Use of a novel relationship between bond length and bond order to calculate accurate bond orders for carbon–carbon bonds

An exact relationship between bond length and bond order has been derived for the first time based on the concept of electron density. This relationship allows the calculation of sufficiently accurate bond orders and also determines the number of bond-forming electrons. According to this novel relationship between bond order and bond length, the bond order of the carbon–carbon bond in ethylene is 1.75, whereas it is 2.50 in acetylene. These bond orders are readily interpreted by the fragmentation of π-bonds and a consequent decrease in bond order, which is further supported by the chemical properties of these molecules. Assuming structure-specific fragmentation of π-bonds (i.e. one structural motif always adheres to one or two types of bond fragmentation scheme), the bond orders can be predicted for molecules containing multiple carbon–carbon bonds in excellent agreement with the experimental findings.     

Structure and Bonding in Cyclic Sulfur-Nitrogen Compounds

The coordination number of sulfur is used in this review as a classification principle; cyclic sulfur-nitrogen compounds in which the sulfur is di-, tri-, and tetracoordinated are discussed. Compounds with sulfur (and nitrogen) of coordination number 2 are electron-rich combinations of elements whose π-electrons are extensively delocalized. A correlation between the coordination number and the bond length can be observed in certain compounds containing tri- and tetracoordinated sulfur.     

Reply to the comment on MORT treatment of bond length alternation in conjugated hydrocarbons

It is shown that in treating bond distortions in the framework of the approach suggested by Nakajima, the contributions of different terms to the total energy are highly sensitive to the choice of parameters and to variations in the functional dependence of the resonance integral as a function of bond length. Hence one can not unambiguously attribute the overall effect to any particular term or terms, and sometimes one has to make a rather careful adjustment in order to avoid qualitatively erroneous results. Though the simple molecular orbital resonance theory (MORT) approach is rather naive, it correctly predicts relative bond lengths in a range of molecules with essentially no parameter adjustment. This approach is hence a rather successful first order approximation to more sophisticated models which progressively incorporate missing contributions. The variation of the resonance integral with bond length and the -bond compression energy should be in these more sophisticated models undoubtedly taken into account. However, the contribution of the charge polarisation can not be totally disregarded, especially in the case of conjugated compounds containing small rings.Theoretica Chimica Acta 65, 77–80 (1984)     

碳原子价轨道电负性对化学键性能的影响

研究了同一类型化学键X―C的键能、键长和H―C键的酸性等性能与碳原子价轨道电负性的定量关系。结果表明,X―C键能随碳原子价轨道电负性增加而线性增大;H―C与C―C键的键长随碳原子价轨道电负性增加而线性减小;H―C的酸性随碳原子价轨道电负性增加而线性增大。因而,对结构类似的有机化合物,可以采用碳原子价轨道电负性对实验测定的化学键性能作图,判断其测定结果正确与否。     

A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.     

棕色环反应产物中铁氧化态的讨论

The oxidation state of iron in the "brown-ring" reaction product[Fe(NO)(H₂O)₅]²⁺ and the bond between Fe and NO in this cation are discussed in detail. After presenting different views from the literature based on experimental evidences and theoretical calculations, the oxidation state of iron resonates between +2 and +3 inclining to +2. The Fe-N-O bond angle is 180°. In addition, we proposed an explanation for the slightly shortening of the bond length of NO after coordination to the iron ion.     

镧系元素相关的键价参数研究

根据镧系元素络合物的晶体结构数据确定了单价键长R0的镧系收缩效应，并对已有的键价参数进行了系统的修订.建立了Ln-O键的R0对原子序数N在普适参数B=0.037 nm下的线性方程R0(nm)=0.2879－0.00132N.用不同参数进行键价和的计算并对结果进行了对比和讨论，最后展望了相关研究的前景.     

A simple method for the calculation of π-bond orders in alternant hydrocarbons

A new method for the calculation of bond orders in alternant hydrocarbons is presented. The method requires a summation over the contributions of various superposition diagrams. Quantitatively, the method is almost as reliable as PPP, and due to its simplicity it can be used for fast and relatively accurate calculation of bond orders. In addition some simple rules are derived, which in many cases can be used to predict the signs of bond orders between nonbonded atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayResearch supported by the Robert A. Welch Foundation of Houston, Texas     

环和纳米管径向呼吸振动模式的一个简单理论模型

用密度泛函方法在B3LYP/6-31G(d)基组下计算了(MgO)n和(BeO)n环(n=3-10)的径向呼吸振动. 大环的径向呼吸振动频率正比于环直径的倒数, 但键长的变化导致频率偏离了这种线性关系. 随着环直径的减小, 直径倒数的三次方和键长的变化将导致频率更大地偏离线性行为. 从化学键的角度出发利用一维谐振子及弹簧的串并联思想, 解释了这种线性关系和偏离现象. 这种模型还可以用于研究纳米管的径向呼吸振动频率.     

共价键稳定性的影响因素

虽然小分子中的共价键强度可以很方便地通过高斯计算而相当准确地得到,一些手册和数据库中也可以直接查出部分键能/离解能数据,但共价键的强弱变化的影响因素分析在化学教学中仍然显得非常重要。共价键的强弱与成键原子及其环境密切相关,其中成键原子因素主要包括原子半径、成键类型、成键轨道类型、相对论效应、电负性、成键数量、反馈效应和孤电子对效应,而成键环境因素包括键间张力效应、离域效应、次级化学键效应、诱导效应和位阻效应。在教学中,我们可以通过对化学键影响因素的分析帮助学生理解共价键键能的变化规律。本文分析了影响共价键强弱的主要因素,并介绍了这种分析思路在化学教学中的应用。     

A Simple Theoretical Model for Ring and Nanotube Radial Breathing Mode

The radial breathing modes (RBMs) of (MgO)_n and (BeO)_n rings (n=3-10) were calculated using the density functional theory at B3LYP/6-31G(d) level. It was found that for large rings, the radial breathing mode (RBM) frequency was inversely proportional to the centre diameter, but the variation of bond length may lead to deviations from a linear behavior. The deviations caused by inverse cubic term of diameter and variation of bond length, became dramatic with the decrease of ring diameter. From the point of chemical bond view, using one-dimensional harmonic oscillator and the method of cascade and parallel connection of “springs”, the linear relation and deviations were explained. The model can be applied to nanotubes.     

ON THE COORDINATION IN METAL SACCHARINATES. IMPLICATIONS FOR BOND-ORDER MODELS OF METAL – LIGAND BINDING

Abstract

The structures of saccharinates retrieved from the Cambridge Structural Database were used to discuss the coordination propcrties of deprotonated saccharin. The series of the first-row metal(II) saccharinato isomorphs and of tnphenylstannyl sacchainates were analyzed within the bond valence model (BVM). The “relative radius” parameter of the saccharinato ligand for the M(Ow)₄(Nsac)₂ type of coordination was estimated (1.424 Å) from correlation of the metal-N(saccharinato) distances with the Shannon-Prewitt ionic radii.

Making use of the exponential bond distance-bond order (BDBO) relation of Pauling within the BVM, ligand-specific mean bond order sums (MBOS) were recently derived for several ligands. Coupled with the coordination number (CN), they are predictive for the metal-ligand bond lengths. Using parameterized power function instead of the exponential form of the BDBO relation, a new set of MBOS's is derived here: isothiocyanate 2.56 ± 0.06; pyridine 1.84 ± 0.16; imidazole 2.02 ± 0.12; chloride 2.05 ± 0.10; water 1.54 ± 0.03. The two sets of MBOS values can be used to predict the metal-ligand distances nearly equally well, showing that the distances are solely predetermined by the MBOS and CN values, independently of the particular form of BDBO relation used.     

Crystallographic and infrared spectroscopic study of bond distances in Ln[Fe(CN)6]·4H2O (Ln=lanthanide)

Along with crystallographic data of Ln[Fe(CN)₆]·4H₂O (Ln=lanthanide), the infrared spectra are reassigned to examine bond length trends across the series of Ln. The changes in mean Ln-O, Ln-N, CN and Fe-C distances are discussed and the bond natures of Ln-N and Ln-O are studied by bond length linear or quadratic fitting and comparisons with relevant ionic radii. The two different CN bond distances have been simulated by the covalo-electrostatic model.     

Exchange Charges and Bond Orders for Homonuclear Diatomic Molecules

A new bond order definition B = βS² is defined which relates the bond order B to the non-classical exchange charges in the bonding region. This definition is successful in correlating the bond order to its bond energy, when the overlap is calculated from a generalized valence-bond pair function and the parameter β is chosen to be the inverse of bond distance.     

Toward a semiempirical density functional theory of chemical binding

The new ideas ofbond electronegativity andbond hardness are introduced, and a semiempirical density functional approach to the theory of molecular electronic structure and chemical binding is outlined. There result effective electronegativity equalization procedures that permit calculation of binding energies as well as partial charges. By a modelling of the bond electronegativity and bond hardness, a density functional interpretation of earlier bond charge models is established. Some numerical results are given for diatomic molecules.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

The effects of fluorine and chlorine substitution on bond lengths in ethanes and disilanes: comparisons of ab initio and experimental information

Ab initio and some density functional theory calculations of bond lengths in fluoro- and chloro-ethanes and disilanes are reported with a precision of ±0.0001 Å under strictly comparable conditions. The resulting changes in MH and MX (M=C, Si; X=F, Cl) bond length are analysed for the effects of halogens substituted in geminal (), or vicinal (gauche or trans) positions. The shortening effect of halogen on an MH bond is markedly reduced or even reversed by the introduction of electron correlation at the MP2 or B3LYP level. MX bonds are little affected. gauche halogen consistently shortens both MH and MX bonds, while trans halogen has no effect on an MH bond but a small and variable effect on the MX bond.

The reality of these calculated changes in bond length is tested in two ways. MH bond lengths are plotted against experimental values of the isolated stretching frequencies ν^isMH, which themselves correlate well with experimental r₀ bond lengths. Agreement on the resulting substituent effects is generally good for the gauche and trans effects of halogen but variable for effects. Unobserved ν^isMH values are predicted from computed bond lengths in fluoroethanes, chloroethanes and chlorodisilanes.

Calculated MX and MM bond lengths are compared with experimental values, notably those from electron diffraction studies amongst the ethanes. Most calculations underestimate the changes found experimentally in CF and CCl bond lengths. CC bond length changes are underestimated in fluoroethanes and overestimated in the chloro-compounds.

The ‘offset’ value (r_e(calc)−r_e(true)) for a CH or SiH bond calculated with a given basis set and level of theory in most cases varies markedly throughout the series of compounds. The same is true for CF, CCl, CC and SiSi bonds if the corresponding offset values for the r_a lengths are constant.

The need is stressed for extended experimental work on many of the compounds, especially the disilanes. It is recommended that structures should be refined with ab initio derived constraints on the bond lengths involved and differences between spectroscopic and diffraction-based geometries reconciled through the calculation of r_z structures.     

The Physical Mechanism of the Chemical Bond

First the interplay of kinetic and potential energy via the uncertainty relation is described with the aid of a variational function for the ground state of the H atom. The H ion is used to illustrate the physical mechanism of the occurrence of the chemical bond. The formation of the chemical bond can be divided into three steps: 1. the quasi-classical (electrostatic) interaction of the unchanged electronic charges of the separate atoms; 2. the interference of the atomic orbitals, which (in the case of positive interference) leads to a displacement of charge into the bonding region and to a decrease in the kinetic energy; 3. deformation of the molecular orbitals to restore the correct balance of kinetic and potential energy. In simple models, it is often sufficient to consider just the second step. A two-electron bond is not fundamentally different from a one-electron bond. In larger molecules it is possible to distinguish between long-range and short-range interatomic contributions to the chemical bond. If the former are small, i. e. in molecules with non-polar bonds, a one-electron molecular orbital theory can be justified. Finally, the possibility of describing molecules by localized bonds is discussed.     

Bond covalency and electronic structure of CaB2O4(III) crystal

The electronic structure of CaB₂O₄(III) crystal obtained by using SIESTA program is reported in this article. It is observed that the band gap values are, respectively, 5.39 and 5.89 eV from our LDA and GGA calculations. The bond covalency and bond valence are calculated with a simplified method. For both Ca–O and B–O types of bond, the bond covalency has a decreasing trend with the increasing bond length. The result of bond covalency in explaining the interaction between atoms has been shown in good agreement with that of Mulliken population analysis. The ionic configuration for CaB₂O₄(III) in the fundamental state is estimated to be Ca^+1.808B^−0.68O^−0.112. A summary of B–O distances for the four phases of CaB₂O₄ crystal from several works is also presented.     

Comparative studies on a maximum bond order principle

A recently proposed maximum bond order principle is studied with respect to choice of basis orbitals, choice of wavefunction and compared with other methods. Results for bond orders support the choice of Schmidt orthogonalized AO's with subsequent Löwdin orthogonalization. Differences between semiempirical andab initio wavefunctions in minimal basis sets usually have only minor effects on bond order values. For hydrocarbons bond order values are quite similar for Cohen's and this method. Finally, the dependence of bond orders on internal rotation and vibration is investigated in a few simple cases.     

Highly polarized dithiafulvenes: synthesis and nonlinear optical properties

Push-pull dithiafulvenes with reduced bond length alternation (BLA) and high optical nonlinearities have been prepared. The interplay between the proaromaticity of the donor and the structural and optical properties of these merocyanines is discussed. The donor ability of dithiafulvenes can reach that of ferrocene or dialkylaminophenyl groups.