Exchange-correlation effects in interatomic energies for pure density functionals and their application to the molecular energy prediction.

In this proof-of-concept paper, we show how exchange-correlation effects can be simply recovered for interatomic energies within the interacting quantum atoms decomposition when local, gradient generalized, or meta-gradient generalized approximations are used in density functional theory (DFT) calculations. We also demonstrate how inhomogeneity and non-local effects can be introduced even from a pure local scheme, without resorting to any orbital information. Finally, we provide numerical evidence on a database of selected energetic molecules that this decomposition scheme can be efficiently used to build accurate models for the prediction of molecular energies from an initial "cheap" DFT calculation.

FFLUX molecular simulations driven by atomic Gaussian process regression models.

Machine learning (ML) force fields are revolutionizing molecular dynamics (MD) simulations as they bypass the computational cost associated with ab initio methods but do not sacrifice accuracy in the process. In this work, the GPyTorch library is used to create Gaussian process regression (GPR) models that are interfaced with the next-generation ML force field FFLUX. These models predict atomic properties of different molecular configurations that appear in a progressing MD simulation. An improved kernel function is utilized to correctly capture the periodicity of the input descriptors. The first FFLUX molecular simulations of ammonia, methanol, and malondialdehyde with the updated kernel are performed. Geometry optimizations with the GPR models result in highly accurate final structures with a maximum root-mean-squared deviation of 0.064 Å and sub-kJ mol-1 total energy predictions. Additionally, the models are tested in 298 K MD simulations with FFLUX to benchmark for robustness. The resulting energy and force predictions throughout the simulation are in excellent agreement with ab initio data for ammonia and methanol but decrease in quality for malondialdehyde due to the increased system complexity. GPR model improvements are discussed, which will ensure the future scalability to larger systems.

Classical versus Collective Interactions in Asymmetric Trigonal Bipyramidal Alkaline Metal-Boron Halide Complexes.

Collective interactions are a novel type of chemical bond formed between metals and electron-rich substituents around an electron-poor central atom. So far only a limited number of candidates for having collective interactions are reported. In this work, we extend the newly introduced concept of collective bonding to a series of neutral boron complexes with the general formula M2BX3 (M=Li, Na, and K; X=F, Cl, and Br). Our state-of-the-art ab initio computations suggest that these complexes form trigonal bipyramidal structures with a D3h to C3v distortion along the C3 axis of symmetry. The BX3 unit in the complexes distorts from planar to pyramidal akin to a sp3 hybridized atom. Interestingly, the interaction of the metals with the pyramidal side of BX3, where the lone pair in a hypothetical [BX3]2- should be located, is weaker than the interactions of metals with the inverted side, i. e., the middle of three halogen atoms. The origin of this stronger interaction can be explained by the formation of collective interactions between metals and halogen atoms as we explored via energy decomposition within the context of the theory of interacting quantum atoms, IQA.

Determining the Factors Accounting for Reaction Selectivity: A Relative Energy Gradient - Interacting Quantum Atoms and Natural Bonding Orbitals Study.

Identifying the main physicochemical properties accounting for the course of a reaction is of utmost importance to rationalize chemical syntheses. To this aim, the relative energy gradient (REG) method is an appealing approach because it is an unbiased and automatic process to extract the most relevant pieces of energy information. Initially formulated within the interacting quantum atoms (IQA) framework for a single reaction, here we extend the REG method to natural bond orbitals (NBO) analysis and to the case of two competitive processes. This development enables the determination of the driving forces of any chemical selectivity. We illustrate the extended REG method on the case study of ring opening in cyclobutenes, which is an important instance of the so-called torquoselectivity.

Does Aromaticity Play a Role in Electronic and Structural Properties of YBn (n=2-14) Clusters?

Nanoclusters exhibit electronic, optical, and magnetic properties that differ significantly from those of extended and molecular systems with comparable stoichiometries. In this work, we examined the structural, energetic, and electronic characteristics of yttrium-doped boron clusters (YBn,  n =2-14) with robust wavefunction analysis tools. Special emphasis is placed on the elucidation of the potential aromatic character exhibited by the resultant molecules and how it can affect their chemical bonding and stability. Our results revealed that the YBn stability is governed by the maximization of the ionic Y-B interactions. This is evidenced from the lowest-energy conformations, which manifest as half-sandwich structures wherein the majority of boron atoms are bonded to yttrium. The stabilization of such chemical contacts comes at the expense of a notorious depletion of the Y local electron density, crystallizing in a considerable ionic character, close to Y2+ + Bn2-. Such a  charge transfer is coupled to the enhancement of the electron delocalization within the YBn lattice, resulting in quite remarkable local and global aromatic characters. Altogether, this study shows how the toolkit of real space chemical bonding descriptors can offer valuable insights into the structural and electronic properties,  of YBn clusters, contributing to a better understanding of their behavior.

Revealing the Critical Role of Global Electron Density Transfer in the Reaction Rate of Polar Organic Reactions within Molecular Electron Density Theory.

The critical role of global electron density transfer (GEDT) in increasing the reaction rate of polar organic reactions has been studied within the framework of Molecular Electron Density Theory (MEDT). To this end, the series of the polar Diels-Alder (P-DA) reactions of cyclopentadiene with cyanoethylene derivatives, for which experimental kinetic data are available, have been chosen. A complete linear correlation between the computed activation Gibbs free energies and the GEDT taking place at the polar transition state structures (TSs) is found; the higher the GEDT at the TS, the lower the activation Gibbs free energy. An interacting quantum atoms energy partitioning analysis allows for establishing a complete linear correlation between the electronic stabilization of the electrophilic ethylene frameworks and the GEDT taking place at the polar TSs. This finding supports Parr's proposal for the definition of the electrophilicity ω index. The present MEDT study establishes the critical role of the GEDT in the acceleration of polar reactions, since the electronic stabilization of the electrophilic framework with the electron density gain is greater than the destabilization of the nucleophilic one, making a net favorable electronic contribution to the decrease in the activation energy.

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.

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

Within substitution reactions, the Bimolecular Nucleophilic Substitution (SN 2) reaction mechanism is one of the most frequently found and studied ones. Among other factors, the easiness of the SN 2 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 (EST ) 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 SN 2 reaction with different organic skeletons (CH3 , CH3 CH2 , (CH3 )2 CH, (CH3 )3 C, (CH3 )3 CCH2 ) and halogens (F, Cl, and Br) as test-bed systems. Our results show that, according to EST , 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 SN 2 reaction over different electrophiles.

A fast approximate extension of the interacting quantum atoms energy decomposition to excited states.

An approach is developed for the fast calculation of the interacting quantum atoms energy decomposition (IQA) from the information contained in the first order reduced density matrix only. The proposed methodology utilizes an approximate exchange-correlation density from Density Matrix Functional Theory without the need to evaluate the correlation-exchange contribution directly. Instead, weight factors are estimated to decompose the exact Vxc into atomic and pairwise contributions. In this way, the sum of the IQA contributions recovers the energy obtained from the electronic structure calculation. This method can, hence, be applied to obtain atomic contributions in excited states on the same footing as in their ground states using any method that delivers the reduced first-order density matrix. In this way, one can locate chromophores from first principles quantum chemical calculations. Test calculations on the ground and excited states of a set of small molecules indicate that the scaled atomic contributions reproduce vertical electronic transition energies calculated exactly. This approach may be useful to extend the applicability of the IQA approach in the study of large photochemical systems especially when the calculations of the second order reduced density matrices is prohibitive or not possible.

Binding Energy Partition of Promising IRAK-4 Inhibitor (Zimlovisertib) for the Treatment of COVID-19 Pneumonia.

The technique of Fragment-Based Drug Design (FBDD) considers the interactions of different moieties of molecules with biological targets for the rational construction of potential drugs. One basic assumption of FBDD is that the different functional groups of a ligand interact with a biological target in an approximately additive, that is, independent manner. We investigated the interactions of different fragments of ligands and Interleukin-1 Receptor-Associated Kinase 4 (IRAK-4) throughout the FBDD design of Zimlovisertib, a promising anti-inflammatory, currently in trials to be used for the treatment of COVID-19 pneumonia. We utilised state-of-the-art methods of wave function analyses mainly the Interacting Quantum Atoms (IQA) energy partition for this purpose. By means of IQA, we assessed the suitability of every change to the ligand in the five stages of FBDD which led to Zimlovisertib on a quantitative basis. We determined the energetics of the interaction of different functional groups in the ligands with the IRAK-4 protein target and thereby demonstrated the adequacy (or lack thereof) of the changes made across the design of this drug. This analysis permits to verify whether a given alteration of a prospective drug leads to the intended tuning of non-covalent interactions with its protein objective. Overall, we expect that the methods exploited in this paper will prove valuable in the understanding and control of chemical modifications across FBDD processes.

A QCT View of the Interplay between Hydrogen Bonds and Aromaticity in Small CHON Derivatives.

The somewhat elusive concept of aromaticity plays an undeniable role in the chemical narrative, often being considered the principal cause of the unusual properties and stability exhibited by certain π skeletons. More recently, the concept of aromaticity has also been utilised to explain the modulation of the strength of non-covalent interactions (NCIs), such as hydrogen bonding (HB), paving the way towards the in silico prediction and design of tailor-made interacting systems. In this work, we try to shed light on this area by exploiting real space techniques, such as the Quantum Theory of Atoms in Molecules (QTAIM), the Interacting Quantum Atoms (IQA) approaches along with the electron delocalisation indicators Aromatic Fluctuation (FLU) and Multicenter (MCI) indices. The QTAIM and IQA methods have been proven capable of providing an unbiased and rigorous picture of NCIs in a wide variety of scenarios, whereas the FLU and MCI descriptors have been successfully exploited in the study of diverse aromatic and antiaromatic systems. We used a collection of simple archetypal examples of aromatic, non-aromatic and antiaromatic moieties within organic molecules to examine the changes in π delocalisation and aromaticity induced by the Aromaticity and Antiaromaticity Modulated Hydrogen Bonds (AMHB). We observed fundamental differences in the behaviour of systems containing the HB acceptor within and outside the ring, e.g., a destabilisation of the rings in the former as opposed to a stabilisation of the latter upon the formation of the corresponding molecular clusters. The results of this work provide a physically sound basis to rationalise the strengthening and weakening of AMHBs with respect to suitable non-cyclic non-aromatic references. We also found significant differences in the chemical bonding scenarios of aromatic and antiaromatic systems in the formation of AMHB. Altogether, our investigation provide novel, valuable insights about the complex mutual influence between hydrogen bonds and π systems.

An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Analysis of the Anomeric Effect.

The explanation of the anomeric effect in terms of underlying quantum properties is still controversial almost 70 years after its introduction. Here, we use a method called Relative Energy Gradient (REG), which is able to compute chemical insight with a view to explaining the anomeric effect. REG operates on atomic energy contributions generated by the quantum topological energy decomposition Interacting Quantum Atoms (IQA). Based on the case studies of dimethoxymethane and 2-fluorotetrahydropyran, we show that the anomeric effect is electrostatic in nature rather than governed by hyperconjugation.

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.

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.

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 SO42- 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.

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.

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.

Efficient implementation of the interacting quantum atoms energy partition of the second-order Møller-Plesset energy.

We describe an efficient implementation of the partition of the second-order Møller-Plesset (MP2) correlation energy within the interacting quantum atoms (IQA) energy decomposition. We simplify the IQA integration bottleneck by considering only the occupied to virtual elements of the second order reduced density matrix, a procedure that reduces substantially the size of the two-electron matrix, which has to be addressed. The algorithmic improvements described herein allow to perform the decomposition of the MP2 correlation energy for medium size molecular systems using moderate computational resources. We expect that the methods developed in this investigation will prove useful to understand electron correlation effects through a real space perspective.

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 Ih ). 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.

Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer.

The development of chemical intuition in photochemistry faces several difficulties that result from the inadequacy of the one-particle picture, the Born-Oppenheimer approximation, and other basic ideas used to build models. It is shown herein how real-space approaches can be efficiently used to gain valuable insights in photochemistry through a simple example of red and blue shift effects: the double hypso- and bathochromic shifts in the low-lying valence excited states of (H2 O)2 . It is demonstrated that 1) the use of these techniques allows the perturbative language used in the theory of intermolecular interactions, even in the strongly interacting short-range regime, to be maintained; 2) one and only one molecule is photoexcited in each of the addressed excited states and 3) the electrostatic interaction between the in-the-cluster molecular dipoles provides a fairly intuitive rationalisation of the observed batho- and hypsochromism. The methods exploited and illustrated herein are able to maintain the individuality and properties of the interacting entities in a molecular aggregate, and thereby they allow chemical intuition in general states, at any geometry and using a broad variety of electronic structure methods to be kept and built.