Interacting Quantum Atoms Research Articles

Determination of the molecular structure of gaseous proline by electron diffraction, supported by microwave and quantum chemical data

The molecular structures of the four most stable conformers of neutral proline (pyrrolidine-2-carbonic acid) were investigated by means of gas-phase electron diffraction. The results were used in conjunction with the experimental rotational constants in combined structural analysis. Small differences between similar structural parameters were constrained on the basis of theoretical calculations at the M062X/aug-cc-pVTZ level of theory. Because intramolecular hydrogen bonds play an important role in the molecular structure and conformational stability of amino acids, the hydrogen bond descriptors calculated by natural bond orbital, atoms in molecules, interacting quantum atoms and noncovalent interactions methods were included.

Comparison of halogen bonds in M-X⋯N contacts (M = C, Si, Ge and X = Cl, Br).

The halogen bonds (XB) formed between some Si-X- and Ge-X- (X is Cl and Br) containing molecules and NCH (as a Lewis base) have been investigated and compared with C-X⋯N halogen bond. Although, in all cases, the existence of a positive electrostatic potential (σ-hole) along the extension of M-X was responsible for halogen bond formation, multipole expansion of electrostatic potential reveals that these positive potentials originate from different atomic multipole moments. Indeed, in addition to the monopole moment of M atoms, the quadrupole moment of X in C-X molecules, the dipole moment of the halogen in Si-X molecules and both the dipole and quadrupole moments of X in Ge-X molecules are mainly responsible for the existence of the σ-hole along the extension of the M-X bond. From a different point of view, the distribution of the Laplacian of electron density shows that all the studied M-X⋯N halogen bonds can be regarded as "lump-hole" interactions; a region of charge depletion (hole) in the valence shell charge concentration (VSCC) of the halogen atom interacts with a region of charge concentration (lump) in the VSCC of nitrogen and forms a halogen bond. On the other hand, interacting quantum atoms (IQA) analysis of atomic energies indicates that, in contrast to C-X⋯N contacts, in which the interaction between halogen and nitrogen is attractive, there is a net repulsive interaction between X and N in Si-X⋯N and Ge-X⋯N complexes. Indeed, the attraction between Si/Ge and nitrogen is mainly responsible for the formation of these halogen bonds.

An interacting quantum atoms analysis of the metal-metal bond in [M2(CO)8]n systems.

The metal-metal interaction in policarbonyl metal clusters remains one of the most challenging and controversial issues in metal-organic chemistry, being at heart of a generalized understanding of chemical bonding and of specific applications of these molecules. In this work, the interacting quantum atoms (IQA) approach is used to study the metal-metal interaction in dimetal polycarbonyl dimers, analyzing bridged (Co2(CO)8)), semibridged ([FeCo(CO)8](-)) and unbridged (Co2(CO)8, [Fe2(CO)8](2-)) clusters. In all systems, a delocalized covalent bond is found to occur, involving the metals and the carbonyls, but the global stability of the dimers mainly originates from the Coulombic attraction between the metals and the oxygens.

Does Fluorine Participate in Halogen Bonding?

When R is sufficiently electron withdrawing, the fluorine in the R-F molecules could interact with electron donors (e.g., ammonia) and form a noncovalent bond (F⋅⋅⋅N). Although these interactions are usually categorized as halogen bonding, our studies show that there are fundamental differences between these interactions and halogen bonds. Although the anisotropic distribution of electronic charge around a halogen is responsible for halogen bond formations, the electronic charge around the fluorine in these molecules is spherical. According to source function analysis, F is the sink of electron density at the F⋅⋅⋅N BCP, whereas other halogens are the source. In contrast to halogen bonds, the F⋅⋅⋅N interactions cannot be regarded as lump-hole interactions; there is no hole in the valence shell charge concentration (VSCC) of fluorine. Although the quadruple moment of Cl and Br is mainly responsible for the existence of σ-holes, it is negligibly small in the fluorine. Here, the atomic dipole moment of F plays a stabilizing role in the formation of F⋅⋅⋅N bonds. Interacting quantum atoms (IQA) analysis indicates that the interaction between halogen and nitrogen in the halogen bonds is attractive, whereas it is repulsive in the F⋅⋅⋅N interactions. Virial-based atomic energies show that the fluorine, in contrast to Cl and Br, stabilize upon complex formation. According to these differences, it seems that the F⋅⋅⋅N interactions should be referred to as "fluorine bond" instead of halogen bond.

On the non-classical contribution in lone-pair-π interaction: IQA perspective.

In the present work the nature of lone-pair-π interactions between water molecules and a number of π-rings with different substituents/hetero-atoms in the light of quantum chemical topology approaches is studied. The Quantum Theory of Atoms in Molecules (QTAIM) and Interacting Quantum Atoms (IQA) were employed for distinguishing the role of heteroatoms and electron withdrawing substituents in the complex formation between water and π-rings. Our IQA study identified three classes of water-π complexes on the basis of the relative role of electrostatics (classical) and exchange-correlation (non-classical) factors in the interaction energy between the oxygen of water (the lone-pair donor) and the sp(2) atoms of the π-ring, i.e. the primary lp-π interaction. Considering both the primary and secondary (the rest of interatomic interactions except Owater-π-ring atoms) interactions demonstrates that the exchange-correlation is the dominant contributor to the binding energy. This proves a non-negligible contribution of non-classical factors in the stabilization of the lone-pair-π complexes. However, in spite of a relatively large contribution of the exchange-correlation, this part of the interaction energy is virtually counterbalanced by the deformation energy, i.e. the increase in atomic kinetic energy upon complexation. This finding clarifies why water-π interactions can be modelled by simple electrostatics without the need to invoke quantum effects.

Understanding the bifurcated halogen bonding N⋯Hal⋯N in bidentate diazaheterocyclic compounds

The nature of bifurcated halogen bonding N1⋯Hal2⋯N2 (Hal2=Cl2, Br2, I2) in complexes with bidentate heterocycles has been studied through an analysis of the electron density and the electrostatic potential. It has been established, that the halogen atom can be specified as an electron acceptor for both the strong primary N1⋯Hal interaction and the weak secondary N2⋯Hal interaction in all the examined complexes. Consideration of two-atomic electrostatic and exchange contributions to the total energy, defined in terms of the Interacting Quantum Atom (IQA) method, reveals that the strengthening of the primary bonding with Cl2 is due to an increase in the exchange energy component. In contrast, the electrostatic contribution dominates both primary and secondary interactions in the complexes with I2. Considering series of bifurcated halogen bonds with two different electron donor centers, we have found simple quantitative correlations between the electronic kinetic and potential energy densities at the bond critical points and the IQA two-atomic exchange energy contribution. Relations linking the delocalization indices and two-atomic exchange energy contributions with the local halogen atom contribution from a source function to the N1⋯Hal2⋯N2 halogen bond critical points have also been established.

An energy partition method based on localized molecular orbitals

A new energy partition scheme based on the use of the molecular orbitals (MO) derived from an isopycnic localization of the natural MOs of the system is presented. The method is inspired in the Interacting Quantum Atoms (IQA) methodology and leads to an exact decomposition of the total energy of the molecule into intra-atomic self-energies and inter-atomic interaction energies. The latter, in turn, can be partitioned into a Coulombic or classical electrostatic part and an exchange–correlation contribution that measures the covalency of the interaction. In principle, the scheme presented can be used with both single- and multi-determinant wavefunctions. However, in the first case, and contrary to what happens in the IQA method, as long as the numerical overlap integrals between the isopycnic MOs over the atomic domains in which the physical space is divided are accurate enough, all the energy components are computed analytically. We have performed calculations in the H2 and LiH molecules, and in several Hydrogen bonded systems, and compared the results with those previously reported using the IQA methodology.

Halogen–halogen interactions in perhalogenated ethanes: An interacting quantum atoms study

In this paper, intramolecular halogen–halogen interactions in perhalogenated ethanes CX3–CX′3 (X, X′=F, Cl, Br) were investigated using Bader’s theory of Atoms in Molecules along the potential energy surface defined by the XCCX′ torsion angle. Besides examining the topology of the electron density in terms of critical points, we made use of Pendás’ interacting quantum atoms energy decomposition scheme in order to cast light on the nature of those interactions. Previous conclusions on the important role of the exchange interaction energy in such non-covalent interactions were confirmed, the presence or absence of bond critical points between halogens being rationalized in terms of the competition between primary and secondary exchange channels. Moreover, additional information was inferred from the source function that enables to quantify the role of distant atoms. Finally, we assessed the influence of the chosen computational protocol (basis set and dispersion correction) on the reported energetic decomposition.

Halogenotrinitromethanes: a combined study in the crystalline and gaseous phase and using quantum chemical methods.

The halogenotrinitromethanes FC(NO2 )3 (1), BrC(NO2 )3 (2), and IC(NO2)3 (3) were synthesized and fully characterized. The molecular structures of 1-3 were determined in the crystalline state by X-ray diffraction, and gas-phase structures of 1 and 2 were determined by electron diffraction. The Hal-C bond lengths in F-, Cl-, and Br-C(NO2 )3 in the crystalline state are similar to those in the gas phase. The obtained experimental data are interpreted in terms of Natural Bond Orbitals (NBO), Atoms in Molecules (AIM), and Interacting Quantum Atoms (IQA) theories. All halogenotrinitromethanes show various intra- and intermolecular non-bonded interactions. Intramolecular N⋅⋅⋅O and Hal⋅⋅⋅O (Hal=F (1), Br (2), I (3)) interactions, both competitors in terms of the orientation of the nitro groups by rotation about the C-N bonds, lead to a propeller-type twisting of these groups favoring the mentioned interactions. The origin of the unusually short Hal-C bonds is discussed in detail. The results of this study are compared to the molecular structure of ClC(NO2 )3 and the respective interactions therein.

Dynamical correlation within the Interacting Quantum Atoms method through coupled cluster theory

The Interacting Quantum Atoms (IQA) approach is an energy partition of an electronic system which has provided new understandings and insightful information about diverse chemical systems and processes from Hartree–Fock, CASSCF as well as truncated and full CI wavefunctions. Nonetheless, the unavailability of an implementation of IQA relying on size extensive correlated methods such as coupled cluster or Møller–Plesset perturbation theory, has prevented the application of this procedure to the study of molecular systems in which these models of electronic structure are necessary to obtain accurate results. This paper uses first and second-order density matrices consistent with a closed shell coupled cluster energy to carry out the IQA splitting. The presented developments are tested and discussed using H2, N2, H2O and CO as representative examples. It is our hope that the implementations discussed in this paper would give new insights in the study of chemical bonding, intermolecular interactions and other important phenomena in chemistry for which the consideration of electron correlation is critical.

Hydrogen-hydrogen interaction in planar biphenyl: a theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods.

The nature of H-H interaction between ortho-hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial-based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H-H bonding, partitioning the atomic energy into intra-atomic and interatomic terms reveals that there is a net attractive interaction between the ortho-hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho-hydrogens remains almost constant when they participate in the H-H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H-H bond, it is almost compensated by the destabilizing effects of the intra-atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra-atomic and interatomic energy terms of ortho-hydrogens during H-H bond formation are very similar to those observed for the H2 molecule.

Modeling biophysical and biological properties from the characteristics of the molecular electron density, electron localization and delocalization matrices, and the electrostatic potential.

The electron density and the electrostatic potential are fundamentally related to the molecular hamiltonian, and hence are the ultimate source of all properties in the ground- and excited-states. The advantages of using molecular descriptors derived from these fundamental scalar fields, both accessible from theory and from experiment, in the formulation of quantitative structure-to-activity and structure-to-property relationships, collectively abbreviated as QSAR, are discussed. A few such descriptors encode for a wide variety of properties including, for example, electronic transition energies, pKa's, rates of ester hydrolysis, NMR chemical shifts, DNA dimers binding energies, π-stacking energies, toxicological indices, cytotoxicities, hepatotoxicities, carcinogenicities, partial molar volumes, partition coefficients (log P), hydrogen bond donor capacities, enzyme–substrate complementarities, bioisosterism, and regularities in the genetic code. Electronic fingerprinting from the topological analysis of the electron density is shown to be comparable and possibly superior to Hammett constants and can be used in conjunction with traditional bulk and liposolubility descriptors to accurately predict biological activities. A new class of descriptors obtained from the quantum theory of atoms in molecules' (QTAIM) localization and delocalization indices and bond properties, cast in matrix format, is shown to quantify transferability and molecular similarity meaningfully. Properties such as “interacting quantum atoms (IQA)” energies which are expressible into an interaction matrix of two body terms (and diagonal one body “self” terms, as IQA energies) can be used in the same manner. The proposed QSAR-type studies based on similarity distances derived from such matrix representatives of molecular structure necessitate extensive investigation before their utility is unequivocally established. © 2014 The Author and the Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Physical Nature of Interactions in ZnIIComplexes with 2,2′-Bipyridyl: Quantum Theory of Atoms in Molecules (QTAIM), Interacting Quantum Atoms (IQA), Noncovalent Interactions (NCI), and Extended Transition State Coupled with Natural Orbitals for Chemical Valence (ETS-NOCV) Comparative Studies

In the present account factors determining the stability of ZnL, ZnL2, and ZnL3 complexes (L = bpy, 2,2′-bipyridyl) were characterized on the basis of various techniques: the quantum theory of atoms in molecules (QTAIM), energy decomposition schemes based on interacting quantum atoms (IQA), and extended transition state coupled with natural orbitals for chemical valence (ETS-NOCV). Finally, the noncovalent interactions (NCI) index was also applied. All methods consistently indicated that the strength of the coordination bonds, Zn–O and Zn–N, decreases from ZnL to ZnL3. Importantly, it has been identified that the strength of secondary intramolecular heteropolar hydrogen bonding interactions, CH···O and CH···N, increases when going from ZnL to ZnL3. A similar trend appeared to be valid for the π-bonding as well as electrostatic stabilization. In addition to the above leading bonding contributions, all techniques suggested the existence of very subtle, but non-negligible additional stabilization from the CH···HC electronic exchange channel; these interactions are the weakest among all considered here. From IQA it was found that the local diatomic interaction energy, Eint(H,H), amounts at HF to −2.5, −2.7, and −2.9 kcal mol(–1) for ZnL, ZnL2, and ZnL3, respectively (−2.1 kcal mol(–1) for ZnL at MP2). NOCV-based deformation density channels showed that formation of CH--HC contacts in Zn complexes causes significant polarization of σ(C–H) bonds, which accordingly leads to charge accumulation in the CH···HC bay region. Charge depletion from σ(C–H) bonds was also reflected in the calculated spin–spin (1)J(C–H) coupling constants, which decrease from 177.06 Hz (ZnL) to 173.87 Hz (ZnL3). This last result supports our findings of an increase in the local electronic CH···HC stabilization from ZnL to ZnL3 found from QTAIM, IQA, and ETS-NOCV. Finally, this work unites for the first time the results from four methods that are widely used for description of chemical bonding.

An anatomy of intramolecular atomic interactions in halogen-substituted trinitromethanes.

The intramolecular interactions in substituted trinitromethanes, XC(NO2)3 (X = F, Cl, I, H) are studied and clarified by using a combination of the Quantum Theory of Atoms in Molecules (QTAIM), the non-covalent interaction analysis and the Interacting Quantum Atoms (IQA) methods. The stretching vibration modes are formed by the concerted displacements of atoms involved in the covalent bonds showing the significant multiatomic influence in substituted trinitromethanes. In agreement with that, the arrangement of the local reduced density gradient minima indicates that the electron density favors the non-covalent intramolecular interactions X···O and N···O. However, the corresponding QTAIM bond paths are not formed; instead, contacts, which we call uncompleted links in this context, are accompanied by "quasi-bonding channels" corresponding to the λ2() ≤ 0 regions on the sign[λ2(r)]ρ(r) contour maps. The intramolecular IQA energy contributions signal the appreciable electron exchange between the pairs of atoms associated with potential atomic interactions or the bond-path-free non-covalent links. The IQA analysis shows that the electrostatic term destabilizes FC(NO2)3 and distinctly stabilizes IC(NO2)3, whereas it is close to neutral in ClC(NO2)3. The exchange energy between the X atom and the NO2 groups, in contrast, stabilizes all the molecules.

Density functional theory and Bader's atoms-in-molecules theory: towards a vivid dialogue

Density functional theory and Bader's atoms-in-molecules theory share the same primary ingredient: the electron density, which is the fundamental physical observable in quantum chemistry. In this paper, we elaborate on the decomposition of the Kohn-Sham molecular energy in terms of Bader's partition, discussing how Pendás' Interacting Quantum Atoms framework could be adapted to a DFT context. Besides, another bridge between these two theories is built through a general formalism able to generate new local descriptors from any second-order density gradient expansion. These approaches are then applied to two classes of intramolecular bonds: between two electronegative atoms and intramolecular hydrogen bonds, illustrating how fruitful a dialog between both theories can be.

On the Physical Nature of Halogen Bonds: A QTAIM Study

In this article, we report a detailed study on halogen bonds in complexes of CHCBr, CHCCl, CH2CHBr, FBr, FCl, and ClBr with a set of Lewis bases (NH3, OH2, SH2, OCH2, OH(-), Br(-)). To obtain insight into the physical nature of these bonds, we extensively used Bader's Quantum Theory of Atoms-in-Molecules (QTAIM). With this aim, in addition to the examination of the bond critical points properties, we apply Pendás' Interacting Quantum Atoms (IQA) scheme, which enables rigorous and physical study of each interaction at work in the formation of the halogen-bonded complexes. In particular, the influence of primary and secondary interactions on the stability of the complexes is analyzed, and the roles of electrostatics and exchange are notably discussed and compared. Finally, relationships between QTAIM descriptors and binding energies are inspected.

Hydrogen‐Bond Cooperative Effects in Small Cyclic Water Clusters as Revealed by the Interacting Quantum Atoms Approach

The cooperative effects of hydrogen bonding in small water clusters (H2 O)n (n=3-6) have been studied by using the partition of the electronic energy in accordance with the interacting quantum atoms (IQA) approach. The IQA energy splitting is complemented by a topological analysis of the electron density (ρ(r)) compliant with the quantum theory of atoms-in-molecules (QTAIM) and the calculation of electrostatic interactions by using one- and two-electron integrals, thereby avoiding convergence issues inherent to a multipolar expansion. The results show that the cooperative effects of hydrogen bonding in small water clusters arise from a compromise between: 1) the deformation energy (i.e., the energy necessary to modify the electron density and the configuration of the nuclei of the isolated water molecules to those within the water clusters), and 2) the interaction energy (Eint ) of these contorted molecules in (H2 O)n . Whereas the magnitude of both deformation and interaction energies is enhanced as water molecules are added to the system, the augmentation of the latter becomes dominant when the size of the cluster is increased. In addition, the electrostatic, classic, and exchange components of Eint for a pair of water molecules in the cluster (H2 O)n-1 become more attractive when a new H2 O unit is incorporated to generate the system (H2 O)n with the last-mentioned contribution being consistently the most important part of Eint throughout the hydrogen bonds under consideration. This is opposed to the traditional view, which regards hydrogen bonding in water as an electrostatically driven interaction. Overall, the trends of the delocalization indices, δ(Ω,Ω'), the QTAIM atomic charges, the topology of ρ(r), and the IQA results altogether show how polarization, charge transfer, electrostatics, and covalency contribute to the cooperative effects of hydrogen bonding in small water clusters. It is our hope that the analysis presented in this paper could offer insight into the different intra- and intermolecular interactions present in hydrogen-bonded systems.

Forced Bonding and QTAIM Deficiencies: A Case Study of the Nature of Interactions in He@Adamantane and the Origin of the High Metastability

Calculations within the framework of the interacting quantum atoms (IQA) approach have shown that the interactions of the helium atom with both tertiary, tC, and secondary, sC, carbon atoms in the metastable He@adamantane (He@adam) endohedral complex are bonding in nature, whereas the earlier study performed within the framework of Bader's quantum theory of atoms in molecules (QTAIM) revealed that only He---tC interactions are bonding. The He---tC and He---sC bonding interactions are shown to be forced by the high pressure that the helium and carbon atoms exert upon each other in He@adam. The occurrence of a bonding interaction between the helium and sC atoms, which are not linked by a bond path, clearly shows that the lack of a bond path between two atoms does not necessarily indicate the lack of a bonding interaction, as is asserted by QTAIM. IQA calculations showed that not only the destabilization of the adamantane cage, but also a huge internal destabilization of the helium atom, contribute to the metastability of He@adam, these contributions being roughly equal. This result disproves previous opinions based on QTAIM analysis that only the destabilization of the adamantane cage accounts for the endothermicity of He@adam. Also, it was found that there is no homeomorphism of the ρ(r) and -v(r) fields of He@adam. Comparison of the IQA and QTAIM results on the interactions in He@adam exposes other deficiencies of the QTAIM approach. The reasons for the deficiencies in the QTAIM approach are analyzed.

Congested molecules. Where is the steric repulsion? An analysis of the electron density by the method of interacting quantum atoms

The computed electron density of several congested saturated hydrocarbons and halogenated derivatives has been analyzed by the method of interacting quantum atoms (IQA). For all the molecules studied, the calculations show the existence of a bond path between the congested atoms and which, according to the Quantum Theory of Atoms in Molecules, indicates that there is a stabilizing interaction between these atoms. The bond path is found to exist up to interatomic distances well‐beyond the sum of the van der Waals radii. The IQA results indicate that steric hindrance is not a repulsive force between the congested atoms but that is the result of an increase in the intra‐atomic or self‐energy of the congested atoms. This increase in self‐energy is caused by the deformation of the atomic basin of the congested atoms. © 2013 Wiley Periodicals, Inc.

Chemical Interactions and Spin Structure in (O2)4: Implications for the ε-O2 Phase.

The chemical interactions and spin structure of (O2)4 in its ground singlet state are analyzed by means of Quantum Chemical Topology descriptors. The energetic contributions of the Interacting Quantum Atoms approach are used to obtain information about the class of interactions displayed along the dissociation path of (O2)4. The exchange-correlation contribution to the binding energy is non-negligible for the O2-O2 interactions at intermolecular distances close to those found for the pressure induced ε phase of solid (O2) and this strengthening of the intermolecular bonding is built up from a simultaneous weakening of the intramolecular bond. This result is of interest in connection with the observed softening of the IR vibron frequency in the lower pressure range of the ε phase. The spin structure in the real space along the dissociation process is interpreted with the help of the so-called electron number distribution functions. At large distances, the four triplet O2 molecules are arranged in a way consistent with an antiferromagnetic structure, whereas at short distances, a significant spin redistribution is driven by the exchange process and it involves a propensity toward a null magnetic moment per molecule. Such probability behavior can be related with the magnetic evolution of solid oxygen across the δ → ε phase transition. Additional calculations of (O2)4 excited states support the conclusion that the relative stabilization and magnetic features of the ground singlet state are due to the onset of the new intermolecular bonds, and not to an exclusive modification of the electronic character within the O2 molecules.