Topological analysis of the charge density of solids: bcc sodium and lithium

Studies of electronic structure of solids have concentrated mainly on Hilbert space properties such as energy-band structures and density of states, as well as some properties that can be reduced from them. Here, we report application of the topological charge density analysis to crystals. It is found that the pseudoatoms (or nonnuclear attractors, which are charge accumulations in nonnuclear regions), first found in Li₂, exist in solid lithium and sodium as well. In the former, the pseudoatoms form a connected network; in the latter, they are separated from one another. Although such networks obey the space group symmetry of the corresponding crystal, their existence is an intrinsic property of a specific crystal. © 1993 John Wiley & Sons, Inc.     

Topological analysis of the electronic charge density in the ethene protonation reaction catalyzed by acidic zeolite

In the present work, the distribution of the electronic charge density in the ethene protonation reaction by a zeolite acid site is studied within the framework of the density functional theory and the atoms in molecules (AIM) theory. The key electronic effects such as topological distribution of the charge density involved in the reaction are presented and discussed. The results are obtained at B3LYP/6-31G(**) level theory. Attention is focused on topological parameters such as electron density, its Laplacian, kinetic energy density, potential energy density, and electronic energy density at the bond critical points (BCP) in all bonds involved in the interaction zone, in the reactants, pi-complex, transition state, and alkoxy product. In addition, the topological atomic properties are determined on the selected atoms in the course of the reaction (average electron population, N(Omega), atomic net charge, q(Omega), atomic energy, E(Omega), atomic volume, v(Omega), and first moment of the atomic charge distribution, M(Omega)) and their changes are analyzed exhaustively. The topological study clearly shows that the ethene interaction with the acid site of the zeolite cluster, T5-OH, in the ethene adsorbed, is dominated by a strong O-H...pi interaction with some degree of covalence. AIM analysis based on DFT calculation for the transition state (TS) shows that the hydrogen atom from the acid site in the zeolitic fragment is connected to the carbon atom by a covalent bond with some contribution of electrostatic interaction and to the oxygen atom by closed shell interaction with some contribution of covalent character. The C-O bond formed in the alkoxy product can be defined as a weaker shared interaction. Our results show that in the transition state, the dominant interactions are partially electrostatic and partially covalent in nature, in which the covalent contribution increases as the concentration and accumulation of the charge density along the bond path between the nuclei linked increases.     

Approximate charge density localization of molecular orbitals

A NDO approximate procedure based on the indirect intrinsic ab initio localization method of von Niessen is developed. It is shown that only when the NDO approximations are introduced at the two electron level, expressions are obtained which are the charge density counterpart of those found in the approximate energy localization methods. The results of these two methods are quite similar both in the CNDO and INDO approximations. The indeterminacies observed in the CNDO localization for unsaturated systems and for molecules with two or three lone pairs on the same atom, are removed by localizing up to an INDO level. The approximate charge density localization is however computationally much easier than the approximate energy localization method and should be more appropriate in LMO studies of large organic molecules.     

Point charge models for molecular properties

A point charge model for the electron density of a molecule is proposed. The model preserves the correct total charge and dipole moment. It also gives the entire asymptotic part of the electrostatic potential. This becomes a very close approximation to the complete electrostatic potential outside the shell of the molecule. The use of the model to simplify various calculations is suggested.     

Topological analysis of the charge density response of a Ni4 cluster to a probe H2 molecule

Local density self-consistent field (SCF) discrete variationalX calculations are performed on a Ni₄ tetrahedron interacting with a probe H₂ molecule in special geometries. Optimized basis functions generated from the spherically averaged SCF potential are used. Topological charge-density analyses and binding energy calculations are used to study a portion of the energy surface for the approach of the H₂ molecule toward the Ni₄ tetrahedron. The effect of the H₂ molecule on Ni-Ni, Ni-H bonds and changes in the H-H covalent bond are investigated with the help of the field and various data at its critical points. The qualitative relationship between these data and the calculated binding energies is exploited.     

Topological analysis of complex molecular surfaces

An algorithm for the calculation of local and global curvatures of molecular surfaces is presented. The analysis is based on a surface representation as a set of points in 3-D space (“dotted surface” representation). The surface data are used to subdivide the surfac into domains with different curvatures. All domains are characterized by a reference point with a corresponding curvature profile specifiying the topological properties in its neighborhood. The curvature profiles provide a method for a systematic comparison of the shapes of different molecules. Such a strategy is important for the treatment of molecular recognition problems. The enzyme-inhibitor complex trypsin/BPTI was chosen to demonstrate the scopes of the method.     

Topology of charge density of flucytosine and related molecules and characteristics of their bond charge distributions

The molecular charge distribution of flucytosine (4-amino-5-fluoro-2-pyrimidone), uracil, 5-fluorouracil, and thymine was studied by means of density functional theory calculations (DFT). The resulting distributions were analyzed by means of the atoms in molecules (AIM) theory. Bonds were characterized through vectors formed with the charge density value, its Laplacian, and the bond ellipticity calculated at the bond critical point (BCP). Within each set of C=O, C-H, and N-H bonds, these vectors showed little dispersion. C-C bonds formed three different subsets, one with a significant degree of double bonding, a second corresponding to single bonds with a finite ellipticity produced by hyperconjugation, and a third one formed by a pure single bond. In N-C bonds, a decrease in bond length (an increase in double bond character) was not reflected as an increase in their ellipticity, as in all C-C bonds studied. It was also found that substitution influenced the N-C, C-O, and C-C bond ellipticity much more than density and its Laplacian at the BCP. The Laplacian of charge density pointed to the existence of both bonding and nonbonding maxima in the valence shell charge concentration of N, O, and F, while only bonding ones were found for the C atoms. The nonbonding maxima related to the sites for electrophilic attack and H bonding in O and N, while sites of nucleophilic attack were suggested by the holes in the valence shell of the C atoms of the carbonyl groups.     

常压下能量与电荷在分子间的传递机制

离子源是质谱仪的心脏,制备待测物的离子是质谱分析的首要前提.如何有效地电离含有复杂基体的实际样品中的痕量待测物分子是制约实际样品直接质谱分析的重要瓶颈.本文提出了用电子云模型帮助理解能量与电荷传递和中性分子电离过程的关系,从分子的基本物性参数、能量耦合方式等角度讨论了能量与电荷在不同相态、组成和维度的复杂基体样品分子间传递的过程,着重阐述了能荷传递过程中分子的电子云变化规律及其对分子电离的影响,并简要讨论了这些影响在质谱分析中的应用.     

Prediction of densities for solid energetic molecules with molecular surface electrostatic potentials

The densities of high energetic molecules in the solid state were calculated with a simplified scheme based on molecular surface electrostatic potentials (MSEP). The MSEP scheme for density estimation, originally developed by Politzer et al., was further modified to calculate electrostatic potential on a simpler van der Waals surface. Forty-one energetic molecules containing at least one nitro group were selected from among a variety of molecular types and density values, and were used to test the suitability of the MSEP scheme for predicting the densities of solid energetic molecules. For comparison purposes, we utilized the group additivity method (GAM) incorporating the parameter sets developed by Stine (Stine-81) and by Ammon (Ammon-98 and -00). The absolute average error in densities from our MSEP scheme was 0.039 g/cc. The results based on our MSEP scheme were slightly better than the GAM results. In addition, the errors in densities generated by the MSEP scheme were almost the same for various molecule types, while those predicted by GAM were somewhat dependent upon the molecule types.     

Electron (charge) density studies of cellulose models

Introductory material first describes electron density approaches and demonstrates visualization of electron lone pairs and bonding as concentrations of electron density. Then it focuses on the application of Bader’s Quantum Theory of Atoms-in-Molecules (AIM) to cellulose models. The purpose of the work is to identify the various interactions that stabilize cellulose structure. AIM analysis aids study of non-covalent interactions, especially those for which geometric criteria are not well established. The models were in the form of pairs of cellotriose molecules, methylated at the O1 and O4 ends. Based on the unit cell of cellulose Iβ, there were corner–corner, and center–center pairs that correspond to (200) sheets, and corner–center pairings that corresponded to (1–10) and (110) stacks. AIM analysis (or charge-density topology analysis) was applied before and after minimization in vacuum and in continuum solvation. Besides the conventional O–H···O hydrogen bonds, all of which were known from geometric criteria, C–H···O hydrogen bonds (some previously reported), and some O···O and H···H interactions were found. Non-covalent bonds in the (200) sheets were maintained in all calculations with the exception of a weak, bifurcated O6–H···O2′′ bond that was not found in the corner–corner pair model and did not survive minimization. Nor did the O6···O4 interactions on the reducing ends of the triosides. Pairs of molecules along the (110) plane had an equal number (12) of non-covalent bonds compared to the pairs along the (1–10) plane, but the AIM parameters indicated the bonds between the pairs in the (110) plane were weaker. Intra-molecular O–H···O hydrogen bonds survived in these minimized pairs, but the relative chain alignments usually did not.     

Probing the weakest bond and the cleavage of p‐chlorobenzaldehyde diperoxide energetic molecule via quantum chemical calculations and theoretical charge density analysis

A high‐level ab initio Hartree‐Fock/Møller‐Plesset 2 and density functional theory quantum chemical calculations were performed on p‐chlorobenzaldehyde diperoxide energetic molecule to understand its bond topological, electrostatic, and energetic properties. The optimized molecular geometry for the basis set 6‐311G** exhibit chair diperoxide ring and planar aromatic side rings. Although the diperoxide ring bear same type of side rings, surprisingly, both the rings are almost perpendicular to each other, and the dihedral angle is 96.1°. The MP2 method predicts the O? O bond distance as ～1.466 Å. The charge density calculation reveals that the C? C bonds of chlorobenzaldehyde ring have rich electron density and the value is ～2.14 e Å^?3. The maximum electron density of the O? O bonds does not lie along the internuclear axes; in view of this, a feeble density is noticed in the ring plane. The high negative values of laplacian of C? C bonds (approximately ?22.4 e Å^?5) indicate the solidarity of these bonds, whereas it is found too small (approximately ?1.8 e Å^?5 for MP2 calculation) in O? O bonds that shows the existence of high degree of bond charge depletion. The energy density in all the C? C bonds are found to be uniform. A high electronegative potential region is found at the diperoxide ring which is expected to be a nucleophilic attack area. Among the bonds, the O? O bond charge is highly depleted and it also has high bond kinetic energy density; in consequence of this, the molecular cleavage is expected to happen across these bonds when the material expose to any external stimuli such as heat or pressure treatment. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Surface migration of branched molecules: analysis of energetic and entropic factors

We have introduced energetic factors into the response theory developed by Wu and Fredrickson [Macromolecules 29, 7919 (1996)] to predict the enrichment of branched molecules due to architectural effects at surfaces. This development simultaneously increases the utility of the theory for guiding experimental investigations, and makes possible a rigorous assessment of theoretical predictions in careful studies of isotopically labeled linear/branched species binary blends at surfaces. For example, the introduction of energetic factors allows us to predict the existence of a crossover molecular weight, below which an energetically unfavorable species at a surface can be enriched entirely due to architecture. For binary blends of linear chains, the degree of polymerization (Kuhn) of the energetically unfavorable species at the crossover point is r(c) approximately =2U(e)/DeltaU(s). Here, U(e) is the attraction of chain ends towards the surface and DeltaU(s) is the difference in the interaction potential of main chain segments to the surface due to chemical differences and/or isotopic labeling. We also show that surface segregation of an additive in a host polymer due to architectural effects alone is significantly enhanced as the spinodal temperature of a branched/linear blend is approached. Detailed comparisons of the modified response theory with lattice simulations are used to evaluate the theory and to determine the limits of its applicability.     

Topological electron density analysis of phosphines,phosphaalkenes and phosphaalkynes

A general survey of the topological properties of various phospines, phosphaalkenes, and phosphaalkynes is presented. Fifteen compounds containing carbon-phosphorus single, aromatic, double, and triple bonds were optimized at the Hartree-Fock-self-consistent field (HF-SCF) level using the 3-21G, 3-21G(*) and 6-31G* basis sets. Inclusion of d-orbitals was necessary to obtain reasonable structures. The electron densities of these compounds were analyzed using the topological method of Bader, revealing a number of trends. The value of the electron density at the P C bond critical point correlates strongly with the bond distance and bond order. Integrated electron populations correlate with coordination number. The integrated charge indicates a strongly polarized C P bond in all compounds. Comparisons with five C N compounds are made.     

Prelude to molecular dynamics: Topography-driven gaussian charge models

A new strategy to develop Gaussian charge models (GCMs) for molecules like ammonia, water, ethene, hydrogen sulfide, formaldehyde and benzene is presented. These molecular models comprising of positive point charges and negative Gaussian charge distributions (GCDs), which represent nuclei and continuous electron charge distribution, are found to correctly represent the ab initio Molecular Electrostatic Potential (MESP) and reproduce its essential topographical features of corresponding molecules. The models use optimized parameters: positive charges at nuclei, negative charges on GCDs, Gaussian exponent and centers. The Potential Energy Surface (PES) of water dimer has been explored using water GCMs. A good agreement has been found between PES obtained using GCMs and wave function. The Gaussian models correctly predict structure of benzene-water complex. It is thus recommended to use GCMs for molecular dynamic simulations.     

Topological analysis and charge density studies of an alpha-diimine macrocyclic complex of cobalt(II)--a combined experimental and theoretical study

A combined experimental and theoretical study of the paramagnetic [Co(II)(C12H20N8)(H2O)2] x 2 ClO4 complex was made on the basis of the electron density distribution and topological analysis. Accurate single-crystal diffraction data were measured on a suitable crystal with Mo(K alpha) radiation at 125 K. The CoII ion is coordinated in a square bipyramidal fashion with four imino nitrogen atoms at the equatorial plane and two water molecules at the axial positions. The hydrogen-bonding interaction at 125 K between the coordinated water molecule and the ClO(4)(-) ion makes the space group different from that at 298 K. Parallel MO calculations were made at UHF and DFT/UB3LYP. The agreement between experiment and theory is reasonably good. The chemical bonding characterization is presented in terms of the topological properties associated with bond critical points and the natural bond orbital (NBO) analysis as well. The Co-N(imino) and Co-O(water) bonds are dative bonds, where the lone-pair electrons of N or O serve as a -donor; however, a certain covalent character is identified in the Co-N(imino) bond. A delocalized C-N, N-N pi-bond model is proposed. The d-orbital energies of Co in this complex are such that E(d(xz)) is approximately equal to E(d(yz)) is approximately equal to E(dx(2-y2)) < E(d(z2)) < E(d(xy)); notice that d(xy) and d(z2) are d(sigma) orbitals in this case. The Co(II) ion is in a low-spin d7 state with the singly occupied d(z2) orbital. The asphericity in electron density at Co and Cl nuclei is nicely demonstrated by the Laplacian of electron density. The envelope plot of the isovalue Laplacian surface around the nucleus gives the exact shape of such asphericity. The isovalue Laplacian surfaces of these two nuclei show significantly different VSCC character in both experimental and theoretical results.     

Site charge models for molecular electrostatic potentials of cycloalkanes and tetrahedrane

The molecular structures of cycloalkanes (from cyclopropane to cyclodecane) and tetrahedrane were optimized at the Hartree–Fock/6–31G** level and their molecular electric potentials (MEPs) were calculated using a geodesic grid. The MEPs were fitted using net atomic charges and several site charge models. The net atomic charge model gave very poor fits to the MEPs in every case. A model with additional methylene bisector charge sites, similar to one successfully used previously for linear alkanes, greatly improved the fits to the MEPs of these cycloalkanes. The MEPs of the highly strained molecules cyclopropane and tetrahedrane were further studied using ring center and displaced bond charge sites. The fitting of the MEP of cyclopropane was consistent with a banana bond model with asymmetrically displaced electron density in the C C bonds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 579–585, 1999     

Topological analysis of the electron density distribution in perturbed systems. I. Effect of charge on the bond properties of hydrogen fluoride

Within the framework of the molecular orbital (MO) theory, the addition of one electron to the 4sigma antibonding orbital of the neutral (F...H) system or the removal of one electron from its pi nonbonding orbitals, leading to (F...H)- and to (F...H)+, has permitted the investigation of these charge perturbations on the bond properties of the hydrogen fluoride molecule by using the topological analysis of rho(r). For (F...H), (F...H)-, and (F...H)+, the topological and energetic properties calculated at the F...H bond critical point (BCP) have been related to the 3sigma bonding molecular orbital (BMO) distribution, as this orbital is the main contributor to rho(r) at the interatomic surface. The analysis has been carried out at several F...H internuclear distances, ranging from 0.8 to 3.0 A. As far as the BMO distribution results from its interaction with the average Coulomb and exchange potential generated by the charge filling the other MOs, and in particular by the pi and 4sigma electrons, the comparison between the BCP properties calculated for the charged systems and those corresponding to the neutral one permits the interpretation of the differences in terms of the charge perturbation on BMO. Along with the BCP properties of (F...H), (F...H)-, and (F...H)+, the interaction energy magnitudes of these systems have been also calculated within the same range of internuclear distances, indicating that the applied perturbations do not break the F-H bond but soften it, giving rise to the stable species (F-H)- and (F-H)+. Comparing the three systems at their equilibrium geometries, the most stable configuration, which corresponds to the unperturbed (F...H) system, shows the highest quantity and the most locally concentrated charge density distribution, along with the largest total electron energy density magnitude, at the interatomic surface as a consequence of the BMO contraction toward the fluorine nucleus in (F...H)+ and of the BMO expansion toward both nuclei in (F...H)-. On the other hand, if the comparison is carried out at the equilibrium distance of (F...H) (d(eq)0), this one exhibits both the smallest total energy density magnitude and the largest quantity of bonding charge at the interatomic surface. Hence, being the signature of the most stable configuration, the characteristic magnitudes of the neutral system rho(d(eq)0), inverted triangle2 rho(d(eq)0), and H(d(eq)0) appear as boundary conditions at the interatomic surface of its unperturbed and relaxed electron distribution.