Negative and Infinite Fukui Functions: The Role of Diagonal Dominance in the Hardness Matrix

The possible genesis of negative atom condensed Fukui functions is discussed based on hardness kernel matrix relationships. The recent hypothesis that diagonal dominance of the hardness matrix is a requirement for positive Fukui functions is proven, and general considerations also predict the possibility of regions with numerically unstable Fukui functions, including discontinuities.     

The Concept of Hard and Soft Acids and Bases as Applied to Multi-Center Chemical Reactions

Many chemical bonds of differing types and strengths have recently been regarded by Pearson^[1] as representing partnerships between (Lewis) acids and (Lewis) bases. Most acceptor molecules or ions (acids) can be placed in one or other of two categories, graphically termed “Hard” and “Soft”. There are also two broad categories of donor molecules or ions (bases) which can also be termed Hard and Soft. On the whole, strong chemical bonds are partnerships between either a Hard base and a Hard acid or a Soft base and Soft acid, whereas weaker bond types most usually result in cases of either Hard base-Soft acid or Soft base-Hard acid interactions. The present paper shows how this concept of acidity and basicity can be applied in the interpretation of multi-center chemical reactions involving interconnected acid-base relationships. In particular, fourcenter substitutions and additions involving cooperative attack by nucleophiles and electrophiles at various chemical bonds have been examined, and a conclusion is reached that especially reactive patterns of reactants can be developed if the substrates contain bonds between either a hard acid and a soft base, or a soft acid and a hard base. Indeed, the arguments can be elaborated to provide two distinct Rules which should be of interest in the interpretation of metal-ion assisted reactions and in the design of novel syntheses.     

On the quality of the hardness kernel and the Fukui function to evaluate the global hardness

An approximated hardness kernel, which includes the second derivative with respect to the density of the kinetic energy, the electron-electron coulomb repulsion, and the exchange density functionals, has been tested for the calculation of the global hardness. The results obtained for a series of 40 cations and neutral systems and 16 anions represent in most cases an improvement of the results obtained using the HOMO-LUMO gap approach and indicate the viability of this approach to evaluate global hardness. In addition, the relevance of the Fukui function approximation and the role of the three components of the hardness kernel in the evaluation of the global hardness have been analyzed.     

Fukui函数和局域软度应用于亲电加成反应的区位选择性的研究

Fukui函数、局域软度、广义Fukui函数以及广义软度通常被称为反应描述符。使用它们研究和探讨了HCl与不对称烯烃以及溴苯硒与不对称苯乙烯的亲电加成反应的区位选择性。在MP2/6-311++G(d, p)理论水平下,采用有限差分方法计算这些反应描述符,同时也使用ABEEMσπ方法进行了计算。ABEEMσπ模型下的局域软度和广义局域软度,分别结合局域硬-软酸碱(HSAB)原理,得出亲电试剂氯化氢与溴苯硒,更容易进攻不对称乙烯和苯乙烯中的马氏碳原子,符合马氏规则。而有限差分方法不能完全地解释该系列反应的区位选择性。此外,主要产物所对应的马氏碳原子的广义局域软度值,就能够预测出此类反应的活性序列,所得结果与速率常数有很好的关联。     

The Fukui matrix: a simple approach to the analysis of the Fukui function and its positive character

The Fukui matrix is introduced as the derivative of the one-electron reduced density matrix with respect to a change in the number of electrons under constant external potential. The Fukui matrix extends the Fukui function concept: the diagonal of the Fukui matrix is the Fukui function. Diagonalizing the Fukui matrix gives a set of eigenvectors, the Fukui orbitals, and accompanying eigenvalues. At the level of theory used, there is always one dominant eigenvector, with an eigenvalue equal to 1. The remaining eigenvalues are either zero or come in pairs with eigenvalues of the same magnitude but opposite sign. Analysis of the frontier molecular orbital coefficient in the eigenvector with eigenvalue 1 gives information on the quality of the frontier molecular orbital picture. The occurrence of negative Fukui functions can be easily interpreted in terms of the nodal character of the dominant eigenvector versus the characteristics of the remaining eigenvectors and eigenvalues.     

Chemical reactivity of hypervalent silicon compounds: The local hard and soft acids and bases principle viewpoint

The silicon atom may increase its coordination number to values greater than four, to form pentacoordinated compounds. It has been observed experimentally that, in general, pentacoordinated compounds show greater reactivity than tetracoordinated compounds. In this work, density functional theory is used to calculate the global softness and the condensed softness of the silicon atom for SiH _n F_4−n and SiH _n F _5−n ¹⁻ . The values obtained show that the global and condensed softness are greater in the pentacoordinated compounds than in the tetracoordinated compounds, a result that explains the enhanced reactivity. If the results are analysed through a local version of the hard and soft acids and bases principle, it is possible to suggest that in nucleophilic substitution reactions, soft nucleophiles preferably react with SiH _n F _5−n ¹⁻ , and hard nucleophiles with SiH _n F_4−n .     

金属萃取平衡与软-硬酸碱规则

软硬酸碱规则从宏观角度描述化合物的形成及性质,在配合物稳定性的判断方面有广泛应用.前文^[1]报道了萃取速率常数与金属离子的软硬酸碱强度的关系,本文研究了萃取平衡常数与金属离子的软硬酸碱强度的关系.     

A study of the nature of coordination in metal monothiocarbamates based on infrared spectroscopy and the HSAB concept

The nature of coordination in metal monothiocarbamates is shown to depend on the hardness or softness of the metal ton. Thus, the monothiocarbamate ion acts as a monodentate ligand with metal-sulphur bending when the metal ion is a soft acid while it acts as a bidentate ligand when the metal ion is a hard acid; it can exhibit either behaviour when the metal ion is a borderline acid. In dialkyltin and dialkylmonocholorotin complexes, the monothiocarbamate ion acts as a bidentate ligand with strong Sn-S bonding while in trialkyl-or triaryl-tin complexes it acts essentially as a monodentate ligand. Thus, R₃Sn(I) seems to be a soft or borderline acid while R₂Sn(II) is a hard acid.     

Surface modification of III–V semiconductors: chemical processes and electronic properties

The possibilities of controlling the surface electronic properties of III–V semiconductors by varying the adsorption chemistry are analyzed. Variations of the adsorption process parameters and the adsorbate reactivity are able to affect the surface atomic and electronic structure of the semiconductor. The adsorbate reactivity is considered within the framework of the density functional theory using the reactivity indices. The easiest way to affect the reactivity of a particular adsorbate is to create a solvation shell around it, as is possible in both liquid solutions and the gas phase (microsolvation). Solvation of ions before their adsorption by different solvents affects considerably the relative nucleophility of the central atom in the ion, which results in a different charge transfer mechanism from the surface states on adsorption, and thus, in a different modification of the surface electronic structure of the semiconductor. The effect of halogen, sulfur and metal atoms reactivity on the electronic structure of the resulting adsorbate-covered surface of III–V semiconductor is discussed.     

二价金属离子萃取速率常数与软硬酸碱规则

用上升液滴法测定了２－乙基己基膦酸单（２－乙基己基）酯－正辛烷从硝酸介质中萃取镁、钙、锌、镍、铜和铅等二价金属离子的正向初始速率，建立了速率方程，计算出正向萃取反应的速率常数、活化能及活化熵，首次将软硬酸碱规则与金属溶萃取速率常数关联。结果表明，在萃取机理相同时，萃取速率常数的大小与金属离子的软硬酸碱标度一致，即萃取过程中，作为酸的被萃取金属离子，其硬度越大，萃取速率常数亦越大，萃取反应的活化能…     

Unusual condensation ofN-phenylsemiquinonediimine ligands coordinated to the NiII atom with an acetone molecule to form a heterocycle

The reaction of a mononuclear Ni^II semiquinonediimine complex,viz., Ni[1,2-(NPh)(NH)C₆H₄]₂, with silver triflate was investigated. The starting monomer was not oxidized in benzene or CH₂Cl₂ solutions; instead, a solvate of the complex with C₆H₆ was formed. According to the X-ray diffraction data, the solvate is characterized by an unusual molecular packing with short C−H(C₆H₆)... Ni and C−H(C₆H₆)... N−H contacts. An analogous effect is observed in the crystals of the solvate Pt[1,2-(NPh)(NH)C₆H₄]₂·C₆H₆. Grinding of the nickel complex with silver triflate (the reagent ratio was 1:5) in the presence of acetone led to the oxidation of the complex, yielding tetrahydroimidazophenazinium triflate, whose structure was established by X-ray diffraction analysis. Published inIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1794–1798, October, 2000.     

Reglochemistry in Electrophilic Reactions of Propanedlthio-Substituted Allylic Anions Influenced by the γ-Substituents

The dienyl anion 1f, generated from metallation of 2-(1,3-pentadienyl)-1,3-dithianc with n-BuLi in THF, reacted exclusively at the C-1 position (α-site) with alkylating agents and ketones, but it showed some tendency toward the C-3 position (γ-site) in the reactions with benzyl bromide and aliphatic aldehydes. No reaction at the C-5 position (?-site) was observed in any studied case. Examination of the related propanedithio-substituted allylic anions having various γ-substituents revealed that the regiochemistry was remarkably influenced by the γ-substituents and the attacking electrophiles. The electronic effect according to the principle of hard and soft acids and bases is proposed to account for the observed regiochemistry, while the steric factor was minor. Two trienes, obtained by alkylations of the dienyl anion 1f with 4-bromo-1-butene and 5-pentenyl methanesulfonate, were applicable to intramolecular Diels-Alder reactions to give bicyclic compounds.     

Coenzyme B12 model studies: An HSAB approach to the equilibria and kinetics of axial ligation of alkyl(aquo)-cobaloximes by imidazole and cyanide

Kinetics and equilibria of the axial ligation of alkyl(aquo)cobaloximes by imidazole and cyanide have been measured spectrophotometrically in aqueous solutions of ionic strength 1.0 M at 25°C as a function of pH. Comparison of K_IMD and K_CN- of CH₃, C₂H₅ and BrCH₂cobaloximes indicates that their stability is in the order BrCH₂>CH₃>C₂H₂. As the electron-withdrawing capacity of the alkyl grouptrans to water increases, the electron density of the cobalt(III) decreases and thus it becomes a stronger Lewis acid and binds more strongly to imidazole and cyanide. The association and dissociation rate constants are better correlated to the relative softness of the ligand showing that cyanide binds 30 times faster than imidazole. These complexes are isolated and are characterized by IR and¹H NMR spectra.     

Chemical reactivity and selectivity using Fukui functions: basis set and population scheme dependence in the framework of B3LYP theory

The use of Fukui functions for the site selectivity of the formaldehyde molecule for nucleophilic, electrophilic and radical attacks has been made with special emphasis to the dependence of Fukui values on the basis sets as well as population schemes in the framework of B3LYP theory. Out of the five population schemes selected viz., Mulliken population analysis, natural population analysis, CHELP, CHELPG and atoms in molecules (AIM), it is found that the CHELPG and AIM schemes predict precise reactive site with less dependency on the basis sets. Charges derived from Hirshfeld partitioning, calculated using the BLYP/dnd method (implemented in the DMOL³ package), provide non-negative Fukui values for all the molecular systems considered in this study. Supporting results have been obtained for acetaldehyde and acetone molecules at the 6-31+G** basis set level. These results support the fact that high Fukui values correspond to soft–soft interaction sites. On the other hand, the correlation of the low Fukui value to the hard–hard interaction site merits further investigation. Received: 10 November 2001 / Accepted: 6 March 2002 / Published online: 13 June 2002     

A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

We report an efficient and consistent method for the solution of Schrödinger wave equation using the Green's function technique and its successful application to the nonrelativistic radial wave equation of hydrogen atom. For the radial wave equation, the Green's function is worked out analytically by means of Laplace transform method and the wave function is proposed under the boundary conditions. Computationally the product of potential term, the proposed wave function and the Green's function are integrated iteratively to get the nonrelativistic radial wave function. The resultant wave after each iteration is normalized and plotted against the standard nonrelativistic radial wave function. The solution converges to the standard wave with the increasing number of iterations. Results are verified for the first 15 states of hydrogen atom. The method adopted here can be extended to many‐body problem and hope that it can enhance our knowledge about complex systems.     

Proton transfer at the carboxylic sites of amino acids: A single water molecule catalyzed process

Ab initio calculations at MP2 level of theory were used to study the proton transfer at the carboxylic sites of amino acids, in the isolated, mono‐ and di‐hydrated forms. In the case of water dimer, two interaction modes with glycine neutral structures (see Fig. 3 ) were explored, corresponding to the concerted and stepwise reaction pathways. Their transition states can be described as (H₂O? H? OH₂)⁺ [Fig. 4 (a)] and (H₂O‐‐‐H? OH₂)⁺ [Fig. 4 (b)], respectively. The energy analysis indicated that the concerted pathway is preferred. In the isolated, mono‐ and di‐hydrated glycine complexes, the activation barriers of the proton transfer at the carboxylic sites were calculated to be 34.49, 16.59, and 13.36 kcal mol^?1, respectively. It was thus shown that the proton transfer is significantly assisted and catalyzed by water monomer so that it can take place at room temperature. Instead, the further addition of water molecules plays solvent effects rather than catalytic effects to this proton transfer process. The above results obtained with discrete water molecules were supported by the solvent continuum calculated data. It was also observed that the heavy dependence of the solvent continuum models on dipole moments may produce misleading results. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009