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.     

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     

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     

Density functional study of ion hydration for the alkali metal ions (Li+, Na+, K+) and the halide ions (F-, Br-, Cl-)

We performed first principles density functional calculations to study the effect of monovalent ions M+ (M = Li,Na,K) and A- (A = F,Cl,Br) in water with the aim of characterizing the local molecular properties of hydration. For this reason, several ion-water clusters, up to five or six water molecules were considered; such structures were optimized, and the Wannier analysis was then applied to determine the average molecular dipole moment of water. We found that with an increasing number of water molecules, the molecular polarization is determined by the water-water interaction rather than the water-ion interaction, as one would intuitively expect. These results are consistent with those obtained in previous density functional calculations and with other results obtained by employing classical polarizable water models. The main message of this work is that as one increases the number of molecules the average dipole moment of all water molecules and the ones in the first shell tends to the same value as the average of a similar sized cluster of pure water. This supports the use of nonpolarizable classical models of water in classical atomistic simulations.     

Nonlinear pair population analysis: The study of basis‐set dependence

The nonlinear pair population analysis recently introduced as a new means of visualization of bonding in molecules with complex bonding patterns was tested for the assumed sensitivity of calculated populations to the quality of the basis set. The testing was performed on a series of several simple molecules ranging from systems well represented by the classical Lewis model of localized two‐center two‐electron (2c–2e) bonds to electron‐deficient boranes containing three‐center bonding. It has been shown that even if this basis‐set sensitivity is slightly greater than for the closely related linear population analysis the dependence is not important enough to question the usefulness of this new approach for the analysis and visualization of bonding molecular systems. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 127–137, 1999     

Accurate prediction of proton chemical shifts. I. Substituted aromatic hydrocarbons

Forty‐five proton chemical shifts in 14 aromatic molecules have been calculated at several levels of theory: Hartree–Fock and density functional theory with several different basis sets, and also second‐order Møller–Plesset (MP2) theory. To obtain consistent experimental data, the NMR spectra were remeasured on a 500 MHz spectrometer in CDCl₃ solution. A set of 10 molecules without strong electron correlation effects was selected as the parametrization set. The calculated chemical shifts (relative to benzene) of 29 different protons in this set correlate very well with the experiment, and even better after linear regression. For this set, all methods perform roughly equally. The best agreement without linear regression is given by the B3LYP/TZVP method (rms deviation 0.060 ppm), although the best linear fit of the calculated shifts to experimental values is obtained for B3LYP/6‐311++G**, with an rms deviation of only 0.037 ppm. Somewhat larger deviations were obtained for the second test set of 4 more difficult molecules: nitrobenzene, azulene, salicylaldehyde, and o‐nitroaniline, characterized by strong electron correlation or resonance‐assisted intramolecular hydrogen bonding. The results show that it is possible, at a reasonable cost, to calculate relative proton shieldings in a similar chemical environment to high accuracy. Our ultimate goal is to use calculated proton shifts to obtain constraints for local conformations in proteins; this requires a predictive accuracy of 0.1–0.2 ppm. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1887–1895, 2001     

Holographic electron density shape theorem and its role in drug design and toxicological risk assessment

Each complete, boundaryless molecular electron density is fully determined by any nonzero volume piece of the electron density cloud. This inherent feature of molecules, called the "holographic" property of molecular electron densities, provides a strong foundation for the local, quantum chemical shape analysis of various functional groups, pharmacophores, and other local molecular moieties. A proof is presented for the relevant molecular shape theorem, the "holographic electron density shape theorem", and the role of this theorem in quantum chemical, quantitative shape-activity relations (QShAR) is discussed. The quantum chemical methods of molecular shape analysis can be extended to ab initio quality electron densities of macromolecules, such as proteins, as well as to local molecular moieties, such as functional groups or pharmacophores, based on the transferability and additivity of local, fuzzy density fragments and the associated local density matrixes within the framework of the ADMA (Adjustable Density Matrix Assembler) approach. In addition to new results on chemical bonding and the development of macromolecular force methods, the new methodologies are also applicable to QShAR studies in computer-aided drug discovery and in toxicological risk assessment.     

Crystallographic and first-principles density functional theory study on the structure,noncovalent interactions,and chemical reactivity of 1,5-benzodiazepin-2-ones derivatives

The present work arose out of a desire to fundamentally understand the molecular geometry, weak interactions, electron density delocalization, and chemical reactivity features of 1,5-benzodiazepines-containing family. Herein, a complete X-ray crystallographic study, supported by trustworthy sets of computational approaches, has been reported for two organic crystals. Quantifying intramolecular and intermolecular interactions by Hirshfeld-Becke surfaces analysis conjointly with noncovalent interaction-reduced density gradient topological study revealed that supramolecular assemblies are stabilized by N-H ^… O (inter) and O-H ^… N (intra) hydrogen bonds, Cg ^… Cg (π ^… π) and C-H(O) ^… π intercontacts, as well as Van der Waals interactions and steric effects. The long-range-corrected functional wB97XD, which uses Grimme's D2 dispersion model, seems to be just right for our systems. The quantum theory of atoms in molecules analysis confirms that both significant O1-H1…N1 and N2-H2A…O2 H-bonds are weak and electrostatic in nature. Furthermore, global reactivity indices computed via the conceptual density functional theory framework allows these molecules to be classified as moderate electrophiles and marginal nucleophiles. The active sites favorable for nucleophilic/electrophilic attacks were also predicted based on local Parr functions. Finally, a comparative evaluation on the aromaticity character and π-π stacking ability has been done for different (pseudo) rings.     

Generalized chirality and symmetry deficiency

Some of the elementary properties of molecular electron densities are studied from the perspectives of generalizations of symmetry, symmetry deficiency, and in particular, chirality. A simple, information‐theoretical proof of the Hohenberg–Kohn theorem is discussed, and the information contents of local and global molecular electron densities are compared using a formulation of quantum chemistry on a compact manifold. One result, the “holographic electron density theorem”, involving a compactification step combined with analytic continuation, gives a tool for comparing local and global symmetry properties. The compact manifold quantum chemistry approach leads to a precise statement on the role of local molecular regions in determining global properties of complete, boundaryless molecules, resulting in constraints on their symmetry, chirality, and other types of symmetry deficiencies. A special similarity measure, the SLT measure, is used for generalized density domain comparisons, suitable in general for the comparison of semilattices with a tree structure. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Site‐Specific Investigation of the Steady‐State Kinetics and Dynamics of the Multistep Binding of Bile Acid Molecules to a Lipid Carrier Protein

The investigation of multi‐site ligand–protein binding and multi‐step mechanisms is highly demanding. In this work, advanced NMR methodologies such as 2D ¹H–¹⁵N line‐shape analysis, which allows a reliable investigation of ligand binding occurring on micro‐ to millisecond timescales, have been extended to model a two‐step binding mechanism. The molecular recognition and complex uptake mechanism of two bile salt molecules by lipid carriers is an interesting example that shows that protein dynamics has the potential to modulate the macromolecule–ligand encounter. Kinetic analysis supports a conformational selection model as the initial recognition process in which the dynamics observed in the apo form is essential for ligand uptake, leading to conformations with improved access to the binding cavity. Subsequent multi‐step events could be modelled, for several residues, with a two‐step binding mechanism. The protein in the ligand‐bound state still exhibits a conformational rearrangement that occurs on a very slow timescale, as observed for other proteins of the family. A global mechanism suggesting how bile acids access the macromolecular cavity is thus proposed.     

Structure investigation of mesalazine drug using thermal analyses,mass spectrometry,DFT calculations,and NBO analysis

Mesalazine (MZ) drug has been used for several decades as a primary treatment for inflammatory bowel diseases. The drug was investigated using thermal analysis (TA) measurements and electron impact mass spectral fragmentation at 70 and 15 eV of electron energy. The optimum molecular geometry and the total energy of the neutral and the positively charged MZ molecules were calculated by density functional theory method with 6-311++G(d,p) basis sets. Stability of the molecules arising from hyperconjugative interactions, charge delocalization, and the natural atomic charges has been analyzed using natural bond orbital analysis. In electron ionization mass spectrometry, the primary rupture is due to successive loss of H₂O (OH from carboxyl and H from phenolic OH of the ring) and CO of the acetyl group. Thermogravimetric results have revealed two stages of mass loss at 75.3 and 25.3 % in ranges 225–350 and 350–650 °C, respectively. The first one may be due to successive losses of different groups or molecules with fast rate of decomposition. A comparison between MS and TA helped in selection the proper pathway representing the fragmentation mechanism of this drug.     

Computational studies of the corrosion‐inhibition efficiency of iron by triazole surfactants

The corrosion‐inhibition efficiency of N‐decyl‐1,2,4‐triazole, N‐undecyl‐1,2,4‐triazole, and N‐dodecyl‐1,2,4‐triazole surfactants and the corresponding protonated molecules have been studied computationally using density functional theory and second‐order Møller–Plesset calculations. Corrosion‐inhibition properties and the strength of the affinity of the iron‐surfactant molecules were estimated by using an appropriate cluster model. The iron‐surfactant complexes were constructed by attaching the triazole ring to the iron surface modeled by one and five iron atoms, respectively. Relations between molecular properties and corrosion‐inhibition efficiency were determined by using linear regression and quantitative structure–activity relationship (QSAR). The QSAR analysis yielded significant correlations between the corrosion‐inhibition activity of the studied molecules with molecular properties such as the highest occupied molecular orbital, the lowest unoccupied molecular orbital, dipole moments (μ), and the total atomic charges. Fukui indexes were also calculated for assessing correlations between them and experimental corrosion‐inhibition efficiencies. Solvent effects were investigated by using the polarized continuum model. The effects of the acidity medium and the local reactivity of the triazole derivatives with iron were also analyzed. The calculated binding energy of 276 kJ/mol for the Fe₅‐N‐dodecyl‐1,2,4‐triazole cluster shows that the surfactant molecules bind strongly to iron surfaces, which is in agreement with experimental data. © 2012 Wiley Periodicals, Inc.     

Theoretical study of Cu(I)Y zeolite: structure and electronic properties

The structural and electronic properties of the accessible Cu(I) site of a faujasite-type zeolite have been studied, by use of large cluster models and a density functional theory-based methodology. We demonstrate that the local ideal C(3) symmetry of the Cu(I) site II is broken. The Cu(I) cation is bonded to the zeolite framework by one bond of about 2.26 A and two shorter ones of 2.07 A. We demonstrate that only one cation position exists at this site. This result is also confirmed by a molecular electrostatic potential analysis. We show that local properties at site II, as well as the global properties of the solid (frontier orbitals), do not depend on the Al and cation distribution and only slightly on the cocation nature. Taking into account the present results and well-known experimental data, we propose that specific catalytic behaviors are correlated with local response properties, such as the local acid strength or, in other reactions, specific local architecture or confinement.     

Structural and dynamic features of water and amorphous ice

Structural properties and microscopic dynamics of water and amorphous ice have been studied by the molecular dynamics method. It has been found that the distribution function of the tetrahedricity parameter exhibits two ranges, which correspond to local molecular formations with low and high degrees of tetrahedricity. The number of molecular clusters with a high degree of tetrahedricity grows as temperature decreases. It has been shown that the vibrational density of states comprises two vibrational modes. A low-frequency vibrational mode strongly depends on pressure and is almost independent of temperature, while a high-frequency mode is relevant to the pressure-independent heat motion of molecules. The geometric criterion of hydrogen bonds has been used to evaluate their continuous lifetime as depending on temperature for molecules with different coordination values. The average lifetime of a hydrogen bond substantially depends on the coordination of molecules, with the temperature dependence of the coordination obeying the activation dynamics.     

Molecular dynamics study of structural and thermodynamic characteristics of nanodroplets of simple fluid

Equilibrium configurations of Lennard-Jones nanodroplets composed of 10–15000 spherically symmetric molecules placed in the center of a spherical container are studied at constant temperature by the molecular dynamics method. The distribution of local density is found and size dependences of density in the center of droplet, first coordination number, and energy surface tension coinciding for equimolecular dividing surface with specific excess free energy of droplet are studied. Radial distribution function is also determined. It is established that the passage of structural characteristics to their macroscopic values is observed for droplets containing as little as about 300 molecules, while, for energy surface tension, analogous passage for energy surface tension occurs for droplets containing 700–6000 molecules.     

The localized electrons detector as an ab initio representation of molecular structures

The local single particle momentum is proposed as a localized‐electrons detector (LED) that provides a direct three‐dimensional representation of bonding interactions in molecules. It is given exclusively in terms of the electron density and its gradient. We show that the graphical representation of bonding interactions given by LED is consistent with the local curvatures of the electron density as given by the eigenvalues of the Hessian matrix, according to a local symmetry classification of the critical points here introduced. LED consistently complements the topological analysis of the electron density given by the quantum theory of atoms in molecules, by providing a graphical representation of the symmetry of the bonding interactions in molecular systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110:2418–2425, 2010     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.