Nine questions on energy decomposition analysis

Chemical Bond Overlap Descriptors From Multiconfiguration Wavefunctions

The chemical bond is a fundamental concept in chemistry, and various models and descriptors have evolved since the advent of quantum mechanics. This study extends the overlap density and its topological descriptors (OP/TOP) to multiconfigurational wavefunctions. We discuss a comparative analysis of OP/TOP descriptors using CASSCF and DCD-CAS(2) wavefunctions for a diverse range of molecular systems, including X-O bonds in X-OH (XH, Li, Na, H2B, H3C, H2N, HO, F) and Li-X' (XF, Cl, and Br). Results show that OP/TOP aligns with bonding models like the quantum theory of atoms in molecules (QTAIM) and local vibrational modes theory, revealing insights such as overlap densities shifting towards the more electronegative atom in polar bonds. The Li-F dissociation profile using OP/TOP descriptors demonstrated sensitivity to ionic/neutral inversion during Li-F dissociation, highlighting their potential for elucidating complex bond phenomena and offering new avenues for understanding multiconfigurational chemical bond dynamics.

Exchange-correlation effects in interatomic energies for pure density functionals and their application to the molecular energy prediction

In this proof-of-concept paper, we show how exchange-correlation effects can be simply recovered for interatomic energies within the interacting quantum atoms decomposition when local, gradient generalized, or meta-gradient generalized approximations are used in density functional theory (DFT) calculations. We also demonstrate how inhomogeneity and non-local effects can be introduced even from a pure local scheme, without resorting to any orbital information. Finally, we provide numerical evidence on a database of selected energetic molecules that this decomposition scheme can be efficiently used to build accurate models for the prediction of molecular energies from an initial "cheap" DFT calculation.

CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems

CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis's enhanced performance, guiding developers of GPU-accelerated code.

Multiple Bonding in AeN- (Ae=Ca, Sr, Ba)

Quantum chemical calculations using ab initio methods at the MRCI+Q(8,9)/def2-QZVPPD and CCSD(T)/def2-QZVPPD levels as well as using density functional theory are reported for the diatomic molecules AeN- (Ae=Ca, Sr, Ba). The anions CaN- and SrN- have electronic triplet (3Π) ground states with nearly identical bond dissociation energies De ~57 kcal/mol calculated at the MRCI+Q(8,9)/def2-QZVPPD level. In contrast, the heavier homologue BaN- has a singlet (1Σ+) ground state, which is only 1.1 kcal/mol below the triplet (3Σ-) state. The computed bond dissociation energy of (1Σ+) BaN- is 68.4 kcal/mol. The calculations at the CCSD(T)-full/def2-QZVPPD and BP86-D3(BJ)/def2-QZVPPD levels are in reasonable agreement with the MRCI+Q(8,9)/def2-QZVPPD data, except for the singlet (1Σ+) state, which has a large multireference character. The calculated atomic partial charges given by the CM5, Voronoi and Hirshfeld methods suggest small to medium-sized Ae←N- charge donation for most electronic states. In contrast, the NBO method predicts for all species medium to large Ae→N- electronic charge donation, which is due to the neglect of the (n)p AOs of Ae atoms as genuine valence orbitals. Neither the bond orders nor the bond lengths correlate with the bond dissociation energies. The EDA-NOCV calculations show that the heavier alkaline earth atoms Ca, Sr, Ba use their (n)s and (n-1)d orbitals for covalent bonding.

Preparation of a Compound with a SiII -SiIV -SiII Bonding Arrangement

Herein, we report the synthesis of a rare bis-silylene, 1, in which two SiII atoms are bridged by a SiIV atom. Compound 1 contains an unusual SiII -SiIV -SiII bonding arrangement with SiII -SiIV bond distances of 2.4212(8) and 2.4157(7) Å. Treatment of 1 with Fe(CO)5 afforded a dinuclear Fe0 complex 2 with two unusually long Si-Si bonds (2.4515(8) and 2.4488(10) Å). We have also carried out a detailed computational study to understand the nature of the Si-Si bonds in these compounds. Natural bond orbital (NBO) and energy decomposition analysis-natural orbital for chemical valence (EDA-NOCV) analyses reveal that the Si-Si bonds in 1 and 2 are of an electron-sharing nature.

The Energetic Origins of Pi-Pi Contacts in Proteins

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

Open shell versus closed shell bonding interaction in cyclopropane derivatives: EDA-NOCV analyses

Cyclopropane ring is a very common motif in organic/bio-organic compounds. The chemical bonding of this strained ring is taught to all chemistry students. This three-membered cyclic, C3 ring is quite reactive which has attracted both, synthetic and theoretical chemists to rationalize/correlate its stability and bonding with its reactivity and physical properties over a century. There are a few bonding models (mainly the Bent-Bond model and Walsh model) of this C3 ring that are debated to date. Herein, we have carried out energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV) to study the two most reactive bonds of cyclopropane rings of 49 different organic compounds containing different functional groups to obtain a much deeper bonding insight toward a more general bonding model of this class of compounds. The EDA-NOCV analyses of fragment orbitals and susequent bond formation revealed that the nature of the CC bond of the cyclopropane (splitting two bonds at a time out of three CC bonds) ring is preferred to form two dative covalent CC bonds (between a singlet olefin-fragment and an excited singlet carbene-fragment with a vacant sp2 orbital and a filled p-orbital) for the majority (37/49) of compounds over two covalent electron sharing bonds in some (7/49) compounds (between an excited triplet olefin and triplet carbene), while a few (5/49) compounds show flexibility to adopt either the electron sharing or dative covalent bond as both are equally possible. The effects of functional groups on the nature of chemical bond in cyclopropane rings have been studied in detail. Our bonding analyses are in line with the QTAIM analyses which produce small negative values of the Laplacian, significantly positive values of bond ellipticity, and accumulation of electron densities around the ring critical point of C3 -rings. These corresponding QTAIM parameters of C3 -rings are quite different for CC single bonds of normal hydrocarbons as expected. The chemical bonding in the majority of cyclopropane rings can be very similar to those of metal-olefin systems.

Multistate Energy Decomposition Analysis of Molecular Excited States

A multistate energy decomposition analysis (MS-EDA) method is described to dissect the energy components in molecular complexes in excited states. In MS-EDA, the total binding energy of an excimer or an exciplex is partitioned into a ground-state term, called local interaction energy, and excited-state contributions that include exciton excitation energy, superexchange stabilization, and orbital and configuration-state delocalization. An important feature of MS-EDA is that key intermediate states associated with different energy terms can be variationally optimized, providing quantitative insights into widely used physical concepts such as exciton delocalization and superexchange charge-transfer effects in excited states. By introducing structure-weighted adiabatic excitation energy as the minimum photoexcitation energy needed to produce an excited-state complex, the binding energy of an exciplex and excimer can be defined. On the basis of the nature of intermolecular forces through MS-EDA analysis, it was found that molecular complexes in the excited states can be classified into three main categories, including (1) encounter excited-state complex, (2) charge-transfer exciplex, and (3) intimate excimer or exciplex. The illustrative examples in this Perspective highlight the interplay of local excitation polarization, exciton resonance, and superexchange effects in molecular excited states. It is hoped that MS-EDA can be a useful tool for understanding photochemical and photobiological processes.

Structure and Bonding of Halonium Compounds

The geometrical parameters and the bonding in [D···X···D]⁺ halonium compounds, where D is a Lewis base with N as the donor atom and X is Cl, Br, or I, have been investigated through a combined structural and computational study. Cambridge Structural Database (CSD) searches have revealed linear and symmetrical [D···X···D]⁺ frameworks with neutral donors. By means of density functional theory (DFT), molecular electrostatic potential (MEP), and energy decomposition analyses (EDA) calculations, we have studied the effect of various halogen atoms (X) on the [D···X···D]⁺ framework, the effect of different nitrogen-donor groups (D) attached to an iodonium cation (X = I), and the influence of the electron density alteration on the [D···I···D]⁺ halonium bond by variation of the R substituents at the N-donor upon the symmetry, strength, and nature of the interaction. The physical origin of the interaction arises from a subtle interplay between electrostatic and orbital contributions (σ-hole bond). Interaction energies as high as 45 kcal/mol suggest that halonium bonds can be exploited for the development of novel halonium transfer agents, in asymmetric halofunctionalization or as building blocks in supramolecular chemistry.

Regiodivergent (3 + 2) annulation reactions of oxyallyl cations

We report a new method for the regiodivergent dearomative (3 + 2) reaction between 3-substituted indoles and oxyallyl cations. Access to both regioisomeric products is possible and is contingent on the presence or absence of a bromine atom on the substituted oxyallyl cation. In this way, we are able to prepare molecules that contain highly-hindered, stereodefined, vicinal, quaternary centers. Detailed computational studies employing energy decomposition analysis (EDA) at the DFT level establishes that regiochemical control arises from either reactant distortion energy or orbital mixing and dispersive forces, depending on the oxyallyl cation. Examination of the Natural Orbitals for Chemical Valence (NOCV) confirms that indole acts as the nucleophilic partner in the annulation reaction.

Bonding and stability of elusive silaboryne (SiB) and germaboryne (GeB) with donor base ligands

Stabilizing the exotic chemical species possessing multiple bonds is often extremely challenging due to insufficient orbital overlap, especially involving one heavier element. Bulky aryl groups and/or carbene as ligand have previously stabilized the SiSi, GeGe, and BB triple bonds. Herein, theoretical calculations have been carried out to shed light on the stability and bonding of elusive silaboryne/germaboryne (Si/GeB triple bond) stabilized by donor base ligands ((cAAC)BE(Me)(L); E = Si, L = cAAC^Me , NHC^Me , PMe₃ ; E = Ge, L = cAAC^Me ). The heavier analogues (Sn, Pb) have been further studied for comparison. Additionally, the effects of bulky substituents at the Si and N atoms on the structural parameters and stability of those species have been investigated. Energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV; for Si) showed that cAAC/NHC ligands could stabilize the exotic BSi-Me species more efficiently than PMe₃ ligands. The BSi partial triple bond of the corresponding species possesses a mixture of one covalent electron sharing BSi σ-bond and two dative π-bonds (B ← Si, B → Si).

Many-Body Effects in Aqueous Systems: Synergies Between Interaction Analysis Techniques and Force Field Development

Interaction analysis techniques, including the many-body expansion (MBE), symmetry-adapted perturbation theory, and energy decomposition analysis, allow for an intuitive understanding of complex molecular interactions. We review these methods by first providing a historical context for the study of many-body interactions and discussing how nonadditivities emerge from Hamiltonians containing strictly pairwise-additive interactions. We then elaborate on the synergy between these interaction analysis techniques and the development of advanced force fields aimed at accurately reproducing the Born-Oppenheimer potential energy surface. In particular, we focus on ab initio-based force fields that aim to explicitly reproduce many-body terms and are fitted to high-level electronic structure results. These force fields generally incorporate many-body effects through (a) parameterization of distributed multipoles, (b) explicit fitting of the MBE, (c) inclusion of many-atom features in a neural network, and (d) coarse-graining of many-body terms into an effective two-body term. We also discuss the emerging use of the MBE to improve the accuracy and speed of ab initio molecular dynamics.

Quantitative Descriptions of Dewar-Chatt-Duncanson Bonding Model: A Case Study of Zeise and Its Family Ions

Historically, Dewar-Chatt-Duncanson (DCD) model is a heuristic device to advance the development of organometallic chemistry and deepen our understanding of the metal-ligand bonding nature. Zeise's ion, the first man-made organometallic compound and a quintessential transition metal-olefin complex, was qualitatively explained using the DCD bonding scheme in 1950s. In this work, we quantified the explicit contributions of the σ donation and π back-donation to the metal-ligand bonding in Zeise and its family ions, [PtX3 L]- (X=F, Cl, Br, I, and At; L=C2 H4 , CO, and N2 ), using state-of-the-art quantum chemical calculations and energy decomposition analysis. The relative importance of the σ donation and π back-donation depends on both X and L, with [PtCl3 (C2 H4 )]- being a critical case in which the σ donation is marginally weaker than the π back-donation. The changes along this series are controlled by the energy levels of the correlated molecular orbitals of PtX3 - and ligand L. This study deepens our understanding of the bonding properties for transition metal complexes beyond the qualitative description of the DCD model.

Excimer Energies

A multistate energy decomposition analysis (MS-EDA) method is introduced for excimers using density functional theory. Although EDA has been widely applied to intermolecular interactions in the ground state, few methods are currently available for excited-state complexes. Here, the total energy of an excimer state is separated into exciton excitation energy ΔE_Ex(|Ψ_X·Ψ_Y⟩*), resulting from the state interaction between locally excited monomer states |Ψ_X^*·Ψ_Y⟩ and |Ψ_X·Ψ_Y^*⟩ , a superexchange stabilization energy ΔE_SE, originating from the mutual charge transfer between two monomers |Ψ_X⁺·Ψ_Y⟩ and |Ψ_X^-·Ψ_Y⁺⟩ , and an orbital-and-configuration delocalization term ΔE_OCD due to the expansion of configuration space and block-localized orbitals to the fully delocalized dimer system. Although there is no net charge transfer in symmetric excimer cases, the resonance of charge-transfer states is critical to stabilizing the excimer. The monomer localized excited and charge-transfer states are variationally optimized, forming a minimal active space for nonorthogonal state interaction (NOSI) calculations in multistate density functional theory to yield the intermediate states for energy analysis. The present MS-EDA method focuses on properties unique to excited states, providing insights into exciton coupling, superexchange and delocalization energies. MS-EDA is illustrated on the acetone and pentacene excimer systems; three configurations of the latter case are examined, including the optimized excimer, a stacked configuration of two pentacene molecules and the fishbone orientation. It is found that excited-state energy splitting is strongly dependent on the relative energies of the monomer excited states and the phase-matching of the monomer wave functions.

Explaining the High Catalytic Activity in Bis(indenyl)methyl Zirconium Cation Using Combined EDA-NOCV/QTAIM Approach

The main purpose of this study is to elucidate some discrepancies already observed in the catalytic activity values of some zirconocene methyl cations. The EDA-NOCV scheme was employed for a theoretical description of the interactions between an ethylene molecule and five catalysts of zirconocene methyl cation. The nature of the chemical interactions has been elucidated through the QTAIM topological analysis. The steric hindrance due to the ligands was evaluated qualitatively by means of an IRI-based analysis and quantitively through Fisher information. The findings prove that the indenyl ligand seems to favor the orbital interaction between the ethylene molecule and the metal centre of zirconocene methyl cation. Both electrostatic and orbital contributions play a crucial role in stabilising the studied complexes. Based on the NOCV deformation density contributions, the strongest orbital interaction is reached with the bis(indenyl)methyl zirconium cation, which is the only one exhibiting covalent interactions. Especially, the strong contribution of π-back donation (occurring from the occupied orbitals of the zirconium atom to the π* anti-bonding orbital of ethylene) may be a key to understand why this catalyst has a higher polymerisation yield than the other studied catalysts. This work suggests a perspective for predicting values of catalytic activity when theoretically designing novel catalysts of zirconocene type.

Multitask Deep Ensemble Prediction of Molecular Energetics in Solution: From Quantum Mechanics to Experimental Properties

The past few years have witnessed significant advances in developing machine learning methods for molecular energetics predictions, including calculated electronic energies with high-level quantum mechanical methods and experimental properties, such as solvation free energy and logP. Typically, task-specific machine learning models are developed for distinct prediction tasks. In this work, we present a multitask deep ensemble model, sPhysNet-MT-ens5, which can simultaneously and accurately predict electronic energies of molecules in gas, water, and octanol phases, as well as transfer free energies at both calculated and experimental levels. On the calculated data set Frag20-solv-678k, which is developed in this work and contains 678,916 molecular conformations, up to 20 heavy atoms, and their properties calculated at B3LYP/6-31G* level of theory with continuum solvent models, sPhysNet-MT-ens5 predicts density functional theory (DFT)-level electronic energies directly from force field-optimized geometry within chemical accuracy. On the experimental data sets, sPhysNet-MT-ens5 achieves state-of-the-art performances, which predict both experimental hydration free energy with a RMSE of 0.620 kcal/mol on the FreeSolv data set and experimental logP with a RMSE of 0.393 on the PHYSPROP data set. Furthermore, sPhysNet-MT-ens5 also provides a reasonable estimation of model uncertainty which shows correlations with prediction error. Finally, by analyzing the atomic contributions of its predictions, we find that the developed deep learning model is aware of the chemical environment of each atom by assigning reasonable atomic contributions consistent with our chemical knowledge.

Dihydrogen Bonding-Seen through the Eyes of Vibrational Spectroscopy

In this work, we analyzed five groups of different dihydrogen bonding interactions and hydrogen clusters with an H3+ kernel utilizing the local vibrational mode theory, developed by our group, complemented with the Quantum Theory of Atoms-in-Molecules analysis to assess the strength and nature of the dihydrogen bonds in these systems. We could show that the intrinsic strength of the dihydrogen bonds investigated is primarily related to the protonic bond as opposed to the hydridic bond; thus, this should be the region of focus when designing dihydrogen bonded complexes with a particular strength. We could also show that the popular discussion of the blue/red shifts of dihydrogen bonding based on the normal mode frequencies is hampered from mode-mode coupling and that a blue/red shift discussion based on local mode frequencies is more meaningful. Based on the bond analysis of the H3+(H2)n systems, we conclude that the bond strength in these crystal-like structures makes them interesting for potential hydrogen storage applications.

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

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

Understanding chemistry: from "heuristic (soft) explanations and reasoning by analogy" to "quantum chemistry"

"Soft theories," i.e., "heuristic models based on reasoning by analogy" largely drove chemistry understanding for 150 years or more. But soft theories have their limitations and with the expansion of chemistry in the mid-20th century, more and more inexplicable (by soft theory) experimental results were being obtained. In the past 50 years, quantum chemistry, most often in the guise of applied theoretical chemistry including computational chemistry, has provided (a) the underlying "hard evidence" for many soft theories and (b) the explanations for chemical phenomena that were unavailable by soft theories. In this publication, we define "hard theories" as "theories derived from quantum chemistry." Both soft and hard theories can be qualitative and quantitative, and the "Houk quadrant" is proposed as a helpful categorization tool. Furthermore, the language of soft theories is often used appropriately to describe quantum chemical results. A valid and useful way of doing science is the appropriate use and application of both soft and hard theories along with the best nomenclature available for successful communication of results and ideas.

Stability and bonding of carbon(0)-iron-N2 complexes relevant to nitrogenase co-factor: EDA-NOCV analyses

The factors/structural features which are responsible for the binding, activation and reduction of N₂ to NH₃ by FeMoco of nitrogenase have not been completely understood well. Several relevant model complexes by Holland et al. and Peters et al. have been synthesized, characterized and studied by theoretical calculations. For a matter of fact, those complexes are much different than real active N₂ -binding Fe-sites of FeMoco, which possesses a central C(4-) ion having an eight valence electrons as an μ₆ -bridge. Here, a series of [(S₃ C(0))Fe(II/I/0)-N₂ ]^n- complexes in different charged/spin states containing a coordinated σ- and π-donor C(0)-atom which possesses eight outer shell electrons [carbone, (Ph₃ P)₂ C(0); Ph₃ P→C(0)←PPh₃ ] and three S-donor sites (i.e. ^- S-Ar), have been studied by DFT, QTAIM, and EDA-NOCV calculations. The effect of the weak field ligand on Fe-centres and the subsequent N₂ -binding has been studied by EDA-NOCV analysis. The role of the oxidation state of Fe and N₂ -binding in different charged and spin states of the complex have been investigated by EDA-NOCV analyses. The intrinsic interaction energies of the Fe-N₂ bond are in the range from -42/-35 to -67 kcal/mol in their corresponding ground states. The S₃ C(0) donor set is argued here to be closer to the actual coordination environment of one of the six Fe-centres of nitrogenase. In comparison, the captivating model complexes reported by Holland et al. and Peter et al. possess a stronger π-acceptor C-ring (S₂ C_ring donor, π-C donor) and stronger donor set like CP₃ (σ-C donor) ligands, respectively.

Binding Energy Partition of Promising IRAK-4 Inhibitor (Zimlovisertib) for the Treatment of COVID-19 Pneumonia

The technique of Fragment-Based Drug Design (FBDD) considers the interactions of different moieties of molecules with biological targets for the rational construction of potential drugs. One basic assumption of FBDD is that the different functional groups of a ligand interact with a biological target in an approximately additive, that is, independent manner. We investigated the interactions of different fragments of ligands and Interleukin-1 Receptor-Associated Kinase 4 (IRAK-4) throughout the FBDD design of Zimlovisertib, a promising anti-inflammatory, currently in trials to be used for the treatment of COVID-19 pneumonia. We utilised state-of-the-art methods of wave function analyses mainly the Interacting Quantum Atoms (IQA) energy partition for this purpose. By means of IQA, we assessed the suitability of every change to the ligand in the five stages of FBDD which led to Zimlovisertib on a quantitative basis. We determined the energetics of the interaction of different functional groups in the ligands with the IRAK-4 protein target and thereby demonstrated the adequacy (or lack thereof) of the changes made across the design of this drug. This analysis permits to verify whether a given alteration of a prospective drug leads to the intended tuning of non-covalent interactions with its protein objective. Overall, we expect that the methods exploited in this paper will prove valuable in the understanding and control of chemical modifications across FBDD processes.

Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecular separation R. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at any R. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.

Electronegativity Equilibration

Controlling the distribution of electrons in materials is the holy grail of chemistry and material science. Practical attempts at this feat are common but are often reliant on simplistic arguments based on electronegativity. One challenge is knowing when such arguments work, and which other factors may play a role. Ultimately, electrons move to equalize chemical potentials. In this work, we outline a theory in which chemical potentials of atoms and molecules are expressed in terms of reinterpretations of common chemical concepts and some physical quantities: electronegativity, chemical hardness, and the sensitivity of electronic repulsion and core levels with respect to changes in the electron density. At the zero-temperature limit, an expression of the Fermi level emerges that helps to connect several of these quantities to a plethora of material properties, theories and phenomena predominantly explored in condensed matter physics. Our theory runs counter to Sanderson's postulate of electronegativity equalization and allows a perspective in which electronegativities of bonded atoms need not be equal. As chemical potentials equalize in this framework, electronegativities equilibrate.

The Labile Nature of Air Stable Ni(II)/Ni(0)-phosphine/Olefin Catalysts/Intermediates: EDA-NOCV Analysis

Metal ions-based inorganic-organic hybrid composites are often reported acting as good to excellent catalysts with various substrate scopes under milder reaction conditions. The active catalyst of a catalytic cycle is sometimes proposed to be a short-lived reactive intermediate species. A three coordinate (L-Me)Ni(II) intermediate species [L-Me = O 2 N donor dianionic ligand] can bind with short-lived carbene-ester ligands to produce four coordinate Ni(II) species which can act as carbene transfer intermediates under suitable reaction conditions for C-H functionalization or cyclopropanation reactions. The dissociation of phosphine (PPh 3 ) from the Ni(II) centre of (L-Me)Ni(II)(PPh 3 ) ( 1a ) and binding of short lived carbene esters (:CR 1 -CO 2 R 2 ; R 1 = H, Ph; R 2 = aliphatic group; 2-4 and other carbenes; 5-10 ) to Ni(II) rationalize the phenomenon in solution. Air stable Ni(0)-olefin complexes/intermediates ( 12-18 ) have recently been shown to mediate a variety of organic transformations. This analysis will further help organic/organometallic chemists to rationalize the design and synthesis of future catalysts for organic transformation. EDA-NOCV calculations have been performed to shed light on the stability and bonding of those species. Additionally, our analysis provides a proper reason why the analogous (L-Me)Pd-PPh 3 complex ( 1b ) does not dissociate in solution and hence, a similar catalytic product has not been isolated from identical reaction conditions. The stability and the labile nature of Ni(II/0) complexes has been investigated by state-of-the-art EDA-NOCV analyses.

Recognition in the Domain of Molecular Chirality: From Noncovalent Interactions to Separation of Enantiomers

It is not a coincidence that both chirality and noncovalent interactions are ubiquitous in nature and synthetic molecular systems. Noncovalent interactivity between chiral molecules underlies enantioselective recognition as a fundamental phenomenon regulating life and human activities. Thus, noncovalent interactions represent the narrative thread of a fascinating story which goes across several disciplines of medical, chemical, physical, biological, and other natural sciences. This review has been conceived with the awareness that a modern attitude toward molecular chirality and its consequences needs to be founded on multidisciplinary approaches to disclose the molecular basis of essential enantioselective phenomena in the domain of chemical, physical, and life sciences. With the primary aim of discussing this topic in an integrated way, a comprehensive pool of rational and systematic multidisciplinary information is provided, which concerns the fundamentals of chirality, a description of noncovalent interactions, and their implications in enantioselective processes occurring in different contexts. A specific focus is devoted to enantioselection in chromatography and electromigration techniques because of their unique feature as "multistep" processes. A second motivation for writing this review is to make a clear statement about the state of the art, the tools we have at our disposal, and what is still missing to fully understand the mechanisms underlying enantioselective recognition.

Uncovering the hidden reactivity of benzyne/aryne precursors utilized under milder condition: Bonding and stability studies by EDA-NOCV analyses

Arenes [C₆ H₃ R(TMS)(OTf); also called benzyne/aryne precursors] containing inter-related leaving groups Me₃ Si (TMS) and CF₃ SO₃ (OTf) on the adjacent positions (1,2-position) are generally converted to their corresponding aryne-intermediates via the addition of fluoride anion (F^- ) and subsequent elimination of TMS and OTf groups. This reaction is believed to proceed via the formation of an anionic intermediate [C₆ H₄ (TMS-F)(OTf)]^- . The EDA-NOCV analysis (EDA-NOCV = energy decomposition analysis-natural orbital for chemical valence) of over 35 such precursors of varied types have been reported to reveal bonding and stability of C_Ar Si and COTf bonds. EDA-NOCV showed that the nature of the C_Ar Si bond of C₆ H₃ R(TMS)(OTf) can be expressed as both dative and electron sharing [C_Ar Si, C_Ar →Si]. The C_Ar OTf bond, on the other hand, can be described explicitly as dative [C_Ar ←OTf]. The nature of C_Ar Si bond of [C₆ H₄ (TMS-F)(OTf)]^- exclusively changes to covalent dative σ-bond C_Ar →S(Me)3F on the attachment of F^- to the TMS group of C₆ H₄ (TMS)(OTf). Introduction of σ-electron withdrawing group (like OMe, NMe₂ , and NO₂ ) to the ortho-position of the TMS group of functionalized arynes C₆ H₃ R(TMS)(OTf) prefer to have a covalent dative σ-bond (C_Ar →Si) over an electron-sharing covalent σ-bond (C_Ar Si). If this σ-electron withdrawing group is shifted from ortho-position to meta- and para-positions, then the preference for a dative bond decreases significantly, implying that the electronic effect on the nature of chemical bonds affects through bond paths. This effect dies with distance, similar to the well-known inductive effect.

The Nature of the Polar Covalent Bond

Quantum chemical calculations using density functional theory are reported for the diatomic molecules LiF, BeO, and BN. The nature of the interatomic interactions is analyzed with the EDA-NOCV method, and the results are critically discussed and compared with data from QTAIM, NBO and Mayer approaches. Polar bonds, like nonpolar bonds, are caused by the interference of wave functions, which lead to an accumulation of electronic charge in the bonding region. Polar bonds generally have a larger percentage of electrostatic bonding to the total attraction, but nonpolar bonds may also possess large contributions from Coulombic interaction. The term "ionic contribution" refers to VB structures and is misleading because it refers to separate fragments with negligible overlap that occur only in the solid state and in solution, not in a molecule. The EDA-NOCV method gives detailed information about the individual orbital contributions, which can nicely be identified by visual inspection of the associated deformation densities. It is very important, particularly for polar bonds to distinguish between the interatomic interactions of the final dissociation products after bond rupture and the interactions between the fragments in the eventually formed bond.

Clarifying notes on the bonding analysis adopted by the energy decomposition analysis

We discuss the fundamental aspects of the EDA-NOCV method and address some critical comments that have been made recently. The EDA-NOCV method unlike most other methods focuses on the process of bond formation between the interacting species and not just only on the analysis of the finally formed bond. This is demonstrated using LiF as an example. There is a difference between the interactions between the initial species which form the bond and are also the final product of bond cleavage, and the interactions between the fragments in the eventually formed molecule. The flexibility of the method allows the choice of the interacting fragments which helps to identify the charge and electron configuration of the fragments which describe the bond. This is very helpful in cases where the bond may be described with several Lewis structures. We reject the idea that it would be a disadvantage to have "bond path functions" as the energy components in the EDA, which actually indicate the variability of the method. The bonding analysis in a different sequence of the bond formation gives important results for the various questions that can be asked. This is demonstrated by using CH₂, CO₂ and the formation of a guanine quartet as examples. The fact that a bond is always defined by the bound molecule, the fragments, and their states is universal and deeply physical, as we show here again for various examples. The results of the EDA-NOCV method are in full accordance with the physical mechanism of the chemical bond as revealed by Ruedenberg.

Anatomy of Classical Boron-Boron Bonding: Overlap and sp Dissonance

Classical bonding is predominantly understood using the insipid spⁿ hybridization for σ-bonds as well as π bonds and their delocalized variants. Because hybridization ignores intricate differences in the energy and size of valence atomic orbitals, its naïve application to classically bonded boron atoms leads to numerous surprises in bond strengths, frontier MOs/bands, and even geometry. Here we show that the sp dissonance caused by size mismatch between the valence s and p orbitals of boron plays a crucial role in its bonding, subtly distinct from that of carbon and silicon. Unlike the heavier p block elements, boron prefers to actively engage its compact 2s orbitals in bonding. This leads to the overreach of p-p σ-type overlap that reduces its magnitude in the entire B─B bonding range. Consequently, the π-type overlap remains substantial, making its electronic structure visibly distinct in saturated and unsaturated regimes. The deltahedral frameworks offer a compromise by breaking this symmetry-enforced dichotomy of classical σ- and π-type bonding and following alternate electron counts that suit the electron deficiency of the boron. The pathological anatomy of classical B─B σ-bonding also explains the origins of puzzling metallic character and disorder in their classical boride networks even with ideal electron count, unlike deltahedral borides. The implications of sp dissonance are illustrated in classical boron networks of various hybridizations, explaining the unusual preference for unique sp³ lattice with strained four-membered rings in CrB₄, origins of observed σ holes in MgB₂ that lead to its superconducting nature, and the absence of Peierls distortion in LiB.

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

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

EDA-NOCV analysis of carbene-borylene bonded dinitrogen complexes for deeper bonding insight: A fair comparison with a metal-dinitrogen system

Binding of dinitrogen (N₂ ) to a transition metal center (M) and followed by its activation under milder conditions is no longer impossible; rather, it is routinely studied in laboratories by transition metal complexes. In contrast, binding of N₂ by main group elements has been a challenge for decades, until very recently, an exotic cAAC-borylene (cAAC = cyclic alkyl(amino) carbene) species showed similar binding affinity to kinetically inert and non-polar dinitrogen (N₂ ) gas under ambient conditions. Since then, N₂ binding by short lived borylene species has made a captivating news in different journals for its unusual features and future prospects. Herein, we carried out different types of DFT calculations, including EDA-NOCV analysis of the relevant cAAC-boron-dinitrogen complexes and their precursors, to shed light on the deeper insight of the bonding secret (EDA-NOCV = energy decomposition analysis coupled with natural orbital for chemical valence). The hidden bonding aspects have been uncovered and are presented in details. Additionally, similar calculations have been carried out in comparison with a selected stable dinitrogen bridged-diiron(I) complex. Singlet cAAC ligand is known to be an exotic stable species which, combined with the BAr group, produces an intermediate singlet electron-deficient (cAAC)(BAr) species possessing a high lying HOMO suitable for overlapping with the high lying π*-orbital of N₂ via effective π-backdonation. The BN₂ interaction energy has been compared with that of the FeN₂ bond. Our thorough bonding analysis might answer the unasked questions of experimental chemists about how boron compounds could mimic the transition metal of dinitrogen binding and activation, uncovering hidden bonding aspects. Importantly, Pauling repulsion energy also plays a crucial role and decides the binding efficiency in terms of intrinsic interaction energy between the boron-center and the N₂ ligand.

Bonding analysis of the C2 precursor Me3E–C2–I(Ph)FBF3 (E = C, Si, Ge)

A series of possible precursors for generating C2 with the general formula Me3E–C2–I(Ph)FBF3 [E = C (1), Si (2), and Ge (3)] has been theoretically investigated using quantum chemical calculations. The equilibrium geometries of all species show a linear E–C2–I+ backbone. The inspection of the electronic structure of the Me3E–C2 bond by energy decomposition analysis coupled with the natural orbital for chemical valence (EDA-NOCV) method suggests a combination of electron sharing C–C σ-bond and v weak π-dative bond between Me3C and C2 fragments in the doublet state for species 1 (E = C). For species 2 (Si) and 3 (Ge), the analysis reveals σ-dative Me3E–C2 bonds (E = Si, Ge; Me3E←C2) resulting from the interaction of singly charged (Me3E)+ and (C2–IPh(BF4))− fragments in their singlet states. The C2–I bond is diagnosed as an electron sharing σ-bond in all three species, 1, 2 and 3.

EDA-NOCV Analysis of Donor-Base-Stabilized Elusive Monomeric Aluminum Phosphides [(L)P-Al(L'); L, L' = cAACMe, NHCMe, PMe3]

Herein, we report on the stability and bonding analysis of donor-base-stabilized monomeric AlP species (1-6) of the general formula (L)P-Al(L'); [L = cAACMe, L' = cAACMe, NHCMe, PMe3, (N i Pr2)2 (1-4); L = L' = NHCMe, PMe3 (5 and 6); cAAC = cyclic alkyl(amino) carbene; NHC = N-heterocyclic carbene]. Energy decomposition analysis coupled with natural orbitals for chemical valence (EDA-NOCV) analysis indicates the synthetic viability of this class of species, stabilized in their singlet ground state, in the laboratory. The CL-P bond is found to be a partial double bond (WBI ∼ 1.45), while the CL/PL-Al bond is a single bond (WBI ∼ 0.42-0.69). These bonds are mostly covalent or dative σ/π bonds depending upon the ligands attached. The central P-Al bond is an electron-sharing covalent polar single bond (WBI ∼ 0.80; P-Al) for 1-4 and a dative σ bond for 5 and 6 (WBI ∼ 0.89-0.93; P-Al). The calculated intrinsic interaction energies of the central P-Al bonds are found to be in the range from -116 to -216 kcal/mol (1-3 and 5 and 6). This value is the highest for compound 3, possibly due to the push and pull effects from the ligands PMe3 and cAAC, respectively.

Bonding and stability of dinitrogen-bonded donor base-stabilized Si(0)/Ge(0) species [(cAACMe-Si/Ge)2(N2)]: EDA-NOCV analysis

Recently, dinitrogen (N₂) binding and its activation have been achieved by non-metal compounds like intermediate cAAC-borylene as (cAAC)₂(B-Dur)₂(N₂) [cAAC = cyclic alkyl(amino) carbene; Dur = aryl group, 2,3,5,6-tetramethylphenyl; B-Dur = borylene]. It has attracted a lot of scientific attention from different research areas because of its future prospects as a potent species towards the metal free reduction of N₂ into ammonia (NH₃) under mild conditions. Two (cAAC)(B-Dur) units, each of which possesses six valence electrons around the B-centre, are shown to accept σ-donations from the N₂ ligand (B ← N₂). Two B-Dur further provide π-backdonations (B → N₂) to a central N₂ ligand to strengthen the B–N₂–B bond, providing maximum stability to the compound (cAAC)₂(B-Dur)₂(N₂) since the summation of each pair wise interaction accounted for the total stabilization energy of the molecule. (cAAC)(B-Dur) unit is isolobal to cAAC–E (E = Si, Ge) fragment. Herein, we report on the stability and bonding of cAAC–E bonded N₂-complex (cAAC–E)₂(N₂) (1–2; Si, Ge) by NBO, QTAIM and EDA-NOCV analyses (EDA-NOCV = energy decomposition analysis coupled with natural orbital for chemical valence; QTAIM = quantum theory of atoms in molecule). Our calculation suggested that syntheses of elusive (cAAC–E)₂(N₂) (1–2; Si, Ge) species may be possible with cAAC ligands having bulky substitutions adjacent to the C_cAAC atom by preventing the homo-dimerization of two (cAAC)(E) units which can lead to the formation of (cAAC–E)₂. The formation of E Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> E bond is thermodynamically more favourable (E = Si, Ge) over binding energy of N₂ inbetween two cAAC–E units.

Dinitrogen (N₂) binding and its activation have been achieved by non-metal compounds like intermediate cAACborylene with the general formula of (cAAC)₂(B-Dur)₂(N₂) [cAAC = cyclic alkyl(amino)carbene; Dur = aryl group, 2,3,5,6-tetramethylphenyl; B-Dur = aryl-borylene].

Using atomic charges to model molecular polarization

We review different models for introducing electric polarization in force fields, with special focus on methods where polarization is modelled at the atomic charge level. While electric polarization has been included in several force fields, the common approach has been to focus on atomic dipole polarizability. Several approaches allow modelling electric polarization by using charge-flow between charge sites instead, but this has been less exploited, despite that atomic charges and charge-flow is expected to be more important than atomic dipoles and dipole polarizability. A number of challenges are required to be solved for charge-flow models to be incorporated into polarizable force fields, for example how to parameterize the models and how to make them computational efficient.

Path-dependency of energy decomposition analysis & the elusive nature of bonding

Here, we provide evidence of the path-dependency of the energy components of the energy decomposition analysis scheme, EDA, by studying a set of thirty-one closed-shell model systems with the D_2h symmetry point group. For each system, we computed EDA components from nine different pathways and numerically showed that the relative magnitudes of the components differ substantially from one path to the other. Not surprisingly, yet unfortunately, the most significant variations in the relative magnitudes of the EDA components appear in the case of species with bonds within the grey zone of covalency and ionicity. We further discussed that the role of anions and their effect on arbitrary Pauli repulsion energy components affects the nature of bonding defined by EDA. The outcome variation by the selected partitioning scheme of EDA might bring arbitrariness when a careful comparison is overlooked.

Here, we provide evidence of the path-dependency of the energy components of the energy decomposition analysis scheme, EDA, by studying a set of thirty-one closed-shell model systems with the D_2h symmetry point group.

Estimations of Fe0/−1–N2 interaction energies of iron(0)-dicarbene and its reduced analogue by EDA-NOCV analyses: crucial steps in dinitrogen activation under mild conditions

Metal complexes containing low valence iron atoms are often experimentally observed to bind with the dinitrogen (N₂) molecule. This phenomenon has attracted the attention of industrialists, chemists and bio-chemists since these N₂-bonded iron complexes can produce ammonia under suitable chemical or electrochemical conditions. The higher binding affinity of the Fe-atom towards N₂ is a bit ‘mysterious’ compared to that of the other first row transition metal atoms. Fine powders of α-Fe⁰ are even part of industrial ammonia production (Haber–Bosch process) which operates at high temperature and high pressure. Herein, we report the EDA-NOCV analyses of the previously reported dinitrogen-bonded neutral molecular complex (cAAC^R)₂Fe⁰–N₂ (1) and mono-anionic complex (cAAC^R)₂Fe⁻¹–N₂ (2) to give deeper insight of the Fe–N₂ interacting orbitals and corresponding pairwise intrinsic interaction energies (cAAC^R = cyclic alkyl(amino) carbene; R = Dipp or Me). The Fe⁰ atom of 1 prefers to accept electron densities from N₂via σ-donation while the comparatively electron rich Fe⁻¹ centre of 2 donates electron densities to N₂via π-backdonation. However, major stability due to the formation of an Fe–N₂ bond arises due to Fe → N₂ π-backdonation in both 1 and 2. The cAAC^R ligands act as a charge reservoir around the Fe centre. The electron densities drift away from cAAC ligands during the binding of N₂ molecules mostly via π-backdonation. EDA-NOCV analysis suggests that N₂ is a stronger π-acceptor rather than a σ-donor.

The stable Fe–N₂ bond of stable complex should have a sufficiently high interaction energy.

In-Situ Electronegativity and the Bridging of Chemical Bonding Concepts

One challenge in chemistry is the plethora of often disparate models for rationalizing the electronic structure of molecules. Chemical concepts abound, but their connections are often frail. This work describes a quantum-mechanical framework that enables a combination of ideas from three approaches common for the analysis of chemical bonds: energy decomposition analysis (EDA), quantum chemical topology, and molecular orbital (MO) theory. The glue to our theory is the electron energy density, interpretable as one part electrons and one part electronegativity. We present a three-dimensional analysis of the electron energy density and use it to redefine what constitutes an atom in a molecule. Definitions of atomic partial charge and electronegativity follow in a way that connects these concepts to the total energy of a molecule. The formation of polar bonds is predicted to cause inversion of electronegativity, and a new perspective of bonding in diborane and guanine-cytosine base-pairing is presented. The electronegativity of atoms inside molecules is shown to be predictive of pKa .

Implementation of the interacting quantum atom energy decomposition using the CASPT2 method

We present an implementation of the interacting quantum atom (IQA) energy decomposition scheme using the complete active space second-order perturbation theory (CASPT2). This combination yields a real-space interpretation tool with a proper account of the static and dynamic correlation that is particularly relevant for the description of processes in electronic excited states. The IQA/CASPT2 approach allows determination of the energy redistribution that takes place along a photophysical/photochemical deactivation path in terms of self- and interatomic contributions. The applicability of the method is illustrated by the description of representative processes spanning different bonding regimes: noble gas excimer and exciplex formation, the reaction of ozone with a chlorine atom, and the photodissociations of formaldehyde and cyclobutane. These examples show the versatility of using CASPT2 with the significant information provided by the IQA partition to describe chemical processes with a large multiconfigurational character.

XEDA, a fast and multipurpose energy decomposition analysis program

A fast and multipurpose energy decomposition analysis (EDA) program, called XEDA, is introduced for quantitative analysis of intermolecular interactions. This program contains a series of variational EDA methods, including LMO-EDA, GKS-EDA and their extensions, to analyze non-covalent interactions and strong chemical bonds in various environments. XEDA is highly efficient with a similar computational scaling of single point energy calculations. Its efficiency and universality are validated by a series of test examples including van der Waals interactions, hydrogen bonds, radical-radical interactions and strong covalent bonds.

EDA-NOCV Calculation for Efficient N2 Binding to the Reduced Ni3S8 Complex: Estimation of Ni-N2 Intrinsic Interaction Energies

The binding of the dinitrogen molecule to the metal center is the first and crucial step toward dinitrogen activation. Favorable interaction energies are desired by chemists and biochemists to study model complexes in the laboratory. An electrochemically reduced form of a previously isolated sulfur-bridged Ni₃S₈ complex is inferred to bind N₂ at multiple Ni centers, and this bonded N₂ undergoes reductive protonation to produce hydrazine (N₂H₄) as the product in the presence of a proton donor. Density functional theory (DFT) calculations and quantum theory of atoms in molecules (QTAIM) analysis have been carried out to shed light on the nature of N₂ binding to an anionic trinuclear Ni₃S₈ complex. Additionally, energy decomposition analysis with the combination of natural orbital for chemical valence (EDA-NOCV) analysis has been performed to estimate the pairwise interaction energies between the Ni center and the N₂ molecule under experimental conditions.

Estimations of Fe-N2 Intrinsic Interaction Energies of Iron-Sulfur/Nitrogen-Carbon Sites: A Deeper Bonding Insight by EDA-NOCV Analysis of a Model Complex of the Nitrogenase Cofactor

The MoFe₇S₉C^1- unit of the nitrogenase cofactor (FeMoco) attracts chemists and biochemists due to its unusual ability to bind aerial dinitrogen (N₂) at ambient condition and catalytically convert it into ammonia (NH₃). The mode of N₂ binding and its reaction pathways are yet not clear. An important conclusion has been made based on the very recent synthesis and isolation of model Fe(I/0)-complexes with sulfur-donor ligands under the cleavage of one Fe-S bond followed by binding of N₂ at the Fe(0) center. These complexes are structurally relevant to the nitrogenase cofactor (MoFe₇S₉C^1-). Herein, we report the EDA-NOCV analyses and NICS calculations of the dinitrogen-bonded dianionic complex Fe⁰-N₂ (1) (having a C_Ar ← Fe π-bond) and monoanionic complex Fe^I-N₂ (2) (having a C_Ar-Fe σ-bond) to provide a deeper insight into the Fe-N₂ interacting orbitals and corresponding pairwise interaction energies (EDA-NOCV = energy decomposition analysis coupled with natural orbital for chemical valence; NICS = nucleus-independent chemical shifts). The orbital interaction in the Fe-N₂ bond is significantly larger than Coulombic interactions, with major pairwise contributions coming from d(Fe) orbitals to the empty π* orbitals of N₂ (three Fe → N₂). ΔE _int values are in the range of -61 to -77 kcal mol^-1. Very interestingly, NICS calculations have been carried out for the fragments before and after binding of the N₂ molecule. The computed σ- and π-aromaticity values are attributed to the position of the Fe atoms, oxidation states of Fe centers, and Fe-C bond lengths of these two complexes.

Triel bonds within anionanion complexes

The ability of two anions to interact with one another is tested in the context of pairs of TrX₄^- homodimers, where Tr represents any of the triel atoms B, Al, Ga, In, or Tl, and X refers to a halogen substituent F, Cl, or Br. None of these pairs engage in a stable complex in the gas phase, but the situation reverses in water where the two monomers are held together by Tr⋯X triel bonds, complemented by stabilizing interactions between X atoms. Some of these bonds are quite strong, notably those involving TrF₄^-, with interaction energies surpassing 30 kcal mol^-1. Others are very much weaker, with scarcely exothermic binding energies. The highly repulsive electrostatic interactions are counteracted by large polarization energies.

Unexpected Charge Effects Strengthen π-Stacking Pancake Bonding

Phenalenyls (PLYs) are important synthons in many functional and electronic materials, which often display favorable molecule-to-molecule overlap for electron or hole transport. They also serve as a prototype for π-stacking pancake bonding based on two-electron multicenter bonding (2e/mc). Unexpected near-doubling of the binding energy is obtained for the positively charged PLY2 + dimer with an effect similar to that seen for the positively charged olympicenyl (OPY) radical dimer. This charge effect is reversed for the perfluorinated (PF) dimers, and the negatively charged perfluorinated (PF) dimers PF-PLY2 - and PF-OPY2 - become strongly bound. Long-range interactions reflect these differences. Also surprising is that in this case the pancake bonding corresponds to single-electron (1e/mc) or a three-electron (3e/mc) multicenter bonding in contrast to the 2e/mc bonding that occurs for the neutral radical dimers. The strong preference for a large intermolecular overlap is maintained in these charged dimers. Importantly, the preference for π-bonding in the charged dimers compared to σ-bonding is strongly enhanced relative to the neutral PLY dimers.

Variational Energy Decomposition Analysis of Charge-Transfer Interactions between Metals and Ligands in Carbonyl Complexes

Variational energy decomposition analyses have been presented to quantify the σ-dative, ligand-to-metal forward charge transfer (CT) and the π-conjugative, metal-to-ligand backward charge delocalization on a series of isolelectronic transition-metal carbonyl complexes M(CO)₆, including M = Ti^2-, V^-, Cr, Mn⁺, and Fe²⁺. Although the qualitative features of these energy terms are understood, well-defined quantitative studies have been scarce. Consistent with early findings, electrostatic and Pauli exchange effects play a key role in σ-donation, resulting in blue shifts in ligand vibrational frequency in the complex geometries. Excluding chemical bonding interactions between the CO ligand and the metal fragments in the energy decomposition analysis, we found that loosely bound electrostatic complexes can be formed at a longer metal-to-ligand distance due to the exponential decay of Pauli exchange. In all complexes, the overall binding stabilization can be attributed to CT effects, with opposing trends between σ-donation and π-back bonding that follows an order of Ti^2- (4.4) > V^1- (2.6) > Cr (1.5) > Mn¹⁺ (1.1) > Fe²⁺ (0.5) in π-to-σ CT ratio. These electronic and energetic features are mirrored in the vibrational frequency shifts induced by different factors. The present investigation may help stimulate the use of energy decomposition techniques to understand the structure and activity of metallocatalysts using density functional theory.

On the question of steric repulsion versus noncovalent attractive interactions in chiral phosphoric acid catalyzed asymmetric reactions

The origin of enantioselectivity in asymmetric catalysis is often built around the differential steric interaction in the enantiocontrolling transition states (TSs). A closer perusal of enantiocontrolling TSs in an increasingly diverse range of reactions has revealed that the cumulative effect of weak noncovalent interactions could even outweigh the steric effects. While enunciating this balance is conspicuously important, quantification of such intramolecular forces within a TS continues to remain scarce and challenging. Herein, we demonstrate the utility of the fragment molecular orbital method in establishing the relative contributions of various attractive and repulsive contributions in the total interaction energy between the suitably chosen fragments in enantiocontrolling TSs. Three types of reactions of high contemporary importance, namely, axially chiral phosphoric acid (CPA) catalyzed kinetic resolution of rac-α-methyl-γ-hydroxy ester (reaction I), asymmetric dearomative amination of β-naphthols by dimethyl azodicarboxylate (IIa and IIb), and intramolecular desymmetrization of β,β-disubstituted methyl oxetanes (IIIa) and hydroxyl oxetane (IIIb), bearing a tethered alcohol (-OCH₂CH₂OH or -(CH₂)₂CH₂OH), are considered. In all the five reactions, the differences in the stabilizing contributions arising due to electrostatic, charge-transfer, and dispersion interactions between the catalyst and the reacting partners in the enantiocontrolling transition states are weighed against the destabilizing exchange interaction. The balancing interactions are found to be between dispersion and exchange repulsion in reaction I, a combination of charge transfer and dispersion energies offsets the repulsive energy in reaction IIb involving the electron rich anthryl groups in the catalyst, whereas the -(CF₃)₂C₆H₄ 3,3'-substituent in the catalyst (reaction IIa) leads to a trade-off between dispersion and exchange energies. In reactions IIIa and IIIb, however, electrostatic and dispersion energies help compensate the repulsive interactions. These quantitative insights on the intramolecular interactions in the stereocontrolling TSs could help in the rational design of asymmetric catalysis.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Neat, Simple, and Wrong: Debunking Electrostatic Fallacies Regarding Noncovalent Interactions

Multipole moments such as charge, dipole, and quadrupole are often invoked to rationalize intermolecular phenomena, but a low-order multipole expansion is rarely a valid description of electrostatics at the length scales that characterize nonbonded interactions. This is illustrated by examining several common misunderstandings rooted in erroneous electrostatic arguments. First, the notion that steric repulsion originates in Coulomb interactions is easily disproved by dissecting the interaction potential for Ar₂. Second, the Hunter-Sanders model of π-π interactions, which is based on quadrupolar electrostatics, is shown to have no basis in accurate calculations. Third, curved "buckybowls" exhibit unusually large dipole moments, but these are ancillary to the forces that control their intermolecular interactions, as illustrated by two examples involving corannulene. Finally, the assumption that interactions between water and small anions are dictated by the dipole moment of H₂O is shown to be false in the case of binary halide-water complexes. These examples present a compelling case that electrostatic explanations based on low-order multipole moments are very often counterfactual for nonbonded interactions at close range and should not be taken seriously in the absence of additional justification.