Frontier orbital and density functional study of the variation of the hard–soft behavior of monoborane (BH3) and boron trifluoride (BF3) as a function of angles of reorganization from planar (D3h) to pyramidal (C3v) shape

In chemical response the BH₃ and BF₃ molecules undergo the physical process of planar (D_3h) to pyramidal (C_3v) reorganization in shape as the condition precedent to the event of chemical reaction under the requirement of symmetry. A frontier orbital and density functional study of the variation of the stability of electronic structures and chemical reactivity of associated with the physical process of D_3h to C_3v geometry reorganization has been performed. The theoretical parameters viz. eigenvalues of HOMO and LUMO, the HOMO and LUMO energy gap, the global hardness and global softness, the chemical potential, the condensed Fukui function, and local softness of B atom, the reaction site, have been computed over a wide range of ∠XBX angles. The nature of variation in the intrinsic chemical reactivity, global and local, of the molecules associated with their geometry reorganization during the chemical event of charge transfer interaction involving their frontier molecular orbitals has been quantitatively explored. The hardness profiles as a function of reaction coordinates are consistent with the principle of maximum hardness (PMH). Results demonstrate that the hardness and softness are not a static and invariable property of molecules but a dynamic and variable function of molecular structure. The hardness parameters and the HOMO–LUMO gap of the molecules are so modified with the distortion of molecular geometry that, after a certain stage of molecular deformation, the profiles of such parameters of the molecules intersect and cross each other, signifying that the relative order of the intrinsic hardness of their equilibrium geometry is reversed. The intrinsically hard molecule BF₃ becomes softer than the intrinsically soft molecule BH₃ as a consequence of structural distortion. The increase in chemical reactivity computed in terms of density functional parameters are transparent and justified in terms of the profiles of the eigenvalues of the frontier orbitals. The profiles of chemical potential reveal the inherent difference in the tendency of backdonation from two molecules. The computed values of Fukui functions and local softness parameters of the B atom site demonstrate that the concept of local softness can be exploited for a theoretical analysis and understanding of the characteristic chemical events of the molecules under consideration. The profiles of the Fukui functions and local softness parameters of the two molecules seem to reflect and reveal their intrinsic difference in the tendency of receiving donation in the LUMO (electrophilicity) and that of backdonation from the HOMO (nucleophilicity) and the inherent difference of overall reactivity of the two molecules by a simultaneous operation of two opposing processes of charge transfer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

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.     

Atom and Bond Fukui Functions and Matrices: A Hirshfeld‐I Atoms‐in‐Molecule Approach

The Fukui function is often used in its atom‐condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms‐in‐molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld‐I atoms‐in‐molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld‐I approach to obtain atom‐ and bond‐condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms‐in‐molecule approach shows low correlation between the two partitioning schemes.     

Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazoles

The chemistry of thiadiazoles and their derivatives is of considerable interest in chemistry owing to their pharmacological and potential industrial applications. In this context, a detailed study of isomeric thiadiazole molecules has been done using local (SVWN; Slater, and Vosko, Wilk and Nusair) and nonlocal (BLYP; Becke, and Lee, Yang and Parr) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecule has been performed by resorting to density functional theory, obtaining several sensitivity coefficients such as the molecular energy, net atomic charges, global and local hardness, global and local softness and Fukui functions. With these results and the analysis of the dipole moments, the molecular electrostatic potentials and the total electron density maps, several conclusions have been inferred about the preferred sites of chemical reaction of the studied compounds. The condensed Fukui functions are shown to be one of the best criteria for predicting chemical reactivity.     

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.     

A misconception concerning the electronic density distribution of an atom

It is shown that the electronic charge density of a ground-state atom decreases monotonically as a function of radial distance from the nucleus, contrary to the widespread belief that the shell structure is reflected by relative maxima in the density. Any proposed relationship between chemical bonding and the maxima in the radial density functions of atoms should therefore be regarded with caution. It is proven that the electrostatic potential of an atom must be monotonically decreasing. The changes in charge distribution upon molecule formation are also discussed.     

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.     

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     

A new approach to local hardness

The applicability of the local hardness as defined by the derivative of the chemical potential with respect to the electron density is undermined by an essential ambiguity arising from this definition. Further, the local quantity defined in this way does not integrate to the (global) hardness-in contrast with the local softness, which integrates to the softness. It has also been shown recently that with the conventional formulae, the largest values of local hardness do not necessarily correspond to the hardest regions of a molecule. Here, in an attempt to fix these drawbacks, we propose a new approach to define and evaluate the local hardness. We define a local chemical potential, utilizing the fact that the chemical potential emerges as the additive constant term in the number-conserving functional derivative of the energy density functional. Then, differentiation of this local chemical potential with respect to the number of electrons leads to a local hardness that integrates to the hardness, and possesses a favourable property; namely, within any given electron system, it is in a local inverse relation with the Fukui function, which is known to be a proper indicator of local softness in the case of soft systems. Numerical tests for a few selected molecules and a detailed analysis, comparing the new definition of local hardness with the previous ones, show promising results.     

Comment on“direct consequences of the bond index statistical interpretation”

It is shown that half the valence of an atom, in MO theory, is equal to the fluctuation of its atomic charge, and that the softness of an atom in a molecule is linearly related to the valence. In consequence the hardness of the atoms in the first row of the periodic table increases symmetrically from carbon to lithium and to fluorine.     

Chemical reactivity trends of ergotamine and butenolide from electrostatic potentials and charge sensitivities

A set of reactivity indices, including maps of the electrostatic potential and local and condensed Fukui function (FF ) indices in the atomic resolution, are reported for two vasoconstricting mycotoxins: butenolide and ergotamine; both the finite difference approach of Parr and Yang as well as charge sensitivity analysis, determining the charge responses via the inversion of the hardness tensor, have been used to generate the FF data. These two routes of arriving at the atomic FF indices provide an opportunity to evaluate the available parametrizations of the semiempirical NDDO -type of methods which have been used to determine the input charge distribution; namely, the best parametrization should generate consistent FF predictions resulting from both approaches. For butenolide, the MNDO parametrization was found to fulfill this consistency requirement. The chemical reactivity information has been used to trace possible similarities in reactivity trends of the butenolide molecule and the related fragment of ergotamine, toward hypothetical nucleophilic, electrophilic, and radical attacks. These predictions have been compared to experimental data available for other unsaturated lactones. © 1995 John Wiley & Sons, Inc.     

Charge sensitivities of the externally interacting open reactants

Effective chemical potential, hardness, softness, and Fukui function quantities of the simultaneously open reactants, e.g., adsorbates in catalytic systems, are examined. The derived reduced expressions in terms of the canonical chemical potentials and condensed hardness matrix elements of such molecular subsystems are compared with the corresponding analogs for the case of the closed complementary subsystem. Implications of the catalyst‐induced changes in the condensed hardness matrix of the reactive system consisting of a pair of donor/acceptor adsorbates, in the preferred complementary arrangement with the acidic/basic active sites of the surface, respectively, are discussed and interpreted as manifestations of the Le Châtelier–Braun principle. Only in such a complementary arrangement is the in‐phase, concerted, mutually enhancing pattern of the polarizational and charge transfer flows of electrons in a catalytic system obtained. The activating influence of the catalyst is identified through its softening, decoupling effect on the adsorbates. The catalyst‐induced chemical potential equalization creates electronic instability in the system of adsorbed species, thus increasing their reactivity. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 168–178, 2000     

Diffusion by chemical bond hopping of single O2 and H on Si(111)-7×7 surfaces

Using a variable temperature STM to trace in detail the path of single particle movement, it is possible to derive diffusion parameters of individual atoms and molecules on solid surfaces as well as to probe the mechanisms. Below ˜370 °C, O₂ molecules adsorb on Si(111)-7×7 surfaces at the top site of Si-adatoms as bright image spots. An O₂ molecule can hop between two adatom sites within the half unit cell it adsorbs via two rest-atom sites. Above this temperature, it can either hop out of the half cell, or can go through other reaction pathways. In contrast, for H atoms, the adsorption sites are rest-atom sites. An H atom darkens the rest-atom in filled state image, but the surrounding adatoms will appear brighter because of a reverse charge transfer. Above ˜280 °C, it can hop to a neighbor rest atom site within the half cell via an adatom site. The adatom in the short lived intermediate state appears darker because of the saturation of its dangling bond. Above ˜340 °C, it can hop out of the half cell via two adatom sites. Thus diffusion of H and O₂ on this surface is achieved by hopping of chemical bonds via intermediate states. We have also derived site and pathway-specific activation energies and frequency factors and the potential energy curves for the hopping of O₂ and H on Si(111)-7×7 surfaces.     

Fragment chemistry of the hydrogen thioperoxide molecule; energy, chemical potential and hardness

In this paper we present a complete theoretical study of the hydrogen thioperoxide molecule (HSOH). We characterize the internal rotation by studying the evolution of the energy, chemical potential and hardness along the torsional angle. We have found that hydrogen thioperoxide in its electronic singlet state is a gauche molecule. Barrier heights, activation chemical potential and activation hardness have been obtained, and it has been found that the trans barrier is lower than the cis one. Good agreement of rotation barriers is obtained on the basis of comparisons with the available literature experimental data for the HOOH and HSSH parent molecules. Another important result is that the maximum hardness principle is verified for the torsional motion. On the other hand, we characterize the thermochemistry of chemical reactions leading to formation of HSOH from the electronic properties associated with the free constituent fragments. The procedure, which involves the use of Sanderson's rule to estimate chemical potentials and hardnesses, is shown to be promising and opens the possibility of rationalizing the behavior of other series of reactions.     

Conceptual DFT based electronic structure principles in a dynamical context

Within the context of quantum fluid density functional theory diverse processes simulating a chemical reaction like interaction of an atom or a molecule with an externally applied electric or magnetic field or its collision with a proton have been analyzed in a dynamical situation. The changes produced in the chemical reactivity parameters namely chemical potential, hardness, polarizability during such processes have been identified and discussed. In addition, confinement is also introduced to observe the necessary variation in the different reactivity parameters.