Interacting Quantum Atoms-A Review

Predicting redox potentials by graph-based machine learning methods

The evaluation of oxidation and reduction potentials is a pivotal task in various chemical fields. However, their accurate prediction by theoretical computations, which is a complementary task and sometimes the only alternative to experimental measurement, may be often resource-intensive and time-consuming. This paper addresses this challenge through the application of machine learning techniques, with a particular focus on graph-based methods (such as graph edit distances, graph kernels, and graph neural networks) that are reviewed to enlighten their deep links with theoretical chemistry. To this aim, we establish the ORedOx159 database, a comprehensive, homogeneous (with reference values stemming from density functional theory calculations), and reliable resource containing 318 one-electron reduction and oxidation reactions and featuring 159 large organic compounds. Subsequently, we provide an instructive overview of the good practice in machine learning and of commonly utilized machine learning models. We then assess their predictive performances on the ORedOx159 dataset through extensive analyses. Our simulations using descriptors that are computed in an almost instantaneous way result in a notable improvement in prediction accuracy, with mean absolute error (MAE) values equal to 5.6 kcal mol- 1 for reduction and 7.2 kcal mol- 1 for oxidation potentials, which paves a way toward efficient in silico design of new electrochemical systems.

Exploring the influence of metal cations on individual hydrogen bonds in Watson-Crick guanine-cytosine DNA base pair: An interacting quantum atoms analysis

This study delves into the nature of individual hydrogen bonds and the relationship between metal cations and hydrogen bonding in the Watson-Crick guanine-cytosine (GC) base pair and its alkali and alkaline earth cation-containing complexes (Mn+-GC). The findings reveal how metal cations affect the nature and strength of individual hydrogen bonds. The study employs interacting quantum atoms (IQA) analysis to comprehensively understand three individual hydrogen bonds within the GC base pair and its cationic derivatives. These analyses unveil the nature and strength of hydrogen bonds and serve as a valuable reference for exploring the impact of cations (and other factors) on each hydrogen bond. All the H ⋯ D interactions (H is hydrogen and D is oxygen or nitrogen) in the GC base pair are primarily electrostatic in nature, with the charge transfer component playing a substantial role. Introducing a metal cation perturbs all H ⋯ D interatomic interactions in the system, weakening the nearest hydrogen bond to the cation (indicated by a) and reinforcing the other (b and c) interactions. Notably, the interaction a, the strongest H ⋯ D interaction in the GC base pair, becomes the weakest in the Mn+-GC complexes. A broader perspective on the stability of GC and Mn+-GC complexes is provided through interacting quantum fragments (IQF) analysis. This approach considers all pairwise interactions between fragments and intra-fragment components, offering a complete view of the factors that stabilize and destabilize GC and Mn+-GC complexes. The IQF analysis underscores the importance of electron sharing, with the dominant contribution arising from the inter-fragment exchange-correlation term, in shaping and sustaining GC and Mn+-GC complexes. From this point of view, alkaline and alkaline earth cations have distinct effects, with alkaline cations generally weakening inter-fragment interactions and alkaline earth cations strengthening them. In addition, IQA and IQF calculations demonstrate that the hydration of cations led to small changes in the hydrogen bonding network. Finally, the IQA interatomic energies associated with the hydrogen bonds and also inter-fragment interaction energies provide robust indicators for characterizing hydrogen bonds and complex stability, showing a strong correlation with total interaction energies.

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.

Photocatalyzed Cascade Hydrogen Atom Transfers for Assembly of Multi-Substituted α-SCF3 and α-SCF2H Cyclopentanones

A photocatalyzed formal (3+2) cycloaddition has been developed to construct original polysubstituted α-SCF3 cyclopentanones in a regio- and diastereoselective manner. This building block approach leverages trifluoromethylthio alkynes and branched/linear aldehydes, as readily available reaction partners, in consecutive hydrogen atom transfers and C-C bond formations. Difluoromethylthio alkynes are also compatible substrates. Furthermore, the potential for telescoped reaction starting from alcohols instead of aldehydes was demonstrated, as well as process automatization and scale-up under continuous microflow conditions. This prompted density functional theory (DFT) calculations to support a radical-mediated cascade process.

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.

Molecular Tailoring Approach for the Direct Estimation of Individual Noncovalent Interaction Energies in Molecular Systems

The noncovalent interactions (NCIs) are omnipresent in chemistry, physics, and biology. The study of such interactions offers insights into various physicochemical phenomena. Some indirect approaches proposed in the literature for exploring the NCIs are briefly reviewed in Section 1 of this Perspective. These include: (i) Shift in the stretching frequency of an X-Y bond involved in X-Y···Z interaction. (ii) Topological analysis of molecular electron density. (iii) Empirical equations derived employing experimental and theoretical quantities. However, a direct method for estimating individual intramolecular/intermolecular interaction energies has been conspicuous by its absence from the literature. We have developed a molecular tailoring approach (MTA)-based method enabling a direct and reliable estimation of the energy of intra- as well as intermolecular interactions. This method offers a direct and reliable estimation of these interactions, in particular of the hydrogen bonds (HB) in molecules/weakly bound clusters along with the respective cooperativity contribution. In Section 2, the basis of our method is discussed, along with some illustrative examples. The application of this method to a variety of molecules and clusters, with a special emphasis on estimating the HB energy along with the energy of other NCIs is presented in Section 3. Section 4 discusses some computational strategies for applying our method to large molecular clusters. The last Section provides a summary and a discussion on future developments.

Unusual quadruple bonds featuring collective interaction-type σ bonds between first octal-row atoms in the alkaline-earth compounds AeOLi2 (Ae = Be-Ba)

Quantum chemical calculations are reported for the complexes of alkaline earth metals AeOLi2 (Ae = Be-Ba) at the BP86-D3(BJ)/def2-QZVPP and CCSD(T)/def2-QZVPPQZVPP levels. The nature of the Ae-OLi2 bond has been analyzed with a variety of methods. The AeOLi2 molecules exhibit an unprecedented σ donor bond Ae→OLi2 where the (n)s2 lone-pair electrons of the Ae atom are donated to vacant O-Li2 antibonding orbitals having the largest coefficient at lithium. This is a covalent bond where the accumulation of the associated electronic charge is located at two positions above and below the Ae-OLi2 axis. The bifurcated component of orbital interactions is structurally related to the recently proposed collective bonding model, but exhibits a completely different type of bonding. The most stable isomer of AeOLi2 has a C 2v geometry and a singlet (1A1) electronic ground state. The bond dissociation energy (BDE) of the Ae-OLi2 bonds exhibits a zig-zag trend from BeOLi2 to BaOLi2, with BeOLi2 having the largest BDE (D e = 73.0 kcal mol-1) and MgOLi2 possessing the lowest BDE (D e = 42.3 kcal mol-1) at the CCSD(T) level. The calculation of the atomic partial charges by the Hirshfeld and Voronoi methods suggests that Be and Mg carry small negative charges in the lighter molecules whereas the heavier atoms Ca-Ba have small positive charges. In contrast, the NBO and QTAIM methods give positive charges for all Ae atoms that are larger for Ca-Ba than that calculated by the Hirshfeld and Voronoi approaches. The molecules AeOLi2 have large dipole moments where the negative end is at the Ae atom with the polarity Ae→OLi2. The largest dipole moments are predicted for the lighter species BeOLi2 and MgOLi2 and the smallest value is calculated for BaOLi2. The calculation of the vibrational spectra shows a significant red-shift toward lower wave numbers for the Ae-OLi2 stretching mode in comparison to diatomic AeO. Besides the Ae→OLi2 σ-donor bonds there are also three dative bonds due to Ae←OLi2 backdonation which consist of one σ bond and two π bonds. The appearance of strong Ae→OLi2 σ donation leads to quadruple bonds AeOLi2 in all systems AeOLi2, even for the lightest species with Ae = Be, Mg. The valence orbitals of Ca, Sr, and Ba, which are involved in the dative interactions, are the (n)s and (n-1)d AOs whereas Be and Mg use their (n)s and (n)p AOs. The EDA-NOCV results are supported by the AdNDP calculations which give four 2c-2e bonding orbitals. Three bonding orbitals have occupation numbers ∼2. One σ orbital has smaller occupation numbers between 1.32 and 1.73 due to the delocalization to the lithium atoms. The analysis of the electronic structure with the ELF method suggests multicenter bonds with mainly trisynaptic and tetrasynaptic basins, which also support the results of the EDA-NOCV calculations.

Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations

The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.

Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions

The molecular dipole polarizability can be decomposed into components corresponding to the charge flow between atoms and changes in atomic dipole moments. Such decompositions are recognized to depend on how atoms are defined within a molecule, as, for example, by Hirshfeld, iterative Stockholder, or quantum topology partitioning of the electron density. For some of these, however, there are significant differences between the numerical results obtained by analytical response methods and finite field calculations. We show that this difference is due to analytical response methods accounting for (only) the change in electron density by a perturbation, while finite field methods may also include a component corresponding to a perturbation-dependent change in the definition of an atom within a molecule. For some atom-in-molecule definitions, such as the iterative Hirshfeld, iterative Stockholder, and quantum topology methods, the latter effect significantly increases the charge flow component. The decomposition of molecular polarizability into atomic charge flow and induced dipole components thus depends on whether the atom-in-molecule definition is taken to be perturbation-dependent.

Explainable chemical artificial intelligence from accurate machine learning of real-space chemical descriptors

Machine-learned computational chemistry has led to a paradoxical situation in which molecular properties can be accurately predicted, but they are difficult to interpret. Explainable AI (XAI) tools can be used to analyze complex models, but they are highly dependent on the AI technique and the origin of the reference data. Alternatively, interpretable real-space tools can be employed directly, but they are often expensive to compute. To address this dilemma between explainability and accuracy, we developed SchNet4AIM, a SchNet-based architecture capable of dealing with local one-body (atomic) and two-body (interatomic) descriptors. The performance of SchNet4AIM is tested by predicting a wide collection of real-space quantities ranging from atomic charges and delocalization indices to pairwise interaction energies. The accuracy and speed of SchNet4AIM breaks the bottleneck that has prevented the use of real-space chemical descriptors in complex systems. We show that the group delocalization indices, arising from our physically rigorous atomistic predictions, provide reliable indicators of supramolecular binding events, thus contributing to the development of Explainable Chemical Artificial Intelligence (XCAI) models.

Questing for homoleptic mononuclear manganese complexes with monodentate O-donor ligands

Compounds containing Mn-O bonds are of utmost importance in biological systems and catalytic processes. Nevertheless, mononuclear manganese complexes containing all O-donor ligands are still rare. Taking advantage of the low tendency of the pentafluoroorthotellurate ligand (teflate, OTeF5) to bridge metal centers, we have synthesized two homoleptic manganese complexes with monomeric structures and an all O-donor coordination sphere. The tetrahedrally distorted MnII anion, [Mn(OTeF5)4]2-, can be described as a high spin d5 complex (S = 5/2), as found experimentally (magnetic susceptibility measurements and EPR spectroscopy) and using theoretical calculations (DFT and CASSCF/NEVPT2). The high spin d4 electronic configuration (S = 2) of the MnIII anion, [Mn(OTeF5)5]2-, was also determined experimentally and theoretically, and a square pyramidal geometry was found to be the most stable one for this complex. Finally, the bonding situation in both complexes was investigated by means of the Interacting Quantum Atoms (IQA) methodology and compared to that of hypothetical mononuclear fluoromanganates. Within each pair of [MnXn]2- (n = 4, 5) species (X = OTeF5, F), the Mn-X interaction is found to be comparable, therefore proving that the similar electronic properties of the teflate and the fluoride are also responsible for the stabilization of these unique species.

Probing Non-Covalent Interactions through Molecular Balances: A REG-IQA Study

The interaction energies of two series of molecular balances (1-X with X = H, Me, OMe, NMe2 and 2-Y with Y = H, CN, NO2, OMe, NMe2) designed to probe carbonyl…carbonyl interactions were analysed at the B3LYP/6-311++G(d,p)-D3 level of theory using the energy partitioning method of Interacting Quantum Atoms/Fragments (IQA/IQF). The partitioned energies are analysed by the Relative Energy Gradient (REG) method, which calculates the correlation between these energies and the total energy of a system, thereby explaining the role atoms have in the energetic behaviour of the total system. The traditional "back-of-the-envelope" open and closed conformations of molecular balances do not correspond to those of the lowest energy. Hence, more care needs to be taken when considering which geometries to use for comparison with the experiment. The REG-IQA method shows that the 1-H and 1-OMe balances behave differently to the 1-Me and 1-NMe2 balances because the latter show more prominent electrostatics between carbonyl groups and undergoes a larger dihedral rotation due to the bulkiness of the functional groups. For the 2-Y balance, REG-IQA shows the same behaviour across the series as the 1-H and 1-OMe balances. From an atomistic point of view, the formation of the closed conformer is favoured by polarisation and charge-transfer effects on the amide bond across all balances and is counterbalanced by a de-pyramidalisation of the amide nitrogen. Moreover, focusing on the oxygen of the amide carbonyl and the α-carbon of the remaining carbonyl group, electrostatics have a major role in the formation of the closed conformer, which goes against the well-known n-π* interaction orbital overlap concept. However, REG-IQF shows that exchange-correlation energies overtake electrostatics for all the 2-Y balances when working with fragments around the carbonyl groups, while they act on par with electrostatics for the 1-OMe and 1-NMe2. REG-IQF also shows that exchange-correlation energies in the 2-Y balance are correlated to the inductive electron-donating and -withdrawing trends on aromatic groups. We demonstrate that methods such as REG-IQA/IQF can help with the fine-tuning of molecular balances prior to the experiment and that the energies that govern the probed interactions are highly dependent on the atoms and functional groups involved.

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.

Hydrogen bond energy estimation (H-BEE) in large molecular clusters: A Python program for quantum chemical investigations

A procedure, derived from the fragmentation-based molecular tailoring approach (MTA), has been proposed and extensively applied by Deshmukh and Gadre for directly estimating the individual hydrogen bond (HB) energies and cooperativity contributions in molecular clusters. However, the manual fragmentation and high computational cost of correlated quantum chemical methods make the application of this method to large molecular clusters quite formidable. In this article, we report an in-house developed software for automated hydrogen bond energy estimation (H-BEE) in large molecular clusters. This user-friendly software is essentially written in Python and executed on a Linux platform with the Gaussian package at the backend. Two approximations to the MTA-based procedure, viz. the first spherical shell (SS1) and the Fragments-in-Fragments (Frags-in-Frags), enabling cost-effective, automated evaluation of HB energies and cooperativity contributions, are also implemented in this software. The software has been extensively tested on a variety of molecular clusters and is expected to be of immense use, especially in conjunction with correlated methods such as MP2, CCSD(T), and so forth.

Transferability of atomic energies from alchemical decomposition

We study alchemical atomic energy partitioning as a method to estimate atomization energies from atomic contributions, which are defined in physically rigorous and general ways through the use of the uniform electron gas as a joint reference. We analyze quantitatively the relation between atomic energies and their local environment using a dataset of 1325 organic molecules. The atomic energies are transferable across various molecules, enabling the prediction of atomization energies with a mean absolute error of 23 kcal/mol, comparable to simple statistical estimates but potentially more robust given their grounding in the physics-based decomposition scheme. A comparative analysis with other decomposition methods highlights its sensitivity to electrostatic variations, underlining its potential as a representation of the environment as well as in studying processes like diffusion in solids characterized by significant electrostatic shifts.

Expanding the Limits of Organic Energetic Materials: High-Performance Alliance of 1,3,4-Thiadiazole and Furazan Scaffolds

A majority of known and newly synthesized energetic materials comprise polynitrogen or nitrogen-oxygen heterocycles with various explosophores. However, available structural combinations of these organic scaffolds are finite and are about to reach their limits. Herein, we present the design and synthesis of a series of sulfur-containing polyazole structures comprising 1,3,4-thiadiazole and furazan rings linked by C-C bonds and enriched with energetic nitro and azo functionalities. In terms of detonation performance, all synthesized 1,3,4-thiadiazole-furazan assemblies (D = 7.7-7.9 km s-1; P = 26-28 GPa) lie between the powerful explosive TATB (D = 8.0 km s-1; P = 31 GPa) and melt-cast material TNT (D = 6.9 km s-1; P = 23 GPa). In the synthesized series, azo-bridged derivative 5 seems to be most practically interesting, as it combines a relatively high energetic performance (D = 7.9 km s-1; P = 28 GPa), a very high thermal stability (271 °C), and insensitivity to friction. By these functional properties, 5 outperforms the benchmark heat-resistant explosive hexanitrostilbene (HNS). To the best of our knowledge, this is the first example of an energetic alliance of furazan and 1,3,4-thiadiazole scaffolds and a rare case of sulfur-containing high-energy materials, which can certainly be considered as an evolutionary step in energetic materials science.

On the nature of the two-positron bond: evidence for a novel bond type

The nature of the newly proposed two-positron bond in (PsH)2, which is composed of two protons, four electrons and two positrons, is considered in this contribution. The study is done at the multi-component-Hartree-Fock (MC-HF) and the Diffusion Monte Carlo (DMC) levels of theory by comparing ab initio data, analyzing the spatial structure of the DMC wavefunction, and applying the multi-component quantum theory of atoms in molecules and the two-component interacting quantum atoms energy partitioning schemes to the MC-HF wavefunction. The analysis demonstrates that (PsH)2 to a good approximation may be conceived of as two slightly perturbed PsH atoms, bonded through a two-positron bond. In contrast to the usual two-electron bonds, the positron exchange phenomenon is quite marginal in the considered two-positron bond. The dominant stabilizing mechanism of bonding is a novel type of classical electrostatic interaction between the positrons, which are mainly localized between nuclei, and the surrounding electrons. To emphasize its uniqueness, this mechanism of bonding is proposed to be called gluonic which has also been previously identified as the main driving mechanism behind formation of the one-positron bond in [H-,e+,H-]. We conclude that the studied two-positron bond should not be classified as a covalent bond and it must be seen as a brand-new type of bond, foreign to the electronic bonding modes discovered so far in the purely electronic systems.

Strong carbon - noble gas covalent bond and fluxionality in hypercoordinate compounds

Thermodynamic, kinetic, and chemical bonding analysis at the coupled cluster level has been carried out for a series of hypercoordinated carbon compounds with formula CH4Ng2+ (Ng = He-Rn). Results show that these compounds could be stable at room temperature and Born-Oppenheimer molecular dynamics simulations (BOMD) in conjunction with activation energies indicate high kinetic stability. In addition, all chemical bonding descriptors agree with a strong C-Ng covalent bond and a bonding pattern similar to that of CH5+. Finally, BOMD simulations showed that these compounds are fluxional, with a continuous formation/breaking of H-H and C-H bonds. To the best of the authors' knowledge, these results represent the first series of fluxional compounds possessing a covalent bond between a main group element and a noble gas atom.

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

Interacting Quantum Atoms and Multipolar Electrostatic Study of XH···π Interactions

The interaction energies of nine XH···π (X = C, N, and O) benzene-containing van der Waals complexes were analyzed, at the atomic and fragment levels, using QTAIM multipolar electrostatics and the energy partitioning method interacting quantum atoms/fragment (IQA/IQF). These descriptors were paired with the relative energy gradient method, which solidifies the connection between quantum mechanical properties and chemical interpretation. This combination provides a precise understanding, both qualitative and quantitative, of the nature of these interactions, which are ubiquitous in biochemical systems. The formation of the OH···π and NH···π systems is electrostatically driven, with the Qzz component of the quadrupole moment of the benzene carbons interacting with the charges of X and H in XH. There is the unexpectedly intramonomeric role of X-H (X = O, N) where its electrostatic energy helps the formation of the complex and its covalent energy thwarts it. However, the CH···π interaction is governed by exchange-correlation energies, thereby establishing a covalent character, as opposed to the literature's designation as a noncovalent interaction. Moreover, dispersion energy is relevant, statically and in absolute terms, but less relevant compared to other energy components in terms of the formation of the complex. Multipolar electrostatics are similar across all systems.

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.

Further Perspectives on the Teflate versus Fluoride Analogy: The Case of a Co(II) Pentafluoroorthotellurate Complex

The pentafluoroorthotellurate group (teflate, OTeF5) is considered as a bulky analogue of fluoride, yet its coordination behavior in transition metal complexes is not fully understood. By reaction of [CoCl4]2- and neat ClOTeF5, we synthesized the first cobalt teflate complex, [Co(OTeF5)4]2-, which exhibits moisture-resistant Co-OTeF5 bonds. Through a combined experimental and theoretical (DFT and NEVPT2) study, the properties and electronic structure of this species have been investigated. It exhibits a distorted tetrahedral structure around the cobalt center and can be described as a d7 system with a quartet (S = 3/2) ground state. A comparative bonding analysis of the (pseudo)tetrahedral [CoX4]2- anions (X = OTeF5, F, Cl) revealed that the strength of the Co-X interaction is similar in the three cases, being the strongest in [Co(OTeF5)4]2-. In addition, an analysis of the charge of the Co center reinforced the similar electron-withdrawing properties of the teflate and fluoride ligands. Therefore, the [Co(OTeF5)4]2- anion constitutes an analogue of the polymeric [CoF4]2- in terms of electronic properties, but with a monomeric structure.

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.

Fragments-in-fragments method for efficient and reliable estimates of individual hydrogen bond energies in large molecular clusters

The knowledge of individual hydrogen bond (HB) strength in molecular clusters is indispensable to get insights into the bulk properties of condensed systems. Recently, we have developed the molecular tailoring approach based (MTA-based) method for the estimation of individual HB energy in molecular clusters. However, the direct use of this MTA-based method to large molecular clusters becomes progressively difficult with the increase in the size of a cluster. To overcome this caveat, herein, we propose the use of linear scaling method (such as the original MTA method) for the estimation of single-point (SP) energies of large-sized parent molecular cluster and their respective fragments. Because the fragments of the MTA-based method, for the estimation of HB energy, are further fragmented, this proposed strategy is called as Fragments-in-Fragments (Frags-in-Frags) method. The SP energies of fragments and parent cluster calculated by the Frags-in-Frags approach were utilized to estimate the individual HB energy. The estimated individual HB energies, in various molecular clusters, by Frags-in-Frags method are found to be in excellent linear agreement with their MTA-based counterparts (R²  = 0.9975 of 348 data points). The difference being less than 0.5 kcal/mol in most of the cases. Furthermore, RMSD is 0.43 kcal/mol, MAE is 0.33 kcal/mol, and the standard deviation is 0.44 kcal/mol. Importantly, the Frags-in-Frags method not only enables the reliable estimation of HB energy in large molecular clusters but also requires less computational time and can be possible even with off-the-shelf hardware.

On the Short-Range Nature of Cooperativity in Hydrogen-Bonded Large Molecular Clusters

The variation in the hydrogen bond (HB) strength has considerable consequences on the physicochemical properties of molecular clusters. Such a variation mainly arises due to the cooperative/anti-cooperative networking effect of neighboring molecules connected by HBs. In the present work, we systematically study the effect of neighboring molecules on the strength of an individual HB and the respective cooperativity contribution toward each of them in a variety of molecular clusters. For this purpose, we propose a use of a small model of a large molecular cluster called the spherical shell-1 (SS1) model. This SS1 model is constructed by placingg the spheres of an appropriate radius centered on X and Y atoms of the X-H···Y HB under consideration. The molecules falling within these spheres constitute the SS1 model. Utilizing this SS1 model, the individual HB energies are calculated within the molecular tailoring approach-based framework and the results are compared with their actual counterparts. It is found that the SS1 is a reasonably good model of large molecular clusters, providing 81-99% of the total HB energy estimated using the actual molecular clusters. This in turn suggests that the maximum cooperativity contribution toward a particular HB is due to the fewer number of molecules (in the SS1 model) directly interacting with two molecules involved in its formation. We further demonstrate that the remaining part of the energy or cooperativity (∼1 to 19%) is captured by the molecules falling in the second spherical shell (SS2) centered on the hetero-atom of the molecules in the SS1 model. The effect of increasing size of a cluster on the strength of a particular HB, calculated by the SS1 model, is also investigated. The calculated value of the HB energy remains unchanged with the increase in the size of a cluster, emphasizing the short-ranged nature of the HB cooperativity in neutral molecular clusters.

Quantum Alchemy Based Bonding Trends and Their Link to Hammett's Equation and Pauling's Electronegativity Model

We present an intuitive and general analytical approximation estimating the energy of covalent single and double bonds between participating atoms in terms of their respective nuclear charges with just three parameters, [E_AB ≈ a - bZ_AZ_B + c(Z_A^7/3 + Z_B^7/3) ]. The functional form of our expression models an alchemical atomic energy decomposition between participating atoms A and B. After calibration, reasonably accurate bond dissociation energy estimates are obtained for hydrogen-saturated diatomics composed of p-block elements coming from the same row 2 ≤ n ≤ 4 in the periodic table. Corresponding changes in bond dissociation energies due to substitution of atom B by C can be obtained via simple formulas. While being of different functional form and origin, our model is as simple and accurate as Pauling's well-known electronegativity model. Analysis indicates that the model's response in covalent bonding to variation in nuclear charge is near-linear, which is consistent with Hammett's equation.

The Ultrashort Spike-Ring Interaction in Substituted Iron Maiden Molecules

The in forms of molecular iron maidens are known for their unique ultrashort interaction between the apical hydrogen atom or its small substituent and the surface of the benzene ring. It is generally believed that this forced ultrashort X⋯π contact is associated with high steric hindrance, which is responsible for specific properties of iron maiden molecules. The main aim of this article is to investigate the influence of significant charge enrichment or depletion of the benzene ring on the characteristics of the ultrashort C-X⋯π contact in iron maiden molecules. For this purpose, three strongly electron-donating (-NH2) or strongly electron-withdrawing (-CN) groups were inserted into the benzene ring of in-[34,10][7]metacyclophane and its halogenated (X = F, Cl, Br) derivatives. It is shown that, despite such extremely electron-donating or electron-accepting properties, the considered iron maiden molecules surprisingly reveal quite high resistance to changes in electronic properties.

MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde

The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.

Two-Step ONIOM Method for the Accurate Estimation of Individual Hydrogen Bond Energy in Large Molecular Clusters

The study of molecular clusters to understand the properties of condensed systems has been the subject of immense interest. To get insight into these properties, the knowledge of various noncovalent interactions present in these molecular clusters is indispensable. Our recently developed molecular tailoring approach-based (MTA-based) method for the estimation of the individual hydrogen bond (HB) energy in molecular clusters is useful for this purpose. However, the direct application of this MTA-based method becomes progressively difficult with the increase in the size of the cluster. This is because of the difficulty in the evaluation of single-point energy at the correlated level of theory. To overcome this caveat, herein, we propose a two-step method within the our own N-layer integrated molecular orbital molecular mechanics (ONIOM) framework. In this method, the HB energy evaluated by the MTA-based method employing the actual molecular cluster at a low Hartree-Fock (HF) level of theory is added to the difference in the HB energies evaluated by the MTA-based method, employing an appropriate small model system, called the shell-1 model, calculated at high (MP2) and low (HF) levels of theory. The shell-1 model of a large molecular cluster is made up of only a few molecules that are in direct contact (by a single HB) with the two molecules involved in the formation of an HB under consideration. We tested this proposed two-step ONIOM method to estimate the individual HB energies in various molecular clusters, viz., water (W_n, n = 10-16, 18 and 20), (H₂O₂)₁₂, (H₂O₃)₈, (NH₃)_n and strongly interacting (HF)₁₅ and (HF)_m(W)_n clusters. Furthermore, these estimated individual HB energies by the ONIOM method are compared with those calculated by the MTA-based method using actual molecular clusters. The estimated individual HB energies by the ONIOM method, in all these clusters, are in excellent linear one-to-one agreement (R² = 0.9996) with those calculated by the MTA-based method using actual molecular clusters. Furthermore, the small values of root-mean-square deviation (0.06), mean absolute error (0.04), |ΔE_max| (0.21) and Sε (0.06) suggest that this two-step ONIOM method is a pragmatic approach to provide accurate estimates of individual HB energies in large molecular clusters.

Energetics and electronics of polar Diels-Alder reactions at the atomic level: QTAIM and IQA analyses of complete IRC paths

The mechanism of Diels-Alder reactions between cyclopentadiene and several cyanoethylenes was studied by means of Density Functional Theory calculations using QTAIM and IQA (Interacting Quantum Atoms) analyses along complete IRC paths. Each geometry from the IRC had its wavefunction computed and the topology of the electronic density for it was then evaluated. By means of IQA, the global energetic profile was partitioned among the various atoms in the molecule, providing insight into what atoms are the main ones responsible for the magnitude of the energy barriers. The (a)synchronicity of the reaction mechanisms featuring non-symmetrically substituted dienophiles was characterized, from QTAIM, by the electron densities and Laplacians over the LCP's as well as by the different atomic energy barriers obtained from IQA. The magnitude of the atomic barrier nicely explains the (a)synchronicity of the reaction mechanisms, and the degree of (a)synchronicity is nicely revealed by the difference between the earlier and later bond breaking and bond formations. The main conclusion is that important energetic and electronic changes are occurring before and after the position of the transition state structure, mainly for those asynchronous mechanisms, and although these provide essential insight into the reaction mechanism, most studies cannot assess this kind of information because they are focusing solely on reactants, transition states, and products. We advocate that the additional computational effort required for such analyses is more than compensated by the great amount of useful information it provides.

Chemical Bonding Perspective on Low-Lying SiC4H2 Isomers: Conceptual Quantum Chemical Views

The nature of the chemical bonding in seven low-lying isomers of SiC₄H₂ is analyzed through quantum chemical concepts. Out of the seven, four isomers, 1-ethynyl-3-silacycloprop-1(2)-en-3-ylidene (1), diethynylsilylidene (2), 1-sila-1,2,3,4-pentatetraenylidene (4), and 1,3-butadiynylsilylidene (5), have already been identified in the laboratory. The other three isomers, 2-methylenesilabicyclo[1.1.0]but-1(3)-en-4-ylidene (3), 4-sila-2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (6), and 3-ethynyl-1-silapropadienylidene (7) remain elusive in the laboratory to date (J. Phys. Chem. A, 2020, 124, 987-1002). Deep insight into the characteristics of chemical bonding is explored with different bonding analysis tools. Quantum theory of atoms in molecules (QTAIM), interaction quantum atoms analysis, natural bond orbital analysis, adaptive natural density partitioning, electron localization function (ELF), Laplacian of electron density, energy decomposition analysis, atomic charge analysis, bond order analysis, and frontier molecular orbital analysis are employed in the present work to gain a better understanding of the chemical bonding perspective in SiC₄H₂ isomers. Different quantum chemical topology approaches (QTAIM, ELF, and Laplacian of electron density) are employed to complement each other. The obtained results dictate that the lone pair of the silicon atom participate in delocalization and influences the structural stability of isomers.

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

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.

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.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

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.

The physical nature of the ultrashort spike-ring interaction in iron maiden molecules

The so-called 'iron maiden' molecules belong to one of the most interesting subgroups of cyclophanes due to the presence of the ultrashort interaction between the CX apical bond and the benzene ring. This article presents an in-depth theoretical study of 16 'iron maiden' molecules, in which X = H, F, Cl or Br and the side chains are of various lengths and types: CSC, CSCC, CCC, and CCCC. It is shown that the H → F → Cl → Br substitution leads to a significant expansion of the 'iron maiden' molecule. Shorter chains lead to more pronounced effects, while insertion of sulfur atoms into the side chains lowers them. Structural changes are associated with an increase in energetic destabilization of X. Moreover, unlike for H, in the case of X = halogen, the out → in isomerization is energetically disadvantageous. The 'iron maiden' molecules are characterized by the presence of only three X⋯C_Ar bond paths. Particularly noteworthy are unusually large (even up to 32) values of the X⋯C_Ar bond ellipticity, which results from flat electron density distribution. The X⋯π interaction in each of the investigated 'iron maiden' molecule turned out to be multi-center, stabilizing and almost purely covalent in nature as indicated by the definitely dominant percentage (94.8%-101.6%) of the exchange-correlation energy. The spatial hindrance within the 'iron maiden' molecules appears to be not so much due to the X⋯π repulsion, but due to unfavorable steric interactions between X and the CC side bonds. It is also confirmed that some CH⋯HC interactions in aliphatic chains can be very weakly stabilizing.

The role of references and the elusive nature of the chemical bond

Chemical bonding theory is of utmost importance to chemistry, and a standard paradigm in which quantum mechanical interference drives the kinetic energy lowering of two approaching fragments has emerged. Here we report that both internal and external reference biases remain in this model, leaving plenty of unexplored territory. We show how the former biases affect the notion of wavefunction interference, which is purportedly recognized as the most basic bonding mechanism. The latter influence how bonding models are chosen. We demonstrate that the use of real space analyses are as reference-less as possible, advocating for their use. Delocalisation emerges as the reference-less equivalent to interference and the ultimate root of bonding. Atoms (or fragments) in molecules should be understood as a statistical mixture of components differing in electron number, spin, etc.

The theory of chemical bonding relies on arbitrary references. Here the authors report a fundamental study on the chemical bond showing that considering the binding fragments as objects in real space enables to eliminate inherent biases.

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 V_xc 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.

Synthesis, structural and photophysical properties of dimethylphosphino(perfluoro-)phenylene-based gold(I) dimers

Starting with 1,2-dibromobenzene and 1,2,3,4-tetrafluorobenzene, dimethyl(2-(trimethylstannyl)phenyl)phosphane, Me₂P(o-C₆H₄)SnMe₃, and dimethyl-[2,3,4,5-tetrafluoro-6-(trimethylstannyl)phenyl]phosphane, Me₂P(o-C₆F₄)SnMe₃, were synthesized and used in tin-gold exchange reactions to prepare two gold(I) dimers, bis[(2-dimethylphosphino)phenyl]di-gold(I), [Au₂(μ-2-C₆H₄PMe₂)₂], and bis[(2-dimethylphosphino)-3,4,5,6-tetrafluorophenyl]di-gold(I), [Au₂(μ-2-C₆F₄PMe₂)₂], respectively. Both tin precursor molecules, as well as the gold(I) complexes, were characterized by multinuclear NMR spectroscopy, CHN analysis and X-ray diffraction experiments. Both gold(I) dimers were further investigated by the means of computational as well as photophysical methods.

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.

DL_FFLUX: A Parallel, Quantum Chemical Topology Force Field

DL_FFLUX is a force field based on quantum chemical topology that can perform molecular dynamics for flexible molecules endowed with polarizable atomic multipole moments (up to hexadecapole). Using the machine learning method kriging (aka Gaussian process regression), DL_FFLUX has access to atomic properties (energy, charge, dipole moment, etc.) with quantum mechanical accuracy. Newly optimized and parallelized using domain decomposition Message Passing Interface (MPI), DL_FFLUX is now able to deliver this rigorous methodology at scale while still in reasonable time frames. DL_FFLUX is delivered as an add-on to the widely distributed molecular dynamics code DL_POLY 4.08. For the systems studied here (10³–10⁵ atoms), DL_FFLUX is shown to add minimal computational cost to the standard DL_POLY package. In fact, the optimization of the electrostatics in DL_FFLUX means that, when high-rank multipole moments are enabled, DL_FFLUX is up to 1.25× faster than standard DL_POLY. The parallel DL_FFLUX preserves the quality of the scaling of MPI implementation in standard DL_POLY. For the first time, it is feasible to use the full capability of DL_FFLUX to study systems that are large enough to be of real-world interest. For example, a fully flexible, high-rank polarized (up to and including quadrupole moments) 1 ns simulation of a system of 10 125 atoms (3375 water molecules) takes 30 h (wall time) on 18 cores.

Noncovalent Interactions in Organometallic Chemistry: From Cohesion to Reactivity, a New Chapter

Noncovalent interactions (NCIs) have long interested a vast community of chemists who investigated their "canonical categories" derived from descriptive crystallography, e.g., H-bonds, π-π interactions, halogen/chalcogen/tetrel bonds, cation-π and C-H-π interactions, metallophilic interactions in the broad sense, etc. Recent developments in theoretical chemistry have enabled the treatment of noncovalent interactions under new auspices: dispersion-force-inclusive density functionals have emerged, which are reliable for modeling small to large molecular systems. It is possible to perform the full analysis of the contributions of London, Debye, and Keesom forces, i.e., the main components of van der Waals forces, by the DFT-D and ab initio methods at a reasonable computational cost. Our research has been focusing for now 15 years on the role of NCIs in the cohesion of organometallic complexes. NCIs are not only effective in Werner's secondary coordination sphere but also in the metal's primary one. The stabilization of electron-unsaturated transition metal complexes by hemichelation, metal-metal donor-acceptor complexes, and self-aggregation of cationic Rh(I) chromophores have indeed outlined the significance of the London dispersion force as an attractive force operating throughout the whole molecule or molecular assembly. The recent outburst of interest in C-H bond functionalization led us to address the broader question of reaction and catalyst engineering: although one can now satisfactorily analyze bonding and molecular cohesion in transition-metal-based organometallic systems, can modern theoretical methods guide reactivity exploration and the engineering of novel catalytic systems? We addressed this question by investigating the ambiphilic metal-ligand activation/concerted metalation-deprotonation mechanism involved in transition-metal-catalyzed directed C-H bond functionalization. This endeavor was initiated having in scope the construction of a rationale for the transposition of 4-5d metal chemistry to earth-abundant 3d metals. In this base-assisted mechanism of C-H bond metalation, agostic interactions are necessary but not sufficient because C-H bond breaking actually relies on the attractive NCI coding of a proton-transfer step and the minimization of metal-H repulsion. This Account introduces the recent shift of our research toward the construction of an NCI-inclusive paradigm of chemical reactivity engineering based on experimental efforts propped up by state-of-the-art theoretical tools.

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.