A relative energy gradient (REG) study of the planar and perpendicular torsional energy barriers in biphenyl

The Analysis of Electron Densities: From Basics to Emergent Applications

The electron density determines all properties of a system of nuclei and electrons. It is both computable and observable. Its topology allows gaining insight into the mechanisms of bonding and other phenomena in a way that is complementary to and beyond that available from the molecular orbital picture and the formal oxidation state (FOS) formalism. The ability to derive mechanistic insight from electron density is also important with methods where orbitals are not available, such as orbital-free density functional theory (OF-DFT). While density topology-based analyses such as QTAIM (quantum theory of atoms-in-molecules) have been widely used, novel, vector-based techniques recently emerged such as next-generation (NG) QTAIM. Density-dependent quantities are also actively used in machine learning (ML)-based methods, in particular, for ML DFT functional development, including machine-learnt kinetic energy functionals. We review QTAIM and its recent extensions such as NG-QTAIM and localization-delocalization matrices (LDM) and their uses in the analysis of bonding, conformations, mechanisms of redox reactions excitations, as well as ultrafast phenomena. We review recent research showing that direct density analysis can circumvent certain pitfalls of the FOS formalism, in particular in the description of anionic redox, and of the widely used (spherically) projected density of states analysis. We discuss uses of density-based quantities for the construction of DFT functionals and prospects of applications of analyses of density topology to get mechanistic insight with OF-DFT and recently developed time-dependent OF-DFT.

A Study of Differential Topology on the Magnetically Induced Isotropically Averaged Lorentz Force Density of a Few Simple Molecules

Quantum chemical topology addresses the study of the chemical structure by applying the tools of differential topology to scalar and vector fields obtained by quantum mechanics. Here, the magnetically induced isotropically averaged Lorentz force density was computed and topologically analyzed for 11 small molecules. Critical points (attractors, repellers, and saddles) were determined and trajectories connecting the attractors computed. It is shown that kinds and numbers of the critical points are to some extent transferable in similar molecules. CC bonds of different orders are endowed with critical points of different kinds close to their center. The sum of topological indices of the isolated critical points is influenced by the presence of repellers on the outer part of the molecules.

Guest-Mediated Modulation of Photophysical Pathways in a Coronene Bisimide Cyclophane

The properties and functions of chromophores utilized by nature are strongly affected by the environment formed by the protein structure in the cells surrounding them. This concept is transferred here to host-guest complexes with the encapsulated guests acting as an environmental stimulus. A new cyclophane host based on coronene bisimide is presented that can encapsulate a wide variety of planar guest molecules with binding constants up to (4.29 ± 0.32) × 1010 M-1 in chloroform. Depending on the properties of the chosen guest, the excited state deactivation of the coronene bisimide chromophore can be tuned by the formation of host-guest complexes toward fluorescence, exciplex formation, charge separation, room-temperature phosphorescence (RTP), or thermally activated delayed fluorescence (TADF). The photophysical processes were investigated by UV/vis absorption, emission, and femto- and nanosecond transient absorption spectroscopy. To enhance the TADF, two different strategies were used by employing suitable guests: the reduction of the singlet-triplet gap by exciplex formation and the external heavy atom effect. Altogether, by using supramolecular host-guest complexation, a versatile multimodal chromophore system is achieved with the coronene bisimide cyclophane.

Theoretical Description of Hydride-hydride Interactions in Selected Hydrogen Storage Materials

In recent years there has been growing interest in the use of metal hydrides as hydrogen rich sources. The high content of hydride-hydride contacts Hδ-⋅⋅⋅δ-H in these materials appears to be relevant for hydrogen formation. At present time there is no consensus whether these contacts are attractive or repulsive. Accordingly, the main goal of this article is to shed light on physical factors which constitute homopolar hydride-hydride interactions Hδ-⋅⋅⋅δ-H in selected transition metal complexes i. e. HCoL4, L=CO,PPh3,PH3. In order to achieve this goal, the charge and energy decomposition ETS-NOCV approach along with the Interacting Quantum Atoms (IQA) and reduced density gradient (NCI) are applied for the bonded adducts L4CoH⋅⋅⋅HCoL4. Based on DFT and correlated methods it has been shown, contrary to classical interpretations, that hydride-hydride interactions might be attractive and even far stronger than classical hydrogen bonds. The stability of the adducts is increased by phosphine ligand installation: overall Hδ-⋅⋅⋅δ-H bonding energy changes in the order: CO≪PPh3~PH3. It has been revealed that depending on monomer's conformations Hδ-⋅⋅⋅δ-H bonds are dominated by charge delocalization or London dispersion forces and the electrostatic term is also relevant. The side carbonyl ligands additionally stabilize the Hδ-⋅⋅⋅δ-H bonded structures through covalent charge delocalizations and Coulombic contributors. Furthermore, the sterically crowded systems containing bulky phosphine ligands are supported by π⋅⋅⋅π stacking, C-H⋅⋅⋅π and C-H⋅⋅⋅H-Co. It is finally determined by IQA energy decomposition, that diatomic hydride-hydride interaction CoH⋅⋅⋅HCo is chameleon-like, namely, it is attractive in CO4CoH⋅⋅⋅HCoCO4 and (PH3)4CoH⋅⋅⋅HCo(PH3)4, whereas the repulsion is unveiled in (CO)3(PPh3)CoH⋅⋅⋅HCo(CO)3(PPh3) where the monomers are of Cs symmetry.

Current developments and trends in quantum crystallography

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

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

CONTEXT

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

METHODS

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

Syntheses and Properties of Hole-Transporting Biindenofluorenes

Described herein is a straightforward approach to synthesizing three biindenofluorene (BIF) derivatives, composed of antiaromatic indenofluorene units, which are the first non-alternant congeners of known bipentacene. Dimerization of indeno[1,2-b]fluorene and indeno[2,1-c]fluorene units by connecting carbons 3 and 3' and carbons 2 and 2', respectively, is shown to influence the highest occupied and lowest unoccupied molecular orbital energy levels of the resulting BIFs, affording band gaps (1.5-1.6 eV) that are smaller than that of a known indenofluorene polymer (2.3 eV). The hole mobilities of BIFs were determined to be ∼10-2 cm2 V-1 s-1.

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.

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.

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.

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'.

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.

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.

Planar in Brooker's mode and twisted in Reichardt's mode: defying the steric forces in biphenyl types of zwitterionic systems through metameric resonance stabilizations

To be planar or to be twisted at the bridge junctions in biphenyls or biaryl types of molecular systems depends on two conflicting forces: (1) steric repulsions (destabilizations) and (2) conjugation assisted electron delocalizations (resonance stabilizations). This work reports an unfamiliar kind of behaviour shown by metamers of a zwitterionic biphenyl type of system, where the Reichardt's metamer was found to be in an usual twisted conformation (delicate balance of conflicting forces), but the Brooker's metamer was found to be in a fully planar conformation. Interestingly, at the ωB97xD/aug-cc-pVDZ level, energetically (ΔE) the planar Brooker's metamer was found to be 16.7 kcal mol^-1 lower (22.9 kcal mol^-1 lower in the CASSCF method) in energy (more stable) than the isoelectronic twisted Reichardt's metamer, and also thermodynamic ΔG values were found to be close to ΔE values for various methods (for example, 15.6 kcal mol^-1 in the above case using the ωB97xD method). When the steric repulsions are in their full potentials at the ring junction site, attainment of a conformational planarity by any biaryl type of system has not been reported previously. Without reducing the steric constraints or even without inducing any attractive forces, determining what other factors were responsible for defying the steric forces is the main focus of this investigation. Using the results of quantum mechanical computations of NBO, rotational barriers, and other saddle points (metastable conformations in singlet and triplet surfaces) in the potential energy surfaces, the dominant contribution of the resonance stabilized quinonoid form to the ground state was delineated as the possible reason for this unusual behaviour.

Towards an atomistic understanding of polymorphism in molecular solids

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

Does Steric Hindrance Actually Govern the Competition between Bimolecular Substitution and Elimination Reactions?

Bimolecular nucleophilic substitution (SN2) and elimination (E2) reactions are prototypical examples of competing reaction mechanisms, with fundamental implications in modern chemical synthesis. Steric hindrance (SH) is often considered to be one of the dominant factors determining the most favorable reaction out of the SN2 and E2 pathways. However, the picture provided by classical chemical intuition is inevitably grounded on poorly defined bases. In this work, we try to shed light on the aforementioned problem through the analysis and comparison of the evolution of the steric energy (EST), settled within the IQA scheme and experienced along both reaction mechanisms. For such a purpose, the substitution and elimination reactions of a collection of alkyl bromides (R-Br) with the hydroxide anion (OH-) were studied in the gas phase at the M06-2X/aug-cc-pVDZ level of theory. The results show that, generally, EST recovers the appealing trends already anticipated by chemical intuition and organic chemistry, supporting the role that SH is classically claimed to play in the competition between SN2 and E2 reactions.

Coordination polymers fabricated from Cd(NO3)2 and N,N′,O-pincer-type isonicotinoylhydrazone-based polytopic ligands – an insight from experimental and theoretical investigations

Three new Cd(ii) coordination polymers based on isonicotinohydrazide ligands (HLI, HLII) differing in the presence of a methyl unit have been obtained and extensively characterized by experimental and computational approaches.

Understanding the Nature and Properties of Hydrogen-Hydrogen Bonds: The Stability of a Bulky Phosphatetrahedrane as a Case Study

Recently, the first mixed C/P phosphatetrahedranes (^tBuC)₃P and (^tBuCP)₂ were reported. Unlike (^tBuCP)₂, (^tBuC)₃P exhibits remarkable thermal stability, which can be partially attributed to a network of nine hydrogen-hydrogen bonds (HHBs) localized between the tert-butyl substituents. The stabilizing contribution arising from this network of HHBs was obtained from local energy decomposition (LED) analysis calculated at the domain-based local pair natural orbital CCSD(T) (DLPNO-CCSD(T)) level of theory. These calculations suggest that each HHB contributes approximately -0.7 kcal/mol of stabilization; however, the net stabilization energy likely lies between -0.25 and -0.5 kcal/mol because of steric repulsion. Spatial analysis of the London dispersion energy via a dispersion interaction density (DID) plot reveals that the DID surface is localized at key C-H groups involved in HHBs, consistent with London dispersion interactions predominantly arising from HHBs. In addition, we present a computed mechanism that supports a phosphinidenoid species as a key reaction intermediate in the synthesis of (^tBuC)₃P.

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.

The CH···HC interaction in biphenyl is a delocalized, molecular-wide and entirely non-classical interaction: Results from FALDI analysis

In this study we aim to determine the origin of the electron density describing a CH···HC interaction in planar and twisted conformers of biphenyl. In order to achieve this, the fragment, atomic, localized, delocalized, intra- and inter-atomic (FALDI) decomposition scheme was utilized to decompose the density in the inter-nuclear region between the ortho-hydrogens in both conformers. Importantly, the structural integrity, hence also topological properties, were fully preserved as no 'artificial' partitioning of molecules was implemented. FALDI-based qualitative and quantitative analysis revealed that the majority of electron density arises from two, non-classical and non-local effects: strong overlap of ortho CH σ-bonds, and long-range electron delocalization between the phenyl rings and ortho carbons and hydrogens. These effects resulted in a delocalized electron channel, that is, a density bridge or a bond path in a QTAIM terminology, linking the H-atoms in the planar conformer. The same effects and phenomena are present in both conformers of biphenyl. We show that the CH···HC interaction is a molecular-wide event due to large and long-range electron delocalization, and caution against approaches that investigate CH···HC interactions without fully taking into account the remainder of the molecule.

The effective isotropy of the hydrogen local potential in biphenyl and other hydrocarbons

We present an experimental investigation of the hydrogen nuclear momentum distribution in biphenyl using deep inelastic neutron scattering. Our experimental results suggest that the local potential affecting hydrogen is both harmonic and isotropic within experimental uncertainties. This feature is interpreted as a consequence of the central limit theorem, whereby the three-dimensional momentum distribution is expected to become a purely Gaussian function as the number of independent vibrational modes in a system increases. We also performed ab initio phonon calculations on biphenyl and other saturated hydrocarbons, from methane to decane. From the results of the simulations, one can observe that the nuclear momentum distribution becomes more isotropic as the number of atoms and normal modes in the molecule increases. Moreover, the predicted theoretical anisotropy in biphenyl is clearly larger than in the experiment. The reason is that the total number of normal modes necessary to reproduce the experimental results is much larger than the number of normal modes encompassed by a single unit cell due to the presence of structural disorder and intermolecular interactions in the real crystal, as well as coupling of different normal modes. Finally, experimental data were collected, over a subset of detectors on the VESUVIO spectrometer at ISIS, with a novel setup to increase the count rate and signal-to-background ratio. We envision that such an optimized experimental setup can provide faster measurements and more stringent constraints for phonon calculations.

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 .

Steric clash in real space: biphenyl revisited

A textbook case of twisted structure due to hydrogen-hydrogen steric clash, the biphenyl molecule, has been studied in real space from a new perspective. Long-term discrepancies regarding the origin of the steric repulsion are now reconciled under the NCI (Non Covalent Interaction) method, which reflects in 3D the balance between attractive and repulsive interactions taking place in the region between the phenyl rings. The NCI method confirms that the steric repulsion does not merely come from the H-H interaction itself, but from the many-atom interactions arising from the Cortho-H region, therefore providing rigorous physical grounds for the steric clash. This method allows a continuous scan of all the subtle changes on the electron density on going from the planar to the perpendicular biphenyl structure. The NCI results agree with other topological approaches (IQA, ELF) and are in line with previous findings in the literature regarding controversial H-H interactions in steric clash situations: H-H interactions are attractive, but repulsion appears between (Cortho-H)(Cortho-H), raising the intraatomic energy of the ortho H. ELF is also used to support these conclusions. Indeed, deformations are observed in compressed basins that allow to visualize the intraatomic effect of steric repulsion. These results can be easily extrapolated to systems with similar topological features in which steric clash is claimed to be the reason for instability.

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.

Molecular Orbitals Support Energy-Stabilizing "Bonding" Nature of Bader's Bond Paths

Our MO-based findings proved a bonding nature of each density bridge (DB, or a bond path with an associated critical point, CP) on a Bader molecular graph. A DB pinpoints universal physical and net energy-lowering processes that might, but do not have to, lead to a chemical bond formation. Physical processes leading to electron density (ED) concentration in internuclear regions of three distinctively different homopolar H,H atom-pairs as well as classical C-C and C-H covalent bonds were found to be exactly the same. Notably, properties of individual MOs are internuclear-region specific as they (i) concentrate, deplete, or do not contribute to ED at a CP and (ii) delocalize electron-pairs through either in- (positive) or out-of-phase (negative) interference. Importantly, dominance of a net ED concentration and positive e^--pairs delocalization made by a number of σ-bonding MOs is a common feature at a CP. This feature was found for the covalently bonded atoms as well as homopolar H,H atom-pairs investigated. The latter refer to a DB-free H,H atom-pair of the bay in the twisted biphenyl (Bph) and DB-linked H,H atom-pairs (i) in cubic Li₄H₄, where each H atom is involved in three highly repulsive interactions (over +80 kcal/mol), and (ii) in a weak attractive interaction when sterically clashing in the planar Bph.

On the Discrepancy between Experimental and Calculated Raman Intensities for Conjugated Phenyl and Thiophene Derivatives

Compared with experimental spectra, calculations for conjugated phenyl and thiophene oligomers tend to overestimate the ground state Raman intensities of higher-frequency vibrations (1200-1800 cm^-1) relative to the intensities at lower frequencies (<1200 cm^-1). The discrepancy was observed in previous benchmarking work that examined the method dependence of the calculated Raman spectra for a series of aromatic molecules. This paper further investigates the nature of the discrepancy by examining the role of anharmonic corrections and the dependence of the calculated Raman spectra on the inter-ring torsion angle for the representative molecules biphenyl (BP), 2-phenylthiophene (PT), and 2,2'-bithiophene (BT). Perturbative anharmonic corrections to the spectra calculated using density functional theory (DFT) provide only slightly better agreement with experiment. On the other hand, calculations at larger torsion angles give up to 30% improvement in the relative Raman intensities compared with the spectra calculated at the optimized geometries. The torsion-angle dependence of the Raman intensities is most pronounced for delocalized C-C and C-S stretching modes, and less pronounced for bending and ring distortion modes that do not involve inter-ring stretching. Higher-level calculations using the coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] method indicate that DFT underestimates the energy barrier for torsion isomerization at small angles, and it overestimates the barriers at large angles, thus predicting minimum geometries at torsion angles that are too small. Therefore, the results suggest that the discrepancy in relative Raman intensities may be related to an overestimation of inter-ring conjugation by DFT, which also tends to favor geometries that are too planar.

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

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

Origin of Hydrocarbons Stability from a Computational Perspective: A Case Study of Ortho-Xylene Isomers

It is shown herein that intuitive and text-book steric-clash based interpretation of the higher energy "in-in" xylene isomer (as arising solely from the repulsive CH⋅⋅⋅HC contact) with respect to the corresponding global-minimum "out-out" configuration (where the clashing C-H bonds are tilted out) is misleading. It is demonstrated that the two hydrogen atoms engaged in the CH⋅⋅⋅HC contact in "in-in" are involved in attractive interaction so they cannot explain the lower stability of this isomer. We have proven, based on the arsenal of modern bonding descriptors (EDDB, HOMA, NICS, FALDI, ETS-NOCV, DAFH, FAMSEC, IQA), that in order to understand the relative stability of "in-in" versus "out-out" xylenes isomers one must consider the changes in the electronic structure encompassing the entire molecules as arising from the cooperative action of hyperconjugation, aromaticity and unintuitive London dispersion plus charge delocalization based intra-molecular CH⋅⋅⋅HC interactions.

Nine questions on energy decomposition analysis

The paper collects the answers of the authors to the following questions: Is the lack of precision in the definition of many chemical concepts one of the reasons for the coexistence of many partition schemes? Does the adoption of a given partition scheme imply a set of more precise definitions of the underlying chemical concepts? How can one use the results of a partition scheme to improve the clarity of definitions of concepts? Are partition schemes subject to scientific Darwinism? If so, what is the influence of a community's sociological pressure in the "natural selection" process? To what extent does/can/should investigated systems influence the choice of a particular partition scheme? Do we need more focused chemical validation of Energy Decomposition Analysis (EDA) methodology and descriptors/terms in general? Is there any interest in developing common benchmarks and test sets for cross-validation of methods? Is it possible to contemplate a unified partition scheme (let us call it the "standard model" of partitioning), that is proper for all applications in chemistry, in the foreseeable future or even in principle? In the end, science is about experiments and the real world. Can one, therefore, use any experiment or experimental data be used to favor one partition scheme over another? © 2019 Wiley Periodicals, Inc.

Does the Intra-Atomic Deformation Energy of Interacting Quantum Atoms Represent Steric Energy?

We show that the mutual, through-space compression of atomic volume experienced by approaching topological atoms causes an exponential increase in the intra-atomic energy of those atoms, regardless of approach orientation. This insight was obtained using the modern energy partitioning method called interacting quantum atoms (IQA). This behaviour is consistent for all atoms except hydrogen, which can behave differently depending on its environment. Whilst all atoms experience charge transfer when they interact, the intra-atomic energy of the hydrogen atom is more vulnerable to these changes than larger atoms. The difference in behaviour is found to be due to hydrogen's lack of a core of electrons, which, in heavier atoms, consistently provide repulsion when compressed. As such, hydrogen atoms do not always provide steric hindrance. In accounting for hydrogen's unusual behaviour and demonstrating the exponential character of the intra-atomic energy in all other atoms, we provide evidence for IQA's intra-atomic energy as a quantitative description of steric energy.