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

Understanding the coupling of non-metallic heteroatoms to CO2 from a Conceptual DFT perspective

CONTEXT

A Conceptual DFT (CDFT) study has been carry out to analyse the coupling reactions of the simplest amine (CH3NH2), alcohol (CH3OH), and thiol (CH3SH) compounds with CO2 to form the corresponding adducts CH3NHCO2H, CH3OCO2H, and CH3SCO2H. The reaction mechanism takes place in a single step comprising two chemical events: nucleophilic attack of the non-metallic heteroatoms to CO2 followed by hydrogen atom transfer (HAT). According to our calculations, the participation of an additional nucleophilic molecule as HAT assistant entails important decreases in activation electronic energies. In such cases, the formation of a six-membered ring in the transition state (TS) reduces the angular stress with respect to the non-assisted paths, characterised by four-membered ring TSs. Through the analysis of the energy and reaction force profiles along the intrinsic reaction coordinate (IRC), the ratio of structural reorganisation and electronic rearrangement for both activation and relaxation energies has been computed. In addition, the analysis of the electronic chemical potential and reaction electronic flux profiles confirms that the highest electronic activity as well as their changes take place in the TS region. Finally, the distortion/interaction model using an energy decomposition scheme based on the electron density along the reaction coordinate has been carried out and the relative energy gradient (REG) method has been applied to identify the most important components associated to the barriers.

METHODS

The theoretical calculation were performed with Gaussian-16 scientific program. The B3LYP-D3(BJ)/aug-cc-pVDZ level was used for optimization of the minima and TSs. IRC calculations has also been carried out connecting the TS with the associated minima. Conceptual-DFT (CDFT) calculations have been carried out with the Eyringpy program and in-house code. The distortion/interaction model along the reaction coordinate have used the decomposition scheme of Mandado et al. and the analysis of the importance of each components have been done with the relative energy gradient (REG) method.

Capture of CO2 by Melamine Derivatives: A DFT Study Combining the Relative Energy Gradient Method with an Interaction Energy Partitioning Scheme

A theoretical study of the interaction between melamine and CO2 was carried out using density functional theory (DFT) with the B3LYP-D3(BJ)/aug-cc-pVTZ level of theory. The presence of anions interacting with melamine transforms the weakly bonded tetrel complexes into adducts. Thus, melamine acts as an FLP (frustrated Lewis pair) with acid groups (NHs as hydrogen bond donors) and a base group (N of the triazine ring). The application of the relative energy gradient formalism (REG) along the reaction coordinate has demonstrated that the ability of the melamine-anion systems to capture CO2 is linked to its capacity to polarize the CO2 molecule. These results have been confirmed by placing the melamine:CO2 complex in a uniform electric field with different strengths.

Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap

Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.

How to Compute Atomistic Insight in DFT Clusters: The REG-IQA Approach

The relative energy gradient (REG) method is paired with the topological energy partitioning method interacting quantum atoms (IQA), as REG-IQA, to provide detailed and unbiased knowledge on the intra- and interatomic interactions. REG operates on a sequence of geometries representing a dynamical change of a system. Its recent application to peptide hydrolysis of the human immunodeficiency virus-1 (HIV-1) protease (PDB code: 4HVP) has demonstrated its full potential in recovering reaction mechanisms and through-space electrostatic and exchange-correlation effects, making it a compelling tool for analyzing enzymatic reactions. In this study, the computational efficiency of the REG-IQA method for the 133-atom HIV-1 protease quantum mechanical system is analyzed in every detail and substantially improved by means of three different approaches. The first approach of smaller integration grids for IQA integrations reduces the computational overhead by about a factor of 3. The second approach uses the line-simplification Ramer-Douglas-Peucker (RDP) algorithm, which outputs the minimal number of geometries necessary for the REG-IQA analysis for a predetermined root mean squared error (RMSE) tolerance. This cuts the computational time of the whole REG analysis by a factor of 2 if an RMSE of 0.5 kJ/mol is considered. The third approach consists of a "biased" or "unbiased" selection of a specific subset of atoms of the whole initial quantum mechanical model wave-function, which results in more than a 10-fold speed-up per geometry for the IQA calculation, without deterioration of the outcome of the REG-IQA analysis. Finally, to show the capability of these approaches, the findings gathered from the HIV-1 protease system are also applied to a different system named haloalcohol dehalogenase (HheC). In summary, this study takes the REG-IQA method to a computationally feasible and highly accurate level, making it viable for the analysis of a multitude of enzymatic systems.

Intermolecular Covalent Interactions: Nature and Directionality

Quantum chemical methods were employed to analyze the nature and the origin of the directionality of pnictogen (PnB), chalcogen (ChB), and halogen bonds (XB) in archetypal F_m Z⋅⋅⋅F^- complexes (Z=Pn, Ch, X), using relativistic density functional theory (DFT) at ZORA-M06/QZ4P. Quantitative Kohn-Sham MO and energy decomposition analyses (EDA) show that all these intermolecular interactions have in common that covalence, that is, HOMO-LUMO interactions, provide a crucial contribution to the bond energy, besides electrostatic attraction. Strikingly, all these bonds are directional (i.e., F-Z⋅⋅⋅F^- is approximately linear) despite, and not because of, the electrostatic interactions which, in fact, favor bending. This constitutes a breakdown of the σ-hole model. It was shown how the σ-hole model fails by neglecting both, the essential physics behind the electrostatic interaction and that behind the directionality of electron-rich intermolecular interactions. Our findings are general and extend to the neutral, weaker ClI⋅⋅⋅NH₃ , HClTe⋅⋅⋅NH₃ , and H₂ ClSb⋅⋅⋅NH₃ complexes.

Factors contributing to halogen bond strength and stretch or contraction of internal covalent bond

The halogen bond formed by a series of Lewis acids TF₃X (T = C, Si, Ge, Sn, Pb; X = Cl, Br, I) with NH₃ is studied by quantum chemical calculations. The interaction energy is closely mimicked by the depth of the σ-hole on the X atom as well as the full electrostatic energy. There is a first trend by which the hole is deepened if the T atom to which X is attached becomes more electron-withdrawing: C > Si > Ge > Sn > Pb. On the other hand, larger more polarizable T atoms are better able to transmit the electron-withdrawing power of the F substituents. The combination of these two opposing factors leaves PbF₃X forming the strongest XBs, followed by CF₃X, with SiF₃X engaging in the weakest bonds. The charge transfer from the NH₃ lone pair into the σ*(TX) antibonding orbital tends to elongate the covalent TX bond, and this force is largest for the heavier X and T atoms. On the other hand, the contraction of this bond deepens the σ-hole at the X atom, which would enhance both the electrostatic component and the full interaction energy. This bond-shortening effect is greatest for the lighter X atoms. The combination of these two opposing forces leaves the T-X bond contracting for X = Cl and Br, but lengthening for I.

The IQA Energy Partition in a Drug Design Setting: A Hepatitis C Virus RNA-Dependent RNA Polymerase (NS5B) Case Study

The interaction of the thumb site II of the NS5B protein of hepatitis C virus and a pair of drug candidates was studied using a topological energy decomposition method called interacting quantum atoms (IQA). The atomic energies were then processed by the relative energy gradient (REG) method, which extracts chemical insight by computation based on minimal assumptions. REG reveals the most important IQA energy contributions, by atom and energy type (electrostatics, sterics, and exchange–correlation), that are responsible for the behaviour of the whole system, systematically from a short-range ligand–pocket interaction until a distance of approximately 22 Å. The degree of covalency in various key interatomic interactions can be quantified. No exchange–correlation contribution is responsible for the changes in the energy profile of both pocket–ligand systems investigated in the ligand–pocket distances equal to or greater than that of the global minimum. Regarding the hydrogen bonds in the system, a “neighbour effect” was observed thanks to the REG method, which states that a carbon atom would rather not have its covalent neighbour oxygen form a hydrogen bond. The combination of IQA and REG enables the automatic identification of the pharmacophore in the ligands. The coarser Interacting Quantum Fragments (IQF) enables the determination of which amino acids of the pocket contribute most to the binding and the type of energy of said binding. This work is an example of the contribution topological energy decomposition methods can make to fragment-based drug design.

Towards an atomistic understanding of polymorphism in molecular solids

Understanding and controlling polymorphism in molecular solids is a major unsolved problem in crystal engineering. While the ability to calculate accurate lattice energies with atomistic modelling provides valuable insight into the associated energy scales, existing methods cannot connect energy differences to the delicate balances of intra- and intermolecular forces that ultimately determine polymorph stability ordering. We report herein a protocol for applying Quantum Chemical Topology (QCT) to study the key intra- and intermolecular interactions in molecular solids, which we use to compare the three known polymorphs of succinic acid including the recently-discovered γ form. QCT provides a rigorous partitioning of the total energy into contributions associated with topological atoms, and a quantitative and chemically intuitive description of the intra- and intermolecular interactions. The newly-proposed Relative Energy Gradient (REG) method ranks atomistic energy terms (steric, electrostatic and exchange) by their importance in constructing the total energy profile for a chemical process. We find that the conformation of the succinic acid molecule is governed by a balance of large and opposing electrostatic interactions, while the H-bond dimerisation is governed by a combination of electrostatics and sterics. In the solids, an atomistic energy balance emerges that governs the contraction, towards the equilibrium geometry, of a molecular cluster representing the bulk crystal. The protocol we put forward is as general as the capabilities of the underlying quantum-mechanical model and it can provide novel perspectives on polymorphism in a wide range of chemical systems.

Theoretical treatment of IO-X (X = N2, CO, CO2, H2O) complexes

Iodine monoxide (IO) is an important component of the biogeochemical cycle of iodine. For instance, it is present in the troposphere, where it plays a crucial role in the physical chemical processes involving iodine containing compounds. Here, we present a theoretical study on a series of atmospherically relevant complexes of IO with N₂, CO, CO₂ and H₂O, where their structural and spectroscopic properties and their interaction energies are computed. Calculations are carried out by means of ab initio post Hartree-Fock (RCCSD(T) and RMP2) methods and density functional theory DFT (PBE0 and M05-2X) based approaches with and without the inclusion of dispersion correction. After comparison to RCCSD(T), we highlight the good performance of M05-2X(+D3) DFT in describing the bonding between IO and X (X = N₂, CO, CO₂, H₂O). Moreover, we found that the IO-X (X = N₂, CO, CO₂, H₂O) complexes are formed by non-covalent interactions between the two monomers. In sum, we characterized two types of complexes: I-bonded and O-bonded, where the former is more stable. The atmospheric implications of the present findings are also discussed such as in the formation of the iodine oxide particles (IOPs).

Proton leap: shuttling of protons onto benzonitrile

The detailed description of chemical transformations in the interstellar medium allows deciphering the origin of a number of small and medium - sized organic molecules. We present density functional theory analysis of proton transfer from the trihydrogen cation and the ethenium cation to benzonitrile, a recently discovered species in the Taurus Molecular Cloud 1. Detailed energy transformations along the reaction paths were analyzed using the interacting quantum atoms methodology, which elucidated how the proton carrier influences the lightness to deliver the proton to benzonitrile's nitrogen atom. The proton carriers' deformation energy represents the largest destabilizing effect, whereas a proton's promotion energy, the benzonitrile-proton Coulomb attraction, as well as non-classical benzonitrile-proton and carrier-proton interaction are the dominant stabilizing energy components. As two ion-molecule reactions proceed without energy barriers, rate constants were estimated using the classical capture theory and were found to be an order of magnitude larger for the reaction with the trihydrogen cation compared to that with the ethenium cation (∼10^-8 and 10^-9 cm³ s^-1, respectively). These results were obtained both with quantum chemical and ab initio molecular dynamics simulations (the latter performed at 10 K and 100 K), confirming that up to 100 K both systems choose energetically undemanding routes by tracking the corresponding minimum energy paths. A concept of a turning point is introduced, which is an equivalent to the transition state in barrierless reactions.

Implementation of the interacting quantum atom energy decomposition using the CASPT2 method

We present an implementation of the interacting quantum atom (IQA) energy decomposition scheme using the complete active space second-order perturbation theory (CASPT2). This combination yields a real-space interpretation tool with a proper account of the static and dynamic correlation that is particularly relevant for the description of processes in electronic excited states. The IQA/CASPT2 approach allows determination of the energy redistribution that takes place along a photophysical/photochemical deactivation path in terms of self- and interatomic contributions. The applicability of the method is illustrated by the description of representative processes spanning different bonding regimes: noble gas excimer and exciplex formation, the reaction of ozone with a chlorine atom, and the photodissociations of formaldehyde and cyclobutane. These examples show the versatility of using CASPT2 with the significant information provided by the IQA partition to describe chemical processes with a large multiconfigurational character.

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺ , Na⁺ , K⁺ , Be²⁺ , Mg²⁺ , and Ca²⁺ together with (ii) the anions F^- , Cl^- , Br^- , NO₃ ^- and SO₄ ^2- with water clusters (H₂ O)_n , n=1-8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.

New insights in chemical reactivity from quantum chemical topology

Based on the quantum chemical topology of the modified electron localization function ELF_x , an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange-correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first-order variation in the coulomb intermolecular energy defined in terms of the response to changes in the number of electrons. Illustrative examples with the formation of the dative bond B-N involved in the BH₃ NH₃ molecule and the typical formation of the hydrogen bond in the canonical water dimer are presented. For these selected systems, our approach unveils a noticeable mimicking of E_dual onto the DFT intermolecular interaction energy surface calculated between the both reactants. An automated reaction-path algorithm aimed to determine the most favorable relative orientations when the two molecules approach each other is also outlined.

The significance of the metal cation in guanine-quartet – metalloporphyrin complexes

The distinct positions of the divalent metal ions with respect to the porphyrin ring are responsible for different interaction energies between metalloporphyrins and the guanine quartet.

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18, 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h ). The strongest HBs within H₂ O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂ O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂ O clusters.

An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study of the Halogen Bond with Explicit Analysis of Electron Correlation

Energy profiles of seven halogen-bonded complexes were analysed with the topological energy partitioning called Interacting Quantum Atoms (IQA) at MP4(SDQ)/6-31+G(2d,2p) level of theory. Explicit interatomic electron correlation energies are included in the analysis. Four complexes combine X₂ (X = Cl or F) with HCN or NH₃, while the remaining three combine ClF with HCN, NH₃ or N₂. Each complex was systematically deformed by translating the constituent molecules along its central axis linking X and N, and reoptimising its remaining geometry. The Relative Energy Gradient (REG) method (Theor. Chem. Acc. 2017, 136, 86) then computes which IQA energies most correlate with the total energy during the process of complex formation and further compression beyond the respective equilibrium geometries. It turns out that the covalent energy (i.e., exchange) of the halogen bond, X…N, itself drives the complex formation. When the complexes are compressed from their equilibrium to shorter X…N distance then the intra-atomic energy of N is in charge. When the REG analysis is restricted to electron correlation then the interatomic correlation energy between X and N again drives the complex formation, and the complex compression is best described by the destabilisation of the through-space correlation energy between N and the "outer" halogen.

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.