Interacting Quantum Atoms Approach Research Articles

Cooperativity and topological hydrogen bonding in aromatic diol complexes

AbstractComplexes of three aromatic diols, catechol, naphthalene‐1,8‐diol, and fluorene‐4,5‐diol, with a series of hydrogen bond acceptors (HBAs) that have oxygen, nitrogen, and sulfur acceptor atoms, have been studied by density functional theory (DFT) at the B3LYP/6‐311+G(d,p) level. Binding energies, geometries, infrared spectroscopic (IR) frequencies, nuclear magnetic resonance (NMR) shifts, and measures of the electron density distribution from the Quantum Theory of Atoms in Molecules (QTAIM) are evaluated and compared with data for the corresponding monohydroxy compounds (monols), phenol, naphth‐1‐ol, and fluorene‐4‐ol, in order to assess the importance of cooperativity between intramolecular and intermolecular hydrogen bonding. All measures for all complexes show positive cooperativity whereby both the intermolecular and intramolecular hydrogen bonds are strengthened upon complexation. Cooperativity is weak for catechol and strong for the other two diols and, for all diols, increases with the hydrogen bond basicity of the acceptor. Correlations of IR and NMR metrics against binding energies for a single HBA and all six monols and diols are excellent, but attempts to correlate the same metrics for all HBAs and a single donor are frustrated by differences in intermolecular hydrogen bonding, depending notably on the identity of the acceptor atom in the HBA. Atom–atom interaction energies, calculated by the Interacting Quantum Atoms approach, are used to discuss the covalency of both types of hydrogen bond.

Exact decompositions of the total KS-DFT exchange-correlation energy into one- and two-center terms.

In the so-called Interacting Quantum Atoms (IQA) approach, the molecular energy is numerically decomposed as a sum of atomic and diatomic contributions. While proper formulations have been put forward for both Hartree-Fock and post-Hartree-Fock wavefunctions, this is not the case for the Kohn-Sham density functional theory (KS-DFT). In this work, we critically analyze the performance of two fully additive approaches for the IQA decomposition of the KS-DFT energy, namely, the one from Francisco et al., which uses atomic scaling factors, and that from Salvador and Mayer based upon the bond order density (SM-IQA). Atomic and diatomic exchange-correlation (xc) energy components are obtained for a molecular test set comprising different bond types and multiplicities and along the reaction coordinate of a Diels-Alder reaction. Both methodologies behave similarly for all systems considered. In general, the SM-IQA diatomic xc components are less negative than the Hartree-Fock ones, which is in good agreement with the known effect of electron correlation upon (most) covalent bonds. In addition, a new general scheme to minimize the numerical error of the sum of two-electron energy contributions (i.e., Coulomb and exact exchange) in the framework of overlapping atoms is described in detail.

Merging the Energy Decomposition Analysis with the Interacting Quantum Atoms Approach.

Energy decomposition analysis (EDA) is a well-established approach to dissect the interaction energy into chemically sound components. Despite the inherent requirement of reference states has been a long-standing object of debate, the direct relation with the molecular orbital analysis helps in building up predictive models. The alternative molecular energy decomposition schemes that decompose the total energy into atomic and diatomic contributions, such as the interacting quantum atoms (IQA), has no external reference requirements and also the intra- and intermolecular interactions are treated on equal footing. However, a connection with heuristic chemical models are limited, bringing about a somewhat narrower predictive power. While efforts to reconcile the bonding picture obtained by both methodologies have been discussed in the past, a synergic combination of them has not been tackled yet. Herein, we present the use of IQA decomposition of the individual terms arising from the EDA in the context of intermolecular interactions, henceforth EDA-IQA. The method is applied to a molecular set covering a wide range of interaction types, including hydrogen bonding, charge-dipole, π-π and halogen interactions. We find that the electrostatic energy from EDA, entirely seen as intermolecular, leads to meaningful and non-negligible intra-fragment contributions upon IQA decomposition, originated from charge penetration. EDA-IQA also affords the decomposition of the Pauli repulsion term into intra- and inter-fragment contributions. The intra-fragment term is destabilizing, particularly for the moieties that are net acceptors of charge, while the inter-fragment Pauli term is actually stabilizing. In the case of the orbital interaction term, the sign and magnitude of the intra-fragment contribution at equilibrium geometries is largely driven by the amount of charge transfer, while the inter-fragment contribution is clearly stabilizing. EDA-IQA terms show a smooth behavior along the intermolecular dissociation path of selected systems. The new EDA-IQA methodology provides a richer energy decomposition scheme that aims at bridging the gap between the two main distinct real-space and Hilbert-space methodologies. Via this approach, the partitioning can be used directionally on all the EDA terms aiding in identifying the causal effects on geometries and/or reactivity.

Boat and Chair Shaped Hexahalogen Synthons.

Non-covalent halogen bonding interactions are quintessential in crystal engineering for the construction of distinctive supramolecular synthons. Here, we report the first crystalline evidences of unique boat and chair shaped cyclic hexahalogen synthons in the crystal structures of α,α,α',α',4-pentabromo-o-xylene (PBX) and α,α,α',α',4,5-hexabromo-o-xylene (HBX) respectively. Nature and stability of constituent interactions in the supramolecular synthons are scrutinized with the help of quantum-chemical calculations. Pendás' interacting quantum atoms approach confirmed the stability of Br⋅⋅⋅Br interactions leading to boat and chair shaped synthons with major contribution from exchange-correlation. Although both the molecules are achiral in nature, the packing forces guide PBX to crystallize in the chiral space group P21 with a helix-like orientation while HBX packs in a centrosymmetric P21 /n space group. The extended furcations in the pentabromo derivative construct a molecular framework consisting of macrocycles realized through halogen bonding.

Wave function analyses of scandium-doped aluminium clusters, AlnSc (n = 1-24), and their CO2 fixation abilities.

Nanoclusters represent a connection between (i) solid state systems and (ii) species in the atomic and molecular domains. Additionally, nanoclusters can also have very interesting electronic, optical and magnetic properties. For example, some aluminium clusters behave as superatoms and the doping of these clusters might strengthen their adsorption capabilities. Thus, we address herein the structural, energetic and electronic characterisation of scandium-doped aluminium clusters (AlnSc (n = 1-24)) by means of density functional theory calculations and quantum chemical topology wave function analyses. We studied the effect of Sc-doping on the structure and charge distribution by considering pure Al clusters as well. The quantum theory of atoms in molecules (QTAIM) reveals that interior Al atoms have large negative atomic charges (≈2a.u.) and hence the atoms surrounding them are considerably electron deficient. The Interacting Quantum Atoms (IQA) energy partition allowed us to establish the nature of the interaction between the Al13 superatom and the Al12Sc cluster with Al to form the complexes Al14 and Al13Sc, respectively. We also used the IQA approach to examine (i) the influence of Sc on the geometry of the AlnSc complexes along with (ii) the cooperative effects in the binding of AlnSc and Aln+1 clusters. We also exploited the QTAIM and IQA approaches to study the interaction of the electrophilic surface of the examined systems with CO2. Overall, we observe that the investigated Sc-doped Al complexes with a marked stability towards disproportionation reactions exhibit strong adsorption energies with CO2. Concomitantly, the carbon dioxide molecule is considerably distorted and destabilised, conditions which might prepare it for further chemical reactions. Altogether, this paper gives valuable insights on the tuning of the properties of metallic clusters for their design and exploitation in custom-made materials.

A real space picture of the role of steric effects in SN 2 reactions.

Within substitution reactions, the Bimolecular Nucleophilic Substitution (SN2) reaction mechanism is one of the most frequently found and studied ones. Among other factors, the easiness of the SN2 pathway is classically considered to be determined by steric hindrance. However, the diffuse nature of the latter inevitably darkens these and other arguments holding the pillars of chemical intuition. In this work, we employ the steric energy (E ST ) descriptor, formulated within the Interacting Quantum Atoms approach, to offer insights regarding this problem. The steric demands of the substrate, nucleophile and leaving group were studied using the gas‐phase SN2 reaction with different organic skeletons (CH3—, CH3CH2—, (CH3)2CH—, (CH3)3C—, (CH3)3CCH2—) and halogens (F, Cl, and Br) as test‐bed systems. Our results show that, according to E ST , the SH experienced along these simple reactions fits, in the general case, the trends predicted by a meticulous and rigorous application of chemical intuition. However, steric clash alone should not be considered as the only argument used to explain the easiness of the SN2 reaction over different electrophiles.

Partition of the electronic energy of the PM7 method via the interacting quantum atoms approach.

Partitions of the electronic energy such as that provided by the Interacting Quantum Atoms (IQA) approach have given valuable insights for numerous chemical systems and processes. Unfortunately, this kind of analysis may involve the integration of scalar fields over very irregular volumes, a condition which leads to a large and often prohibitive computational effort. These circumstances have limited the use of these energy partitions to systems comprising a few tens of atoms at most. On the other hand, semiempirical methods have proved useful in the study of systems of several thousands of atoms. Therefore, the goal of this work is to carry out partitions of the semiempirical method PM7 in compliance with the IQA approach. For this purpose, we computed one- and two-atomic energetic contributions whose sum equals the PM7 electronic energy. We illustrate how one might exploit the partition of electronic energies computed via the PM7 method by considering small organic and inorganic molecules and the energetics of individual hydrogen bond interactions within several water clusters which include (H2O)30, (H2O)50 and (H2O)100. We also considered the solvation of the amphiphilic caprylate anion to exemplify how to exploit the energy partition proposed in this paper. Overall, this investigation shows how the approach put forward herein might give further insights of the interactions occurring within complex systems in physical and biological chemistry.

Interacting Quantum Atoms Analysis of the Reaction Force: A Tool to Analyze Driving and Retarding Forces in Chemical Reactions.

The analysis of the reaction force and its topology has provided a wide range of fruitful concepts in the theory of chemical reactivity over the years, allowing to identify chemically relevant regions along a reaction profile. The reaction force (RF), a projection of the Hellmann-Feynman forces acting on the nuclei of a molecular system onto a suitable reaction coordinate, is partitioned using the interacting quantum atoms approach (IQA). The exact IQA molecular energy decomposition is now shown to open a unique window to identify and quantify the chemical entities that drive or retard a chemical reaction. The RF/IQA coupling offers an extraordinarily detailed view of the type and number of elementary processes that take reactants into products, as tested on two sets of simple reactions.

A Quantum Chemical Topology Picture of Intermolecular Electrostatic Interactions and Charge Penetration Energy.

Based on the Interacting Quantum Atoms approach, we present herein a conceptual and theoretical framework of short-range electrostatic interactions, whose accurate description is still a challenging problem in molecular modeling. For all the noncovalent complexes in the S66 database, the fragment-based and atomic decomposition of the electrostatic binding energies is performed using both the charge density of the dimers and the unrelaxed densities of the monomers. This energy decomposition together with dispersion corrections gives rise to a pairwise approximation to the total binding energy. It also provides energetic descriptors at varying distance that directly address the atomic and molecular electrostatic interactions as described by point-charge or multipole-based potentials. Additionally, we propose a consistent definition of the charge penetration energy within quantum chemical topology, which is mainly characterized in terms of the intramolecular electrostatic energy. Finally, we discuss some practical implications of our results for the design and validation of electrostatic potentials.

Energetic Descriptors of Steric Hindrance in Real Space: An Improved IQA Picture*.

Steric hindrance (SH) plays a central role in the modern chemical narrative, lying at the core of chemical intuition. As it however happens with many successful chemical concepts, SH lacks an underlying physically sound root, and multiple mutually inconsistent approximations have been devised to relate this fuzzy concept to computationally derivable descriptors. We here argue that being SH related to spatial as well as energetic features of interacting systems, SH can be properly handled if we chose a real space energetic stance like the Interacting Quantum Atoms (IQA) approach. Drawing on previous work by Popelier and coworkers (ChemistryOpen 8, 560, 2019) we build an energetic estimator of SH, referred to as EST . We show that the rise in the self-energy of a fragment that accompanies steric congestion is a faithful proxy for the chemist's SH concept if we remove the effect of charge transfer. This can be done rigorously, and the EST here defined provides correct sterics even for hydrogen atoms, where the plain use of deformation energies leads to non-chemical results. The applicability of EST is validated in several chemical scenarios, going from atomic compressions to archetypal SN2 reactions. EST is shown to be a robust steric hindrance descriptor.

Challenging the electrostatic σ-hole picture of halogen bonding using minimal models and the interacting quantum atoms approach.

Among the different noncovalent interactions, halogen bonds have captured wide attention in the last years. Their stability has been rationalized in electrostatic terms by appealing to the σ-hole concept, a charge-depleted region that is able to interact favorably with electron rich moieties. This interpretation has been questioned, and in this work a set of anionic halogen model systems are used to shed some light on this issue. We use the interacting quantum atoms method, which provides an orbital invariant energy decomposition in which pure electrostatic terms are well isolated, and we complement our insights with the analysis of electrostatic potentials (ESPs) as well as with traditional descriptors of charge accumulation like the Laplacian of the electron density. The total electrostatic interaction between the interacting species is surprisingly destabilizing in many of the systems examined, demonstrating that although σ-holes might be qualitatively helpful, much care has to be taken in ascribing the stability of these systems to electrostatics. It is clearly shown that electron delocalization is essential to understand the stability of the complexes. The evolution of atomic charges as the aggregates forms reveals a charge transfer picture in which the central, σ-hole bearing halogen acts as a mere spectator. These systems may then be not far from engaging in a classical 3c-4e interaction. Since the presence of a σ-hole as characterized by the ESP mapped on a suitable molecular envelope isosurface does not guarantee attractive electrostatic interactions, we encourage to employ a wider perspective that takes into account the full charge distribution.

Energetics of Electron Pairs in Electrophilic Aromatic Substitutions.

The interacting quantum atoms approach (IQA) as applied to the electron-pair exhaustive partition of real space induced by the electron localization function (ELF) is used to examine candidate energetic descriptors to rationalize substituent effects in simple electrophilic aromatic substitutions. It is first shown that inductive and mesomeric effects can be recognized from the decay mode of the aromatic valence bond basin populations with the distance to the substituent, and that the fluctuation of the population of adjacent bonds holds also regioselectivity information. With this, the kinetic energy of the electrons in these aromatic basins, as well as their mutual exchange-correlation energies are proposed as suitable energetic indices containing relevant information about substituent effects. We suggest that these descriptors could be used to build future reactive force fields.

High coordination number actinide-noble gas complexes; a computational study.

The geometries, electronic structures and bonding of early actinide-noble gas complexes are studied computationally by density functional and wavefunction theory methods, and by ab initio molecular dynamics. AcHe183+ is confirmed as being an 18-coordinate system, with all of the He atoms accommodated in the primary coordination shell, and this record coordination number is reported for the first time for Th4+ and Th3+. For Pa and U in their group valences of 5 and 6 respectively, the largest number of coordinated He atoms is 17. For AnHe17q+ (An = Ac, q = 3; An = Th, q = 4; An = Pa, q = 5; An = U, q = 6), the average An-He binding energy increases significantly across the series, and correlates linearly with the extent of He → Anq+ charge transfer. The interatomic exchange-correlation term Vxc obtained from the interacting quantum atoms approach correlates linearly with the An-He quantum theory of atoms-in-molecules delocalization index, both indicating that covalency increases from AcHe173+ to UHe176+. The correlation energy in AnHe163+ obtained from MP2 calculations decreases in the order Pa > Th > U > Ac, the same trend found in Vxc. The most stable complexes of Ac3+ with the heavier noble gases Ar-Xe are 12 coordinate, best described as Ng12 cages encapsulating an Ac3+ ion. There is enhanced Ng → Ac3+ charge transfer as the Ng gets heavier, and Ac-Ng covalency increases.

The X-ray constrained wavefunction of the [Mn(CO)4{(C6H5)2P-S-C(Br2)-P(C6H5)2}]Br complex: a theoretical and experimental study of dihalogen bonds and other noncovalent interactions.

The synthesis and X-ray structure determination of the [Mn(CO)4{(C6H5)2P-S-C(Br2)-P(C6H5)2}]Br complex (1) are described. The C-Br...Br dihalogen bond present in 1 has been characterized by means of topological studies of the electron density. Both the quantum theory of atoms in molecules and the electron localization function approaches have been applied to several theoretically calculated wavefunctions as well as to an X-ray constrained wavefunction. In addition, a number of theoretical techniques, such as the source function, the reduced density gradient method and the interacting quantum atoms approach, among others, have been used to analyse the dihalogen bond as well as several intramolecular interactions of the type C-H...Br-C which have also been detected in 1. The results show clearly that while bonding in the latter interactions are dominated by electrostatic components, the former has a high degree of covalency.

Interatomic exchange‐correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

Reactivity of α,ω-Dihydrofluoropolyethers toward OH Predicted by Multiconformer Transition State Theory and the Interacting Quantum Atoms Approach.

We report rate constants for the tropospheric reaction between the OH radical and α,ω-dihydrofluoropolyethers, which represent a specific class of the hydrofluoropolyethers family with the formula HF2C(OCF2CF2)p(OCF2)qOCF2H. Four cases were considered: p0q2, p0q3, p1q0, and p1q1 (pxqy denoting p = x and q = y) with the calculations performed by a cost-effective protocol developed for bimolecular hydrogen-abstraction reactions. This protocol is based on multiconformer transition state theory and relies on computationally accessible M08-HX/apcseg-2//M08-HX/pcseg-1 calculations. Within the protocol's approximations, the results show that (1) the calculated rate constants are within a factor of five of the experimental results (p1q0 and p1q1) and (2) the chain length and composition have a negligible effect on the rate constants, which is consistent with the experimental work. The interacting quantum atoms energy decomposition scheme is used to analyze the observed trends and extract chemical information related to the imaginary frequencies and barrier heights that are key parameters controlling the reactivity of the reaction. The intramolecular exchange-correlation contributions in the reactants and transition states were found to be the dominating factor.

Cooperativity in alkane-1,2- and 1,3-polyols: NMR, QTAIM, and IQA study of O─H… OH and C─H… OH bonding interactions.

Proton nuclear magnetic resonance chemical shifts and atom-atom interaction energies for alkanepolyols with 1,2-diol and 1,3-diol repeat units, and for their 1:1 pyridine complexes, are computed by density functional theory calculations. In the 1,3-polyols, based on a tG'Gg' repeat unit, the only important intramolecular hydrogen bonding interactions are O─H… OH. By quantum theory of atoms in molecules analysis of the electron density, unstable bond and ring critical points are found for such interactions in 1,2-polyols with tG'g repeat units, from butane-1,2,3,4-tetrol onwards and in their pyridine complexes from propane-1,2,3-triol onwards. Several features (OH proton shifts and charges, and interaction energies computed by the interacting quantum atoms approach) are used to monitor the dependence of cooperativity on chain length: This is much less regular in 1,2-polyols than in 1,3-polyols and by most criteria has a higher damping factor. Well defined C─H… OH interactions are found in butane-1,2,3,4-tetrol and higher members of the 1,2-polyol series, as well as in their pyridine complexes: There is no evidence for cooperativity with O─H… OH bonding. For the 1,2-polyols, there is a tenuous empirical relationship between the existence of a bond critical point for O─H… OH hydrogen bonding and the interaction energies of competing exchange channels, but the primary/secondary ratio is always less than unity.

Theoretical scrutinization of nine benzoic acid dimers: Stability and energy decomposition analysis

AbstractAromatic carboxylic acids are able to form diverse dimers and multimers due to their hydrogen bond donor and acceptor cites, as well as the aromatic rings. In this work, we examine nine benzoic acid dimers stabilized by hydrogen bonding and stacking interactions. Interacting quantum atoms methodology revealed that dominant attractive interactions in all of them, including hydrogen bonded systems, are due to exchange‐correlation. Coulomb interactions are significant only in the most stable dimer with a double hydrogen bond, although the corresponding energy term is almost two times lower compared to the nonclassical one. Since interacting quantum atoms approach treats monomers binding by considering electronic energy only, in order to examine dissociation kinetics we performed density functional theory‐based molecular dynamics simulations of selected stacked dimers: in 40% of the studied systems at 300 K thermal energy was sufficient to overpower barrier for dissociation within 1 ps, which resulted in the separation of the monomers, whereas 20% of them remained in the stacked position even after 5 ps. These results highlight the importance of noncovalent interactions, particularly weak stacking interactions, on the structure and dynamics of carboxylic acids and their derivatives.

Featuring I···N Halogen Bond and Weaker Interactions in Iodoperfluoroalkylimidazoles: An Experimental and Theoretical Charge Density Study

The experimental charge density distribution of two new iodoperfluoroalkylimidazole derivatives has been determined with the aspherical atom model against single-crystal X-ray diffracted intensities and analyzed by means of the Bader Quantum Theory of Atoms In Molecules. The compounds self-assemble in the solid state forming infinite chains through strong I···N halogen bonds. The topological and energetic features of these interactions have been determined and compared with those of a previously reported I···N interaction formed by an iodoperfluoroarene derivative, allowing elucidation of the role of hybridization of the carbon atom bonded to the halogen atom in the nature of the halogen bonding interaction. The weaker interactions present in the crystal structures have been investigated as well, with particular attention to F···F interactions. They have also been analyzed through the Interacting Quantum Atoms approach in order to elucidate their role in stabilizing the crystal structure.

Interacting Quantum Atoms Approach and Electrostatic Solvation Energy: Assessing Atomic and Group Solvation Contributions.

The interacting quantum atoms (IQA) method decomposes the total energy of a molecular system in terms of one- and two-center (atomic) contributions within the context of the quantum theory of atoms in molecules. Here we incorporate electrostatic continuum solvent effects into the IQA energy decomposition. To this end, the interaction between the solute electrostatic potential and the solvent screening charges as defined within the COSMO solvation model is now included in a new version of the PROMOLDEN code, allowing thus to apply IQA in combination with COSMO-quantum chemical methods as well as to partition the electrostatic solvation energy into effective atomic and group contributions. To test the robustness of this approach, we carry out COSMO-HF/aug-cc-pVTZ calculations followed by IQA calculations on more than 400 neutral and ionic solutes extracted from the MNSol database. The computational results reveal a detailed atomic mapping of the electrostatic solvation energy that is useful to assess to what extent the solvation energy can be decomposed into atomic and group contributions of various parts of a solute molecule, as generally assumed by empirical methodologies that estimate solvation energy and/or logP values.