Local and nonlocal density functional calculations of the molecular structure of isomeric thiadiazole monoxides

Conjugated organic heterocycles are systems of growing interest in materials science in view of the potential applications in fields such as electronics, photonics, sensors, or corrosion protection. The study of their molecular properties serves as a model for the prediction of the behavior of potentially conductive oligomers and polymers. A detailed analysis of isomeric thiadiazole monoxide molecules has been done using Hartree–Fock and local (SVWN) and nonlocal (BLYP, B3LYP) density functionals and optimizing the molecular geometries by means of the gradient technique. A charge sensitivity analysis of the studied molecules 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. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 105–115, 2001     

Polarization justified Fukui functions: the theory and applications for molecules

The Fukui functions based on the computable local polarizability vector have been presented for a group of simple molecules. The necessary approximation for the density functional theory softness kernel has been supported by a theoretical analysis unifying and generalizing early concepts produced by the several authors. The exact relation between local polarizability vector and the derivative of the nonlocal part of the electronic potential over the electric field has been demonstrated. The resulting Fukui functions are unique and represent a reasonable refinement when compared to the classical ones that are calculated as the finite difference of the density in molecular ions. The new Fukui functions are strongly validated by their direct link to electron dipole polarizabilities that are reported experimentally and by other computational methods.     

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     

Face-integrated Fukui function: understanding wettability anisotropy of molecular crystals from density functional theory

Wettability is one of the anisotropic surface properties of molecular crystals that exhibit the structural variance of chemical moieties on various growth faces. The divergence in liquid-solid interactions at different faces is thought to be related to the inherent responding capacity or sensitivity of a solid surface to the perturbation in electronic structures and atomic positions as a result of the contact by a liquid. Since the Fukui function, according to density functional theory (DFT), is a local function for describing such sensitivity to the structural perturbation and is directly related to local softness, it has been proposed and tested to use an integrated Fukui function over a crystallographic plane for describing the anisotropy of solid-liquid interactions. It is found that the contact angle of a polar solvent, such as water, on a crystal surface shows an intimate connection to the integrated Fukui functions of the surface, illustrating an extension of Pearson's HSAB (hard and soft acids and bases) to crystal systems. The concept of face-integrated Fukui function and the approach to apply the HSAB with the DFT-based concepts may provide a powerful means for describing anisotropic properties, including wettability of organic crystals.     

Phenomenological chemical reactivity theory for mobile electrons

We present herein a model to deal with the chemical reactivity, selectivity and site activation concepts of π electron systems derived by merging the classical Coulson–Longuet-Higgins response function theory based on the Hückel molecular orbital (HMO) theory and the conceptual density functional theory. HMO-like expressions for the electronic chemical potential, chemical hardness and softness, including their local counterparts, atomic and bond Fukui functions and non-local response functions are derived. It is shown that sophisticated non-local concepts as site activation may be cast into deeper physical grounds by introducing a simplified version of static response functions. In this way, useful quantities such as self and mutual polarizabilities originally defined through the HMO parameters can be redefined as self and mutual softnesses. The model is illustrated by discussing the classical Hammett free energy relationship describing inductive substituent effects on the reactivity of benzoic acids.     

Analytical evaluation of Fukui functions and real-space linear response function

Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism. In the present work, we obtain the analytical expressions for the real-space linear response function using the coupled perturbed Kohn-Sham and generalized Kohn-Sham equations, and the Fukui functions using the previous analytical expressions for chemical potentials of Cohen, Mori-Sánchez, and Yang. The analytical expressions are exact within the given exchange-correlation functional. They are applicable to all commonly used approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. The analytical expressions obtained here for Fukui function and linear response functions, along with that for the chemical potential by Cohen, Mori-Sánchez, and Yang, provide the rigorous and efficient evaluation of the key quantities in conceptual density functional theory within the computational framework of the Kohn-Sham and generalized Kohn-Sham approaches. Furthermore, the obtained analytical expressions for Fukui functions, in conjunction with the linearity condition of the ground state energy as a function of the fractional charges, also lead to new local conditions on the exact functionals, expressed in terms of the second-order functional derivatives. We implemented the expressions and demonstrate the efficacy with some atomic and molecular calculations, highlighting the importance of relaxation effects.     

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     

1,3-Dipolar cycloadditions of nonstabilized azomethine ylides to planar chalcones via regio- and stereoselective route: A three-component strategy

Simple and efficient strategies toward the synthesis of trisubstituted pyrrolizidines and disubstituted oxazolidine systems by 1,3-dipolar cycloaddition reactions using arylaldehydes and α-amino acids have been developed, followed by a one-pot, three-component strategy. Electron-deficient dipolarophiles, chalcones, were reacted with nonstabilized azomethine ylides derived from arylaldehyde and L-proline in dry dimethyl formamide, leading to substituted pyrrolizidines. The route to substituted oxazolidines involved cycloaddition to the C?O bond of a second molecule of the aldehyde. The structures and stereochemistry of the cycloadducts were established by infrared (IR), NMR spectroscopy, and single-crystal x-ray crystallographic analyses. Condensed Fukui functions and local electrophilicity indices have been computed to characterize the reactive sites and predict the preferred interactions of azomethine ylides to planar chalcones. The softness-matching indices have been evaluated to determine the regioselectivity of the cycloaddition reactions. The theoretical predictions were found to be in complete agreement with the experimental results, implying that the density functional theory (DFT)-based reactivity indices correctly predict the regioselectivities of 1,3-dipolar cycloadditions of azomethine ylides to planar chalcones. The frontier molecular orbital (FMO) energies, electronic chemical potentials, chemical hardness, chemical softness, and global electrophilicity indices of azomethine ylides have been calculated at the DFT/B3LYP/6-31 + G (d, p) level of theory.     

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.     

Theoretical study of the reactivity of cesium with benzene and graphitic C(x)H(y) clusters

The adsorption of a Cs atom on planar (C6H6 and C24H12) and nonplanar (C20H10 and C21H9) carbon clusters has been studied using the density-functional theory, with the local-density approximation and atomic pseudopotentials. Binding energies as a function of separation have been calculated for several configurations of the Cs atom on the different substrates. The adsorption on sites above the center of carbon rings is more stable than adsorption on top of carbon atoms and C-C bonds. In the case of the curved clusters, adsorption on the concave side is preferred compared to the convex side. The Cs bonding is stronger on the nonplanar clusters. The strength of the binding energy depends on two effects: the magnitude of the highest occupied molecular orbital-lowest unoccupied molecular orbital (LUMO) energy gap of the substrate, and the energy of the valence state of Cs relative to the LUMO of the substrate. Due to a favorable relative position of those two energy levels, charge transfer occurs from Cs to the two nonplanar clusters, and this provides an ionic contribution to the bonding. The analysis of the electronic density redistribution and of the local Fukui functions helps in the interpretation of the charge transfer and the reactivity.     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Comprehensive quantum chemical calculations and molecular docking analysis of uracil mustard by first principle

Uracil mustard belongs to the nitrogen mustard family and is primarily used in anticancer drugs. The research that follows, investigates many quantum chemical features such as the computation of global minimum energies with no negative wavenumber values using the Density Functional Theory (DFT) with Becke three functional and 6-311G (d, p)/6–311++G (d, p) basis sets. All the vibrational modes have been calibrated and justified in comparison to their experimental counterparts. Mustard's polarizability and hyperpolarizability components, Natural Bond Analysis (NBO), electronic properties, Fukui function analysis, various global parameters, Quantum Theory of Atoms In Molecule (QTAIM) analysis, ADMET analysis, and docking analysis have all been investigated using the same theory and basis sets, indicating its biochemical significance. The biological activity of the molecule is reported by using PASS software. The Full fitness score and binding affinity parameters are utilized to determine the binding strength with 6cq3 protein. The acidity of the title molecule is calculated in water solvent by polarizable continuum model (PCM) solvent effects (estimated in water). The HOMO, LUMO, and MESP plots are used to explore the nature of binding and surfaces. The Fukui functions are computed using Mulliken atomic charges for neutral atoms, cations, and anions. The Ultraviolet–visible (UV–vis) of the molecule is computed employing the TD-DFT method.