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.     

Directionality of Halogen Bonds: An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study

Interacting Quantum Atoms (IQA) and Interacting Quantum Fragments (IQF) analyses are used to study (X=Cl and Br) model complexes in order to determine the origin of halogen bond directionality. IQA allows for the calculation of intra- and interatomic classical and exchange-correlation energies, which can be used to determine the energetic nature of the changes that occur when deviating from the preferred halogen bond approach. The Relative Energy Gradient (REG) method is also applied to rank the IQA energies and reveal which energy contributions best describe the total behavior of the system. Indeed, all the pairwise interactions and atomic self-energies are angularly dependent; some terms favor the linear structure and some tend toward nonlinear arrangements. For instance, when the C−X−N angle is altered, the halogen-nitrogen interaction energy behaves like the total energy of the system while the carbon-nitrogen interaction works against the total energy profile. Furthermore, the REG values reveal that the contribution of the halogen-nitrogen interaction to the total behavior of the system is small. Instead, the secondary interactions (e. g., fluorine-nitrogen and carbon-hydrogen interactions) and atomic self-energies are mainly responsible for the angular preference of these halogen bonds. Finally, IQF calculations followed by REG analysis reveal the importance of the self-energy of the fragments.     

A Re-evaluation of Factors Controlling the Nature of Complementary Hydrogen-Bonded Networks

The energy profiles of hydrogen-bonded heterocyclic aromatics have been decomposed into atomistic energy contributions using the Interacting Quantum Atoms (IQA) method. The resulting energy contributions have been sequenced by the Relative Energy Gradient (REG) approach to determine their influence upon the shape of these energy profiles. The results show inadequacies in Jorgensen's secondary interaction hypothesis (SIH). A novel method of finding a condensed analogy for the interaction between the molecules is presented. The findings of this work further doubt the validity of the SIH, and reinforce previous warnings against its misguided use.     

On the Relationship between Hydrogen Bond Strength and the Formation Energy in Resonance-Assisted Hydrogen Bonds

Resonance-assisted hydrogen bonds (RAHB) are intramolecular contacts that are characterised by being particularly energetic. This fact is often attributed to the delocalisation of π electrons in the system. In the present article, we assess this thesis via the examination of the effect of electron-withdrawing and electron-donating groups, namely −F, −Cl, −Br, −CF₃, −N(CH₃)₂, −OCH₃, −NHCOCH₃ on the strength of the RAHB in malondialdehyde by using the Quantum Theory of Atoms in Molecules (QTAIM) and the Interacting Quantum Atoms (IQA) analyses. We show that the influence of the investigated substituents on the strength of the investigated RAHBs depends largely on its position within the π skeleton. We also examine the relationship between the formation energy of the RAHB and the hydrogen bond interaction energy as defined by the IQA method of wave function analysis. We demonstrate that these substituents can have different effects on the formation and interaction energies, casting doubts regarding the use of different parameters as indicators of the RAHB formation energies. Finally, we also demonstrate how the energy density can offer an estimation of the IQA interaction energy, and therefore of the HB strength, at a reduced computational cost for these important interactions. We expected that the results reported herein will provide a valuable understanding in the assessment of the energetics of RAHB and other intramolecular interactions.     

Mechanistic insights on how hydroquinone disarms OH and OOH radicals

Phenol derivatives are distinguished as successful free radical scavengers. We present a detailed analysis of hydroxyl hydrogen abstraction from hydroquinone by hydroxyl and hydroperoxyl radical with emphasis on changes that take place in the vicinity of the transition state. Quantum theory of atoms in molecules is employed to elucidate the sequence of positive and negative charge transfer by studying selected properties of the three key atoms (the transferring hydrogen, the donor atom, and the acceptor atom) along intrinsic reaction path. The presented results imply that in both reactions, which are examples of proton coupled electron transfer, proton, and electron get simultaneously transferred to the radical oxygen atom. The fact that the hydrogen's charge and volume do not monotonously change in the vicinity of the transition state in the product valley results from the adjacency of the proton and the electron to the donor and the acceptor oxygen atoms. Obtaining a detailed understanding of mechanisms by which free radicals are disarmed is of paramount importance given the effects of those highly reactive species on biological systems. A comprehensive analysis of hydroxyl hydrogen abstraction from hydroquinone by hydroxyl and hydroperoxyl radicals, based on changes of selected electronic properties of the three most relevant atoms (hydrogen donor, hydrogen acceptor, and the hydrogen itself), along the reaction coordinate, can be obtained by first‐principles calculations.     

Aza-Michael Addition in Explicit Solvent: A Relative Energy Gradient–Interacting Quantum Atoms Study

Aza-Michael additions are key reactions in organic synthesis. We investigate, from a theoretical and computational point of view, several examples ranging from weak to strong electrophiles in dimethylsulfoxide treated as explicit solvent. We use the REG-IQA method, which is a quantum topological energy decomposition (Interacting Quantum Atoms, IQA) coupled to a chemical-interpretation calculator (Relative Energy Gradient, REG). We focus on the rate-limiting addition step in order to unravel the different events taking place in this step, and understand the influence of solvent on the reaction, with an eye on predicting the Mayr electrophilicity. For the first time, a link is established between an REG-IQA analysis and experimental values.     

Incorporation of local structure into kriging models for the prediction of atomistic properties in the water decamer

Machine learning algorithms have been demonstrated to predict atomistic properties approaching the accuracy of quantum chemical calculations at significantly less computational cost. Difficulties arise, however, when attempting to apply these techniques to large systems, or systems possessing excessive conformational freedom. In this article, the machine learning method kriging is applied to predict both the intra‐atomic and interatomic energies, as well as the electrostatic multipole moments, of the atoms of a water molecule at the center of a 10 water molecule (decamer) cluster. Unlike previous work, where the properties of small water clusters were predicted using a molecular local frame, and where training set inputs (features) were based on atomic index, a variety of feature definitions and coordinate frames are considered here to increase prediction accuracy. It is shown that, for a water molecule at the center of a decamer, no single method of defining features or coordinate schemes is optimal for every property. However, explicitly accounting for the structure of the first solvation shell in the definition of the features of the kriging training set, and centring the coordinate frame on the atom‐of‐interest will, in general, return better predictions than models that apply the standard methods of feature definition, or a molecular coordinate frame. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

The effects of higher orders of perturbation theory on the correlation energy of atoms and bonds in molecules

We examine, for the first time, the effects of higher orders of Møller–Plesset perturbation theory on the individual atoms within a molecule and the bonds between them, via the topological energy partitioning method of interacting quantum atoms. In real terms (i.e., not by absolute value) MP3 decreases the correlation energy of a bond, and MP4SDQ also decreases the energy of the atoms at either end of the bond. In addition, we investigated long‐range through‐space dispersive effects on a H₂ oligomer. Overall, MP3 is the largest correction to the correlation energy, and most of that energy is allocated to chemical bonds, reducing their values in actual terms. The MP4SDQ bond correlation correction, despite being relatively small, tends to have two effects: (i) for small or negative correlation energies MP4SDQ tends to decrease the bond correlation values even more, and (ii) for large (positive) bond correlation energies MP4SDQ tends to restore the bond correlation energies from the MP3 back toward the MP2 values. Furthermore, each individual part of a molecule or complex (atom or bond) has a specific convergence pattern for the MPn series: through‐space interactions converge at MP2 but bonds converge at MP3 level. The atomic correlation energy appears to head toward convergence at the MP4 level.     

A multipolar approach to the interatomic covalent interaction energy

Interatomic exchange‐correlation energies correspond to the covalent energetic contributions to an interatomic interaction in real space theories of the chemical bond, but their widespread use is severely limited due to their computationally intensive character. In the same way as the multipolar (mp ) expansion is customary used in biomolecular modeling to approximate the classical Coulomb interaction between two charge densities and , we examine in this work the mp approach to approximate the interatomic exchange‐correlation (xc) energies of the Interacting Quantum Atoms method. We show that the full xc mp series is quickly divergent for directly bonded atoms (1–2 pairs) albeit it works reasonably well most times for 1– n (n > 2) interactions. As with conventional perturbation theory, we show numerically that the xc series is asymptotically convergent and that, a truncated xc mp approximation retaining terms up to usually gives relatively accurate results, sometimes even for directly bonded atoms. Our findings are supported by extensive numerical analyses on a variety of systems that range from several standard hydrogen bonded dimers to typically covalent or aromatic molecules. The exact algebraic relationship between the monopole‐monopole xc mp term and the inter‐atomic bond order, as measured by the delocalization index of the quantum theory of atoms in molecules, is also established. © 2017 Wiley Periodicals, Inc.     

A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two-Particle Density-Matrices of MP4SDQ and CCSD

Within the quantum topological energy partitioning method called Interacting Quantum Atoms (IQA) we transition from Møller-Plesset (MP4SDQ) to CCSD in calculating intra- and interatomic electron correlation energies for a set of hydrides, diatomics, a few simple molecules and non-covalently bonded complexes, using the uncontracted basis set 6-31++G(2d,2p). CCSD-IQA allows a more rigorous analysis of atomic electron correlation than that offered by Møller-Plesset, which returns IQA contributions that are identical to Hartree–Fock counterparts except for two-electron terms. The CCSD-IQA analysis returns bond and other interatomic correlation energies that are typically much larger in magnitude than the MP4SDQ values. Crisp patterns of energy transferability are detected in water clusters, both for intra-atomic and interatomic correlation energies. CCSD determines that the intra-atomic correlation energy of an oxygen drops by 15 kJ · mol^–1 for donating a hydrogen and by 25 kJ · mol^–1 for accepting a hydrogen.     

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.     

Structures,vibrational frequencies,topologies, and energies of hydrogen bonds in cysteine‐formaldehyde complexes

The hydrogen bonding interactions between cysteine (Cys) and formaldehyde (FA) were studied with density functional theory regarding their geometries, energies, vibrational frequencies, and topological features of the electron density. The quantum theory of atoms in molecules and natural bond orbital analyses were employed to elucidate the interaction characteristics in the Cys‐FA complexes. The intramolecular hydrogen bonds (H‐bonds) formed between the hydroxyl and the N atom of cysteine moiety in some Cys‐FA complexes were strengthened because of the cooperativity. Most of intermolecular H‐bonds involve the O atom of cysteine/FA moiety as proton acceptors, while the strongest H‐bond involves the O atom of FA moiety as proton acceptor, which indicates that FA would rather accept proton than providing one. The H‐bonds formed between the CH group of FA and the S atom of cysteine in some complexes are so weak that no hydrogen bonding interactions exist among them. In most of complexes, the orbital interaction of H‐bond is predominant during the formation of complex. The electron density (ρ_b) and its Laplace (?²ρ_b) at the bond critical point significantly correlate with the H‐bond parameter δR, while a linearly relationship between the second‐perturbation energy E(2) and ρ_b has been found as well. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Evidence for site‐specific intra‐ionic hydrogen/deuterium exchange in the low‐energy collision‐induced dissociation product ion spectra of protonated small molecules generated by electrospray ionisation

The experimental investigation of site‐specific intra‐ionic hydrogen/deuterium (H/D) exchange in the low‐energy collision‐induced dissociation (CID) product ion spectra of protonated small molecules generated by electrospray ionisation (ESI) is presented. The observation of intra‐ionic H/D exchange in such ions under low‐energy CID conditions has hitherto been rarely reported. The data suggest that the intra‐ionic H/D exchange takes place in a site‐specific manner between the ionising deuteron, localised at either a tertiary amine or a tertiary amine‐N‐oxide, and a γ‐hydrogen relative to the nitrogen atom. Nuclear magnetic resonance (NMR) spectroscopy measurements showed that no H/D exchange takes place in solution, indicating that the reaction occurs in the gas phase. The compounds analysed in this study suggested that electron‐withdrawing groups bonded to the carbon atom bearing the γ‐hydrogen can preclude exchange. The effect of the electron‐withdrawing group appears dependent upon its electronegativity, with lower χ value groups still allowing exchange to take place. However, the limited dataset available in this study prevented robust conclusions being drawn regarding the effect of the electron‐withdrawing group. The observation of site‐specific intra‐ionic H/D exchange has application in the area of structural elucidation, where it could be used to introduce an isotopic label into the carbon skeleton of a molecule containing specific structural features. This could increase the throughput, and minimise the cost, of such studies due to the obviation of the need to produce a deuterium‐labelled analogue by synthetic means. Copyright © 2010 John Wiley & Sons, Ltd.     

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 (H₂O)_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 (E_int) of these contorted molecules in (H₂O)_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 E_int for a pair of water molecules in the cluster (H₂O)_n?1 become more attractive when a new H₂O unit is incorporated to generate the system (H₂O)_n with the last‐mentioned contribution being consistently the most important part of E_int 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.     

On the role of substituent in noncovalent functionalization of graphene and organophosphor recognition: IQA and SAPT perspective

Despite importance of integrating organic molecules with graphene to fabricate graphene‐based electronic devices, the role of substituents and interface stabilizing forces are poorly understood. In this work, the interactions of 7,7,8,8‐tetracyanoquinodimethane (TCNQ), 2,3,5,6‐tetrafluoro‐7,7,8,8‐tetracyanoquinodimethane (F4TCNQ), hydroquinone (Q), and tetrafluorohydroquinone (TFQ) with graphene have been investigated by means of interacting quantum atoms and SAPT(DFT). In addition, in context of potential design of a graphene‐based sensor for detection of the nerve agent sarin, we studied the interaction of graphene and the organic molecules with the dimethyl methylphosphonate (DMMP)—the molecule that mimics sarin. The results show that the organic molecules attach to graphene via C(sp²)?C(sp²), C(sp²)?C(sp) and H?π bonds. In addition, they trap DMMP via various linkages such as hydrogen, lonepair?π and H?π . The quantum effects play a significant role. The Pauli repulsion is responsible for p‐doping of graphene. The substituents are stabilized on graphene by the exchange‐correlation energy. The fluorination of the benzenoid ring raises the electron‐sharing . The through space and through bond effects of the fluorine atoms (‐F) increase the classical attraction of the cyano groups and benzenoid ring with graphene, respectively. When comparing performance of the ab initio and DFT methods, MP2 predicts too much attraction due to well‐known overestimation of the dispersion energy by the uncoupled dispersion component for benzene rings, while ω B97xD functional and SAPT(DFT) provide weaker interaction energies, in good agreement with each other.     

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. © 2014 Wiley Periodicals, Inc.