Charge transfer associated with the physical process of hardness equalization and the chemical event of the molecule formation and the dipole moments

In this article, we have basically launched a search whether the dipole charge and dipole moment of heteronuclear diatomics can be justifiably evaluated in terms of charge transfer kernel using the hardness equalization principle as basis. We have derived a formula for computing dipole charge (q) on the basis of hardness equalization principle as q = aδ + b, where “a” and “b” are the constants and “δ” is the kernel of charge transfer from less hard atom to more hard atom during the rearrangement of charge on molecule formation. We have computed the dipole charges and dipole moments of as many as six different sets of compounds of widely diverse physicochemical behavior in terms of the algorithm derived in the present work. The computed dipole charge nicely reveals the known chemicophysical behavior of such compounds as are brought under the study. A comparative study of the nature of variation of theoretically evaluated and experimentally determined dipole moments reveals that there is an excellent agreement between the two sets of dipole data. Thus, the new algorithm derived for the calculation of the dipole charge using the hardness equalization principle as a basis is efficacious in computing the distribution and rearrangement of charge associated with the chemical event of molecule formation. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

电负性均衡

电负性是分子中一个原子把电子拉向它自身的能力,是化学理论的基本概念之一。继Pauling建立第一个电负性标度后,提出了众多的电负性标度。只是在密度泛函理论的基础上,电负性概念和电负性均衡原理,才被精密地论证。近二十多年来,电负性理论的重要发展是:应用电负性均衡模型或方法,可以快速地计算分子体系的电荷分布,从而确定分子的其他性质,甚至包括分子的结构和反应性指标。通常的电负性均衡方法只把分子划分到原子区域,虽然简单直观,但其精度和应用范围受到限制。原子与键电负性均衡方法,把分子划分到包括原子区域、化学键区域和孤对电子区域,能够较快速精密地计算分子的电荷分布和其他性质,并被应用到构建新一代可极化或浮动电荷力场的探索中,有广阔的应用前景。     

Molecular electronegativity in density functional theory (II) --Direct calculation of group electronegativity and the atomic charges in a group

On the basis of a more precise expression of the atomic effective electronegativity deduced from the density functional theory and electronegativity equalization principle, a new scheme for calculating the group electronegativity and the atomic charges in a group is proposed and programed, and various parameters of electronegativity and hardness are given for some common atoms. Through calculation, analysis and comparison of more than one hundred groups, it is shown that the results from this scheme are reasonable and may be extended.     

异构现象与最大硬度原理

利用原子-键电负性均衡方法计算了700多个异构体的硬度, 通过与标准生成焓所确定的相对稳定性比较后发现, 多数异构体并不遵守最大硬度原理.     

Semiempirical evaluation of the global hardness of the atoms of 103 elements of the periodic table using the most probable radii as their size descriptors

Relying upon the fact that the density functional computation of the global hardness of the atoms of the elements are still at large and there is some mathematical in congruency between the theory and operational formula of finite difference approximation, we have suggested a radial‐dependent ansatz for evaluating global hardness of atoms as: η=a(7.2/r)+b (in eV), where, “a” and “b” are the constants and r is the absolute radius of atoms in angstrom unit. The ansatz is invoked to evaluate the global hardness of atoms of 103 element of the periodic table. The evaluated new set of global hardness is found to satisfy the sine qua non of a reasonable scale of hardness by exhibiting perfect periodicity of periods and groups and correlating the gross physicochemical properties of elements. The inertness of Hg and extreme reactivity Cs atoms are nicely correlated. The chemical reactivity and its variation in small steps in the series of lanthanide elements are also nicely reproduced. The results of the present semiempirical calculation also have strong correlation with the result of some sophisticated DFT calculation for a set of atoms. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

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     

Calculation of molecular energies by atom-bond electronegativity equalization method

The atom-bond electronegativity equalization method (ABEEM), based on the equalization of the “effective electronegativity” of an atom or a bond in a molecule, allows the direct calculation of the charge distribution and the molecular electronegativity of a large molecule. We now demonstrate how the another important quantity, the total molecular energy, can be computed directly and rapidly. It is shown that, based on the ABEEM, the corresponding ab initio values of the total molecular energy can be reproduced with very satisfactory accuracy. In addition, it has been found that in the expression of the energy functional E[ρ] of the ABEEM, the charge-dependent term C correlates quite well with the total molecular bonding energy.     

Charge distribution in homonuclear bonds: A semiempirical modeling

Atoms characterized by nonequivalent electronegativities form chemical bonds by exchanging electrical charge. The fraction of charge exchanged is dictated by the electronegativity differences among the system atoms. In the electronegativity equalization method, the charge distribution is estimated by forcing the system to relax to a common chemical potential, which corresponds to its configuration of energy minimum. By definition, this method cannot be applied to homonuclear bonds. A model is proposed to estimate the charge shared in molecular orbitals of homonuclear molecules. The model expands upon the electronegativity equalization method by adding formalism to describe the spin coupling characteristic of homonuclear bonds. Results are in excellent agreement with other quantum mechanical estimations of the charge distributions. © 2013 Wiley Periodicals, Inc.     

Tautomerism and the maximum hardness principle

Through the application of the atom–bond electronegativity equalization method (ABEEM) to the calculation of the hardnesses of more than 300 tautomers, it can be seen that the maximum hardness principle is nearly useless to account for their relative stabilities. Moreover, by calculating the energies of these tautomers with the HF, B3LYP, B3PW91, and MP2 methods at the 6‐31G, 6‐31G*, 6‐31G**, 6‐31+G**, 6‐311G**, or 6‐311++G** level, it is found that all these methods may not be always reliable in predicting their relative stabilities. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

青霉素基团性质的分析

以密度泛函理论和电负性均衡原理为基础,应用修正的电负性均衡方法,并自编程序,用最小二乘法,拟合确定了H,C,O,N,F和Cl以及S等各种类型原子的价态电负性、价态硬度和能量的相关参数;从电负性均衡原理的观点,利用这些参数确定了一些青霉素基团的电负性和电荷分布,并进行了讨论.     

应用ABEEM模型计算铁(Ⅱ)配合物的电荷分布

以密度泛函理论和电负性均衡原理为基础,在原子-键电负性均衡模型中,利用最小二乘法,并结合自编程序,拟合确定了氢、碳、氮、硫以及铁(Ⅱ)等各种类型的原子及相关化学键区域的参数.利用上述参数计算了一些铁(Ⅱ)配合物的电荷分布,计算结果可以和从头算结果很好地相关联.     

Electronegativity and chemical hardness of organoelement groups

The experimental approaches to estimation of comparative electronegativity and chemical hardness of organometallic groups have been proposed. Qualitative data on the electronegativity of L _nM groups were obtained from ¹⁹F NMR study of model systems 4‐FC₆H₄QML_n (Q = CC, N(R), O, C(O)O, S), (4‐FC₆H₄)₃ SnML _n and (4‐FC₆H₄)₃SnQML _n (Q = O, S), containing a great variety of different organometallic groups containing transition or heavy main‐group metals. The data on chemical hardness of L _nM groups were obtained from NMR study of distribution of different L _nM groups between hard and soft anions. The following basic results have been obtained. (1) The relative electronegativity and chemical hardness of L _nM groups can change in parallel or not with the electronegativity and hardness of the central metal atom. (2) The substituents in Ar can substantially modify electronegativity and hardness of Ar _nM groups; the influence of Ar groups has an inductive nature; the increase in electron‐donating ability of aryl ligands enhances the hardness of Ar _nM cations. (3) The relative electronegativity and hardness of L _nM groups in L _nMX are invariant and do not depend on X.     

Ab initio calculations, electronegativity equalisation and group electronegativity

A correspondence betweenab initio calculations, the principle of electronegativity equalisation and group electronegativity has been established within the framework of Mulliken population analysis. Using this we have calculated electronegativities of some 37 groups/atoms. These electronegativities show excellent linear correlation with¹ J _CC coupling constants in monosubstituted benzenes and Inamoto’si scale and a satisfactory one with Wells’ group electronegativity data. The correspondence however required a scaling of charge (obtained byab initio calculations) and a proportionality between the electronegativity of the neutral group and its hardness. It is shown that using these electronegativity values it is possible to calculate group charges in molecules where groups under consideration interact with each other through σ bond only.     

Electronegativity equalization method: parameterization and validation for organic molecules using the Merz-Kollman-Singh charge distribution scheme

The electronegativity equalization method (EEM) was developed by Mortier et al. as a semiempirical method based on the density-functional theory. After parameterization, in which EEM parameters A(i), B(i), and adjusting factor kappa are obtained, this approach can be used for calculation of average electronegativity and charge distribution in a molecule. The aim of this work is to perform the EEM parameterization using the Merz-Kollman-Singh (MK) charge distribution scheme obtained from B3LYP/6-31G* and HF/6-31G* calculations. To achieve this goal, we selected a set of 380 organic molecules from the Cambridge Structural Database (CSD) and used the methodology, which was recently successfully applied to EEM parameterization to calculate the HF/STO-3G Mulliken charges on large sets of molecules. In the case of B3LYP/6-31G* MK charges, we have improved the EEM parameters for already parameterized elements, specifically C, H, N, O, and F. Moreover, EEM parameters for S, Br, Cl, and Zn, which have not as yet been parameterized for this level of theory and basis set, we also developed. In the case of HF/6-31G* MK charges, we have developed the EEM parameters for C, H, N, O, S, Br, Cl, F, and Zn that have not been parameterized for this level of theory and basis set so far. The obtained EEM parameters were verified by a previously developed validation procedure and used for the charge calculation on a different set of 116 organic molecules from the CSD. The calculated EEM charges are in a very good agreement with the quantum mechanically obtained ab initio charges.     

Systematic formulations for electronegativity and hardness and their atomic scales within density functional softness theory

A unified Mulliken valence with Parr ground‐state electronegativity picture is presented. It provides a useful analytical tool on which the absolute hardness as well ionization potential and electron affinity functionals are based. For all these chemical reactivity indices, systematic approximate density functionals are formulated within density functional softness theory and are applied to atomic systems. For the absolute hardness, a special relationship with the new electronegativity ansatz and a particular atomic trend paralleling the absolute electron affinity are established that should complement and augment the earlier finite‐difference energetic approach. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Ruling out any electrophilicity equalization principle

Two gas-phase electrophilicity indices, ω(1) and ω(2), introduced by Parr, von Szentpa?ly, and Liu are tested with respect to the recently proposed "principle of electrophilicity equalization." Although electronegativity is equalized in many cases, there is no functioning "hardness equalization principle" nor are the electrophilicity indices principally equalized during molecule formation: they cannot be generally expressed as the mean of the corresponding atomic indices. For large metal clusters and [n]fullerenes, both electrophilicity indices increase proportional to n(1/3) and n(1/2), respectively, as the hardness values converge to zero. Two "principles" are shown to be obsolete: the "geometric mean principle for hardness equalization" and the "principle of electrophilicity equalization", with the latter somewhat relying on the former. An appeal is made to exercise careful judgment before proposing and publishing new structural principles.