Relativistic effects on the Fukui function

The extent of relativistic effects on the Fukui function, which describes local reactivity trends within conceptual density functional theory (DFT), and frontier orbital densities has been analysed on the basis of three benchmark molecules containing the heavy elements: Au, Pb, and Bi. Various approximate relativistic approaches have been tested and compared with the four-component fully relativistic reference. Scalar relativistic effects, as described by the scalar zeroth-order regular approximation methodology and effective core potential calculations, already provide a large part of the relativistic corrections. Inclusion of spin–orbit coupling effects improves the results, especially for the heavy p-block compounds. We thus expect that future conceptual DFT-based reactivity studies on heavy-element molecules can rely on one of the approximate relativistic methodologies.     

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.     

Relation between the Fukui function and the Coulomb hole

By using a coarse-grain representation of the molecular electronic density, we demonstrate that the value of the condensed Fukui function at an atomic site is directly related to the polarization charge (Coulomb hole) induced by a test electron removed (or added) from (at) the atom. The link between the formation of an electron-hole pair and the condensed Fukui function provides insights on the possible negativity of the Fukui function which is interpreted in terms of two phenomena: overscreening and over-strengthening.     

An example where orbital relaxation is an important contribution to the Fukui function

Density-functional electronic structure calculations are performed on the molecules Cr2(hpp)4, Mo2(hpp)4, and W2(hpp)4, where the bridging ligand, hpp, is the anion of 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine. The calculated electronic densities are used to determine the Fukui functions. These molecules are unique not only in their ability as electron donors but also because orbital relaxation plays a decisive role in their reactivity. Unlike other examples in the literature, the reactivity of these compounds cannot be expressed solely in terms of the highest occupied and lowest unoccupied Kohn-Sham orbitals but only using the Fukui function, which includes the effects of orbital relaxation.     

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.     

Modeling temporary anions in density functional theory: calculation of the Fukui function

Two approaches are investigated for modeling electron densities of temporary anions in density functional theory (DFT). Both rely on an artificial binding of the excess electron, in one case by a compact basis set and in the other by a potential wall. The key feature of the calculations is that the degree of binding is controlled in both cases by knowledge of the negative electron affinity of the corresponding neutral, approximated in terms of DFT local functional frontier orbital eigenvalues and vertical ionization potential, A=-(epsilon(LUMO)+epsilon(HOMO))-I. To illustrate the two approaches, Fukui functions for nucleophilic attack are determined in four molecules with increasingly negative electron affinities. They yield very similar results, which are notably different to those determined without artificial electron binding. The use of a potential wall has the attractive feature that large, diffuse basis sets can be used, avoiding the need for a compact basis, tailored to a particular molecule.     

Radial behavior of gradient expansion approximation to atomic Fukui function and shell structure of atoms

An approximation to the Fukui function in atoms recently proposed in the form of a gradient correction to the local density approximation expression is here investigated. The spatial behavior of this function is analyzed, focusing on the gradient correction term. Physical information on the shell structure of atoms is shown to be conveyed by the radial distribution of that term. The analytically modeled densities (AMD) procedure is also implemented, and global atomic hardnesses are calculated with Hartree-Fock and AMD representations of atomic electron densities. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 488–503, 1998     

h function: A protonic take on the numerical Fukui function as a graphical descriptor for deprotonation

In this work, a graphical tool for postdeprotonation analysis of molecular systems is presented. This tool was applied to a series of molecules to distinguish the information given by its resulting graphics. The outcome identified the h function sensitivity toward electron density rearrangement, being able to recognize bond cleavage and increments in π electron population through simple visual analysis.     

Studies of chemical hardness and Fukui function using the exact solution of the density functional theory

Neal's procedure has been applied to determine the electron density ρ(x) for the H₂ molecule. The chemical hardness has been calculated employing the ab initio and density functional theory methods and the values are found to be reasonably good. The principle of maximum hardness (PMH) was tested. Fukui functions and the distribution of electron density around the internuclear distance were studied employing the electron density of the H₂ molecule. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 4–10, 2001     

Group electronegativity and Fukui function studies of the substituent effects in aromatic and inorganic systems

The group electronegativities (GE ) of molecular fragments, including the environmental contributions due to both the electrostatic interactions and electron distribution relaxation, and the Fukui function (FF ) indices of the charge sensitivity analysis (CSA ) are correlated with the known substituent effects in molecular systems. The semiempirical CSA in the atoms-in-molecules (AIM ) resolution has been applied to substituted benzenes and square platinum complexes treated as illustrative examples. The calculated FF indices and GE are both shown to constitute adequate reactivity criteria that qualitatively reproduce the known substituent effects. The FF index (second-order property) is found to be a more sensitive detector of the substituent influence than is the corresponding GE parameter (first-order property). © 1992 John Wiley & Sons, Inc.     

The Fukui function of an atom in a molecule: A criterion to characterize the reactive sites of chemical species

The principle of hard and soft acids and bases is interpreted as the result of two opposing tendencies, one related to the charge transfer process (chemical potential equalization principle), and the other one related to the reshuffling of the electronic density (maximum hardness or minimum softness principle). A local version of the principle is elucidated by assuming that these tendencies are dominated by the local properties rather than by the global properties of the molecule. This principle is used together with the Fukui function of the atoms in the molecule to characterize the reactive sites. The results presented for the nucleophilic addition to the pyridinium ion, and for the electrophilic substitution on pyridine oxide show the usefulness of these concepts in describing the inherent reactivity of chemical species.     

Computing the Fukui function from ab initio quantum chemistry: approaches based on the extended Koopmans’ theorem

The extended Koopmans’ theorem is related to Fukui function, which measures the change in electron density that accompanies electron attachment and removal. Two approaches are used, one based on the extended Koopmans’ theorem differential equation and the other based directly on the expression of the ionized wave function from the extended Koopmans’ theorem. It is observed that the Fukui function for electron removal can be modeled as the square of the first Dyson orbital, plus corrections. The possibility of useful generalizations to the extended Koopmans’ theorem is considered; some of these extensions give approximations, or even exact expressions, for the Fukui function for electron attachment.     

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。     

DFT-based chemical reactivity indices in the Hartree-Fock method. II. Fukui function, chemical potential, and hardness

A derivation of the density-functional-theory- (DFT) based reactivity indices in the ensemble unrestricted Hartree-Fock (eUHF) method is presented. The comparison between the properties of the reactivity indices evaluated in one and two sets of spin-orbital approach of the eUHF and hyper-unrestricted Hartree-Fock (UHF) methods are shown. All approaches give similar Fukui function irrespective of methodology used, but significantly differ for the global indices, containing important chemical information, and so their interpretation in terms of DFT- based indices can be questionable. The calculation scheme for the indices using the first- and second-order coupled perturbed eHF equations is proposed. A method for the identification of the spinorbitals involved in the change of the total number of electrons is included. The illustrative examples (water and hydrogen cyanide) show that the ground-state (GS) properties of the (Z +/- 1)-electron systems can be predicted from the GS properties of the Z-electron systems with an accuracy comparable with the UHF calculations. The relaxation effect, important for the HCN system in which a change in the symmetry of the highest-occupied spin-orbital occurs, is effectively predicted.     

Comparison of different algorithms to calculate electrophoretic mobility of analytes as a function of binary solvent composition

Ten different mathematical models representing the electrophoretic mobility of analytes in capillary electrophoresis in mixed solvents of different composition have been compared using 32 experimental data sets. The solvents are binary mixtures of water-methanol, water-ethanol and methanol-ethanol, respectively. Mean percentage deviation (MPD), overall MPD (OMPD) and individual percentage deviation (IPD) have been considered as comparison criteria. The results showed that a reorganized solution model, namely the combined nearly ideal binary solvent/Redlich-Kister equation, is the most accurate model among other similar models concerning both correlation ability and prediction capability.     

Comparison of temperature and work function measurements obtained with different GTA electrodes

This work was carried out on one standard electrode (W-ThO₂,) and other electrodes developed by additions of La₂O₃, CeO₂, and Y₂O₃,. The effect of rare-earth metal oxides on GTAW electrode phenomena, concerning electrode temperature, emissivity, and work function, was analyzed and compared from the point of view of those oxides' behavior during arcing. The experimental results indicate that the electrode temperature, emissivity, and work (unction .strongly depend on the behavior of the rare-earth metal oxides during arcing. The investigation demonstrates good stability of La₂O₃ during arcing compared with the other oxides. The temperature distributions along the electrode axis of these electrodes were measured by using infrared pyrometer and grooved electrodes. The W-La₂O₃ electrode showed the lowest temperature values, followed by W-CeO₂ and W-ThO₂ electrodes in that order. Also W-La₂O₃ electrodes have a higher emissivity and lower work Junction, followed by W-CeO₂ and W-ThO₂ electrodes in that order.     

不同煤燃烧方式降低NOx排放比较及解耦燃烧应用

采用两段反应器研究了三种煤在不同燃烧方式下抑制NO_x生成的效果。结果表明,煤的热解气和部分气化生成气再燃均能较好的抑制NO_x生成,抑制效果优于空气分级燃烧,解耦燃烧方式抑制NO_x生成的效果最显著,相对于传统燃烧其NO_x排放降低了32%以上。煤种对各种燃烧方式降低NO_x的程度有明显影响,煤中单位氮含量的燃料比(固定碳/挥发分)越小,煤的热解气和部分气化生成气再燃以及解耦燃烧方式下NO_x的排放量越低。在煤部分气化生成气再燃烧方式中,部分氧化气化段通氧量不同,降低NO_x排放的效果也不同,在氧气体积分数为8%~10%时的NO_x生成量最低。基于解耦燃烧技术原理,研制了1.4 MW解耦燃烧工业锅炉,在燃烧同一煤种时,解耦燃烧锅炉和传统立式锅炉相比,烟气中NO_x排放量降低了32.9%。     

Rational syntheses of porphyrins bearing up to four different meso substituents

Porphyrins bearing specific patterns of substituents are crucial building blocks in biomimetic and materials chemistry. We have developed methodology that avoids statistical reactions, employs minimal chromatography, and affords up to gram quantities of regioisomerically pure porphyrins bearing predesignated patterns of up to four different meso substituents. The methodology is based upon the availability of multigram quantities of dipyrromethanes. A procedure for the diacylation of dipyrromethanes using EtMgBr and an acid chloride has been refined. A new procedure for the preparation of unsymmetrical diacyl dipyrromethanes has been developed that involves (1) monoacylation with EtMgBr and a pyridyl benzothioate followed by (2) introduction of the second acyl unit upon reaction with EtMgBr and an acid chloride. The scope of these acylation methods has been examined by preparing multigram quantities of diacyl dipyrromethanes bearing a variety of substituents. Reduction of the diacyl dipyrromethane to the corresponding dipyrromethane-dicarbinol is achieved with NaBH(4) in methanolic THF. Porphyrin formation involves the acid-catalyzed condensation of a dipyrromethane-dicarbinol and a dipyrromethane followed by oxidation with DDQ. Optimal conditions for the condensation were identified after examining various reaction parameters (solvent, temperature, acid, concentration, time). The conditions identified (2.5 mM reactants in acetonitrile containing 30 mM TFA at room temperature for <7 min) provided reaction without detectable scrambling (LD-MS) for aryl-substituted dipyrromethanes, and trace scrambling for alkyl-substituted dipyrromethanes. The desired porphyrins were obtained in 14-40% yield. The synthesis is compatible with diverse functionalities: amide, aldehyde, carboxylic acid, ester, nitrile, ether, bromo, iodo, ethyne, TMS-ethyne, TIPS-ethyne, perfluoroarene. In total 30 porphyrins of the types A(3)B, trans-A(2)B(2), trans-AB(2)C, cis-A(2)B(2), cis-A(2)BC, and ABCD were prepared, including >1-g quantities of three porphyrins.