C library for topological study of the electronic charge density

The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid‐based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton–Raphson method (to find the critical points, where the gradient is null) and the Cash–Karp Runge–Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three‐dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. © 2012 Wiley Periodicals, Inc.     

Self-assembly mechanism based on charge density topological interaction energies

The packing interactions have been evaluated in the context of the self-assembly mechanism of crystal growth and also for its impacts on the aromaticity of the trimesate anion. The structure of ethylammonium trimesate hydrate (1) measured at 100 K and a charge density model, derived in part from theoretical structures, is reported. Theoretical structure factors were obtained from the geometry-optimized periodic wave function. The trimesic acid portion of 1 is fully deprotonated and participates in a variety hydrogen bonding motifs. Topological analysis of the charge density model reveals the most significant packing interactions and is then compared to a complementary analysis performed by the Hirshfeld surface method. The results presented herein demonstrate that in organic salt crystals the small structural motifs are most stable and once formed as stand-alone structures, may direct the self-assembly process. Moreover, when intermolecular interactions supported by the electrostatic forces are analyzed, the care must be taken with interpretation of the results of Hirshfeld surface analysis for organic salts crystals.     

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.     

Influence of electronic correlation in monoelectronic density in p-space

The radial molecular monoelectronic density and their orbital contributions have been calculated in the momentum space. For these purposes, densities for the ground state of several atoms and molecules, using a cc-pVTZ basis set at HF level, as well as some post-HF and DFT methods are computed. The difference between the radial monoelectronic density computed with each method and that using the HF wave function is used as a tool to study the influence of the electronic correlation in the momentum space. Densities obtained with post HF calculations show a similar behavior around p = 1.0 and 2.0, that are different from the DFT results. Radial momentum densities (p-densities) are more influenced by the electronic correlation than the exchange part of the DFT methods. CISD p-density is more affected than DFT p-density when the intermolecular distance increases. An analysis of the powers of moments calculated with different methods has been carried out. Contribution to the Serafin Fraga Memorial Issue.     

Substituent effects on the charge density in the formyl group

SCF wavefunctions with similar extended Gaussian bases for the series HCOX with X = H, OH (syn and anti), NH₂, CN, and F yield closely similar charge deformation density maps in the formyl region of all six molecules. The differences, measured by moments of partitioned atomic deformation densities, correlate almost linearly with the Hammett substituent parameters σ_I and σ_R of the several substituents X. However, systematic deviations, especially in the carbon fragment, suggest the need for modified values of the inductive parameters σ_I for the correlation of these molecular charge densities.     

The Laplacian of the electronic density at the valence-shell charge concentration (VSCC): A comparative study of effective core potential and full-electron calculations in Mo compounds. II

The effective core potential (ECP), using a basis set of different qualities, and ab initio full-electron (FE) calculations were carried out for MoS⁻²₄, MoO⁻²₄, and MoOCl₄ molecules. The topology of − ▿²p(r_cp) (the negative Laplacian of the charge density at its critical points) in the atomic valence shell was studied. Results clearly indicate that semicore (ECP2) approaches are able to reproduce, in a qualitative way, the topology of the Laplacian distribution with respect to those obtained by the FE method. Modifications of basis sets, such as introduction of polarization functions on the ligands, affect the electronic charge distribution (number of critical points in MoOCl₄) for FE as well as for ECP2 approaches. The ECP2 scheme predicts correctly the order of − ▿²p_x(r_cp) (X = O, S, Cl, Mo) in the valence shell; nevertheless, it fails in the relative magnitudes of − ▿²p_Mo(r_cp) between Mo compounds in respect to FE calculations. A scaling factor consistently improves the values of − ▿²p(r_cp) and p(r_cp), which are larger than those obtained with FE, particularly the − ▿²p(r_c) values. © 1996 John Wiley & Sons, Inc.     

First ionization potentials of amines and electronic effects in their radical cations

The possibility of application of linear free energy relationships for studying the effects of substituents on the first vertical ionization potentials of amines, I(n_N), was substantiated. The I(n_N) values depend on the inductive, resonance, and polarizability effects of substituents and are also affected by hyperconjugation. The _R ⁺ resonance parameters of substituents MR₃ (M = Si, Ge, Sn) and CH₂SiMe₃ bound to the N ^·+ radical cation center were calculated for the first time.     

On topological charge stabilization in heterocyclic compounds

According to Gimarc's principle of topological chargestabilization, heteroatomic molecules are topologically stabilized when more electronegative atoms are placed in those positions where atom-atom connectivity and the electron-filling level provide the highest electron charge in the reference hydrocarbon frame. Recently, we showed that the relative atomic moments of energy (the frequencies of atomic self-returning walks) in such uniform molecular skeletons are equal to the respective squared principal eigenvector coefficients. We show here that for conjugated heteroryclic molecules these partial atomic charges follow closely the patterns mirrored by topological charge stabilization and, by producing a nonuniform charge distribution in alternant molecules, enable the broader application of this principle to such molecules.Texas A&M university, Galveston, Texas. Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1011–1022,August, 1995. Original article submitted May 19, 1995.Dedicated to N. S. Zefirov for his important contributions to mathematical chemistry, as well as for his friendly help to those who need it.     

Three-center-two-electron and four-center-four-electron bonds. A study by electron charge density over the structure of methonium cations

We study the electronic density charge topology of CH(5)(+) species 1 (C(s)()), 2 (C(s)()), and 3 (C(2)(v)) at ab initio level using the theory of atoms in molecules developed by Bader. Despite the reports of previous studies concerning carbocationic species, the methane molecule is protonated at the carbon atom, which clearly shows its pentacoordination. In addition to the fact that hydrogen atoms in the methonium molecule behave in a very fluxional fashion and that the energy difference among the species 1, 2, and 3 are very low, is important to point out that two different topological situations can be defined on the basis of our study of the topology of the electronic charge density. Then, the species 1 and 2 present a three-center-two-electron (3c-2e) bond of singular characteristics as compared with other carbocationic species, but in the species 3, the absence of a 3c-2e bond is noteworthy. This structure can be characterized through the three bond critical points found, corresponding to saddle points on the path bonds between the C-H(2,3,5) that lie in the same plane. These nuclei define a four-center interaction where the electronic delocalization produced among the sigma(C-H) bonds provide a stabilization of the three C-H bonds involved in this interaction (the remaining two C-H bonds are similar to those belonging to the nonprotonated species). Our results show that bonding situations with a higher number of atom arrays are possible in protonated hydrocarbons.     

On the electronic structure of dihalogenophosphenium cations

The bonding properties of the dihalogenophosphenium cations, PX₂⁽⁺⁾, X = F, Cl, Br, I, are evaluated by relativistic effective core potential calculations with a DZP basis set. Our investigations include an analysis of the singlet-triplet energy separation in the cations and the determination of the relative cation and anion stabilities in the gas phase, via corresponding group transfer reactions. A comparison is made with other stabilized, previously reported low-coordinated π-bonded phosphorus cations.     

Reproducibility and transferability of topological data: experimental charge density study of two modifications of L-alanyl-L-tyrosyl-L-alanine

Two crystalline modifications of the tripeptide L-Ala-L-Tyr-L-Ala, which have different solvent molecules in the crystal structure (water and ethanol for modifications 1 and 2), were the subject of experimental charge density studies based on high resolution X-ray data collected at ultra-low temperatures of 9 K (1) and 20 K (2), respectively. The molecular structures and the intermolecular interactions were found to be rather similar in the two crystal lattices, so that this study allowed the reproducibility of the charge density of a given molecule in different (but widely comparable) crystalline environments to be examined. With respect to bond topological and atomic properties, the agreement between the two modifications of the title tripeptide was in the same range as found from the comparison with the previously reported results of tri-L-alanine. It follows that the reproducibility and transferability of quantitative topological data are comparable and that within the accuracy of experimental charge density work the replacement of the central amino acid residue L-Ala by L-Tyr has no significant influence, neither on bond nor on the atomic properties of the oligopeptide main chain. Intermolecular interactions in the form of hydrogen bonds were characterized quantitatively and qualitatively by topological criteria and by mapping the charge density distribution on the Hirshfeld surface.     

Electron density topological analysis of hydrogen bonding in glucopyranose and hydrated glucopyranose

Topological analysis of the electron density profiles and the atomic basin integration data for the most energetically favorable (4)C(1) and (1)C(4) conformers of beta-D-glucopyranose, calculated at the B3LYP/6-31+G(d), MPWlPW91/6-311+G(2d,p), and MP2/6-31+G(d) levels, demonstrates that intramolecular hydrogen bonding between adjacent ring OH groups does not occur in glucopyranose, given the need to demonstrate a bond critical point (BCP) of correct (3,-1) topology for such an interaction to be termed a hydrogen bond. On the other hand, pyranose ring OH groups separated by three, rather than just two, carbon atoms are able to form an intramolecular hydrogen bond similar in topological properties and geometry to that found for propane-1,3-diol. Vicinal, equatorial OH groups in the (4)C(1) conformer of glucopyranose are, however, able to form strong bidentate hydrogen bonds with water molecules in a cooperative manner, each water molecule acting simultaneously as both hydrogen bond donor and acceptor, and characterized by (3,-1) bond critical points with increased values for the electron density and the Laplacian of rho(r) compared to an isolated ethane-1,2-diol/water complex.     

The effect of electron correlation on the topological and atomic properties of the electron density distributions of molecules

The topological properties of the electron density and the properties of an atom in a molecule are calculated by means of second-order Møller-Plesset perturbation theory (MP2) and compared with the results of configuration interaction calculations (C12) which include all single and double substitutions from the Hartree-Fock reference configuration. A software package for analyzing the effects of electron correlation on the topological properties of the electron density of molecules is described. H₂CO is used to provide a numerical example and to indicate that the number of bond critical points is unaffected by the inclusion of electron correlation. Correlation leads to only a small shift in the positions of bond critical points and a small change in the electron density at bond critical points. It is further shown that the energy of an atom in a molecule can be calculated to an accuracy of 1 kcal/mol and the electron population of an atom to about 0.001e. A statistical method is used to show that the deviation of the MP2 correlation correction relative to the CI2 correlation correction for a variety of atomic properties is about 25%.     

Linear free energy correlation analysis on the electronic effects of Rh(II) carbene O-H insertion

The relative rate constants for the Rh(II)-catalyzed insertion of diazoacetone into the O-H bond have been measured through intermolecular competitions. The kinetic data were subjected to Hammett correlation analysis, and mechanistic implication of the results with respect to a stepwise vs a concerted O-H insertion pathway is discussed.     

Laplacian field of the effectively unpaired electron density: determination of many-body effects on electron distributions

This work carries out the study of the Laplacian field function of the electron density L(r) = -nabla2rho(r) splitted in two contributions rho(r) = rho(p)(r) + rho(u)(r), which correspond to the effectively paired and effectively unpaired electron densities, respectively. The visualization of the concentration and depletion of these fields and their spatial localization show no contribution of the effectively unpaired electrons to the conventional bonding among two centers, but the field -nabla2rho(u)(r) provides an interesting structure. We also study the reliability of the information contained in the partitioning of this electron density field function for describing nonclassical bondings as the three-center two-electron ones.     

An analysis of the topology of the electron charge density and the reactant–product electronic structure variation along the intrinsic reaction coordinate

In this work the topology of the electron charge density and the variations in the reactant and product electronic structures are analyzed along the Fukui intrinsic reaction coordinate (IRC). The systems studied are the ionic and the Menschutkin S_N2 reactions. This study is performed at ab initio RHF and MP2 levels, and density functional level, employing the B3LYP functional. The basis set in all cases is of split valence type and includes diffuse and polarization functions in nonhydrogen atoms 6‐31+G*. As a measure of the variations of reactant and product electronic structures, we calculate at the RHF level, the overlap integral between the total wavefunction and the wavefunction based on the reactant (or product) localized fragment orbitals. This integral can be interpreted, in Hilbert space, as the cosine of the angle between the vector representing the electronic structure of the molecule in each point of the IRC and that of reactant (or product) electronic structure. The calculated molecular properties were analyzed in light of the valence bond approach, and qualitative differences were noted depending on the property studied. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001