To What Extent are “Atoms in Molecules” Structures of Hydrocarbons Reproducible from the Promolecule Electron Densities?

The “atoms in molecules” structures of 225 unsubstituted hydrocarbons are derived from both the optimized and the promolecule electron densities. A comparative analysis demonstrates that the molecular graphs derived from these two types of electron densities at the same geometry are equivalent for almost 90 % of the hydrocarbons containing the same number and types of critical points. For the remaining 10 % of molecules, it is demonstrated that by inducing small perturbations, through the variation of the used basis set or slight changes in the used geometry, the emerging molecular graphs from both densities are also equivalent. Interestingly, the (3, ?1) critical point between two “non‐bonded” hydrogen atoms, which triggered “H?H bonding” controversy is also observed in the promolecule densities of certain hydrocarbons. Evidently, the topology of the electron density is not dictated by chemical bonds or strong interactions and deformations induced by the interactions of atoms in molecules have a quite marginal role, virtually null, in shaping the general traits of the topology of molecular electron densities of the studied hydrocarbons, whereas the key factor is the underlying atomic densities.     

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     

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     

Blue‐shifted and red‐shifted hydrogen bonds: Theoretical study of the CH3CHO· · ·HNO complexes

The blue‐shifted and red‐shifted H‐bonds have been studied in complexes CH₃CHO…HNO. At the MP2/6‐31G(d), MP2/6‐31+G(d,p) MP2/6‐311++G(d,p), B3LYP/6‐31G(d), B3LYP/6‐31+G(d,p) and B3LYP/6‐311++G(d,p) levels, the geometric structures and vibrational frequencies of complexes CH₃CHO…HNO are calculated by both standard and CP‐corrected methods, respectively. Complex A exhibits simultaneously red‐shifted C? H…O and blue‐shifted N? H…O H‐bonds. Complex B possesses simultaneously two blue‐shifted H‐bonds: C? H…O and N? H…O. From NBO analysis, it becomes evident that the red‐shifted C? H…O H‐bond can be explained on the basis of the two opposite effects: hyperconjugation and rehybridization. The blue‐shifted C? H…O H‐bond is a result of conjunct C? H bond strengthening effects of the hyperconjugation and the rehybridization due to existence of the significant electron density redistribution effect. For the blue‐shifted N? H…O H‐bonds, the hyperconjugation is inhibited due to existence of the electron density redistribution effect. The large blue shift of the N? H stretching frequency is observed because the rehybridization dominates the hyperconjugation. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Theoretical study of the red‐ and blue‐shifted hydrogen bonds of nitroxyl and acetylene dimers

Ab initio molecular orbital and density functional theory (DFT) in conjunction with different basis sets calculations were performed to study the C? H…O red‐shifted and N? H…π blue‐shifted hydrogen bonds in HNO? C₂H₂ dimers. The geometric structures, vibrational frequencies and interaction energies were calculated by both standard and counterpoise (CP)‐corrected methods. In addition, the G3B3 method was employed to calculate the interaction energies. The topological and natural bond orbital (NBO) analysis were investigated the origin of N? H…π blue‐shifted hydrogen bond. From the NBO analysis, the electron density decrease in the σ* (N? H) is due to the significant electron density redistribution effect. The blue shifts of the N? H stretching frequency are attributed to a cooperative effect between the rehybridization and electron density redistribution. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Experimental and Theoretical Charge Density Study on Di‐2‐pyrazylamine (Hdpza) Molecule in Crystal

Electron density distribution of Di‐2‐pyrazylamine ( Hdpza ) is studied both by single‐crystal X‐ray diffraction method at 100K and theoretical calculation. Structural determination reveals that Hdpza molecules crystalize in a syn‐anti conformation with an intramolecular C? H?N hydrogen bond between two pyrazine rings and then gather together via two intermolecular N? H?N and C? H?N hydrogen interaction and π? π stacking interaction between pyrazine rings. Charge density analysis is made in terms of deformation density (Δπ), Laplacian distribution and topological analysis of total electron density based on multipole model and theoretical calculation. The agreement between experiment and theory is good. The topological properties at bond critical points of C? C and C? N bonds reveal a covalent bond character, and those of intermolecular interactions, such as hydrogen bonds and π? π stacking interactions, reveal a closed‐shell interaction. The potential energy curve of Hdpza molecule shows that the syn‐anti conformation is the most stable one (global minima) than the other two of syn‐syn and anti‐anti conformations.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

New insight into the electronic structure of iron(IV)‐oxo porphyrin compound I. A quantum chemical topological analysis

The electronic structure of iron‐oxo porphyrin π‐cation radical complex Por^·+Fe^IV?O (S? H) has been studied for doublet and quartet electronic states by means of two methods of the quantum chemical topology analysis: electron localization function (ELF) η(r) and electron density ρ(r). The formation of this complex leads to essential perturbation of the topological structure of the carbon–carbon bonds in porphyrin moiety. The double C?C bonds in the pyrrole anion subunits, represented by pair of bonding disynaptic basins V_i=1,2(C,C) in isolated porphyrin, are replaced by single attractor V(C,C)_i=1–20 after complexation with the Fe cation. The iron–nitrogen bonds are covalent dative bonds, N→Fe, described by the disynaptic bonding basins V(Fe,N)_i=1–4, where electron density is almost formed by the lone pairs of the N atoms. The nature of the iron–oxygen bond predicted by the ELF topological analysis, shows a main contribution of the electrostatic interaction, Fe^δ+···O^δ?, as long as no attractors between the C(Fe) and C(O) core basins were found, although there are common surfaces between the iron and oxygen basines and coupling between iron and oxygen lone pairs, that could be interpreted as a charge‐shift bond. The Fe? S bond, characterized by the disynaptic bonding basin V(Fe,S), is partially a dative bond with the lone pair donated from sulfur atom. The change of electronic state from the doublet (M = 2) to quartet (M = 4) leads to reorganization of spin polarization, which is observed only for the porphyrin skeleton (?0.43e to 0.50e) and S? H bond (?0.55e to 0.52e). © 2012 Wiley Periodicals, Inc.     

Interaction of the important species HNO and HFSO2 in the atmosphere: Theoretical study of the N?H and S?H blue‐shifted hydrogen bonds

Ab initio molecular orbital and density functional theory (DFT) in conjunction with different basis sets calculations were performed to study the N? H…O and S? H…O blue‐shifted H‐bonds in the HNO…HFSO₂ complex. The geometric structures, vibrational frequencies, and interaction energies were calculated by both standard and CP‐corrected methods. Natural bond orbital (NBO) analysis was used to investigate the origin of blue‐shifted H‐bonds, showing that the decrease in the σ*(N? H) and σ*(S? H) is due to the electron density redistribution effect. The structure reorganization effect on the blue‐shifted hydrogen bonds was discussed in detail. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

A Combined Experimental and Theoretical Electron Density Study of Intra‐ and Intermolecular Interactions in Thiourea S,S‐Dioxide

The thiourea S,S‐dioxide molecule is recognized as a zwitterion with a high dipole moment and an unusually long C? S bond. The molecule has a most interesting set of intermolecular interactions in the crystalline state—a relatively strong O???H? N hydrogen bond and very weak intermolecular C???S and N???O interactions. The molecule has C_s symmetry, and each oxygen atom is hydrogen‐bonded to two hydrogen atoms with O???H? N distances of 2.837 and 2.826 Å and angles of 176.61 and 158.38°. The electron density distribution is obtained both from Xray diffraction data at 110 K and from a periodic density functional theory (DFT) calculation. Bond characterization is made in terms of the analysis of topological properties. The covalent characters of the C? N, N? H, C? S, and S? O bonds are apparent, and the agreement on the topological properties between experiment and theory is adequate. The features of the Laplacian distributions, bond paths, and atomic domains are comparable. In a systematic approach, DFT calculations are performed based on a monomer, a dimer, a heptamer, and a crystal to see the effect on the electron density distribution due to the intermolecular interactions. The dipole moment of the molecule is enhanced in the solid state. The typical values of ρ_b and H_b of the hydrogen bonds and weak intermolecular C???S and N???O interactions are given. All the interactions are verified by the location of the bond critical point and its associated topological properties. The isovalue surface of Laplacian charge density and the detailed atomic graph around each atomic site reveal the shape of the valence‐shell charge concentration and provide a reasonable interpretation of the bonding of each atom.     

An Excursion from Normal to Inverted C?C Bonds Shows a Clear Demarcation between Covalent and Charge‐Shift C?C Bonds

What is the nature of the C? C bond? Valence bond and electron density computations of 16 C? C bonds show two families of bonds that flesh out as a phase diagram. One family, involving ethane, cyclopropane and so forth, is typified by covalent C? C bonding wherein covalent spin‐pairing accounts for most of the bond energy. The second family includes the inverted bridgehead bonds of small propellanes, where the bond is neither covalent nor ionic, but owes its existence to the resonance stabilization between the respective structures; hence a charge‐shift (CS) bond. The dual family also emerges from calculated and experimental electron density properties. Covalent C? C bonds are characterized by negative Laplacians of the density, whereas CS‐bonds display small or positive Laplacians. The positive Laplacian defines a region suffering from neighbouring repulsive interactions, which is precisely the case in the inverted bonding region. Such regions are rich in kinetic energy, and indeed the energy‐density analysis reveals that CS‐bonds are richer in kinetic energy than the covalent C? C bonds. The large covalent–ionic resonance energy is precisely the mechanism that lowers the kinetic energy in the bonding region and restores equilibrium bonding. Thus, different degrees of repulsive strain create two bonding families of the same chemical bond made from a single atomic constituent. It is further shown that the idea of repulsive strain is portable and can predict the properties of propellanes of various sizes and different wing substituents. Experimentally (M. Messerschmidt, S. Scheins, L. Bruberth, M. Patzel, G. Szeimies, C. Paulman, P. Luger, Angew. Chem. 2005 , 117, 3993–3997; Angew. Chem. Int. Ed. 2005 , 44, 3925–3928), the C? C bond families are beautifully represented in [1.1.1]propellane, where the inverted C? C is a CS‐bond, while the wings are made from covalent C? C bonds. What other manifestations can we expect from CS‐bonds? Answers from experiment have the potential of recharting the mental map of chemical bonding.     

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.     

Comparative analysis of blue‐shifted hydrogen bond versus conventional hydrogen bond in methyl radical complexes

Methyl radical complexes H₃C…HCN and H₃C…HNC have been investigated at the UMP2(full)/aug‐cc‐pVTZ level to elucidate the nature of hydrogen bonds. To better understand the intermolecular H‐bond interactions, topological analysis of electron density at bond critical points (BCP) is executed using Bader's atoms‐in‐molecules (AIM) theory. Natural bond orbital (NBO) analysis has also been performed to study the orbital interactions and change of hybridization. Theoretical calculations show that there is no essential difference between the blue‐shift H‐bond and the conventional one. In H₃C…HNC complex, rehybridization is responsible for shortening of the N? H bond. The hyperconjugative interaction between the single electron of the methyl radical and N? H antibonding orbital is up to 7.0 kcal/mol, exceeding 3.0 kcal/mol, the upper limit of hyperconjugative n(Y)→σ*(X–H) interaction to form the blue‐shifted H‐bond according to Alabugin's theory. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

α‐Halogenoacetanilides as Hydrogen‐Bonding Organocatalysts that Activate Carbonyl Bonds: Fluorine versus Chlorine and Bromine

α‐Halogenoacetanilides (X=F, Cl, Br) were examined as H‐bonding organocatalysts designed for the double activation of C?O bonds through NH and CH donor groups. Depending on the halide substituents, the double H‐bond involved a nonconventional C?H???O interaction with either a H?CX_n (n=1–2, X=Cl, Br) or a H?C_Ar bond (X=F), as shown in the solid‐state crystal structures and by molecular modeling. In addition, the catalytic properties of α‐halogenoacetanilides were evaluated in the ring‐opening polymerization of lactide, in the presence of a tertiary amine as cocatalyst. The α‐dichloro‐ and α‐dibromoacetanilides containing electron‐deficient aromatic groups afforded the most attractive double H‐bonding properties towards C?O bonds, with a N?H???O???H?CX₂ interaction.     

A theoretical investigation on the structures,densities, detonation properties,and pyrolysis mechanism of the nitro derivatives of phenols

The nitro derivatives of phenols are optimized to obtain their molecular geometries and electronic structures at the DFT‐B3LYP/6‐31G* level. Detonation properties are evaluated using the modified Kamlet–Jacobs equations based on the calculated densities and heats of formation. It is found that there are good linear relationships between density, detonation velocity, detonation pressure, and the number of nitro and hydroxy groups. Thermal stability and pyrolysis mechanism of the title compounds are investigated by calculating the bond dissociation energies (BDEs) at the unrestricted B3LYP/6‐31G* level. The activation energies of H‐transfer reaction is smaller than the BDEs of all bonds and this illustrates that the pyrolysis of the title compounds may be started from breaking O? H bond followed by the isomerization reaction of H transfer. Moreover, the C? NO₂ bond with the smaller bond overlap population and the smaller BDE will also overlap may be before homolysis. According to the quantitative standard of energetics and stability as a high‐energy density compound, pentanitrophenol essentially satisfies this requirement. In addition, we have discussed the effect of the nitro and hydroxy groups on the static electronic structural parameters and the kinetic parameter. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

A computational study of the effect of an external electric field on the geometry of selected donor–acceptor complexes

To understand the effect of Au and thiol atoms in octane molecule, a structural and charge density analysis has been carried out by high level ab initio quantum chemical calculations using MP2 and B3PW91 methods with the basis sets 6-311G(d,p) and LANL2DZ. The optimized geometries, specifically, the geometry obtained from both levels reveal the effect of S- and Au-atoms in octane molecule. An introduction of sulfur atom in octane molecule lengthen its backbone C–C bond distances, and further adding of Au-atom at the terminals of octane dithiolate stabilizes these distances. The bond densities of the C–C bonds of octane are 1.6 eÅ⁻³, these values are decreased significantly and the charges are largely depleted, when thiol and Au-atoms added in the octane molecule. The presence of negative Laplacian ²ρ(r) at bond critical points of C–C and C–H bonds, indicate, the charges are concentrated in these bonds, confirm that these bonds exhibit an open shell type interaction. The moderate values of density and the negative Laplacian of S–C bonds confirm the covalent character. The positive ²ρ(r) value of Au–S bonds, characterize, the bonding interaction is a closed shell interaction. The combined observed low value of electron density and the positive Laplacian of Au–S bond comprises, the gold and S interaction is not a covalent interaction, but it is a very weak coordination bond interaction. The small positive value of total energy density in Au–S bond indicates, the charges in these bonds are highly depleted and this is further confirmed by the Laplacian of bond characterization.     

Polyacetylenes and Cumulenes,Potential Elements for Molecular Machines and Precursors of Carbon Clusters: A Theoretical Study

A recently described very simple procedure for estimating Hartree–Fock (H. F.) energy and accurate nonrelativistic energy has been used with simple hydrocarbons possessing C?C or C?C bonds and for the acetylene dimer. Experimental characteristics (heats of formation, ionization potentials, electron affinities), structural features, and reactivity have been discussed in terms of quantum‐chemistry characteristics at the H. F. level and also at a level including a part of electron correlation. Deviations from linearity with derivatives of long polyacetylenes and cumulenes are ascribed to the lowest‐energy deformation vibrations, which decrease rapidly when passing from short to long acetylenic and cumulenic chains. The role of derivatives and heteroanalogues of hydrocarbons under study in atmospheric and interstellar chemistry is briefly mentioned. Derivatives with enhanced stability represent potentially promising construction materials for molecular devices and also resources for the preparation of defined clusters of C‐atoms.     

Quantum chemical calculations of geometries and gas‐phase deprotonation energies of linear polyyne chains

The molecular geometries of polyyne chains H(CC)_nH with their deprotonated forms (anions) have been optimized using ab initio LCAO‐SCF molecular orbital (MO) method and density functional theory at different basis set levels. The polyynes possess a series of alternating single and triple bonds. On the theoretical side the persistence of bond alternation and the effect of chain lengthening on the individual bond length in linear conjugated polyyne chains has been investigated. The common conclusion has been drawn that the bond alternation will persist and that bond length variation will be small. The triple bond length increases progressively toward the asymptotic limits as the value of n increases progressively. If the split‐valence basis set was employed, the total charges obtained using the Mulliken population analysis yielded unrealistic values. Using natural bond orbital (NBO) analysis or Bader's analysis, the net charges of the individual atoms converge very rapidly to their asymptotic limits, and the central atoms have almost zero charges in contrast to the Mulliken population analysis results. The reliability of deprotonation energies of neutral polyynes and their monoanionic derivatives calculated from the differences in molecular energy of the parent chains and the corresponding anions E(H(CC)_n⁻)–E(H(CC)_nH) and E(⁻(CC)_n⁻)–E(H(CC)_n⁻) was tested for different basis sets. The increase of the number of CC bonds in the chain decreases these differences asymptotically. The studied compounds are the best available building blocks in bimetallic compounds with useful properties in molecular electronics and nonlinear optics. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 73–85, 2001