Energy decomposition analysis of single bonds within Kohn-Sham density functional theory

Chemical Bonding and the Role of Node-Induced Electron Confinement

The chemical bond is the cornerstone of chemistry, providing a conceptual framework to understand and predict the behavior of molecules in complex systems. However, the fundamental origin of chemical bonding remains controversial and has been responsible for fierce debate over the past century. Here, we present a unified theory of bonding, using a separation of electron delocalization effects from orbital relaxation to identify three mechanisms [node-induced confinement (typically associated with Pauli repulsion, though more general), orbital contraction, and polarization] that each modulate kinetic energy during bond formation. Through analysis of a series of archetypal bonds, we show that an exquisite balance of energy-lowering delocalizing and localizing effects are dictated simply by atomic electron configurations, nodal structure, and electronegativities. The utility of this unified bonding theory is demonstrated by its application to explain observed trends in bond strengths throughout the periodic table, including main group and transition metal elements.

Mechanistic Insights into the Origins of Selectivity in a Cu-Catalyzed C-H Amidation Reaction

The catalytic transformation of C-H to C-N bonds offers rapid access to fine chemicals and high-performance materials, but achieving high selectivity from undirected aminations of unactivated C(sp3)-H bonds remains an outstanding challenge. We report the origins of the reactivity and selectivity of a Cu-catalyzed C-H amidation of simple alkanes. Using a combination of experimental and computational mechanistic studies and energy decomposition techniques, we uncover a switch in mechanism from inner-sphere to outer-sphere coupling between alkyl radicals and the active Cu(II) catalyst with increasing substitution of the alkyl radical. The combination of computational predictions and detailed experimental validation shows that simultaneous minimization of both Cu-C covalency and alkyl radical size increases the rate of reductive elimination and that both strongly electron-donating and electron-withdrawing substituents on the catalyst accelerate the selectivity-determining C-N bond formation process as a result of a change in mechanism. These findings offer design principles for the development of improved catalyst scaffolds for radical C-H functionalization reactions.

Directionality of Halogen-Bonds: Insights from 2D Energy Decomposition Analysis

Halogen bonds are typically observed to have a linear arrangement with a 180° angle between the nucleophile and the halogen bond acceptor X-R. This linearity is commonly explained using the σ-hole model, although there have been alternative explanations involving exchange repulsion forces. We employ two-dimensional Distortion/Interaction and Energy Decomposition Analysis to examine the archetypal H3 N⋯X2 halogen bond systems. Our results indicate that although halogen bonds are predominantly electrostatic, their directionality is largely due to decreased Pauli repulsion in linear configurations as opposed to angled ones in the I2 and Br2 systems. As we move to the smaller halogens, Cl2 and F2 , the influence of Pauli repulsion diminishes, and the energy surface is shaped by orbital interactions and electrostatic forces. These results support the role of exchange repulsion forces in influencing the directionality of strong halogen bonds. Additionally, we demonstrate that the 2D Energy Decomposition Analysis is a useful tool for enhancing our understanding of the nature of potential energy surfaces in noncovalent interactions.

Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

Long but Strong C-C Single Bonds: Challenges for Theory

Theoretical challenges in describing molecules with anomalously long single C-C bonds are analyzed in terms of the relative contributions of stabilizing and destabilizing intramolecular interactions. Diamondoid dimers that are stable despite the presence of C-C bonds up to 1.7 Å long, as well as other bulky molecules stabilized due to intramolecular noncovalent interactions (London dispersions) are discussed. The unexpected stability of highly crowded molecules, such as diamondoid dimers and tert-butyl-substituted hexaphenylethanes, calls for reconsideration of the "steric effect" traditionally thought to destabilize the molecule. Alternatively, "steric attraction" helps to understand bonding in sterically overloaded molecules, whose structural and energetic analysis requires a proper theoretical description of noncovalent interactions.

Properties of Local Electronic Structures

The simulation of intrinsic contributions to molecular properties holds the potential to allow for chemistry to be directly inferred from changes to electronic structures at the atomic level. In the present study, we demonstrate how such local properties can be readily derived from suitable molecular orbitals to yield effective fingerprints of various types of atoms in organic molecules. In contrast, corresponding inferences from schemes that instead make use of individual atomic orbitals for this purpose are generally found to fail in expressing much uniqueness in atomic environments. By further studying the extent to which entire chemical reactions may be decomposed into meaningful and continuously evolving atomic contributions, schemes based on molecular rather than atomic orbitals are once again found to be the more consistent, even allowing for intricate differences between seemingly uniform nucleophilic substitutions to be probed.

When Is a Bond Broken? The Polarizability Perspective

The question of when a chemical bond can be said to be broken is of fundamental chemical interest but has not been widely studied. Herein we propose that the maxima of static polarizability along bond dissociation coordinates naturally define cutoff points for bond rupture, as they represent the onset of localization of shared electron density into constituent fragments. Examples of computed polarizability maxima over the course of bond cleavage in main-group and transition metal compounds are provided, across covalent, dative and charge-shift bonds. The behavior along reaction paths is also considered. Overall, the static polarizability is found to be a sensitive reporter of electronic structure reorganization associated with bond stretching, and thus can serve as a metric for describing bond cleavage (or diagnose the absence of a chemical bond).

Molecular simulation of Cu, Ag, and Au-decorated Si-doped graphene quantum dots (Si@QD) nanostructured as sensors for SO2 trapping

In view of the numerous environmental hazards and health challenges linked to sulfur (iv) oxide (SO2), an indirect greenhouse gas, and the resultant need to develop efficient gas nanosensor devices, this research had as its principal focus on the theoretical evaluation of the gas sensing potential of metals: Ag, Au and Cu functionalized silicon-doped quantum dots (Si@QD) for the detection and adsorption of SO2 gas investigated using the first-principles density functional theory (DFT) computation at the B3LYP-D3(BJ)/def2-SVP level of theory. Eight (8) possible adsorption modes: SO2_O_Si@QD, SO2_O_Ag_Si@QD, SO2_O_Au_Si@QD, SO2_O_Cu_Si@QD, SO2_S_Si@QD, SO2_S_Ag_Si@QD, SO2_S_Au_Si@QD, and SO2_S_Cu_Si@QD were considered based on SO2 interactions with the studied materials at the -S and -O sites of the SO2 molecule. The counterpoise correction (BSSE) showed that five of the eight interactions had favorable Ead + BSSE values ranging from -0.31 to -1.98 eV. All the eight interactions were observed to be thermodynamically favorable with ΔG and ΔH ranging from -129.01 to -200.24 kcal/mol and -158.26 to -229.73 kcal/mol respectively. Results from the topology analysis reveal that van der Waals forces occurred the greatest at the gas-sensor interphase while SO2_S_ Cu_Si@QD is predicted to have the highest sensing potency based on the conductivity and recovery time estimations. These results confirm the potential efficient feasibility of real-world device application of the metals (Ag, Au, Cu) functionalized Si-doped QDs.

Decoding Chemical Bonds: Assessment of the Basis Set Effect on Overlap Electron Density Descriptors and Topological Properties in Comparison to QTAIM

Quantum chemical bonding descriptors based on the total and overlap density can provide valuable information about chemical interactions in different systems. However, these descriptors can be sensitive to the basis set used. To address this, different numerical treatments of electron density have been proposed to reduce the basis set dependency. In this work, we introduce overlap properties (OPs) obtained through numerical treatment of the electron density and present the topology of overlap density (TOP) for the first time. We compare the basis set dependency of numerical OP and TOP descriptors with their quantum theory of atoms in molecules (QTAIM) counterparts, considering the total electron density. Three single (C-C, C-O, and C-F) bonds in ethane, methanol, and fluoromethane and two double (C═C and C═O) bonds in ethene and formaldehyde were analyzed. Diatomic molecules Li-X with X = F, Cl, and Br were also analyzed. Eight parameters, including QTAIM descriptors and OP/TOP descriptors, are used to assess the basis dependency at the ωB97X-D level of theory using 28 basis sets from three classes: Pople, Ahlrichs, and Dunning. The study revealed that the topological overlap electron density properties exhibit comparatively lesser dependence on the basis set compared to their total electron density counterparts. Remarkably, these properties retain their chemical significance even with reduced basis set dependency. Similarly, numerical OP descriptors show less basis set dependency than their QTAIM counterparts. The excess of polarization functions increases charge concentration in the interatomic region and influences both QTAIM and OP descriptors. The basis sets Def2TZVP, 6-31++G(d,p), 6-311++G(d,p), cc-pVDZ, cc-pVTZ, and cc-pVQZ demonstrate reduced variability for the tested bond classes in this study, with particular emphasis on the triple-ζ quality Ahlrichs' basis set. We recommend against using basis sets with numerous polarization functions, such as augmented Dunning's and Ahlrichs' quadruple-ζ.

Valence Bond Theory Allows a Generalized Description of Hydrogen Bonding

This paper describes the nature of the hydrogen bond (HB), B:---H-A, using valence bond theory (VBT). Our analysis shows that the most important HB interactions are polarization and charge transfer, and their corresponding sum displays a pattern that is identical for a variety of energy decomposition analysis (EDA) methods. Furthermore, the sum terms obtained with the different EDA methods correlate linearly with the corresponding VB quantities. The VBT analysis demonstrates that the total covalent-ionic resonance energy (RECS) of the HB portion (B---H in B:---H-A) correlates linearly with the dissociation energy of the HB, ΔEdiss. In principle, therefore, RECS(HB) can be determined by experiment. The VBT wavefunction reveals that the contributions of ionic structures to the HB increase the positive charge on the hydrogen of the corresponding external/free O-H bonds in, for example, the water dimer compared with a free water molecule. This increases the electric field of the external O-H bonds of water clusters and contributes to bringing about catalysis of reactions by water droplets and in water-hydrophobic interfaces.

Charge-Shift Bonding Propensity in Halogen-Bonded BXY (B Is a Small Lewis Base H2O or NH3; X and Y Are Halogen Atoms) Complexes: An NBO/NRT/AIM Investigation

Charge-shift (CS) bonding is a new bonding paradigm in the field of chemical bonds. Our recent study has revealed that certain Cu/Ag/Au-bonds display both CS bonding and ω-bonding characters. In this investigation, we extend our study to halogen bonding. Our focus is on scrutinizing the CS bonding in halogen-bonded BXY (B is a small Lewis base H2O or NH3; X and Y are halogen atoms) complexes by using natural bond orbital (NBO) analysis, natural resonance theory (NRT), and atoms in molecules (AIM) methods. The primary objective is to establish a connection between halogen bonding (B-X) in BXY and CS bonding in free XY (di-halogens). The calculations indicate that the studied BXY can be classified into two types. One type with a weak halogen bond shows closed-shell interaction. The other type with a stronger B-X interaction exhibits both CS bonding and ω-bonding characters (as seen in NH3ClF, NH3BrF, and NH3IF). Another interesting finding is a novel propensity that the CS bonding in free XY tends to carry over the halogen bonding in BXY, and the same propensity is found in Cu/Ag/Au ω-bonded species. The present study may offer an approach to probe CS bonding in many more 3c/4e ω-bonded molecules.

DFT-based analysis of siderophore-metal ion interaction for efficient heavy metal remediation

Siderophores have great application potential in metal pollutant remediation because of their effective cost and friendly impact on the environment. However, the practical use of siderophores in the remediation of specific metals is rather limited because of the weak nonspecific interactions between the siderophores and different metals. Thus, screening for a siderophore with optimal interaction with a specific metal would be necessary. In this study, the interaction between metal ions and moieties that donate the oxygen ligands for the coordination of four types of siderophore (hydroxamates, catecholates, phenolates, and carboxylates) was modeled and analyzed. As revealed by DFT-based analysis, the four types of siderophore generally exhibited selection preference for different metal ions in the order Ga3+  > Al3+  > Fe3+  > Cr3+  > Ni2+  > Cu2+  > Zn2+  > Co2+  > Mn2+  > Hg2+  > Pb2+  > Cd2+, which was determined mainly by the electronegativity of the siderophore functional groups, the electronegativity of the metals, and the ionic radius of the metals, as well as the interaction between the siderophores and the metals. Moreover, the effect of linear or nonlinear (cyclic) structure on the affinity of each siderophore for different metal ions was evaluated. In most situations, metal-bound cyclic siderophores were found to be more stable than their linear counterparts. Thus, proper siderophores for the remediation of metal pollution may be rapidly screened using this model.

Computational Insights on the Chemical Reactivity of Functionalized and Crosslinked Polyketones to Cu2+ Ion for Wastewater Treatment

Today, the high concentrations of copper found in water resources result in an urgent problem to solve since human health and aquatic ecosystems have been affected. Functionalized crosslinked polyketone resins (XLPK) have demonstrated high performance for the uptake of heavy metals in water solutions. In addition, its green chemical synthesis makes these resins very attractive as sorbents for metal ions contained in wastewater. XLPK are not soluble in aqueous media and do not require any catalyst, solvent, or harsh conditions to carry out the uptake process. In this paper, a series of functionalized XLPK with pending amino-derivatives namely; butylamine (BA), amino 2-propanol (A2P), 4-(aminomethyl) benzoic acid (HAMC), 6-aminohexanoic acid (PAMBA), and 1,2 diamino propane (DAP) directly attached to the pyrrole backbone of the polymers and crosslinked by di-amine derivatives was investigated using Density Functional Theory (DFT) calculations. Our computational analysis revealed that dipole-dipole interactions played a crucial role in enhancing the adsorption of Cu2+ ions onto XLPKs. The negatively charged ketone moieties and functional groups within XLPKs were identified as key adsorption sites for the selective binding of Cu2+ ions. Additionally, we found that XLPKs exhibited strong electrostatic interactions primarily through the -NH2 and -C=O groups. Evaluation of the adsorption energies in XLPK-Cu(II) complexes showed that the DAP-Cu(II) complex exhibited the highest stability, attributed to strong Cu(II)-N binding facilitated by the amino moiety (-NH2). The remaining XLPKs displayed binding modes involving oxygen atoms (Cu(II)-O) within the ketone moieties in the polymer backbone. Furthermore, the complexation and thermochemical analysis emphasized the role of the coordinator atom (N or O) and the coordinating environment, in which higher entropic effects involved in the adsorption of Cu2+ ions onto XLPKs describes a lower spontaneity of the adsorption process. The adsorption reactions were favored at lower temperatures and higher pressures. These findings provide valuable insights into the reactivity and adsorption mechanisms of functionalized and crosslinked polyketones for Cu2+ uptake, facilitating the design of high-performance polymeric resins for water treatment applications.

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.

Analysis of Bonding by Quantum Chemistry─Resolving Delocalization Stabilization in a Mechanistic Basis and New Hückel Model

No general and unique understanding of the mechanism of covalent bonding in physical terms is provided by current computational methods or by a consensus among experts. Bonding is studied by energy decomposition analysis but may also be related to the interatomic motion of valence electrons within the molecule. This dynamical view of the mechanism of bonding is not widely appreciated. The aim here is to make it accessible by translation into a corresponding form of quantum chemical energy analysis. The interatomic electron motion is directly related to the delocalization taking place when atomic basis functions are combined into molecular orbitals. A "tribasis method" is introduced, allowing an atomic basis set to form subsets of (1) strictly localized atomic functions and (2) interatomic bridge functions which allow delocalization. Calculations can then identify ground states without (no bridge functions) and with delocalization. The scheme is based on exact quantum mechanics but demonstrated by a minimal basis treatment of H₂⁺ and H₂ in Hartree-Fock and valence bond approximations which show that the bond energy is a sum of repulsive localization and more strongly attractive delocalization energies. The tribasis method is used to reconstruct the Hückel theory of π-electron delocalization in planar hydrocarbon molecules to account for the "overlap problem". In its empirically fitted form, the new theory can accurately resolve both π → π* transition energy and aromatic stabilization energy. The picture of covalent bonding emerging from both hydrogenic and Hückel calculations is that there is a presence of a Pauli repulsion of localization which is overcome by a roughly twice as strong delocalization stabilization to form the bond.

Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory

Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B covalently connected via a linker C. However, the existing ISAPT algorithm displays several issues for many fragmentation patterns (that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive electrostatic energy (even when the fragments are hydrogen-bonded) and very large and mutually cancelling induction and exchange-induction terms. We attribute those issues to the presence of artificial dipole moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing electrons on one of their hybrid orbitals. Therefore, we propose several new partitioning algorithms which reassign one electron, on a singly occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals are added to fragment density matrices, the computation of ISAPT electrostatic, induction, and dispersion energies proceeds exactly as normal, and the exchange energy expressions need only minor modifications. Among the link partitioning algorithms introduced, the so-called ISAPT(SIAO1) approach (in which the link orbital is obtained by a projection onto the intrinsic atomic orbitals (IAOs) of a given fragment followed by orthogonalization to this fragment's occupied space) leads to reasonable values of all ISAPT corrections for all fragmentation patterns, and exhibits a fast and systematic basis set convergence. This improvement is made possible by a significant reduction in magnitude (even though not a complete elimination) of the unphysical dipole moments at the interfragment boundaries. We demonstrate the utility of the improved ISAPT partitioning by examining intramolecular interactions in several pentanediol isomers, examples of linear and branched alkanes, and the open and closed conformations of a family of N-arylimide molecular torsion balances.

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.

Prediction of Multiple Hydrogen Ligation at a Vanadium(II) Site in a Metal-Organic Framework

Densifying hydrogen in a metal-organic framework (MOF) at moderate pressures can circumvent challenges associated with high-pressure compression. The highly tunable structural and chemical composition in MOFs affords vast possibilities to optimize binding interactions. At the heart of this search are the nanoscale characteristics of molecular adsorption at the binding site(s). Using density functional theory (DFT) to model binding interactions of hydrogen to the exposed metal site of cation-exchanged MFU-4l, we predict multiple hydrogen ligation of H₂ at the first coordination sphere of V(II) in V(II)-exchanged MFU-4l. We find that the strength of this binding between the metal site and H₂ molecules can be tuned by altering the halide counterion adjacent to the metal site and that the fluoride containing node affords the most favorable interactions for high-density H₂ storage. Using energy decomposition analysis, we delineate electronic contributions that enable multiple hydrogen ligation and demonstrate its benefits for hydrogen adsorption and release at modest pressures.

A Bond-Energy/Bond-Order and Populations Relationship

We report an analytical bond energy from bond orders and populations (BEBOP) model that provides intramolecular bond energy decompositions for chemical insight into the thermochemistry of molecules. The implementation reported here employs a minimum basis set Mulliken population analysis on well-conditioned Hartree-Fock orbitals to decompose total electronic energies into physically interpretable contributions. The model's parametrization scheme is based on atom-specific parameters for hybridization and atom pair-specific parameters for short-range repulsion and extended Hückel-type bond energy term fitted to reproduce CBS-QB3 thermochemistry data. The current implementation is suitable for molecules involving H, Li, Be, B, C, N, O, and F atoms, and it can be used to analyze intramolecular bond energies of molecular structures at optimized stationary points found from other computational methods. This first-generation model brings the computational cost of a Hartree-Fock calculation using a large triple-ζ basis set, and its atomization energies are comparable to those from widely used hybrid Kohn-Sham density functional theory (DFT, as benchmarked to 109 species from the G2/97 test set and an additional 83 reference species). This model should be useful for the community by interpreting overall ab initio molecular energies in terms of physically insightful bond energy contributions, e.g., bond dissociation energies, resonance energies, molecular strain energies, and qualitative energetic contributions to the activation barrier in chemical reaction mechanisms. This work reports a critical benchmarking of this method as well as discussions of its strengths and weaknesses compared to hybrid DFT (i.e., B3LYP, M062X, PBE0, and APF methods), and other cost-effective approximate Hamiltonian semiempirical quantum methods (i.e., AM1, PM6, PM7, and DFTB3).

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.

The role of references and the elusive nature of the chemical bond

Chemical bonding theory is of utmost importance to chemistry, and a standard paradigm in which quantum mechanical interference drives the kinetic energy lowering of two approaching fragments has emerged. Here we report that both internal and external reference biases remain in this model, leaving plenty of unexplored territory. We show how the former biases affect the notion of wavefunction interference, which is purportedly recognized as the most basic bonding mechanism. The latter influence how bonding models are chosen. We demonstrate that the use of real space analyses are as reference-less as possible, advocating for their use. Delocalisation emerges as the reference-less equivalent to interference and the ultimate root of bonding. Atoms (or fragments) in molecules should be understood as a statistical mixture of components differing in electron number, spin, etc.

The theory of chemical bonding relies on arbitrary references. Here the authors report a fundamental study on the chemical bond showing that considering the binding fragments as objects in real space enables to eliminate inherent biases.

Exploring the nature of electron-pair bonds: an energy decomposition analysis perspective

In this paper, the nature of electron-pair bonds is explored from an energy decomposition perspective. The recently developed valence bond energy decomposition analysis (VB-EDA) scheme is extended for the classification of electron-pair bonds, which divides the bond dissociation energy into frozen, reference state switch, quasi-resonance and polarization terms. VB-EDA investigations are devoted to a series of electron-pair bonds, including the covalent bonds (H-H, H₃C-CH₃, H₃C-H, and H₂N-NH₂), the ionic bonds (Na-Cl, Li-F), the charge-shift (CS) bonds (HO-OH, F-F, Cl-Cl, Br-Br, H-F, F-Cl, H₃Si-F and H₃Si-Cl), and the inverted central carbon-carbon bond in [1.1.1] propallene. It is shown that the VB-EDA approach at the VBSCF level is capable of predicting the characters of the electron-pair bonds. The perspective from VB-EDA illustrates that a relatively high value of quasi-resonance term indicates a CS bond while a large portion of polarization term suggests a classical covalent bond.

Partial Double Metal-Carbon Bonding Model in Transition Metal Methyl Compounds

The chemical bond between a transition metal and a methyl group (M-CH₃) is typically defined as a single covalent bond, which is of fundamental significance and general interest in understanding the structural properties and reactivity of transition metal alkyl compounds. Herein, we demonstrate that the M-CH₃ bonding involves varying σ and π components and thus should be best described in terms of the partial double M═CH₃ bond. The often-neglected π bonding stems from an occupied π-symmetric orbital of the methyl group comprising all three C-H σ bonds (but one C-H' contributes more than the other two) and a vacant low-lying metal d(π) orbital, and is associated with the intramolecular C-H'···M agostic effect (i.e., an acute M-C-H' angle and a short H'···M distance), whose origin is still controversial. We quantify the geometric and energetic impacts of the π interaction involved in the M-CH₃ bond by explicitly computing the intramolecular π_CH' → d_M interaction with the ab initio valence bond (VB) theory. Our computations of the ligand-free [TiCH₃]³⁺ and a series of metallocene catalysts provide a direct proof for the presence of the π bonding in M-CH₃ bonds, which is the cause for the agostic effect. The partial double M═CH₃ bonding model is not only validated by a range of bonding analyses including VB self-consistent field (VBSCF)-based energy decomposition and quantum theory of atoms in molecules (QTAIM) but also authenticated by the specific activity of double M═CH₃ bonds in the C-H activation and olefin insertion. More importantly, the σ bond gradually switches from a classical covalent bond to a novel charge-shift bond with the π bonding becoming increasingly significant. We anticipate that the recognition of the π interaction between electrophilic metal centers and C-H bonds can benefit the understanding of the nature of metal-carbon bonds in transition metal ethyl, alkyl, and carbene compounds.

Nature of the Trigger Linkage in Explosive Materials Is a Charge-Shift Bond

Explosion begins by rupture of a specific bond, in the explosive, called a trigger linkage. We characterize this bond in nitro-containing explosives. Valence-bond (VB) investigations of X-NO₂ linkages in alkyl nitrates, nitramines, and nitro esters establish the existence of Pauli repulsion that destabilizes the covalent structure of these bonds. The trigger linkages are mainly stabilized by covalent-ionic resonance and are therefore charge-shift bonds (CSBs). The source of Pauli repulsion in nitro explosives is unique. It is traced to the hyperconjugative interaction from the oxygen lone pairs of NO₂ into the σ_(X-N)^* orbital, which thereby weakens the X-NO₂ bond, and depletes its electron density as X becomes more electronegative. Weaker trigger bonds have higher CSB characters. In turn, weaker bonds increase the sensitivity of the explosive to impacts/shocks which lead to detonation. Application of the analysis to realistic explosives supports the CSB character of their X-NO₂ bonds by independent criteria. Furthermore, other families of explosives also involve CSBs as trigger linkages (O-O, N-O, Cl-O, N-I, etc. bonds). In all of these, detonation is initiated selectively at the CSB of the molecule. A connection is made between the CSB bond-weakening and the surface-electrostatic potential diagnosis in the trigger bonds.

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.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N₂, and BF bound to a [Ru(II)(NH₃)₅]^{2 +} moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential.

Elucidating the co-transport of bisphenol A with polyethylene terephthalate (PET) nanoplastics: A theoretical study of the adsorption mechanism

Polyethylene terephthalate (PET) is a possible key component of nanoplastics in water environments, which can migrate pollutants through co-transport. In this regard, the co-transport of endocrine disruptors (such as bisphenol A, BPA) by nanoplastics is of emergent concern because of its cytotoxicity/bioaccumulation effects in aquatic organisms. In this work, a computational study is performed to reveal the BPA adsorption mechanism onto PET nanoplastics (nanoPET). It is found that the outer surface of nanoPET has a nucleophilic nature, allowing to increase the mass transfer and intraparticle diffusion into the nanoplastic to form stable complexes by inner and outer surface adsorption. The maximum adsorption energy is similar (even higher) in magnitude with respect to nanostructured adsorbents such as graphene, carbon nanotubes, activated carbon, and inorganic surfaces, indicating the worrying adsorption properties of nanoPET. The adsorption mechanism is driven by the interplay of dispersion (38-49%) and electrostatics effects (43-50%); specifically, dispersion effects dominate the inner surface adsorption, while electrostatics energies dominate the outer surface adsorption. It is also determined that π-π stacking is not a reliable interaction mechanism for aromatics on nanoPET. The formed complexes are also highly soluble, and water molecules behave as non-competitive factors, establishing the high risk of nanoPET to adsorb and migrate pollutants in water ecosystems. Furthermore, the adsorption performance is decreased (but not inhibited) at high ionic strength in salt-containing waters. Finally, these results give relevant information for environmental risk assessment, such as quantitative data and interaction mechanisms for non-biodegradable nanoplastics that establish strong interactions with pollutants in water.

Towards developing a criterion to characterize non-covalent bonds: a quantum mechanical study

Chemical bonds are central to chemistry, biology, and allied fields, but still, the criterion to characterize an interaction as a non-covalent bond has not been studied rigorously.

Data of interaction of supported ionic liquids phases onto copper nanoparticles: A density functional theory study

This work contains data on the computational, structural, and electronic characterization of supported ionic liquids phases anchored to copper nanoparticles using Density Functional theory calculations. The data supplement the paper "Interaction of supported ionic liquids phases onto copper nanoparticles: A Density Functional Theory study" [1], based on the adsorption of ionic liquid onto a Cu nanoparticle is analyzed from a chemical and physical point of view. The chemical analysis is based on Atoms in Molecule theory (AIM) and allows us to differentiate the chemical binding nature between ionic liquid and copper nanoparticle. On the other hand, the energy decomposition analysis based on absolutely localized molecular orbital (ALMO-EDA) describes the physical contributions that govern the interaction between ionic liquid and the copper nanoparticles. Herein, detailed and extended information in the synthesis and computational characterization are presented.

Halogen-bonded haloamine trimers - modelling the X3 synthon

Halogen-halogen bonded haloamine trimers serve as model systems for the X3 synthon present in numerous crystal structures and in two-dimensional self-assembled nanoarchitectures. Halogen bonds forming the synthon are often considered to display cooperativity. Synergy effects were previously found for halogen-halogen bonded bromoamine and iodoamine tetramers. In the present study comparison between haloamine cyclic trimers and tetramers is made. The cooperativity occurring in bromoamine and iodoamine clusters is significantly weaker in the case of the trimers. The present study demonstrates that the bromoamine and iodoamine trimers display weaker cooperativity due to a smaller number of synergy components in comparison to the corresponding tetramers of stronger cooperativity. Moreover, the halogen-halogen interactions in bromoamine and iodoamine dimers with the geometries of the corresponding trimers and tetramers are examined using energy decomposition analysis methods (supermolecular, canonical EDA and SAPT) and the Kohn-Sham molecular orbital model. The results of the analysis indicate that although the interaction energy values for the dimers of the different spatial arrangement are very close to each other, their origin is substantially different. For pairs with the geometry of the trimers orbital interactions and electrostatic attraction are both weaker than for the corresponding dimers with the geometry of the tetramers. This is especially important because both donor-acceptor interactions and electrostatic attraction were previously proven to be responsible for cooperative effects occurring in the bromoamine and iodoamine tetramers.

Computational analysis of vibrational frequencies and rovibrational spectroscopic constants of hydrogen sulfide dimer using MP2 and CCSD(T)

Previous studies have shown that the weakly bonded H₂S dimer demands high level quantum chemical calculations to reproduce experimental values. We investigated the hydrogen bonding of H₂S dimer using MP2 and CCSD(T) levels of theory in combination with aug-cc-pV(D,T,Q)Z basis sets. More precisely, the binding energies, potential energy curves, rovibrational spectroscopic constants, decomposition lifetime, and normal vibrational frequencies were calculated. In addition, we introduced the local mode analysis of Konkoli-Cremer to quantify the hydrogen bonding in the H₂S dimer as well as providing for the first time the comprehensive decomposition of normal vibrational modes into local modes contributions, and a decomposition lifetime based on rate constant. The local mode force constant of the H₂S dimer hydrogen bond is smaller than that of the water dimer, in accordance with the weaker hydrogen bonding in the H₂S dimer.

Clarifying the quantum mechanical origin of the covalent chemical bond

Lowering of the electron kinetic energy (KE) upon initial encounter of radical fragments has long been cited as the primary origin of the covalent chemical bond based on Ruedenberg's pioneering analysis of H[Formula: see text] and H₂ and presumed generalization to other bonds. This work reports KE changes during the initial encounter corresponding to bond formation for a range of different bonds; the results demand a re-evaluation of the role of the KE. Bonds between heavier elements, such as H₃C-CH₃, F-F, H₃C-OH, H₃C-SiH₃, and F-SiF₃ behave in the opposite way to H[Formula: see text] and H₂, with KE often increasing on bringing radical fragments together (though the total energy change is substantially stabilizing). The origin of this difference is Pauli repulsion between the electrons forming the bond and core electrons. These results highlight the fundamental role of constructive quantum interference (or resonance) as the origin of chemical bonding. Differences between the interfering states distinguish one type of bond from another.

Covalent vs Charge-Shift Nature of the Metal-Metal Bond in Transition Metal Complexes: A Unified Understanding

We present here a general conceptualization of the nature of metal-metal (M-M) bonding in transition-metal (TM) complexes across the periods of TM elements, by use of ab initio valence-bond theory. The calculations reveal a dual-trend: For M-M bonds in groups 7 and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving down to the 5d-series, the bonds become gradually covalent. In contrast, M-M bonds of metals having filled d-orbitals (groups 11 and 12) behave oppositely; initially the M-M bond is covalent, but upon moving down the Periodic Table, the CSB character increases. These trends originate in the radial-distribution-functions of the atomic orbitals, which determine the compactness of the valence-orbitals vis-à-vis the filled semicore orbitals. Key factors that gauge this compactness are the presence/absence of a radial-node in the valence-orbital and relativistic contraction/expansion of the valence/semicore orbitals. Whenever these orbital-types are spatially coincident, the covalent bond-pairing is weakened by Pauli-repulsion with the semicore electrons, and CSB takes over. Thus, for groups 3-10, which possess (n - 1)s²(n - 1)p⁶ semicores, this spatial-coincidence is maximal at the 3d-transition-metals which consequently form charge-shift M-M bonds. However, in groups 11 and 12, the relativistic effects maximize spatial-coincidence in the third series, wherein the 5d¹⁰ core approaches the valence 6s orbital, and the respective Pauli repulsion generates M-M bonds with CSB character. These considerations create a generalized paradigm for M-M bonding in the transition-elements periods, and Pauli repulsion emerges as the factor that unifies CSB over the periods of main-group and transition elements.

Local Vibrational Mode Analysis of π–Hole Interactions between Aryl Donors and Small Molecule Acceptors

11 aryl–lone pair and three aryl–anion π –hole interactions are investigated, along with the argon–benzene dimer and water dimer as reference compounds, utilizing the local vibrational mode theory, originally introduced by Konkoli and Cremer, to quantify the strength of the π –hole interaction in terms of a new local vibrational mode stretching force constant between the two engaged monomers, which can be conveniently used to compare different π –hole systems. Several factors have emerged which influence strength of the π –hole interactions, including aryl substituent effects, the chemical nature of atoms composing the aryl rings/ π –hole acceptors, and secondary bonding interactions between donors/acceptors. Substituent effects indirectly affect the π –hole interaction strength, where electronegative aryl-substituents moderately increase π –hole interaction strength. N-aryl members significantly increase π –hole interaction strength, and anion acceptors bind more strongly with the π –hole compared to charge neutral acceptors (lone–pair donors). Secondary bonding interactions between the acceptor and the atoms in the aryl ring can increase π –hole interaction strength, while hydrogen bonding between the π –hole acceptor/donor can significantly increase or decrease strength of the π –hole interaction depending on the directionality of hydrogen bond donation. Work is in progress expanding this research on aryl π –hole interactions to a large number of systems, including halides, CO, and OCH3− as acceptors, in order to derive a general design protocol for new members of this interesting class of compounds.

Probing radical-molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals

Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical-molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical-molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A "polarize-then-depolarize" (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the "vertical" and "adiabatic" variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H₂O˙F and FH˙OH. It is then applied to several chemically interesting radical-molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H₂O) and ˙OH(H₂O)₂), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH₃CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical-molecule interactions.

CASSCF with Extremely Large Active Spaces Using the Adaptive Sampling Configuration Interaction Method

The complete active space self-consistent field (CASSCF) method is the principal approach employed for studying strongly correlated systems. However, exact CASSCF can only be performed on small active spaces of ∼20 electrons in ∼20 orbitals due to exponential growth in the computational cost. We show that employing the Adaptive Sampling Configuration Interaction (ASCI) method as an approximate Full CI solver in the active space allows CASSCF-like calculations within chemical accuracy (<1 kcal/mol for relative energies) in active spaces with more than ∼50 active electrons in ∼50 active orbitals, significantly increasing the sizes of systems amenable to accurate multiconfigurational treatment. The main challenge with using any selected CI-based approximate CASSCF is the orbital optimization problem; they tend to exhibit large numbers of local minima in orbital space due to their lack of invariance to active-active rotations (in addition to the local minima that exist in exact CASSCF). We highlight methods that can avoid spurious local extrema as a practical solution to the orbital optimization problem. We employ ASCI-SCF to demonstrate a lack of polyradical character in moderately sized periacenes with up to 52 correlated electrons and compare against heat-bath CI on an iron porphyrin system with more than 40 correlated electrons.

Energy decomposition analysis based on broken symmetry unrestricted density functional theory

In this paper, the generalized Kohn-Sham energy decomposition analysis (GKS-EDA) scheme is extended to molecular interactions in open shell singlet states, which is a challenge for many popular EDA methods due to the multireference character. Based on broken symmetry (BS) unrestricted density functional theory with a spin projection approximation, the extension scheme, named GKS-EDA(BS) in this paper, divides the total interaction energy into electrostatic, exchange-repulsion, polarization, correlation, and dispersion terms. Test examples include the pancake bond in the phenalenyl dimer, the ligand interactions in the Fe(ii)-porphyrin complexes, and the radical interactions in dehydrogenated guanine-cytosine base pairs and show that GKS-EDA(BS) is a practical EDA tool for open shell singlet systems.

On generalized partition methods for interaction energies

The breakdown of interaction energy has always been a very important means to understand chemical bonding and it has become a seamlessly useful tool for modern supramolecular chemistry.

Metal-Halogen Bonding Seen through the Eyes of Vibrational Spectroscopy

Incorporation of a metal center into halogen-bonded materials can efficiently fine-tune the strength of the halogen bonds and introduce new electronic functionalities. The metal atom can adopt two possible roles: serving as halogen acceptor or polarizing the halogen donor and acceptor groups. We investigated both scenarios for 23 metal–halogen dimers trans-M(Y₂)(NC₅H₄X-3)₂ with M = Pd(II), Pt(II); Y = F, Cl, Br; X = Cl, Br, I; and NC₅H₄X-3 = 3-halopyridine. As a new tool for the quantitative assessment of metal–halogen bonding, we introduced our local vibrational mode analysis, complemented by energy and electron density analyses and electrostatic potential studies at the density functional theory (DFT) and coupled-cluster single, double, and perturbative triple excitations (CCSD(T)) levels of theory. We could for the first time quantify the various attractive contacts and their contribution to the dimer stability and clarify the special role of halogen bonding in these systems. The largest contribution to the stability of the dimers is either due to halogen bonding or nonspecific interactions. Hydrogen bonding plays only a secondary role. The metal can only act as halogen acceptor when the monomer adopts a (quasi-)planar geometry. The best strategy to accomplish this is to substitute the halo-pyridine ring with a halo-diazole ring, which considerably strengthens halogen bonding. Our findings based on the local mode analysis provide a solid platform for fine-tuning of existing and for design of new metal–halogen-bonded materials.