Elba Ortiz

Electronegativities and hardnesses of open shell atoms

A Taylor series expansion of the energy of an atomic system around the neutral atom value, which introduces the first and second derivatives of the energy with respect to the number of electrons (electronegativity χ, and hardness η, respectively) is proposed. The relaxed first derivative and the unrelaxed second derivative of the Xα and hyper‐Hartree–Fock methods are used to relate χ and η with the Lagrange multiplier ei, and the self‐repulsion integral J(i) of the highest occupied atomic orbital for the case of an open shell. A simple model, based on screening effects, is developed to get a better representation of a relaxed second derivative. This model replaces J(i) by 1/2 〈r−1〉i and leads to η= 1/4 〈r−1〉i. The use of this relation, together with the Xα expression for electronegativity, χ=−ei, and a simple charge transfer model for electronegativity equalization leads to values of molecular electronegativities which are in very good agreement with the values obtained through the use of atomic or molecu...

Self-interaction and interelectromc exchange in the electron gas model for atoms

Abstract The exchange potential is separated into self-interaction and interelectronic exchange components which are modeled through the properties of the cne- and two-particle density matrices. The resulting functional has the correct asymptotic behaviour.

Molecular Description of Indigo Oxidation Mechanisms Initiated by OH and OOH Radicals

In this work, we report a quantum chemistry mechanistic study of the hydroxyl (•OH) and hydroperoxyl (•OOH) radicals initiated oxidation of indigo, within the density functional theory framework. All possible hydrogen abstraction and radical addition reaction pathways have been considered. We find that the reaction between a free indigo molecule and an •OH radical occurs mainly through two competing mechanisms: H-abstraction from an NH site and •OH addition to the central C═C double bond. Although the latter is favored, both channels occur, the indigo chromophore group structure is modified, and thus the color is changed. This mechanism adequately accounts for the loss of chromophore in urban air, including indoor air such as in museums and in urban areas. Regarding the reactivity of indigo toward •OOH radicals, only •OOH-addition to the central double bond is thermodynamically feasible. The corresponding transition state free energy value is about 10 kcal/mol larger than the one for the •OH initiated oxidation. Therefore, even considering that the •OOH concentration is considerably larger than the one of •OH, this reaction is not expected to contribute significantly to indigo oxidation under atmospheric conditions.

Indigo stability: an ab initio study

This work shows that indigos high stability can be attributed both to the large π conjugation inside the molecule and to intra- and intermolecular hydrogen bonds. The theoretical investigation of indigos electronic structure has been performed using high-level methods. To understand the interactions in solid state, calculations of the dimer system with both molecules in the same plane was carried out. In the monomer, two intramolecular hydrogen bridges between amino and carbonyl groups occupy positions that would otherwise be the most reactive ones for nucleophilic and electrophilic attacks. In the dimer, amino and carbonyl groups on different monomers form intermolecular multicentred non-linear hydrogen bonds in six-member rings, protecting again the same reactive centres and explaining the limited solubility of indigo. The addition of the free radical OH breaks the central C = C double bond, the conjugation and the hydrogen bridges as a first step. The Gibbs energy calculation favours the addition of OH radical over C1.

Electronic properties of poly(vinylidene fluoride): a density functional theory study

We present a theoretical study of the piezoelectric polymer poly(vinylidene fluoride), PVDF. By density functional theory calculations, some of the distinct properties of this material have been obtained. Among such properties are hardness, capacitance, dipolar moment and energy associated with the conformational structural changes. For the calculations, we employed the B3LYP functional and the 6311+G(d,p) basis set. Five chain molecules of varying length were studied, H–(CH2–CF2) x –H, where x = 1–4 and 6 for the four different PVDF conformations, namely, I = Tp, II = TGa, III = TGp and IV = T3G, where T means trans and G means gauche.

An exchange energy functional based on the Dirac and the Fermi–Amaldi approximations

The exchange energy density functional of an N electron atom is approximated by a combination of the Dirac and the Fermi–Amaldi approximations. The unknown coefficients of the combination are estimated by requiring that the sum of the Coulombic and exchange energies vanish when evaluated with the exact one‐electron density. Evaluating the present functional with the Hartree–Fock densities of 1785 atoms and ions, and comparing the resulting exchange energies with the corresponding Hartree–Fock values gave an average error of 2%. The functional derivative has the correct long‐range behavior, and leads to an Euler–Lagrange equation whose solutions gave energies which were in very good agreement with the Hartree–Fock values.

Thomas–Fermi limit and leading corrections for atoms and ions

The Z−1 perturbation expansion is used to derive a formula of the energy of an ion in the limit of large nuclear charge Z and number of electrons N of the form E=∑nZ(7−n)/3 fn(q) where q=N/Z and fn(q)=q(1−n)/3[b0n+b 1nq+b2nq2] with b1n≂[(7−n)/3]Cn−2b0n and b2n≂b0n −[(4−n)/3]Cn. The constants b0n correspond to the asymptotic expansion of the zero‐order perturbation coefficient e0(N) and the constants Cn correspond to the neutral atom binding energy E=∑nCnZ(7−n)/3. The first function f0(q), which corresponds to the Thomas‐Fermi limit, is then used to obtain approximate analytical expressions for the first derivative at the origin S(q) and the radius of the ion, χ0(q), of the Thomas‐Fermi screening function. The expressions for f0(q), S(q), and χ0(q) provide an excellent representation of the numerical solutions. The function f1(q) is used to show that the value of the coefficient of the leading correction to the Thomas‐Fermi energy C1 is 1/2. Finally, it is shown that the description of the ratio of the tot...

Indigo adsorption on a silicate surface: a theoretical density functional study

AbstractThe applicability of naturally available low-cost and eco-friendly adsorbent materials for the removal of hazardous dyes from aqueous waste is of increasing environmental interest. Among the adsorption treatments available, clays seem to be economically attractive due to their abundance and adsorption capabilities. Indeed, many ancient coloring materials utilized clays mixed with natural dyes (e.g., indigo in Maya Blue). In this work, we performed a quantum-mechanical theoretical study of the adsorption of the indigo molecule onto the (001) surface of a phyllosilicate. Different methods and approaches were applied and compared. We found that the presence of a tetrahedral charge and a sodium counterion significantly increased the adsorption energy of the indigo molecule. The vibrational spectrum of the dye–surface system was also studied, and some interesting shifts in the frequencies of the main vibrational modes of indigo due to its interaction with the surface of the clay mineral were identified. FigureIndigo molecule adsorbed on a silicate surface

First trial and physicochemical studies on the loading of basic fuchsin, crystal violet and Black Eriochrome T on HKUST-1

The highly porous metal–organic framework based on copper-benzenetricarboxylate (HKUST-1, Cu3(BTC)2, MOF-199) is used for a loading study of basic fuchsin (BF, neutral charge, ϕ = 12.40 A molecular diameter, 50 ppm solution), crystal violet (CV, cationic charge, ϕ = 15.10 A, 50 ppm solution) and Eriochrome Black T (EBT, anionic charge, ϕ = 15.50 A, 80 ppm solution), as chosen molecular probes for physicochemical analysis and interactions. Characterization is carried out using XRD, FTIR, SEM, and TGA, and UV-Vis is used to determine the differential concentration of loaded dye in the MOF. The adsorption process is evaluated by three incorporation methodologies: post-synthesis (PS) and one-pot in organic (OPO) or metallic (OPM) solution. XRD cell parameters reveal the general compactness of the net through ionic (CV and EBT), dipolar (BF, CV and EBT) and van der Waals (BF, CV and EBT) dye–MOF interactions. Enhanced compactness is observed for CV due to its cationic nature and medium size; the effect is not as strong in EBT, which is anionic in nature but bigger in size, and the least compactness is observed for BF, which lacks ionic interaction with the net. The samples have crystal sizes between 34 and 57 nm, which indicate the generation of nanomaterials. The employed procedures yield crystallite size in the following order: PS < OPO < OPM. The (%) adsorption of all the dyes is above 86.93%, which is observed for the EBT-PS sample as the lowest and 99.42% for BF-PS as the highest, which evidences the high displacement of equilibrium in the studied systems to the Cu3(BTC)2·dye occluded state. Thus, MOFs can be suggested as potential adsorbents/loaders of BF/CV/EBT dyes for composite material generation as well as MOF·molecule interaction studies because of their high loading ability and obtained stability as well as facile synthesis.

Atoms and Ions in the Limit of Large Nuclear Charge

The Z-1 perturbation expansion is used to derive an expression for the atomic binding energy E in the limit of large nuclear charge Z and number of electrons N. The coefficients appearing in this expression are determined from conditions related to the general behavior of E as a function of N. It is shown that through this expression one can: 1) obtain an excellent representation of Thomas-Fermi ions; 2) derive an expression for the chemical potential of neutral atoms in the limit of large Z, which accounts for the general behavior of this property in atoms of the periodic table; and 3) describe rather well ratios between different energy components.