Extension of the interacting quantum atoms (IQA) approach to B3LYP level density functional theory (DFT)

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⋯ $$ \cdots $$ 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⋯ $$ \cdots $$ 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⋯ $$ \cdots $$ 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.

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.

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.

Significant cell uptake of Gd(III)-diphenylphosphoryl-diphenylphosphonium complexes: evidence for a new conformationally-dependent tumour cell targeting vector

The synthesis, characterisation, and tumour cell uptake of six novel Gd(III)-diphenylphosphoryl-diphenylphosphonium complexes are reported. The propyl-linked Gd(III) complexes can accumulate inside human glioma cells at prodigious levels, approaching 1200%, over the parent triphenylphosphonium salts. DFT and quantum chemical topology analyses support a new type of conformationally-dependent tumour cell targeting vector.

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.

Fluorescent deactivation behaviors based on ESIPT and TICT of novel double target fluorescent probe and its sensing mechanism for Al3+/Mg2+: A TD-DFT study

Based on density functional theory (DFT) and time-dependent DFT (TD-DFT) methods with integral equation formula polarized continuum model (IEFPCM), the fluorescent behavior and recognizing mechanism of probe N'-((1-hydroxynaphthalen-2-yl)methylene)isoquinoline-3-carbohydrazide (NHMI) for Al³⁺/Mg²⁺ ion were investigated in more detail. Excited state intramolecular proton transfer (ESIPT) process in probe NHMI occurs in the stepwise pattern. The proton H₅ of enol structure (E1) firstly moves from O₄ to N₆ to form single proton-transfer (SPT2) structure, and then the proton H₂ of SPT2 transfers from N₁ to N₃ to form the stable double proton-transfer (DPT) structure. Subsequently, the transformation from DPT to its isomer (DPT1) induces the twisted intramolecular charge transfer (TICT) process. Two non-emissive TICT states (TICT1 and TICT2) were obtained, and TICT2 state quenches the fluorescence observed in the experiment. With the addition of aluminum (Al³⁺) or magnesium (Mg²⁺) ion, TICT process is prohibited by the coordination interaction between NHMI and Al³⁺/Mg²⁺, and the strong fluorescent signal is turned on. For probe NHMI, the twisted C-N single bond of acylhydrazone part leads to the TICT state. This sensing mechanism may inspire researchers to develop new probes from a different direction.

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

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

IGMPlot: A program to identify, characterize, and quantify molecular interactions

We describe the development and features of a program called IGMPlot, which is based on the independent gradient model (IGM) and its local descriptor δ g $$ \delta g $$ . The IGM approach analyzes the gradient of the electron density (ED) in a molecular system to identify regions of space where chemical interactions take place. IGMPlot is intended for use by both experimental scientists and theoretical chemists. It is standalone software written in C++, with versions available for multiple platforms. Some key features are: probing and quantifying interactions between two given molecular fragments, determining bond strength (IBSI), estimating the atomic contributions to an intermolecular interaction and preparing data to build 2D and 3D representations of interaction regions. The software has been updated to include new features: critical point analysis of the ED, assessing ED asymmetry of a given bond (PDA) and a new descriptor called q g $$ qg $$ designed to enhance the IGM- δ g $$ \delta g $$ analysis. The program can be found at: http://igmplot.univ-reims.fr.

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.

Extracting Quantitative Information at Quantum Mechanical Level from Noncovalent Interaction Index Analyses

The noncovalent interaction (NCI) index is nowadays a well-known strategy to detect NCIs in molecular systems. Even though it initially provided only qualitative descriptions, the technique has been recently extended to also extract quantitative information. To accomplish this task, integrals of powers of the electron distribution were considered, with the requirement that the overall electron density can be clearly decomposed as sum of distinct fragment contributions to enable the definition of the (noncovalent) integration region. So far, this was done by only exploiting approximate promolecular electron densities, which are given by the sum of spherically averaged atomic electron distributions and thus represent too crude approximations. Therefore, to obtain more quantum mechanically (QM) rigorous results from NCI index analyses, in this work, we propose to use electron densities obtained through the transfer of extremely localized molecular orbitals (ELMOs) or through the recently developed QM/ELMO embedding technique. Although still approximate, the electron distributions resulting from the abovementioned methods are fully QM and, above all, are again partitionable into subunit contributions, which makes them completely suitable for the NCI integral approach. Therefore, we benchmarked the integrals resulting from NCI index analyses (both those based on the promolecular densities and those based on ELMO electron distributions) against interaction energies computed at a high quantum chemical level (in particular, at the coupled cluster level). The performed test calculations have indicated that the NCI integrals based on ELMO electron densities outperform the promolecular ones. Furthermore, it was observed that the novel quantitative NCI-(QM/)ELMO approach can be also profitably exploited both to characterize and evaluate the strength of specific interactions between ligand subunits and protein residues in protein-ligand complexes and to follow the evolution of NCIs along trajectories of molecular dynamics simulations. Although further methodological improvements are still possible, the new quantitative ELMO-based technique could be already exploited in situations in which fast and reliable assessments of NCIs are crucial, such as in computational high-throughput screenings for drug discovery.

Gaussian Process Regression Models for Predicting Atomic Energies and Multipole Moments

Developing a force field is a difficult task because its design is typically pulled in opposite directions by speed and accuracy. FFLUX breaks this trend by utilizing Gaussian process regression (GPR) to predict, at ab initio accuracy, atomic energies and multipole moments as obtained from the quantum theory of atoms in molecules (QTAIM). This work demonstrates that the in-house FFLUX training pipeline can generate successful GPR models for six representative molecules: peptide-capped glycine and alanine, glucose, paracetamol, aspirin, and ibuprofen. The molecules were sufficiently distorted to represent configurations from an AMBER-GAFF2 molecular dynamics run. All internal degrees of freedom were covered corresponding to 93 dimensions in the case of the largest molecule ibuprofen (33 atoms). Benefiting from active learning, the GPR models contain only about 2000 training points and return largely sub-kcal mol^-1 prediction errors for the validation sets. A proof of concept has been reached for transferring the model produced through active learning on one atomic property to that of the remaining atomic properties. The prediction of electrostatic interaction can be assessed at the intermolecular level, and the vast majority of interactions have a root-mean-square error of less than 0.1 kJ mol^-1 with a maximum value of ∼1 kJ mol^-1 for a glycine and paracetamol dimer.

Uncovering the dependence of ESIPT behaviors and fluorescence properties of two new benzothiazole-based fluorophores on solvent polarity: A TD-DFT study

We have studied the spectral features and excited state intramolecular proton transfer (ESIPT) processes of 2-(2',4'-dihydroxyphenyl)benzothiazole (OHBT) and 2-(2'-hydroxy-5'-chlorophenyl)benzothiazole (CHBT) using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). To consider the impact of solvent polarity and intermolecular hydrogen bond (H-bond) on the ESIPT behavior and photophysical properties, four solvents including toluene (TL), tetrahydrofuran (THF), methanol (MeOH) and dimethylsulfoxide (DMSO) were used. The simulated absorption and fluorescence wavelengths of OHBT and CHBT are well consistent with the experimental values. According to the results of structures, electron density and infrared (IR) vibrational frequencies, we found that the intramolecular H-bonds in OHBT/CHBT and OHBT-MeOH/CHBT-MeOH are strengthened in the first singlet excited state (S₁), which will be benefical to the ESIPT process. The potential energy curves (PECs) verified that the ESIPT processes in OHBT/CHBT and OHBT-MeOH/CHBT-MeOH can take place much easier because of their lower energy barrier. The influences of solvent polarity on ESIPT behaviors and photophysical properties of OHBT and CHBT are summarized below. As the solvent polarity becomes stronger from TL to DMSO, the energy gaps enlarges a little, the maximum absorption and fluorescence peaks at normal form red-shift slightly, and the strengths of H-bond in S₁ state become weaker, which makes the ESIPT process occur much harder. The formation of intermolecular H-bond between OHBT/CHBT and MeOH is conducive to promote the ESIPT process of OHBT/CHBT.

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'.

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.

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.

The performance of exchange-correlation functionals in describing electron density parameters of saddle point structures along chemical reactions

This work is focused on evaluating the performance of exchange-correlation functionals from density functional theory in providing descriptor values derived from the electron density of saddle point structures (transition states) in chemical reactions. The properties investigated were obtained from the quantum theory of atoms in molecules, including atomic charges and electron density topological data at the bond critical points. In addition, parameters from the Interacting quantum atom energy partition were used as well in this comparative study. The reference values are attained in coupled cluster calculations with iterative single and double excitations (CCSD). Six elementary reactions are considered here: CO + H₂  ↔ H₂ CO, CO + H₂ O ↔ HCOOH, HCN ↔ HNC, H + F₂  ↔ HF + F, H + N₂  ↔ HN₂ , and H + CO ↔ HCO. In general, the BB1K functional (hybrid-meta-generalized gradient approximation) provides the best description of these properties. Our study indicates that an intermediate percentage of nonlocal exact exchange, around 40%-55% (perhaps even larger), is probably required for attaining more accurate values with actual functionals, although this condition is not able of explaining all the trends observed.

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.

The Importance of Electrostatics and Polarization for Noncovalent Interactions: Ionic Hydrogen Bonds vs Ionic Halogen Bonds

A series of 26 hydrogen-bonded complexes between Br⁻ and halogen, oxygen and sulfur hydrogen-bond (HB) donors is investigated at the M06-2X/6–311 + G(2df,2p) level of theory. Analysis using a model in which Br⁻ is replaced by a point charge shows that the interaction energy (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}$$\end{document}ΔEInt) of the complexes is accurately reproduced by the scaled interaction energy with the point charge (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}^{PC}$$\end{document}ΔEIntPC).This is demonstrated by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}=0.86{\Delta E}_{Int}^{PC}$$\end{document}ΔEInt=0.86ΔEIntPC with a correlation coefficient, R² =0.999. The only outlier is (Br-H-Br)⁻, which generally is classified as a strong charge-transfer complex with covalent character rather than a HB complex. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}^{PC}$$\end{document}ΔEIntPC can be divided rigorously into an electrostatic contribution (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{ES}^{PC}$$\end{document}ΔEESPC) and a polarization contribution (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Pol}^{PC}$$\end{document}ΔEPolPC).Within the set of HB complexes investigated, the former varies between -7.2 and -32.7 kcal mol⁻¹, whereas the latter varies between -1.6 and -11.5 kcal mol⁻¹. Compared to our previous study of halogen-bonded (XB) complexes between Br⁻ and C–Br XB donors, the electrostatic contribution is generally stronger and the polarization contribution is generally weaker in the HB complexes. However, for both types of bonding, the variation in interaction strength can be reproduced accurately without invoking a charge-transfer term. For the Br⁻···HF complex, the importance of charge penetration on the variation of the interaction energy with intermolecular distance is investigated. It is shown that the repulsive character of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Delta E}_{Int}$$\end{document}ΔEInt at short distances in this complex to a large extent can be attributed to charge penetration.

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.

Coordination of Ethylamine on Small Silver Clusters: Structural and Topological (ELF, QTAIM) Analyses

Amine ligands are expected to drive the organization of metallic centers as well as the chemical reactivity of silver clusters early growing during the very first steps of the synthesis of silver nanoparticles via an organometallic route. Density functional theory (DFT) computational studies have been performed to characterize the structure, the atomic charge distribution, and the planar two-dimensional (2D)/three-dimensional (3D) relative stability of small-size silver clusters (Ag_n, 2 ≤ n ≤ 7), with or without an ethylamine (EA) ligand coordinated to the Ag clusters. The transition from 2D to 3D structures is shifted from n = 7 to 6 in the presence of one EA coordinating ligand, and it is explained from the analysis of the Ag-N and Ag-Ag bond energies. For fully EA saturated silver clusters (Ag_n-EA_n), the effect on the 2D/3D transition is even more pronounced with a shift between n = 4 and 5. Subsequent electron localization function (ELF) and quantum theory of atoms in molecules (QTAIM) topological analyses allow for the fine characterization of the dative Ag-N and metallic Ag-Ag bonds, both in nature and in strength. Electron transfer from ethylamine to the coordinated silver atoms induces an increase of the polarization of the metallic core.

Collective interactions among organometallics are exotic bonds hidden on lab shelves

Recent discovery of an unusual bond between Na and B in NaBH₃^- motivated us to look for potentially similar bonds, which remained unnoticed among systems isoelectronic with NaBH₃^-. Here, we report a novel family of collective interactions and a measure called exchange-correlation interaction collectivity index (ICI_XC; [Formula: see text]) to characterize the extent of collective versus pairwise bonding. Unlike conventional bonds in which ICI_XC remains close to one, in collective interactions ICI_XC may approach zero. We show that collective interactions are commonplace among widely used organometallics, as well as among boron and aluminum complexes with the general formula [M^a+AR₃]^b- (A: C, B or Al). In these species, the metal atom interacts more efficiently with the substituents (R) on the central atoms than the central atoms (A) upon forming efficient collective interactions. Furthermore, collective interactions were also found among fluorine atoms of XF_n systems (X: B or C). Some of organolithium and organomagnesium species have the lowest ICI_XC among the more than 100 studied systems revealing the fact that collective interactions are rather a rule than an exception among organometallic species.

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.

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 E_ST . 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 E_ST here defined provides correct sterics even for hydrogen atoms, where the plain use of deformation energies leads to non-chemical results. The applicability of E_ST is validated in several chemical scenarios, going from atomic compressions to archetypal S_N2 reactions. E_ST is shown to be a robust steric hindrance descriptor.

Theoretical investigations on forward-backward ESIPT processes of three fluorophores deriving from 2-(2'-hydroxyphenyl)thiazole

The photophysical properties and excited-state intramolecular proton transfer (ESIPT) processes for 2-(2'-hydroxyphenyl)-4-chloromethylthiazole (1), 2-(2'-hydroxyphenyl)-4-phenylthiazole (2), 2-(2'-hydroxyphenyl)-4-hydroxymethyl-thiazole (3) were studied at the TD-B3PW91/6-31 + G(d, p)/IEFPCM level. The structures of 1-3 were fully optimized and the corresponding structural parameters, infrared spectra and electron densities in the ground (S₀) and the first excited (S₁) states were analyzed. The calculated absorption and fluorescence wavelengths of 1-3 reproduced the experimental data. The potential energy curves of the S₀ and S₁ states were built and the ESIPT processes were clarified. Our results showed that the intramolecular H-bonds of 3 and 2 in the S₁ state were the strongest and the weakest, respectively, and then the ESIPT potential barriers of 3 and 2 were the lowest and highest, respectively. Among the three phenol-thiazole type probes, the compound 2 with phenyl ring group at the 4 position of the thiazole ring had the larger π-conjugation, and had the higher ESIPT potential barrier at the same time. The corresponding compound 1 and 3 with CH₂Cl and CH₂OH had the lower ESIPT barrier.

New insights in chemical reactivity from quantum chemical topology

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

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.

A Step toward the Quantification of Noncovalent Interactions in Large Biological Systems: The Independent Gradient Model-Extremely Localized Molecular Orbital Approach

The independent gradient model (IGM) is a recent electron density-based computational method that enables to detect and quantify covalent and noncovalent interactions. When applied to large systems, the original version of the technique still relies on promolecular electron densities given by the sum of spherically averaged atomic electron distributions, which leads to approximate evaluations of the inter- and intramolecular interactions occurring in systems of biological interest. To overcome this drawback and perform IGM analyses based on quantum mechanically rigorous electron densities also for macromolecular systems, we coupled the IGM approach with the recently constructed libraries of extremely localized molecular orbitals (ELMOs) that allow fast and reliable reconstructions of polypeptide and protein electron densities. The validation tests performed on small polypeptides and peptide dimers have shown that the novel IGM-ELMO strategy provides results that are systematically closer to the fully quantum mechanical ones and outperforms the IGM method based on the crude promolecular approximation, but still keeping a quite low computational cost. The results of the test calculations carried out on proteins have also confirmed the trends observed for the IGM analyses conducted on small systems. This makes us envisage the future application of the novel IGM-ELMO approach to unravel complicated noncovalent interaction networks (e.g., in protein-protein contacts) or to rationally design new drugs through molecular docking calculations and virtual high-throughput screenings.

Local spin and open quantum systems: clarifying misconceptions, unifying approaches

The theory of open quantum systems (OQSs) is applied to partition the squared spin operator into fragment (local spin) and interfragment (spin-coupling) contributions in a molecular system.

From the Linnett-Gillespie model to the polarization of the spin valence shells of metals in complexes

In this paper, we present a novel approach to track the origin of the metal complex structure from the topology of the α and β spin densities as an extension of the Linnett-Gillespie model. Usually, the theories that explain the metal-ligand interactions consider the disposition and the relative energies of the empty or occupied set of d orbitals, ignoring the spin contribution explicitly. Our quantum topological approach considers the spatial distribution of the α and β spin valence shells, and the energy interaction between them. We used the properties of the atomic graph, a topological object that summarises the charge concentrations and depletions on the valence shell of an atom in a molecule, and the interacting quantum atoms (IQA) energy partition scheme. Unlike the Linnett-Gillespie model, which is based on electron-electron repulsion, our approach states that the ligands provoke a redistribution of the electron density to maximize the nuclear-electron interactions in each spin valence shell to bypass the concentration of electron-electron interactions, resulting in a polarization pattern which determines the position of the ligands.

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.

Cooperativity in a cycloalkane-1,2/1,3-polyol corona: Topological hydrogen bonding in 1,2-diol motifs

A corona, consisting of 18 carbon atoms bearing 12 hydroxy groups in a continuous hydrogen-bonded chain, is built up by alternating degenerate conformations of alternating alkane-1,2-diol and 1,3-diol motifs. Geometries, proton nuclear magnetic resonance shifts and interaction energies for the dodecahydroxycyclo-octadecane and selected fragments are determined by density functional calculations at the B3LYP/6-311+G(d,p) level. Cooperative effects of O-H⋯O-H bonding are evident from the simple juxtaposition of these two motifs with a common OH group in butane-1,2,4-triol conformers. Bracketing a 1,2-diol motif with two 1,3-diol motifs in hexane-1,3,4,6-tetrol leads to a structure in which the 1,2-diol motif displays a bond critical point for hydrogen bonding. This is associated with enhancement of the shift of the hydrogen-bonded OH proton and of the corresponding H⋯O interaction energy. The full corona has a complete outer ring of O-H⋯O-H bond paths, and an inner ring of bond paths, due to C-H⋯H-C hydrogen-hydrogen bonding, which result in a central ring critical point. The topological O-H⋯O-H hydrogen bond, never seen in simple alkane-1,2-diols, is associated with cooperative enhancement of the H⋯O interaction energy, but this is not a necessary condition for a bond path: values for topological C-H⋯H-C hydrogen-hydrogen bonds can be as low as -0.4 kcal mol^-1 .

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.

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

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