Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions

Discovering trends in the Lewis acidity of beryllium and magnesium hydrides and fluorides with increasing clusters size

We have reported in the last years the strong effect that Be- and Mg-containing Lewis acids have on the intrinsic properties of typical bases, which become acids upon complexation. In an effort to investigate these changes when the Be and Mg derivatives form clusters of increasing size, we have examined the behavior of the (MX2)n (M = Be, Mg; X = H, F; n = 1, 2, 3) clusters when they interact with ammonia, methanimine, hydrogen cyanide and pyridine, and with their corresponding deprotonated forms. The complexes obtained at the M06-2X/aug-cc-pVTZ level were analyzed using the MBIE energy decomposition formalism, in parallel with QTAIM, ELF, NCIPLOT and AdNDP analyses of their electron density. For n = 1 the interaction enthalpy for the different families of monomers, Be (Mg) hydrides and Be (Mg) fluorides, follows the same trend as the intrinsic basicity of the base that interacts with them. This interaction is greatly reinforced after the deprotonation of the base, resulting in a significant enhancement of the intrinsic acidity of the corresponding MX2-Base complex. For (MX2)2 clusters a further reinforcement of the interaction with the base is observed, this reinforcement being again larger for the deprotonated complexes. However, the concomitant increase of their intrinsic acidity is one order of magnitude larger for hydrides than for fluorides. Unexpectedly, the cyclic conformers (MX2)3, which are more unstable than the linear ones, become the global minima after association with the base and the same is true for the deprotonated complex. Accordingly, a further increase of the intrinsic acidity of the (MX2)3-Base complexes with respect to the (MX2)2-Base ones is observed. This effect is maximum for (MgF2)3 clusters, to the point that the (MgF2)3-Base complexes become more acidic than nitric acid, the extreme case being the cluster (MgF2)3-NCH, whose acidity is higher than that of perchloric acid.

Transferability of Buckingham Parameters for Short-Range Repulsion between Topological Atoms

The repulsive part of the Buckingham potential, with parameters A and B, can be used to model deformation energies and steric energies. Both are calculated using the interacting quantum atom energy decomposition scheme where the latter is obtained from the former by a charge-transfer-based energy correction. These energies relate to short-range interactions, specifically the deformation of electron density and steric hindrance, respectively, when topological atoms approach each other. In this work, we calculate and fit the energies of carbonyl carbon, carbonyl oxygen, and, where possible, amine nitrogen atoms to the repulsive part of the Buckingham potential for 26 molecules. We find that while the steric energies of all atom pairs studied display exponential behavior with respect to distance, some deformation energy data do not. The obtained parameters are shown to be transferable by calculating root-mean-square errors of fitted potentials with respect to energy data of the same atom in, as far as possible, all other molecules from our data set. We observed that 36% and 10% of these errors were smaller than 4 kJ mol-1 for steric and deformation energy, respectively. Thus, we find that steric energy parameters are more transferable than deformation energy parameters. Finally, we speculate about the physical meaning of the A and B parameters and the implications of the strong exponential and exponential-linear piecewise relationships that we observe between them.

Systematic Study of Different Types of Interactions in α-, β- and γ-Cyclodextrin: Quantum Chemical Investigation

In this work, comprehensive ab initio quantum chemical calculations using the DFT level of theory were performed to characterize the stabilization interactions (H-bonding and hyperconjugation effects) of two stable symmetrical conformations of α-, β-, and γ-cyclodextrins (CDs). For this purpose, we analyzed the electron density using "Atom in molecules" (AIM), "Natural Bond Orbital" (NBO), and energy decomposition method (CECA) in 3D and in Hilbert space. We also calculated the H-bond lengths and OH vibrational frequencies. In every investigated CD, the quantum chemical descriptors characterizing the strength of the interactions between the H-bonds of the primary OH (or hydroxymethyl) and secondary OH groups are examined by comparing the same quantity calculated for ethylene glycol, α-d-glucose (α-d-Glcp) and a water cluster as reference systems. By using these external standards, we can characterize more quantitatively the properties of these bonds (e.g., strength). We have demonstrated that bond critical points (BCP) of intra-unit H-bonds are absent in cyclodextrins, similar to α-d-Glcp and ethylene glycol. In contrast, the CECA analysis showed the existence of an exchange (bond-like) interaction between the interacting O…H atoms. Consequently, the exchange interaction refers to a chemical bond, namely the H-bond between two atoms, unlike BCP, which is not suitable for its detection.

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.

The Exciton Model for Molecular Materials: Past, Present and Future?

In assemblies of identical molecules or chromophores, electronic excitations can be described as excitons, bound electron-hole pairs that can move from site to site as a pair in a coherent manner. The understanding of excitons is crucial when trying to engineer favorable photophysical properties through structuring organic molecular matter. In recent decades, limitations of the concept of an exciton have become clear. The exciton can hybridize with phonon and photons. To clarify these issues, the exciton is discussed within the broader context of the gauge properties of the electromagnetic force.

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.

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.

Linking the Interatomic Exchange-Correlation Energy to Experimental J-Coupling Constants

The main aim of the current work is to find an experimental connection to the interatomic exchange-correlation energy as defined by the energy decomposition method Interacting Quantum Atoms (IQA). A suitable candidate as (essentially) experimental quantity is the nuclear magnetic resonance (NMR) J-coupling constant denoted ³J(H,H'), which a number of previous studies showed to correlate well with QTAIM's delocalization index (DI), which is essentially a bond order. Inspired by Karplus equations, here, we investigate correlations between ³J(H,H') and a relevant dihedral angle in six simple initial compounds of the shape H₃C-YH_n (Y = C, N, O, Si, P, and S), N-methylacetamide (as prototype of the peptide bond), and five peptide-capped amino acids (Gly, Ala, Val, Ile, and Leu) because of the protein direction of the force field FFLUX. In conclusion, except for methanol, the inter-hydrogen exchange-correlation energy V_xc(H,H') makes the best contact with experiment, through ³J(H,H'), when multiplied with the internuclear distance R_HH'.

How deeply should we analyze non-covalent interactions?

CONTEXT

Just how much effort and detail should we invest in analyzing interactions of the order of 5 kcal mol^-1? This comment attempts to provide a conciliatory overview of what is often a contentious field and to pose some questions that I hope will eventually lead at least to some consensus.

METHODS

This is an opinion article without calculations or data.

Nature and Strength of Weak O⋅⋅⋅O Interactions in Nitryl Halide Dimers

The use of real space functions and molecular graphs has pushed some chemists to wonder: Are interactions between negatively charged oxygen atoms possible? In this contribution we analyze whether there is a real interaction between oxygen atoms in nitryl halide dimers (XNO₂ )₂ (X=F, Cl, Br and I) and in tetranitromethane and derivatives. Based on ab-initio and density functional theories (DFT) methods, we show these complexes are weakly stabilized. Energy decomposition analyses based on local molecular orbitals (LMOEDA) and interacting quantum atoms (IQA) reveal both dispersion and exchange play a crucial role in the stabilization of these complexes. Electron charge density and IQA analyses indicate that the oxygen atoms are connected by privileged exchange channels. In addition, electrostatic interactions between O and N atoms are also vital for the stabilization of the complexes. Finally, a reasonable explanation is given for the dynamic behavior of nitryl groups in tetranitromethane and derivatives.

Producing chemically accurate atomic Gaussian process regression models by active learning for molecular simulation

Machine learning is becoming increasingly more important in the field of force field development. Never has it been more vital to have chemically accurate machine learning potentials because force fields become more sophisticated and their applications expand. In this study a method for developing chemically accurate Gaussian process regression models is demonstrated for an increasingly complex set of molecules. This work is an extension to previous work showing the progression of the active learning technique in producing more accurate models in much less CPU time than ever before. The per-atom active learning approach has unlocked the potential to generate chemically accurate models for molecules such as peptide-capped glycine.

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.

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.

Electrostatics Explains the Reverse Lewis Acidity of BH3 and Boron Trihalides: Infrared Intensities and a Relative Energy Gradient (REG) Analysis of IQA Energies

The reaction path for the formation of BX₃–NH₃ (X = H, F, Cl, Br) complexes was divided into two processes: (i) rehybridization of the acid while adopting a pyramidal geometry, and (ii) the complex formation from the pyramidal geometries of the acid and base. The interacting quantum atom (IQA) method was used to investigate the Lewis acidity trend of these compounds. This topological analysis suggests that the boron–halogen bond exhibits a considerable degree of ionicity. A relative energy gradient (REG) analysis on IQA energies indicates that the acid–base complex formation is highly dependent on electrostatic energy. With increasing halogen electronegativity, a higher degree of ionicity of the B–X is observed, causing an increase in the absolute value of X and B charges. This increases not only the attractive electrostatic energy between the acid and base but also enhances the repulsive energy. The latter is the main factor behind the acidity trend exhibited by trihalides. Changes in geometry are relevant only for complexes where BH₃ acts as an acid, where lower steric hindrance facilitates the adoption of the pyramidal geometry observed in the complex. The CCTDP analysis shows that infrared intensities of BX₃–NH₃ are determined mostly by the atomic charges and not by the charge transfer or polarization. The opposite is observed in covalent analogues.

The explicit role of electron exchange in the hydrogen bonded molecular complexes

We applied a set of advanced bonding descriptors to establish the hidden electron density features and binding energy characteristics of intermolecular DH∙∙∙A hydrogen bonds (OH∙∙∙O, NH∙∙∙O and SH∙∙∙O) in 150 isolated and solvated molecular complexes. The exchange-correlation and Pauli potentials as well as corresponding local one-electron forces allowed us to explicitly ascertain how electron exchange defines the bonding picture in the proximity of the H-bond critical point. The electron density features of DH∙∙∙A interaction are governed by alterations in the electron localization in the H-bond region displaying itself in the exchange hole. At that, they do not depend on the variations in the exchange hole mobility. The electrostatic interaction mainly defines the energy of H-bonds of different types, whereas the strengthening/weakening of H-bonds in complexes with varying substituents depends on the barrier height of the exchange potential near the bond critical point. Energy variations between H-bonds in isolated and solvated systems are also caused the electron exchange peculiarities as follows from the corresponding potential and the interacting quantum atom analyses complemented by electron delocalization index calculations. Our approach is based on the bonding descriptors associated with the characteristics of the observable electron density and can be recommended for in-depth studies of non-covalent bonding.

On the many-body nature of intramolecular forces in FFLUX and its implications

FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3N_atoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to N_atoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

Interacting Quantum Atoms-A Review

The aim of this review is threefold. On the one hand, we intend it to serve as a gentle introduction to the Interacting Quantum Atoms (IQA) methodology for those unfamiliar with it. Second, we expect it to act as an up-to-date reference of recent developments related to IQA. Finally, we want it to highlight a non-exhaustive, yet representative set of showcase examples about how to use IQA to shed light in different chemical problems. To accomplish this, we start by providing a brief context to justify the development of IQA as a real space alternative to other existent energy partition schemes of the non-relativistic energy of molecules. We then introduce a self-contained algebraic derivation of the methodological IQA ecosystem as well as an overview of how these formulations vary with the level of theory employed to obtain the molecular wavefunction upon which the IQA procedure relies. Finally, we review the several applications of IQA as examined by different research groups worldwide to investigate a wide variety of chemical problems.