关于生成函数法的基本定理

生成函数CF或称生成轨道GO法是用于求SALC轨道的图解方法,由于其简明直观而广泛地用于化学教学中。生成函数法的群论基础可归结为以下基本定理:对位置坐标矢量为r,的原子p的轨道φ_p。,若它们在该分子所属点群对称操作作用下的变换性质与坐标矢量的变换性质一样(简称共交),即     

磷的d轨道在H~3PO分子中的作用

用分子片轨道在分子环境中发生极化的概念研究d轨道在H~3PO分子中的作用。H~3PO分子被分为两个分子片---H~3P和O.在RHF/6-31G^*水平上计算出分子环境中的极化了的分子片轨道(FOM)。再剔除d函数为主的FOM,用剩余的FOM为基进行构型优化,得到与RHF/6-31G^*相近的结果。这一结果说明磷原子的d函数在H~3PO分子中仅仅起一个极化函数的作用,而不是起价轨道作用。     

密度矩阵旋转法 - 绕过波函数直接求密度矩阵

本文首次提出了一种直接求闭壳层体系密度矩阵的方法 - 密度矩阵旋转法(PMatrix Botanon method). PMR法的特点是不必象自洽场法(SCF)那样解HFR方程,也不必象分子轨道酉变换法(UTMO)那样考虑分子轨道系数,而是绕过波函数直接求体系的密度矩阵,进而从密度矩阵求出体系的所有性质,PMR法能够保证求解过程收敛,克服了传统的HFR-SCF法不能保证收敛的根本缺点.此外,PMR法的计算比SCF法和UTMO法更简便.在CNDO/2近似下,比较了PMR,UTMO和SCF三种方法的计算结果,表明PMR法较优越。     

休克尔分子轨道(HMO)的三角函数法求解

用HMO法求解分子轨道和能量时,有二个不易解决的问题:其一是休克尔行列式不易直接展开求解能量;其二是解久期方程组求分子轨道(特别是环状共轭烯烃)时,常会出现不定解的情况。这两个问题给结构化学教学带来一定的困难,采用三角函数法求解     

化学反应势能面理论研究及其新发展(Ⅱ)

五、用分子轨道法,逐点优化求位能面1.自洽场分子轨道法大意对闭壳层分子(电子均成对地排在占据的 M.O.上),多电子(2n 个电子)分子的波函数可用单行列式表示:     

线形碳元素簇合物的成键性质

在ab initio 3-21G水平上, 用能量梯度法优化了线性碳元素簇合物C_n~e(n为成簇原子个数, e为电荷)的平衡几何结构. 所得的电离势随成簇原子个数的改变, 呈现出不同程度的奇偶交替变化趋势. 在ab initio计算基础上, 用Boys方法, 对其占据正则分子轨道进行定域化变换, 得到了它们的定域分子轨道. 对定域分子轨道性质的分析表明, 线性碳元素簇合物中, 主要键型有双中心σ和π健, 双中心弯键和三中心香蕉健, 以及多中心σ和π健. 这种键型的多样化可视为小元素簇的成健特征. 此外, 通过对其成键性质的分析, 讨论了线性碳元素簇的稳定性. 对于小碳元素簇, 化学键的共轭性对其稳定性具有十分显著的作用.     

描述分子轨道成键性质的H-F力方法

提出了用Hellmann-Feynman静电力描述分子轨道成键能力的方法, 从能量梯度和静电力两种观点论述了分子轨道对化学键的作用。H-F力的矢量特性从数值和方向两方面反映了分子轨道的成键性质。同一分子轨道对不同化学键可能有不同的作用。用从头算法计算了乙烯和环丙烷的各分子轨道的H-F力, 指出了H-F力与分子轨道不可约表示闻的关系, 提出了用前线轨道的H-F力判断激发态分子构型畸变的方法。     

多基分子的能级和分子轨道

本文用差分方程法研究多基分子的π轨道和能级.证明了多基分子的轨道系数是基的编号的调谐函数或二重调谐函数.证明了求特征行列式的增补法则,利用特征行列式可直接计算能级和轨道.     

C_(16)H_(14)SNF分子中不共面共轭环上π轨道通过键的相互作用的研究

本文根据我们测定的C_(16)H_(14)SNF(1)和C_(16)H_(16)SNF(2)晶体结构数据,用MNDO2方法进行分子轨道研究,发现1和2的几何构型虽然相近,但其分子轨道中的原子轨道组成有着质的差异:在HOMO和临近HOMO的占据分子轨道中,2的两个苯环的π轨道彼此没有相互作用;1的两个夹角为80°的苯环的π轨道同时出现在一个分子轨道中,彼此通过(?)C=N—键导通,显示出相互作用,与实验观察到的核磁共振谱一致.     

带有分子轨道能量的3D-QSAR对N-氨基咪唑的研

N-氨基咪唑(NAIMs)能通过三种不同的作用方式抑制HIV-1的复制. 用比较分子场（CoMFA）方法对一系列有共同骨架的NAIM分子建立3D-QSAR模型. 与以往模型不同的是，在偏最小二乘（PLS）分析中尝试引入分子轨道能量的信息来研究生物活性与分子轨道能量的关系. 结果得到了几个模型，分子轨道能量对模型的贡献能为21.7%，轨道HOMO5对模型的贡献最大.     

Structure of Organic Crystals with Molecules Lying on Twofold Crystallographic Axes. Structural Class P21212, Z = 2(2)

Molecular arrangement in crystals of a rare structural class P2₁2₁2, Z = 2(2), with molecules occupying a system of special positions on 2 axes is considered. The Cambridge Structural Database (CSD) contains 58 organic crystal substances belonging to this class; 54 of these have clear-cut chains P_c2, Z = 1(2) (shashlyks) and form two subclasses. In crystals of the first subclass (23 representatives), there are layers possessing one of two remarkable features: molecules in a layer have an extraordinarily high molecular coordination number (m.c.n. is 8 in a layer), or molecules in a layer are linked by halogen...halogen specific short contacts (m.c.n. in a layer equals 4). In crystals of the second subclass (31 representative), layers are absent, and the structure is formed directly from chains.     

Flexible organic crystals. Understanding the tractable co-existence of elastic and plastic bending

As an emerging class of flexible materials, mechanically bendable molecular crystals are broadly classified as elastic or plastic. Nevertheless, flexible organic crystals with mutually exclusive elastic and plastic traits, with contrasting structural requirements, co-existing under different stress settings are exceptional; hence, it is imperative to establish the concurring factors that beget this rare occurrence. We report a series of halogen-substituted benzil crystals showing elastic bending (within ∼2.45% strain), followed by elastoplastic deformation under ambient conditions. Under higher stress settings, they display exceptional plastic flexibility that one could bend, twist, or even coil around a capillary tube. X-ray diffraction, microscopy, and computational data reveal the microscopic and macroscopic basis for the exciting co-existence of elastic, elastoplastic, and plastic properties in the crystals. The layered molecular arrangement and the weak dispersive interactions sustaining the interlayer region provide considerable tolerance towards breaking and making upon engaging or releasing the external stress; it enables restoring the original state within the elastic strain. Comparative studies with oxalate compounds, wherein the twisted diketo moiety in benzil was replaced with a rigid and coplanar central oxalate moiety, enabled us to understand the effect of the anisotropy factor on the crystal packing induced by the C O⋯C tetral interactions. The enhanced anisotropy depreciated the elastic domain, making the oxalate crystals more prone to plastic deformation. Three-point bending experiments and the determined Young''s moduli further corroborate the co-existence of the elastic and plastic realm and highlight the critical role of the underlying structural elements that determine the elastic to plastic transformation. The work highlights the possible co-existence of orthogonal mechanical characteristics in molecular crystals and further construed the concurrent role of microscopic and macroscopic elements in attaining this exceptional mechanical trait.

Structural and mechanical studies of benzil and oxalate crystals highlight the microscopic and macroscopic basis for the co-existence of orthogonal mechanical traits and the elastic to plastic transformation under different stress settings.     

Single Crystals Popping Under UV Light: A Photosalient Effect Triggered by a [2+2] Cycloaddition Reaction

The extremely rare examples of dynamic single crystals where excitation by light or heat induces macroscopic motility present not only a visually appealing demonstration of the utility of molecular materials for conversion of energy to work, but they also provide a unique opportunity to explore the mechanistic link between collective molecular processes and their consequences at a macroscopic level. Here, we report the first example of a photosalient effect (photoinduced leaping) observed with crystals of three coordination complexes which is induced by a [2+2] photocycloaddition reaction. Unlike a plethora of other dimerization reactions, when exposed to even weak UV light, single crystals of these materials burst violently, whereby they are propelled to travel several millimeters. The results point to a multistep mechanism where the strain energy that has been accumulated during the dimerization triggers a rapid structure transformation which ultimately results in crystal disintegration.     

Dip-coating crystallization on a superhydrophobic surface: a million mounted crystals in a 1 cm2 array

Silicon wafers (silicon dioxide surfaces) were patterned by photolithograpy to contain 3 μm (width) × 6 μm (length) × 40 μm (height) staggered rhombus posts in a square array (20 μm center-to-center spacing). These surfaces were hydrophobized using a vapor phase reaction with tridecafluorooctyldimethylchlorosilane and exhibit "superhydrophobicity" (water contact angles of θ(A)/θ(R) = 169°/156°). When a section of a wafer is submerged in and withdrawn from water, the superhydrophobic surface emerges, apparently completely dry. If the same procedure is performed using aqueous sodium chloride as the liquid bath, individual crystals of the salt can be observed on the top of each of the posts. "Dip-coating crystallization" using an aqueous sodium chloride solution of 4.3 M produces crystals with ～1 μm dimensions. A less concentrated solution, 1 M NaCl, renders crystals with ～500 nm dimensions. These experiments suggest that superhydrophobic surfaces that emerge from water and are "apparently completely dry" are, in fact, decorated with micrometer-size (several femtoliters) sessile water drops that rapidly evaporate. This simple technique is useful for preparation of very small liquid drops or puddles (of controlled composition) and for preparation of arrays of controlled size, crystalline substances (dip-coating crystallization).     

Modeling of the elementary step in the chemical transformation of crystals. I. Statement of the problem; description of the model

A model is proposed within the framework of activated-complex (AC) theory for analyzing the elementary chemical step (ECS) in the case of solid state reactions. By ECS is understood the synchronous restructuring (change in configuration, decomposition) of polyatomic structural units (SU) of the crystal or synchronous formation of new molecular groupings from poly- or monatomic SU. Simple physical observations lead to the conclusion that the ECS of solid state transformations does not have high molecularity. The mechanism which controls activation and deactivation is not directly considered. For activated SU that do not experience deactivation, it is suggested that interaction of these reacting SU with their surroundings in the crystal is constant throughout the course of the ECS. In conformity with this, an analysis of elementary steps of chemical transformation in crystals leads to an examination of the transformation of groupings composed of a small number of the SU of the crystal. A comparison of the ECS is carried out based on a comparison of the energies of activation (E_a) corresponding to the transformations. The E_a for various paths of transformation are evaluated by using the correlation diagram (CD) method. In a correlation analysis, experimental data for crystals should be used. Orbital symmetry and multiplicity of terms should be examined on the basis of specific quantum chemical analysis. The problem is formally reduced to a molecular one; however, the separable SU are bearers of properties of the crystal which are important for the ECS (enthalpy of formation, symmetry, electron composition, spectroscopic properties, etc.).     

Concerted molecular displacements in a thermally-induced solid-state transformation in crystals of DL-norleucine

Martensitic transformations are of considerable technological importance, a particularly promising application being the possibility of using martensitic materials, possibly proteins, as tiny machines. For organic crystals, however, a molecular level understanding of such transformations is lacking. We have studied a martensitic-type transformation in crystals of the amino acid DL-norleucine using molecular dynamics simulation. The crystal structures of DL-norleucine comprise stacks of bilayers (formed as a result of strong hydrogen bonding) that translate relative to each other on transformation. The simulations reveal that the transformation occurs by concerted molecular displacements involving entire bilayers rather than on a molecule-by-molecule basis. These observations can be rationalized on the basis that at sufficiently high excess temperatures, the free energy barriers to concerted molecular displacements can be overcome by the available thermal energy. Furthermore, in displacive transformations, the molecular displacements can occur by the propagation of a displacement wave (akin to a kink in a carpet), which requires the molecules to overcome only a local barrier. Concerted molecular displacements are therefore considered to be a significant feature of all displacive transformations. This finding is expected to be of value toward developing strategies for controlling or modulating martensitic-type transformations.     

Transmission electron microscope observations of fibrillar-to-lamellar transformations in melt-drawn polymers — I. Isotactic polypropylene

The transformation during heat treatment from a fibrillar to a lamellar morphology in highly oriented polypropylene is followed by transmission electron microscopy (TEM) and small angle electron scattering (SAES). While the as drawn films exhibit long (up to 1m) continuous fibrillar crystals, those crystals disintegrate into short crystalline blocks which finally aggregate into a lamellar morphology during the heat treatment. After even longer heat treatment the lamellar crystals start to thicken.Work supported by the Alexander von Humboldt Stiftung and Deutsche ForschungsgemeinschaftOn leave from Department of Chemical Engineering University of Delaware, Newark, DE 19711, USA     

An approach to developing a force field for molecular simulation of martensitic phase transitions between phases with subtle differences in energy and structure

d,l-Norleucine is one of only a few molecules whose crystals exhibit a martensitic or displacive-type phase transformation where the emerging phase shows a topotaxial relationship with the parent phase. The molecular mechanism for such phase transformations, particularly in molecular crystals, is not well understood. Crystalline phases that exhibit displacive phase transitions tend to be very similar in structure and energy. Consequently, the development of a force field for such phases is challenging as the phase behavior is determined by subtle differences in their lattice energies and entropies. We report an approach for developing a force field for such phases with an application to d,l-norleucine. The proposed procedure includes calculation of the phase diagram of the crystalline phases as a function of temperature to identify the best force field. d,l-Norleucine also presents an additional problem since in the solid state it exists as a zwitterion that is unstable in vacuo and therefore cannot be characterized using high-level ab initio calculations in the gas phase. However, a stable zwitterion could be obtained using Onsager's reaction-field continuum model for a solvent (SCRF) using both Hartree-Fock and density functional theory. A number of force fields and the various sets of partial charges obtained from the SCRF calculations were screened for their ability to reproduce the crystal structures of the two known phases, alpha and beta, of d,l-norleucine. Selected parameter sets were then employed in free energy minimizations to identify the best set on the basis of a correct prediction of the alpha-beta phase transition. The Williams' nonbonded parameters combined with partial charges from SCRF-Polarized Continuum Model calculation were found to reproduce the structures of the phases accurately and also maintained their stability in extended molecular dynamics simulations in the Parrinello-Rahman constant stress ensemble. Moreover, we were also able to successfully simulate the phase transformation of the beta- to the alpha-phase. The identified force field should enable detailed studies of the phase transformations exhibited by crystals of d,l-norleucine and hence enhance our understanding of martensitic-type transformations in molecular crystals.     

Reactions between or within molecular crystals

Reactions that occur within or between molecular crystals, in particular those reactions that are activated by mechanical methods, are reviewed. The focus is on processes (whether intrasolid or intersolid) that are controlled primarily by supramolecular bonding, such as template cycloadditions, formation of inclusion compounds, reactions between molecular crystals by the reassembling of noncovalent bonds, and the formation of complexes and coordination compounds. It is proposed that solvent-free mechanochemical methods, for example, cogrinding, milling, and kneading, represent viable "green" routes for the preparation of novel molecular and supramolecular solids.     

Magnetic and optical bistability driven by thermally and photoinduced intramolecular electron transfer in a molecular cobalt-iron prussian blue analogue

A soluble molecular analogue of photoresponsive Co/Fe Prussian blues is described within this report. As judged via a variety of spectroscopic, magnetic, and crystallographic methods, electron transfer within the octanuclear complex (below 250 K) converts paramagnetic red crystals into green diamagnetic ones. The color and magnetic changes are associated with the transformation of FeIIILS-CN-CoIIHS units into FeIILS-CN-CoIIILS fragments in manner that is identical to that found for the An[Co(OH2)(6-6m)][Fe(CN)6]m.xH2O (An = alkali metal cation) family of three-dimensional Prussian blues. Moreover, this intramolecular electron transfer can be quantitatively circumvented via rapid thermal quenching and reversed via simple white light irradiation at low temperatures. Remarkably the data suggests that thermally or photoinduced paramagnetic metastable phases are identical and exhibit long relaxation times that approach 10 years at 120 K.