Comparison among four different ways to condense the Fukui function

Four different ways to condense the Fukui function are compared. Three of them perform a numerical integration over different basins to define the condensed Fukui function, and the other one is the most traditional Fukui function using Mulliken population analysis. The basins are chosen to be the basins of the electron density (AIM), the basins of the electron localization function (ELF), and the basins of the Fukui function itself. The use of the last two basins is new and presented for the first time here. It is found that the last three methods yield results which are stable against a change in the basis set. The condensed Fukui function using the basins of the ELF is not able to give information on the reactivity of an acceptor molecule. In general, the condensed Fukui function using the basins of the density or the basins of the Fukui function describe the reactivity trends well. The latter is preferred, because it only contains information about the Fukui function itself and it gives the right information for donor as well as acceptor centers.     

Theoretical study of the interaction of molecular oxygen with copper clusters

A new method based on frontier orbital theory has been used to investigate the binding site of molecular oxygen to neutral and anion copper clusters. It has been shown that one can make useful predictions of the binding sites based on the knowledge of the donor local reactivity of the cluster using the condensed Fukui function, f(-)(Ff). In this way, it was found that Cu(3), Cu(5), and Cu(5)(-) have the highest reactivity toward molecular oxygen.     

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.     

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.     

Critical thoughts on computing atom condensed Fukui functions

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.     

Application of density functional theory concepts to the study of the chemical reactivity of thiadiazoles

Several useful concepts derived from Density Functional Theory have been applied to study the chemical reactivity of 1,2,5- and 1,3,4-thiadiazoles. Total hardness of the molecules in terms of the HOMO-LUMO gap as a measure of aromaticity and the condensed Fukui functions related to the variations of the net charges of the atoms resulting from a Mulliken population analysis were calculated in order to determine the reactivity of different sites within the molecules studied. The net charges have been obtained from calculations made in the context of the Hartree-Fock-LCAO approximation and the results compared with the existing experimental evidence on thiadiazoles and related compounds.     

Computing Fukui functions without differentiating with respect to electron number. I. Fundamentals

By using perturbations in the molecular external potential, the authors deduce the Fukui function from the change in Kohn-Sham orbital energies, avoiding the troublesome differentiation of the density with respect to electron number. Though this paper focuses on the Fukui function, the same general technique can be used to compute the functional derivative of any observable with respect to the external potential. In this paper, the method is used to compute the Fukui function for the beryllium atom and the formaldehyde molecule. The follow-up paper (part II) addresses the problem of computing condensed reactivity indicators.     

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.     

Size effects in electronic and catalytic properties of unsupported palladium nanoparticles in electrooxidation of formic acid

We report a combined X-ray photoelectron spectroscopy (XPS), cyclic voltammetry (CV), and chronoamperometry (CA) study of formic acid electrooxidation on unsupported palladium nanoparticle catalysts in the particle size range from 9 to 40 nm. The CV and CA measurements show that the most active catalyst is made of the smallest (9 and 11 nm) Pd nanoparticles. Besides the high reactivity, XPS data show that such nanoparticles display the highest core-level binding energy (BE) shift and the highest valence band (VB) center downshift with respect to the Fermi level. We believe therefore that we found a correlation between formic acid oxidation current and BE and VB center shifts, which, in turn, can directly be related to the electronic structure of palladium nanoparticles of different particle sizes. Clearly, such a trend using unsupported catalysts has never been reported. According to the density functional theory of heterogeneous catalysis, and mechanistic considerations, the observed shifts are caused by a weakening of the bond strength of the COOH intermediate adsorption on the catalyst surface. This, in turn, results in the increase in the formic acid oxidation rate to CO2 (and in the associated oxidation current). Overall, our measurements demonstrate the particle size effect on the electronic properties of palladium that yields different catalytic activity in the HCOOH oxidation reaction. Our work highlights the significance of the core-level binding energy and center of the d-band shifts in electrocatalysis and underlines the value of the theory that connects the center of the d-band shifts to catalytic reactivity.     

Sampling Potential Energy Surfaces in the Condensed Phase with Many-Body Electronic Structure Methods

Sampling potential energy surfaces (PES) is pivotal for understanding chemical structure, energetics and reactivity and is of special importance for complex condensed-phase systems. Until recently such simulations based on electronic structure theory have been performed only by density functional theory and semiempirical methods. Many-body electronic structure methods, almost routinely used for molecules, have been practically unavailable for sampling PES in the condensed-phase. This has changed during the last few years, as efficient algorithms and software implementations for the evaluation of electronic energies and forces on atoms have been developed, allowing for geometry optimization, molecular dynamics and Monte-Carlo simulations, which was previously unthinkable. Herein, we introduce the theory and software developments and overview the applications in the field, the most encouraging results being obtained for aqueous chemistry. Requiring state-of-the-art computer resources PES sampling with many-body electronic structure methods in the condensed phase provides high-quality benchmarks and will gradually become more available due to fast progress in reduced scaling algorithms and computational technologies.     

Quantum chemical study of the inhibitive properties of 2-pyridyl-azoles

Four molecules that have been proven to act as corrosion inhibitors of mild steel in acidic media are studied. The inhibitive efficiency of these molecules is explained by means of electronic structure calculations of the protonated species that seem to represent better the actual situation of the experimental conditions. By assuming that the interaction between the inhibitor and the metallic surface occurs through donation and back-donation, it is shown, with a simple charge transfer model, that the interaction energy is favored when hardness increases, in agreement with the experimentally observed inhibition efficiencies. A local analysis with Hirshfeld condensed Fukui functions, and local Fukui functions, provides further support to the donation and back-donation mechanism.     

Rational design of selective, sulfur-resistant oxidation emissions catalysts

A new catalyst design strategy based on optimizing electronic structure has been proposed and then applied to a very important environmental application, the design of selective, sulfur-resistant oxidation emissions catalysts. The modified d-band center model developed by us in a previous study, together with an energy decomposition scheme, is used to correlate measures of reactivity with reaction barriers of SO2 + O --> SO3 and NO + O --> NO2 on surfaces. Our objective is to find a catalyst which is active in oxidizing NO to NO2 but relatively inactive in oxidizing SO2 to SO3. The Ir alloyed Pt(111) surface is found to have the highest selectivity for oxidation of NO over SO2 at 700 K. Unfortunately, there is a slope change in the correlation of the weighted d-band center with the adsorption of NO at the transition state, which narrows down the range of the theoretical selectivity. Our ongoing study aims at understanding the reason for this. The general importance of this study for surface catalysis is also discussed.     

Understanding Chemical Reactivity in Extended Systems:Exploring Models of Chemical Softness in Carbon Nanotubes

Chemical reactivity towards electron transfer is captured by the Fukui function.However,this is not well defined when the system or its ions have degenerate or pseudo-degenerate ground states.In such a case,the first-order chemical response is not independent of the perturbation and the correct response has to be computed using the mathematical formalism of perturbation theory for degenerate states.Spatialpseudo-degeneracy is ubiquitous in nanostructures with high symmetry and totally extended systems.Given the size of these systems,using degenerate-state perturbation theory is impractical because it requires the calculation of many excited states.Here we present an alternative to compute the chemical response of extended systems using models of local softness in terms of the local density of states.The local softness is approximately equal to the density of states at the Fermi level.However,such approximation leaves out the contribution of inner states.In order to include and weight the contribution of the states around the Fermi level,a model inspired by the long-range behavior of the local softness is presented.Single wall capped carbon nanotubes(SWCCNT) illustrate the limitation of the frontier orbital theory in extended systems.Thus,we have used a C360 SWCCNT to test the proposed model and how it compares with available models based on the local density of states.Interestingly,a simple Hü ckel approximation captures the main features of chemical response of these systems.Our results suggest that density-of-states models of the softness along simple tight binding Hamiltonians could be used to explore the chemical reactivity of more complex system,such a surfaces and nanoparticles.     

Nuclear reactivity indices in the context of spin polarized density functional theory

In this work, the nuclear reactivity indices of density functional theory have been generalized to the spin polarized case and their relationship to electron spin polarized indices has been established. In particular, the spin polarized version of the nuclear Fukui function has been proposed and a finite difference approximation has been used to evaluate it. Applications to a series of triatomic molecules demonstrate the ability of the new functions to predict the geometrical changes due to a change in the spin multiplicity. The main equations in the different ensembles have also been presented.