Two-electron integrations in the quantum theory of atoms in molecules

Planar Tetracoordinate Oxygen Atoms

Planar tetracoordinate oxygen (ptO) atoms are rare, with only a few examples confirmed to date. This study systematically investigates 515 potential structures, formulated as OXnYm q, where n+m=4, q ranging from +2 to -2, and following the 18-valence electron rule. High-level ab initio calculations identified 35 global minima containing a ptO atom, predominantly stabilized by Group 13 elements. Bonding analysis reveals a spectrum of interactions, from covalent to polar ionic, and confirms high electron delocalization. The findings challenge traditional bonding paradigms, improve the understanding of ptO-containing clusters, and propose viable ptO clusters for gas-phase detection, advancing the study of unconventional oxygen bonding.

Pentagonal Star-like Three-Layered Aromatic Sandwich Structure of the [Li10Be2B5]+/0/- Cluster

Boron-based sandwich structures have garnered significant interest in recent years. However, species containing pentagonal boron rings are particularly rare. Herein, we theoretically predict an energetically low-lying three-layered sandwich structure of Li10Be2B5- (of D5h symmetry). The central layer features a pentagonal planar B5 ring staggeringly intercalated between two Be-centered pentagonal Li5Be rings. Bonding analysis reveals that the entire cluster demonstrates σ/π aromaticity. Specifically, the inner B5 layer contributes 6π/10σ-electron aromaticity, while each of the top and bottom layers contributes 2σ-electron aromaticity, leading to high symmetry in both the geometry and bonding patterns. Such a sandwich structure can also exist as the most stable conformation in both neutral and cationic states despite one of the delocalized σ bonds associated with the two outer Li5Be layers being absent. Additionally, this aromaticity is clearly supported by a negative NICS_zz value and local diatropic contributions from the B5 fragment. Our discovery enriches the sandwich family and provides a possible class of cluster units to form nanostructures.

Unraveling the Bonding and Aromaticity of Pentazole, Pentaphosphole, and Cyclopentadiene Anions: A Comprehensive Study

This study investigates π-delocalization, π-bonding situations, and aromaticity of the pentazolate anion ([cyclo-N5-], (a)), which was detected by Christe et al. in 2002. To gain a broader perspective, we investigated the iso-π-electronic species [cyclo-P5-] (b) and [cyclo-(CH)5-] (c). VB analyses reveal that the three studied molecules display significant resonance stabilization, as indicated by their high resonance energy values. A comprehensive analysis of aromaticity was conducted using electronic and magnetic aromaticity indices, revealing that all three anions exhibit strong π-aromaticity and relatively weak σ-aromaticity.

Doubly σ- and π-aromatic planar pentacoordinate boron polyanions

Ten planar pentacoordinate boron (ppB) systems are reported, each featuring a pentagonal ring composed of tetrels, pnictogens, or their combination around boron. These structures exhibit double aromaticity (σ and π), consistent with Hückel's 4n+2 rule, as confirmed by magnetically induced current density analysis.

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

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

Exploring aromatic rings with planar tetracoordinate group 13-15 atoms

This study examines systems containing planar tetracoordinate group 13-15 atoms (E) within pentagonal C4H2E rings bridged by Si or Ge atoms. A detailed chemical bonding analysis of eleven candidates shows that true tetracoordination is achieved only in the C4H2NGe2+ system.

Kohn-Sham fragment energy decomposition analysis

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

Affinity of Telluronium Chalcogen Bond Donors for Lewis Bases in Solution: A Critical Experimental-Theoretical Joint Study

Telluronium salts [Ar2 MeTe]X were synthesized, and their Lewis acidic properties towards a number of Lewis bases were addressed in solution by physical and theoretical means. Structural X-ray diffraction analysis of 21 different salts revealed the electrophilicity of the Te centers in their interactions with anions. Telluroniums' propensity to form Lewis pairs was investigated with OPPh3 . Diffusion-ordered NMR spectroscopy suggested that telluroniums can bind up to three OPPh3 molecules. Isotherm titration calorimetry showed that the related heats of association in 1,2-dichloroethane depend on the electronic properties of the substituents of the aryl moiety and on the nature of the counterion. The enthalpies of first association of OPPh3 span -0.5 to -5 kcal mol-1 . Study of the affinity of telluroniums for OPPh3 by state-of-the-art DFT and ab-initio methods revealed the dominant Coulombic and dispersion interactions as well as an entropic effect favoring association in solution. Intermolecular orbital interactions between [Ar2 MeTe]+ cations and OPPh3 are deemed insufficient on their own to ensure the cohesion of [Ar2 MeTe ⋅ Bn ]+ complexes in solution (B=Lewis base). Comparison of Grimme's and Tkatchenko's DFT-D4/MBD-vdW thermodynamics of formation of higher [Ar2 MeTe ⋅ Bn ]+ complexes revealed significant molecular size-dependent divergence of the two methodologies, with MBD yielding better agreement with experiment.

Anti-electrostatic cation⋯π-hole and cation⋯lp-hole interactions are stabilized via collective interactions

Collective interactions are a novel type of bond between metals and AX3 fragments with an electropositive central atom, A, and electronegative X substituents. Here, using electrostatic potential maps and state-of-the-art bonding analysis tools we have shown that collective interactions are anti-electrostatic cation⋯π-Hole or cation⋯lp-Hole interactions.

Dual Chalcogen-Bonding Interactions for the Conformational Control of Urea

Dual chalcogen-bonding interactions is proposed as a novel means for the conformational control of urea derivatives. The formation of a chalcogen-bonding interaction at both sides of the urea carbonyl group was unambiguously confirmed by X-ray diffraction as well as computational studies including non-covalent interaction (NCI) plot index analysis, quantum theory of atoms in molecules (QTAIM) analysis, and natural bond orbital (NBO) analysis via DFT calculations. By virtue of this dual interaction, urea derivatives that bear chalcogen atoms (X=S and Se) adopt a planar structure via the carbonyl oxygen (O) with an X⋅⋅⋅O⋅⋅⋅X arrangement on the same side of the molecule. The rigidity of the conformational lock was evaluated using the molecular arrangement in the crystal and the rotational barrier of benzochalcogenophene ring, which indicated a stronger conformational lock in benzoselenophene than in benzothiophene urea derivatives. Furthermore, the acidity of the urea derivatives increases according to the Lewis-acidic properties of the chalcogen-bonding interactions, whereby benzoselenophene urea is more acidic than benzothiophene urea. Tweezer-shaped urea derivatives were prepared, and their stereostructure proved the viability of the conformational control for defining the location of the substituents on the urea framework.

Planar pentacoordinate s-block metals

The presence of a delocalized π-bond is often considered an essential criterion for achieving planar hypercoordination. Herein, we show that σ-delocalization could be sufficient to make the planar configuration the most stable isomer in a series of planar pentacoordinate s-block metals. High-level ab initio computations reveal that the global minimum of a series of interalkali and interalkali-alkaline earth clusters (LiNa5, Li5Mg+, Na5Mg+, K5Ca+, CaRb5+, Rb5Sr+, and SrCs5+) adopts a singlet D5h structure with a planar pentacoordinate lithium or alkaline earth metal (AE = Mg, Ca, Sr). These clusters are unusual combinations to stabilize a planar pentacoordinate atom, as all their constituents are electropositive. Despite the absence of π-electrons, Hückel's rule is fulfilled by the six σ-electrons. Furthermore, the systems exhibit a diatropic ring current in response to an external magnetic field and a strong magnetic shielding, so they might be classified as σ-aromatic. Therefore, multicenter σ-bonds and the resulting σ-delocalization stabilize these clusters, even though they lack π-aromaticity.

Exact decompositions of the total KS-DFT exchange-correlation energy into one- and two-center terms

In the so-called Interacting Quantum Atoms (IQA) approach, the molecular energy is numerically decomposed as a sum of atomic and diatomic contributions. While proper formulations have been put forward for both Hartree-Fock and post-Hartree-Fock wavefunctions, this is not the case for the Kohn-Sham density functional theory (KS-DFT). In this work, we critically analyze the performance of two fully additive approaches for the IQA decomposition of the KS-DFT energy, namely, the one from Francisco et al., which uses atomic scaling factors, and that from Salvador and Mayer based upon the bond order density (SM-IQA). Atomic and diatomic exchange-correlation (xc) energy components are obtained for a molecular test set comprising different bond types and multiplicities and along the reaction coordinate of a Diels-Alder reaction. Both methodologies behave similarly for all systems considered. In general, the SM-IQA diatomic xc components are less negative than the Hartree-Fock ones, which is in good agreement with the known effect of electron correlation upon (most) covalent bonds. In addition, a new general scheme to minimize the numerical error of the sum of two-electron energy contributions (i.e., Coulomb and exact exchange) in the framework of overlapping atoms is described in detail.

Searching for Systems with Planar Hexacoordinate Carbons

Here, we present evidence that the D2h M2C50/2+ (M = Li-K, Be-Ca, Al-In, and Zn) species comprises planar hexacoordinate carbon (phC) structures that exhibit four covalent and two electrostatic interactions. These findings have been made possible using evolutionary methods for exploring the potential energy surface (AUTOMATON program) and the Interacting Quantum Atoms (IQA) methodology, which support the observed bonding interactions. It is worth noting, however, that these structures are not the global minimum. Nonetheless, incorporating two cyclopentadienyl anion ligands (Cp) into the CaC52+ system has enhanced the relative stability of the phC isomer. Moreover, cycloparaphenylene ([8]CPP) provides system protection and kinetic stability. These results indicate that using appropriate ligands presents a promising approach for expanding the chemistry of phC species.

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.

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 (ICIXC; [Formula: see text]) to characterize the extent of collective versus pairwise bonding. Unlike conventional bonds in which ICIXC remains close to one, in collective interactions ICIXC 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 [Ma+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 XFn systems (X: B or C). Some of organolithium and organomagnesium species have the lowest ICIXC among the more than 100 studied systems revealing the fact that collective interactions are rather a rule than an exception among organometallic species.

QM/MM Energy Decomposition Using the Interacting Quantum Atoms Approach

The interacting quantum atoms (IQA) method decomposes the quantum mechanical (QM) energy of a molecular system in terms of one- and two-center (atomic) contributions within the context of the quantum theory of atoms in molecules. Here, we demonstrate that IQA, enhanced with molecular mechanics (MM) and Poisson-Boltzmann surface-area (PBSA) solvation methods, is naturally extended to the realm of hybrid QM/MM methodologies, yielding intra- and inter-residue energy terms that characterize all kinds of covalent and noncovalent bonding interactions. To test the robustness of this approach, both metal-water interactions and QM/MM boundary artifacts are characterized in terms of the IQA descriptors derived from QM regions of varying size in Zn(II)- and Mg(II)-water clusters. In addition, we analyze a homologous series of inhibitors in complex with a matrix metalloproteinase (MMP-12) by carrying out QM/MM-PBSA calculations on their crystallographic structures followed by IQA energy decomposition. Overall, these applications not only show the advantages of the IQA QM/MM approach but also address some of the challenges lying ahead for expanding the QM/MM methodology.

Interacting Quantum Atoms Method for Crystalline Solids

An implementation of the Interacting Quantum Atoms method for crystals is presented. It provides a real space energy decomposition of the energy of crystals in which all energy components are physically meaningful. The new package ChemInt enables one to compute intra-atomic and inter-atomic energies, as well as electron population measures used for quantitative description of chemical bonds in crystals. The implementation is tested and applied to characteristic molecular and crystalline systems with different types of bonding.

Metal-CO Bonding in Mononuclear Transition Metal Carbonyl Complexes

DFT calculations have been carried out for coordinatively saturated neutral and charged carbonyl complexes [M(CO) _n ] ^q where M is a metal atom of groups 2-10. The model compounds M(CO)₂ (M = Ca, Sr, Ba) and the experimentally observed [Ba(CO)]⁺ were also studied. The bonding situation has been analyzed with a variety of charge and energy partitioning approaches. It is shown that the Dewar-Chatt-Duncanson model in terms of M ← CO σ-donation and M → CO π-backdonation is a valid approach to explain the M-CO bonds and the trend of the CO stretching frequencies. The carbonyl ligands of the neutral complexes carry a negative charge, and the polarity of the M-CO bonds increases for the less electronegative metals, which is particularly strong for the group 4 and group 2 atoms. The NBO method delivers an unrealistic charge distribution in the carbonyl complexes, while the AIM approach gives physically reasonable partial charges that are consistent with the EDA-NOCV calculations and with the trend of the C-O stretching frequencies. The AdNDP method provides delocalized MOs which are very useful models for the carbonyl complexes. Deep insight into the nature of the metal-CO bonds and quantitative information about the strength of the [M] ← (CO)₈ σ-donation and [M(d)] → (CO)₈ π-backdonation visualized by the deformation densities are provided by the EDA-NOCV method. The large polarity of the M-CO π orbitals toward the CO end in the alkaline earth octacarbonyls M(CO)₈ (M = Ca, Sr, Ba) leads to small values for the delocalization indices δ(M-C) and δ(M···O) and significant overlap between adjacent CO groups, but the origin of the charge migration and the associated red-shift of the C-O stretching frequencies is the [M(d)] → (CO)₈ π-backdonation. The heavier alkaline earth metals calcium, strontium and barium use their s/d valence orbitals for covalent bonding. They are therefore to be assigned to the transition metals.

Origin of the Ir-Si bond shortening in Ir-NSiN complexes

The Ir-Si bond distances reported for Ir-(fac-κ3-NSiNOPy) and Ir-(fac-κ3-NSiN4MeOPy) species (NSiNOPy = bis(pyridine-2-yloxy)methylsilyl and NSiN4MeOPy = bis(4-methyl-pyridine-2-yloxy)methylsily) are in the range of 2.220-2.235 Å. These values are in the lowest limit of the Ir-Si bond distances found in the Cambridge Structural Database (CSD). To understand the origin of such remarkable shortening, a computational study of the bonding situation of representative examples of Ir-(fac-κ3-NSiN) species has been carried out. It is found that the Ir-Si bond can be described as an electron-sharing (i.e. covalent) bond. Despite that, this bond is highly polarized and as a result, the contribution of the electrostatic attractions to the bonding is rather significant. Indeed, there exists a linear relationship (R2 = 0.97) between the Ir-Si bond distance and the extent of the computed electrostatic interactions, which indicates that the ionic contribution to the bonding is mainly responsible for the observed Ir-Si bond shortening.

TWOE Code: An Efficient Tool for Explicit Partition of Coupled Cluster and Configuration Interaction Energies into Atomic and Diatomic Contributions

The efficient implementation of the TWOE program for evaluating the atomic and interatomic energy components at post-HF level was developed. The systematic convergence of these terms up to a near full-CI limit was performed for the first time for a series of coupled cluster methods: CCSD → CCSDT → CCSDTQ → CCSDTQP. A comparison with corresponding CI approaches (up to fifth excitation level) is additionally discussed. For a set of diatomic systems, it was demonstrated that, along with a full molecular energy convergence, all its components are also converged but with different patterns. It was found that not all components are decreased in their values at increasing computational rank. For instance, atomic energy parts are decreased while interatomic (interaction) energies are increased as the limiting level is approached. Two schemes were employed for atomic partition of molecules: the Baders approach and planes dissection. Influence of dynamical correlation effects on atomic energy components was analyzed in detail. Current TWOE implementation allows one, in principle, to work with any ab initio method providing the two-particle density matrix. It is believed that the developed program will be a useful tool for a real space energy decomposition that helps to reveal the most peculiar points in the structure of the total and correlation energies of a molecule.

Chemical Bonding in Homoleptic Carbonyl Cations [M{Fe(CO)5 }2 ]+ (M=Cu, Ag, Au)

Syntheses of the copper and gold complexes [Cu{Fe(CO)5 }2 ][SbF6 ] and [Au{Fe(CO)5 }2 ][HOB{3,5-(CF3 )2 C6 H3 }3 ] containing the homoleptic carbonyl cations [M{Fe(CO)5 }2 ]+ (M=Cu, Au) are reported. Structural data of the rare, trimetallic Cu2 Fe, Ag2 Fe and Au2 Fe complexes [Cu{Fe(CO)5 }2 ][SbF6 ], [Ag{Fe(CO)5 }2 ][SbF6 ] and [Au{Fe(CO)5 }2 ][HOB{3,5-(CF3 )2 C6 H3 }3 ] are also given. The silver and gold cations [M{Fe(CO)5 }2 ]+ (M=Ag, Au) possess a nearly linear Fe-M-Fe' moiety but the Fe-Cu-Fe' in [Cu{Fe(CO)5 }2 ][SbF6 ] exhibits a significant bending angle of 147° due to the strong interaction with the [SbF6 ]- anion. The Fe(CO)5 ligands adopt a distorted square-pyramidal geometry in the cations [M{Fe(CO)5 }2 ]+ , with the basal CO groups inclined towards M. The geometry optimization with DFT methods of the cations [M{Fe(CO)5 }2 ]+ (M=Cu, Ag, Au) gives equilibrium structures with linear Fe-M-Fe' fragments and D2 symmetry for the copper and silver cations and D4d symmetry for the gold cation. There is nearly free rotation of the Fe(CO)5 ligands around the Fe-M-Fe' axis. The calculated bond dissociation energies for the loss of both Fe(CO)5 ligands from the cations [M{Fe(CO)5 }2 ]+ show the order M=Au (De =137.2 kcal mol-1 )>Cu (De =109.0 kcal mol-1 )>Ag (De =92.4 kcal mol-1 ). The QTAIM analysis shows bond paths and bond critical points for the M-Fe linkage but not between M and the CO ligands. The EDA-NOCV calculations suggest that the [Fe(CO)5 ]→M+ ←[Fe(CO)5 ] donation is significantly stronger than the [Fe(CO)5 ]←M+ →[Fe(CO)5 ] backdonation. Inspection of the pairwise orbital interactions identifies four contributions for the charge donation of the Fe(CO)5 ligands into the vacant (n)s and (n)p AOs of M+ and five components for the backdonation from the occupied (n-1)d AOs of M+ into vacant ligand orbitals.

Planar Tetracoordinate Carbons in Allene-Type Structures

The exhaustive exploration of the potential energy surfaces of CE₂M₂ (E = Si-Pb; M = Li and Na) revealed seven global minima containing a planar tetracoordinate carbon (ptC). The design, based on a π-localization strategy, resulted in a ptC with two double bonds forming a linear or a bent allene-type E═C═E motif. The magnetic response of the bent E═C═E fragments support a σ-aromaticity. The bonding analysis indicated that the ptCs form C-E covalent bonds and C-M electrostatic interactions.

Planar Hexacoordinate Carbons: Half Covalent, Half Ionic

Herein, the first global minima containing a planar hexacoordinate carbon (phC) atom are reported. The fifteen structures belong to the CE₃ M₃ ⁺ (E=S-Te and M=Li-Cs) series and satisfy both geometric and electronic criteria to be considered as a true phC. The design strategy consisted of replacing oxygen in the D_3h  CO₃ Li₃ ⁺ structure with heavy and less electronegative chalcogens, inducing a negative charge on the C atom and an attractive electrostatic interaction between C and the alkali-metal cations. The chemical bonding analyses indicate that carbon is covalently bonded to three chalcogens and ionically connected to the three alkali metals.

Bonding and Aromaticity in Electron-Rich Boron and Aluminum Clusters

In this work bonding and aromaticity of triply bonded atoms of group 13 elements (M≡M, M = B and Al) in recently characterized B₂Al₃^-, Na₃Al₂^-, and Na₄Al₂ are studied. Here, I show that although molecular orbital-based analyses characterize triple bonds, the electropositive nature of group 13 elements gives these bonds unique characteristics. The bond orders derived from the delocalization index, topology of the electron density, and local characteristics of (3, -1) critical points, as defined within the context of quantum theory of atoms in molecules, do not conform with those of ordinary triple bonds. In Na₃Al₂^- and Na₄Al₂ clusters non-nuclear attractors form between the electropositive Al atoms acting like pseudo atoms. The bond between boron atoms in B₂Al₃^- is more similar to an ordinary triple covalent bond benefiting from the exchange-correlation component of the interatomic interaction energy as defined via interacting quantum atom theory. However, extreme electrostatic repulsion between negatively charged boron atoms attenuates this bond. Finally, current density analysis suggests that B₂Al₃^- is a magnetic aromatic system, nearly 50% more aromatic compared to benzene.

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.

Anatomy of Base Pairing in DNA by Interacting Quantum Atoms

The formation of purine and pyrimidine base pairs (BPs), which contributes to shaping of the canonical and noncanonical 3D structures of nucleic acids, is one the most investigated phenomena in chemistry and life sciences. In this contribution, the anatomy of the bond energy (BDE) of the base-pairing interaction in 39 different arrangements found experimentally or predicted for DNA structures containing the four common nucleobases (A, C, G, T) in their neutral or protonated forms is described in light of the theory of interacting quantum atoms within the context of the quantum theory of atoms in molecules. The interplay of individual energy components involved in the three stages of the bond formation process (structural deformation, electron-density promotion, and intermolecular interaction) is studied. We recognized that for the neutral BPs, variations in the kinetic and electrostatic contributions to the BDE are rather negligible, leaving the exchange-correlation energy as the main stabilizing component. It is shown that the contribution of the exchange-correlation term can be recovered by including atoms that are formally assumed to be hydrogen bonded (primary interaction). In contrast, to recover the electrostatic component of interaction, one must consider both the primary and secondary (formally nonbonded atoms) interatomic interactions. The results of our study were employed to design new types of BPs with altered bonding anatomy. We demonstrate that improving the electrostatic characteristics of the BPs does not necessarily result in greater interaction energies if weak secondary hydrogen bonding is destroyed. However, the main tuning factor for systems with conserved interacting faces (primary interactions) is the electrostatic component of the interaction energy resulting from the secondary atom-atom electrostatics.

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 .

The Na⋅⋅⋅B Bond in NaBH3 - : A Different Type of Bond

A newly introduced Na-B bond in NaBH₃ ^- has been a challenge for the chemical bonding community. Here, a series of MBH₃ ^- (M=Li, Na, K) species and NaB(CN)₃ ^- are studied within the context of quantum chemical topology approaches. The analyses suggest that M-B interaction cannot be classified as an ordinary covalent, dative, or even simple ionic interaction. The interactions are controlled by coulombic forces between the metals and the substituents on boron, for example, H or CN, more than the direct M-B interaction. On the other hand, while the characteristics of the (3, -1) critical points of the bonds are comparable to weak hydrogen bonds, not covalent bonds, the metal and boron share a substantial sum of electrons. To the best of the author's knowledge, the characteristics of these bonds are unprecedented among known molecules. Considering all paradoxical properties of these bonds, they are herein described as ionic-enforced covalent bonds.

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.

Cooperativity in alkane-1,2- and 1,3-polyols: NMR, QTAIM, and IQA study of O─H… OH and C─H… OH bonding interactions

Proton nuclear magnetic resonance chemical shifts and atom-atom interaction energies for alkanepolyols with 1,2-diol and 1,3-diol repeat units, and for their 1:1 pyridine complexes, are computed by density functional theory calculations. In the 1,3-polyols, based on a tG'Gg' repeat unit, the only important intramolecular hydrogen bonding interactions are O─H^… OH. By quantum theory of atoms in molecules analysis of the electron density, unstable bond and ring critical points are found for such interactions in 1,2-polyols with tG'g repeat units, from butane-1,2,3,4-tetrol onwards and in their pyridine complexes from propane-1,2,3-triol onwards. Several features (OH proton shifts and charges, and interaction energies computed by the interacting quantum atoms approach) are used to monitor the dependence of cooperativity on chain length: This is much less regular in 1,2-polyols than in 1,3-polyols and by most criteria has a higher damping factor. Well defined C─H^… OH interactions are found in butane-1,2,3,4-tetrol and higher members of the 1,2-polyol series, as well as in their pyridine complexes: There is no evidence for cooperativity with O─H^… OH bonding. For the 1,2-polyols, there is a tenuous empirical relationship between the existence of a bond critical point for O─H^… OH hydrogen bonding and the interaction energies of competing exchange channels, but the primary/secondary ratio is always less than unity.

The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds

The concept of a connectivity matrix, essential for the reaction fragility (RF) spectra technique for monitoring electron density evolution in a chemical reaction, has been supported with a novel formulation for the diagonal matrix elements; their direct link to the electron density function ρ(r) has been demonstrated. By combining the concept with the atomization energy of a system, the separation of the potential energy into atomic and/or bond contributions has been achieved. The energy derivative diagrams for atoms and bonds that are variable along a reaction path provide new insight into the reaction mechanism. Diagonalization of the connectivity matrix resulted in the eigenvectors that provide information on a role of individual atoms in the development of structural changes along a reaction path.

Energy components in energy decomposition analysis (EDA) are path functions; why does it matter?

Here, we discuss that unlike bond dissociation energy (BDE) that is a state function quantity, the energy components of the energy decomposition analysis (EDA), i.e. electrostatic interaction, Pauli repulsion, and orbital interaction, are path (process) function quantities. Being a path function means that EDA energy components are not uniquely defined, i.e. the relative magnitudes of the orbital interaction, Pauli repulsion, and electrostatic components may vary depending on the selected pathway for EDA. Therefore, at best, EDA can define whether closely related chemical bonds are more or less ionic/covalent compared with each other. However, a precise assessment of the nature of a certain type of chemical bond using EDA is a questionable task. Besides, we briefly discuss that the widely used EDA pathway, which is merely an arbitrary choice among infinite possible paths, comes to conclusions not consistent with our widely accepted knowledge of bond formation even for the simplest molecules.

Relationships between NMR shifts and interaction energies in biphenyls, alkanes, aza-alkanes, and oxa-alkanes with X─H… H─Y and X─H… Z (X, Y = C or N; Z = N or O) hydrogen bonding

Hydrogen-hydrogen C─H^… H─C bonding between the bay-area hydrogens in biphenyls, and more generally in congested alkanes, very strained polycyclic alkanes, and cis-2-butene, has been investigated by calculation of proton nuclear magnetic resonance (NMR) shifts and atom-atom interaction energies. Computed NMR shifts for all protons in the biphenyl derivatives correlate very well with experimental data, with zero intercept, unit slope, and a root mean square deviation of 0.06 ppm. For some congested alkanes, there is generally good agreement between computed values for a selected conformer and the experimental data, when it is available. In both cases, the shift of a given proton or pair of protons tends to increase with the corresponding interaction energy. Computed NMR shift differences for methylene protons in polycyclic alkanes, where one is involved in a very short contact ("in") and the other is not ("out"), show a rough correlation with the corresponding C─H^… H─C exchange energies. The "in" and "in,in" isomers of selected aza- and diaza-cycloalkanes, respectively, are X─H^… H─N hydrogen bonded, whereas the "out" and "in,out" isomers display X─H^… N hydrogen bonds (X = C or N). Oxa-alkanes and the "in" isomers of aza-oxa-alkanes are X─H^… O hydrogen bonded. There is a very good general correlation, including both N─H^… H─Y (Y = C or N) and N─H^… Z (Z = N or O) interactions, for NH proton shifts against the exchange energy. For "in" CH protons, the data for the different C─H^… H─Y and C─H^… Z interactions are much more dispersed and the overall shift/exchange energy correlation is less satisfactory.

On the applicability of functional-group symmetry-adapted perturbation theory and other partitioning models for chiral recognition - the case of popular drug molecules interacting with chiral phases

The applicability of symmetry-adapted perturbation theory (SAPT) and functional-group SAPT (F-SAPT) to study chiral recognition is investigated on an example of three popular chiral drug molecules: ibuprofen, norepinephrine, and baclofen, interacting with phenethylamine or proline - two molecules that are often used as chiral phases in chromatography. The comparison of the F-SAPT with the interacting quantum atoms (IQA) approach is also provided. Accurate estimation of energetic differences of the non-covalent intermolecular complexes composed of two chiral molecules is a necessary prerequisite for the possibility of a prediction of the chiral recognition. The SAPT method with interacting molecules described on the density functional theory level provides accurate total interaction energies, while the F-SAPT approach is the most useful in determining which functional groups are responsible for strengthening or weakening of the interaction between chiral molecules. The largest difference in the interaction energies has been calculated for the baclofen-phenethylamine and norepinephrine-phenethylamine pairs, while the smallest for the ibuprofen-proline and baclofen-proline ones. In most cases, the intermolecular interaction is found to be composed of a strong directional hydrogen bond, which was stabilized by two or more weaker non-covalent interactions between groups (in accordance with the phenomological three-point rule), but in several cases more subtle factors are responsible for larger stability of one diastereoisomer, like the stabilization of the conformation involving two noninteracting functional groups attached to a chiral atom through intramolecular attraction. Additionally, the simulated IR spectra were analyzed for all pairs of diastereoisomeric complexes and the red- and blue-shifts of characteristic bond vibrations were discussed in the context of inter-group interactions.

Valence-Shell Electron-Pair Repulsion Theory Revisited: An Explanation for Core Polarization

Valence-shell electron-pair repulsion (VSEPR) theory constitutes one of the pillars of theoretical predictive chemistry. It was proposed even before the advent of the concept of "spin", and it is still a very useful tool in chemistry. In this article we propose an extension of VSEPR theory to understand the core structure and predict core polarization in the main-group elements. We show from first principles (Electron Localization Function analysis) how the inner- and outer-core shells are organized. In particular, electrons in these regions are structured following the shape of the dual polyhedron of the valence shell (3^rd period) or the equivalent polyhedron (4^th and 5^th periods). We interpret these results in terms of "hard" and "soft" core character. All the studied systems follow this trend, providing a framework for predicting electron distribution in the core. We also show that lone pairs behave as "standard ligands" in terms of core polarization. The predictive character of the model was tested by proposing the core polarization in different systems not included in the original set (such as XeF₄ and [Fe(CN)₆ ]^3- ) and checking the hypothesis by means of a posteriori calculations. From the experimental point of view, the extension of VSEPR to the core region has consequences for current crystallography research. In particular, it explains the core polarization revealed by high resolution X-ray experiments.

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.

Tetrel Interactions from an Interacting Quantum Atoms Perspective

Tetrel bonds, the purportedly non-covalent interaction between a molecule that contains an atom of group 14 and an anion or (more generally) an atom or molecule with lone electron pairs, are under intense scrutiny. In this work, we perform an interacting quantum atoms (IQA) analysis of several simple complexes formed between an electrophilic fragment (A) (CH₃F, CH₄, CO₂, CS₂, SiO₂, SiH₃F, SiH₄, GeH₃F, GeO₂, and GeH₄) and an electron-pair-rich system (B) (NCH, NCO-, OCN-, F-, Br-, CN-, CO, CS, Kr, NC-, NH₃, OC, OH₂, SH-, and N₃-) at the aug-cc-pvtz coupled cluster singles and doubles (CCSD) level of calculation. The binding energy ( E bind AB ) is separated into intrafragment and inter-fragment components, and the latter in turn split into classical and covalent contributions. It is shown that the three terms are important in determining E bind AB , with absolute values that increase in passing from electrophilic fragments containing C, Ge, and Si. The degree of covalency between A and B is measured through the real space bond order known as the delocalization index ( δ AB ). Finally, a good linear correlation is found between δ AB and E xc AB , the exchange correlation (xc) or covalent contribution to E bind AB .

Substituent effects in the so-called cationπ interaction of benzene and its boron-nitrogen doped analogues: overlooked role of σ-skeleton

Despite massive efforts to pinpoint the substituent effects in the so-called cationπ systems, no consensus has been yet reached on how substituents exercise their effects in the interaction of the aromatic molecule with the metal ion. The π-polarization (the Hunter model) and the direct local effect (the Wheeler-Houk model) are two lines of thought applied to this problem, but the justification of both approaches is based on insufficiently proven assumptions and approximations. In order to shed more light on this issue we propose a new approach which enables us to gauge directly the energetic trends resulting from the interaction of the ring with the cation. In our method we add one more partitioning level to the interacting quantum atoms (IQA) scheme and decompose the IQA interaction energies into contributions resulting from σ and π electron densities of the aromatic ring. The new approach, which is named partitioned-IQA, abbreviated as p-IQA, has been applied to complexes of derivatives of benzene or azaborine interacting with a sodium cation. The p-IQA approach reveals that in these systems both σ and π electronic moieties are polarized. Interestingly, for the majority of cases the σ-polarization outweighs the π one, contrary to the Hunter model. However, the Wheeler-Houk model is not precise, either, since the σ-polarization shows some degree of non-locality. In addition, the substituents are found to have a negligible influence on the ring orbital-overlapping capability, i.e. the covalency. Therefore, the substituent effect in the cationπ interaction is a nonlocal classical effect, indicating that neither Hunter model nor Wheeler-Houk model is able to fully describe all the aspects of the substituent effects. The p-IQA conclusions for the considered systems have been compared with the results from the functional-group SAPT (F-SAPT) method. We believe that the presented partitioning in the IQA framework will provide a deeper insight into the substituent effects in the cationπ interactions, which is beyond the σ-π atomic charge population separation.

A first step towards quantum energy potentials of electron pairs

A first step towards the construction of a quantum force field for electron pairs in direct space is taken. Making use of topological tools (Interacting Quantum Atoms and the Electron Localisation Function), we have analysed the dependency of electron pairs electrostatic, kinetic and exchange-correlation energies upon bond stretching. Simple correlations were found, and can be explained with elementary models such as the homogeneous electron gas. The resulting energy model is applicable to various bonding regimes: from homopolar to highly polarized and even to non-conventional bonds. Overall, this is a fresh approach for developing real space-based force fields including an exchange-correlation term. It provides the relative weight of each of the contributions, showing that, in common Lewis structures, the exchange correlation contribution between electron pairs is negligible. However, our results reveal that classical approximations progressively fail for delocalised electrons, including lone pairs. This theoretical framework justifies the success of the classic Bond Charge Model (BCM) approach in solid state systems and sets the basis of its limits. Finally, this approach opens the door towards the development of quantitative rigorous energy models based on the ELF topology.

Interacting Quantum Atoms Approach and Electrostatic Solvation Energy: Assessing Atomic and Group Solvation Contributions

The interacting quantum atoms (IQA) method decomposes the total energy of a molecular system in terms of one- and two-center (atomic) contributions within the context of the quantum theory of atoms in molecules. Here we incorporate electrostatic continuum solvent effects into the IQA energy decomposition. To this end, the interaction between the solute electrostatic potential and the solvent screening charges as defined within the COSMO solvation model is now included in a new version of the PROMOLDEN code, allowing thus to apply IQA in combination with COSMO-quantum chemical methods as well as to partition the electrostatic solvation energy into effective atomic and group contributions. To test the robustness of this approach, we carry out COSMO-HF/aug-cc-pVTZ calculations followed by IQA calculations on more than 400 neutral and ionic solutes extracted from the MNSol database. The computational results reveal a detailed atomic mapping of the electrostatic solvation energy that is useful to assess to what extent the solvation energy can be decomposed into atomic and group contributions of various parts of a solute molecule, as generally assumed by empirical methodologies that estimate solvation energy and/or logP values.

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

Biphenyl is a prototype molecule, the study of which is important for a proper understanding of stereo-electronic effects. In the gas phase it has an equilibrium central torsion angle of ~ 45° and shows both a planar (0°) and a perpendicular (90°) torsional energy barrier. The latter is analysed for the first time. We use the newly proposed REG method, which is an exhaustive procedure that automatically ranks atomic energy contributions according to their importance in explaining the energy profile of a total system. Here, the REG method operates on energy contributions computed by the interacting quantum atoms method. This method is minimal in architecture and provides a crisp picture of well-defined and well-separated electrostatic, steric and exchange (covalent) energies at atomistic level. It is shown that the bond critical point occurring between the ortho-hydrogens in the planar geometry has been wrongly interpreted as a sign of repulsive interaction. A convenient metaphor of analysing football matches is introduced to clarify the role of a REG analysis.