 2s2p ³P⁰, B: 2s2p^{2 4}P, C: 2s2p^{3 5}S⁰, Si: 3s3p^{3 5}S⁰, O: 2s2p^{5 3}P⁰, S: 3s²3p³3d ³P⁰, N: 2s2p^{4 4}P, P: 3s3p³3d ⁴P⁰, S: 3s3p³3d^{2 7}F⁰, and Ti: 3d²4s4p ⁵G⁰. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 321–328, 1998     

Enantiotropy of Simvastatin as a Result of Weakened Interactions in the Crystal Lattice: Entropy-Driven Double Transitions and the Transient Modulated Phase as Seen by Solid-State NMR Spectroscopy

In crystalline molecular solids, in the absence of strong intermolecular interactions, entropy-driven processes play a key role in the formation of dynamically modulated transient phases. Specifically, in crystalline simvastatin, the observed fully reversible enantiotropic behavior is associated with multiple order–disorder transitions: upon cooling, the dynamically disordered high-temperature polymorphic Form I is transformed to the completely ordered low-temperature polymorphic Form III via the intermediate (transient) modulated phase II. This behavior is associated with a significant reduction in the kinetic energy of the rotating and flipping ester substituents, as well as a decrease in structural ordering into two distinct positions. In transient phase II, the conventional three-dimensional structure is modulated by periodic distortions caused by cooperative conformation exchange of the ester substituent between the two states, which is enabled by weakened hydrogen bonding. Based on solid-state NMR data analysis, the mechanism of the enantiotropic phase transition and the presence of the transient modulated phase are documented.     

Crystal structure and conformational disorder of poly(hexamethylene terephthalate)

Packing polymorphism and conformational disorder of poly(hexamethylene terephthalate) were analyzed by x-ray diffraction technique. The measurements were performed in the temperature range from 20 to 135°C. At high temperature, several unassignable reflections were found to disappear, and all reflections were satisfactorily indexed by single-chain unit cell. The crystal structures of β form (135°C) and β form (20°C) were similarly triclinic. The β′ unit cell assumed the double b-axis dimension, and the centrosymmetric conformations of the two chains adjacent along the b-axis differed in the orientation of the phenylene rings. At the elevated temperature (β form), the chains were indistinguishable by x-ray diffraction owing to the ring-flipping motion. The β and β′ structures were different in the local conformational disorder around the terephthaloyl groups. Conformational polymorphism of homologous poly(oligomethylene terephthalate)s was considered to originate from the difference in bulkiness of the aromatic and aliphatic residues. © 1996 John Wiley & Sons, Inc.     

基于多模板子空间的支持向量机多类自然形状识别

自然物体的检测与识别是机器视觉以及模式识别的重要任务。由于自然物体形状的多样性与柔性以及视觉判别的复杂性,使基于计算机的自然形状物体的准确检测与识别变得比较困难。提出了基于多模板子空间的支持向量机(SVM)多类自然形状识别方法。利用广义Hough变换表示自然形状物体轮廓,针对每个类别通过训练得到多个匹配模板;检测时利用多模板最近邻相关匹配进行粗检测,使用支持向量机进行分类。在相关匹配限定的子空间内收集训练样本,有效地降低了训练样本数目。实验结果证明所提出的自然形状检测与识别方法是十分有效的,大大改进了经典检测算法的检测效果以及自动化程度。     

联合变换相关中输出相关点形状与输入相关物长宽比的关系

根据联合变换相关理论和光的衍射理论,定量分析了联合变换相关中两相关输入物长宽比与输出相关点形状间的关系.结果表明:输入相关物长宽比影响相关点的形状,当相关物长宽比过大时,将使相关点形状严重偏离圆斑形状,从而影响相关点的探测和精确定位.     

EMG模型中参数τ的一种关系式

利用一个关系式δ＝ａ＋ｂ／Ｆ＋ｃτ将标准偏差σ、时间衰减常数τ和流动相流速Ｆ很好地关联起来,取得了很好的结果,相关系数达到０．９９以上。     

Rolling bearing fault detection using correlation technique

It's known that auto-correlation technique is effective in extracting periodical signals from random noises. In the case of fault monitoring of rolling element bearing, we can't acquire the.fault information directly from the original signal because of the difference of signal phases. And the signal is shown as the wide band random signal in auto-correlation function. In this paper, the signal is pre-processed and the results are proved effctive. Moreow, by taking the auto-correlation fumction we can obtain the determined and comparable samples. This is very important for establishing the data base of running condition and for detecting the faults.