Local reactivity index defined through the density of states describes the basicity of alkaline-exchanged zeolites

Reactivity of Single Transition Metal Atoms on a Hydroxylated Amorphous Silica Surface: A Periodic Conceptual DFT Investigation

The drive to develop maximal atom-efficient catalysts coupled to the continuous striving for more sustainable reactions has led to an ever-increasing interest in single-atom catalysis. Based on a periodic conceptual density functional theory (cDFT) approach, fundamental insights into the reactivity and adsorption of single late transition metal atoms supported on a fully hydroxylated amorphous silica surface have been acquired. In particular, this investigation revealed that the influence of van der Waals dispersion forces is especially significant for a silver (98 %) or gold (78 %) atom, whereas the oxophilicity of the Group 8-10 transition metals plays a major role in the interaction strength of these atoms on the irreducible SiO₂ support. The adsorption energies for the less-electronegative row 4 elements (Fe, Co, Ni) ranged from -1.40 to -1.92 eV, whereas for the heavier row 5 and 6 metals, with the exception of Pd, these values are between -2.20 and -2.92 eV. The deviating behavior of Pd can be attributed to a fully filled d-shell and, hence, the absence of the hybridization effects. Through a systematic analysis of cDFT descriptors determined by using three different theoretical schemes, the Fermi weighted density of states approach was identified as the most suitable for describing the reactivity of the studied systems. The main advantage of this scheme is the fact that it is not influenced by fictitious Coulomb interactions between successive, charged reciprocal cells. Moreover, the contribution of the energy levels to the reactivity is simultaneously scaled based on their position relative to the Fermi level. Finally, the obtained Fermi weighted density of states reactivity trends show a good agreement with the chemical characteristics of the investigated metal atoms as well as the experimental data.

Conceptual DFT: the chemical relevance of higher response functions

In recent years conceptual density functional theory offered a perspective for the interpretation/prediction of experimental/theoretical reactivity data on the basis of a series of response functions to perturbations in the number of electrons and/or external potential. This approach has enabled the sharp definition and computation, from first principles, of a series of well-known but sometimes vaguely defined chemical concepts such as electronegativity and hardness. In this contribution, a short overview of the shortcomings of the simplest, first order response functions is illustrated leading to a description of chemical bonding in a covalent interaction in terms of interacting atoms or groups, governed by electrostatics with the tendency to polarize bonds on the basis of electronegativity differences. The second order approach, well known until now, introduces the hardness/softness and Fukui function concepts related to polarizability and frontier MO theory, respectively. The introduction of polarizability/softness is also considered in a historical perspective in which polarizability was, with some exceptions, mainly put forward in non covalent interactions. A particular series of response functions, arising when the changes in the external potential are solely provoked by changes in nuclear configurations (the "R-analogues") are also systematically considered. The main part of the contribution is devoted to third order response functions which, at first sight, may be expected not to yield chemically significant information, as turns out to be for the hyperhardness. A counterexample is the dual descriptor and its R analogue, the initial hardness response, which turns out to yield a firm basis to regain the Woodward-Hoffmann rules for pericyclic reactions based on a density-only basis, i.e. without involving the phase, sign, symmetry of the wavefunction. Even the second order nonlinear response functions are shown possibly to bear interesting information, e.g. on the local and global polarizability. Its derivatives may govern the influence of charge on the polarizability, the R-analogues being the nuclear Fukui function and the quadratic and cubic force constants. Although some of the higher order derivatives may be difficult to evaluate a comparison with the energy expansion used in spectroscopy in terms of nuclear displacements, nuclear magnetic moments, electric and magnetic fields leads to the conjecture that, certainly cross terms may contain new, intricate information for understanding chemical reactivity.

Condensed-to-atoms electronic Fukui functions within the framework of spin-polarized density-functional theory

A simple formalism devised to calculate the condensed-to-atoms Fukui function [R. R. Contreras, P. Fuentealba, M. Galván, and P. Pérez, Chem. Phys. Lett. 304, 405 (1999)] has been further analyzed within a spin-polarized density-functional theory framework. The model is based on a frozen-core approximation to these local reactivity indices [M. Galván, A. Vela, and J. L. Gázquez, J. Phys. Chem. 92, 6470 (1988)], giving us an extended local reactivity description of systems based on the frontier spin-up and spin-down molecular orbitals. Degenerate molecular spin orbitals have been explicitly included in our model equations. Computational results for the nitric oxide (NO) and some simple carbene systems are presented in order to test the model. These quantities have been discussed in the context of changes both in charge density and spin density within the context of electron charge transfer or spin-polarization processes.

Theoretical Study on CDK2 Inhibitors Using a Global Softness Obtained from the Density of States

We report a theoretical study on a series of CDK2 inhibitors using a set of global reactivity indices defined in terms of the density of states. The statistical analysis was performed on the basis of two groups of 11 and 6 compounds, respectively, reported by Hardcastle et al. (J. Med. Chem. 2004, 47, 3710-3722). Both series were classified on the basis of the correlations obtained for the complete set of compounds and the sites targeted within the active site of CDK2. The comparison between the biological activity and the electronic chemical potential approached as the Fermi level yields poor results, thereby suggesting that the interaction between the hinge region (HR) of CDK2 and the ligands may have a marginal contribution from the charge transfer (CT) component. Comparison between the biological activity and global softness shows a better correlation, thereby suggesting that polarization effects outweigh the CT contribution in the HR-ligand interaction. We stress the importance to include in the evaluation of the reactivity indices all of the occupied energy states in order to assess the effects coming from the internal electronic structure involved in the HR-ligand interaction.

The Influence of Electric Field on the Global and Local Reactivity Descriptors: Reactivity and Stability of Weakly Bonded Complexes

The response of the global and local reactivity density-based descriptors (chemical potential, hardness, softness, Fukui function, and local softness) in the presence of external electric field has been studied for some of the simple prototype molecular systems. In addition to the analysis on the reactivity of these systems, the influence of the electric field on the interaction energy of the complexes formed by these systems has also been studied using the recently proposed semiquantitative model based on the local hard-soft acid-base principle. By using the inverse relationship between the global hardness and softness parameters, a simple relationship is obtained for the variation of hardness in terms of the Fukui function under the external electric field. It is shown that the increase in the hardness values for a particular system in the presence of external field does not necessarily imply that the reactivity of the system would be deactivated or vice versa.

Understanding the Concept of Basicity in Zeolites. A DFT Study of the Methylation of Al−O−Si Bridging Oxygen Atoms

DFT calculations on a 4-ring cluster and on ONIOM models of faujasite were carried out to assess the concept of basicity in zeolites, exchanged with alkali cations. The considered reaction is the methylation of the Si-O-Al bridging oxygen by methanol and methyl iodide. The reaction involves both the dissociation of the H3C-OH or H3C-I bonds and the formation of the C-O-zeolite bond. The former involves the hardness of the alkaline cation. The latter reflects the charge density of the basic oxygen, well described by the "hard" descriptor: the molecular electrostatic potential. The harder is the alkali metal, the easier is the H3C-OH or H3C-I bond dissociation, and the lower is the basicity of the bridging oxygen, and thus the more difficult is the C-O-zeolite bond formation. The fact that these two processes compete has been established by comparing the energy profiles for the methylation with methyl iodide and methanol. For methanol the role of the alkaline metal on the bond dissociation prevails because of the larger hardness of the OH group as compared to that of the iodine atom. For methyl iodide the oxygen basicity prevails over the interaction of I with metal. This study clearly shows that in both experimental and theoretical studies the role of the Lewis acidity or hardness of the alkali metal ion and the role of the basicity of the framework oxygen have to be separated from each other for a good interpretation of zeolite basicity. Also, the hardness of the probe molecule is particularly important when considering the interaction with the alkali metal ion.

Incorporation of Anthracene into Zeolites: Confinement Effect on the Recombination Rate of Photoinduced Radical Cation-Electron Pair

FT-Raman spectrometry in combination with diffuse reflectance UV/Vis absorption (DRUVv) and fluorescence emission indicate that complete anthracene (ANT) sorption as intact molecules takes place over 6 months in the medium pores of non-Brønsted acidic M(n)ZSM-5 zeolites (n=0.0, 3.4, 6.6; M=Na+, K+, Rb+, Cs+) with 1 ANT per unit cell loading. The combined effect of confinement and electrostatic field induced by bulky cations (Rb+, Cs+) leads to specific changes in the occluded ANT Raman spectra after very long organization periods (one year). The laser photolysis (266 nm, 355 nm) of ANT@M(n)ZSM-5 equilibrated samples generates long-lived charge separated species in aluminum rich zeolites (n=3.4, 6.6). The very long-lived radical pairs are characterized by conventional DRUVv and CW-EPR spectroscopy. The direct charge recombination rates of ANT.+-electron pairs are dispersive, extending over a broad range of timescales. The kinetic constant values are found to increase dramatically with the aluminum content and increase markedly with M+ according to the following order Na+ < K+ < Rb+ < Cs+. The small reorganization energy (lambda) of ZSM-5 zeolite pores coupled with large negative free energy changes (-DeltaG degrees ) between the ground state ANT oxidation potential and Fermi level of aluminum rich M(n)ZSM-5 explain the observed trends of the ANT.+@M(n)ZSM-5.- charge recombination rates.