Energy Partitioning Scheme Research Articles

Understanding the Electronic Effects of Lewis Acid Catalysts in Accelerating Polar Diels-Alder Reactions.

The electronic effects of Lewis acid (LA) catalysts in reducing the activation energies of polar Diels-Alder (P-DA) reactions have been studied within Molecular Electron Density Theory. To this end, a quantum topological energy partitioning scheme, namely, the Relative Interacting Atomic Energy (RIAE) analysis, is applied to the transition state structures (TSs) and the ground state of the reagents of two different LA-catalyzed P-DA reactions. Analyses of the ξEtotalX total energies of the two interacting frameworks f(X) show that the electronic energy stabilization of the electrophilic frameworks, resulting from the global electron density transfer (GEDT), is the cause of an effective decrease of the activation energies. On the other hand, an in-depth analysis of the ξEintraA intra-atomic energies of the atoms belonging to the electrophilic ethylenic framework in the LA-catalyzed P-DA reactions of cyclopentadiene with acrolein indicates that the strong electronic stabilization of the carbonyl carbon, resulting from the GEDT taking place at the TSs, is the main factor responsible for the decrease of the activation energies in these LA-catalyzed P-DA reactions. Finally, the increase in GEDT at the TSs of these P-DA reactions causes an increase in the larger C-C distance, resulting from the stabilization of the electrophilic framework, thereby decreasing the suggested Pauli repulsion.

Capture of CO2 by Melamine Derivatives: A DFT Study Combining the Relative Energy Gradient Method with an Interaction Energy Partitioning Scheme.

A theoretical study of the interaction between melamine and CO2 was carried out using density functional theory (DFT) with the B3LYP-D3(BJ)/aug-cc-pVTZ level of theory. The presence of anions interacting with melamine transforms the weakly bonded tetrel complexes into adducts. Thus, melamine acts as an FLP (frustrated Lewis pair) with acid groups (NHs as hydrogen bond donors) and a base group (N of the triazine ring). The application of the relative energy gradient formalism (REG) along the reaction coordinate has demonstrated that the ability of the melamine-anion systems to capture CO2 is linked to its capacity to polarize the CO2 molecule. These results have been confirmed by placing the melamine:CO2 complex in a uniform electric field with different strengths.

Seamless Multilayer─A Novel Total Energy Partition Scheme for Embedded and Hybrid Calculations.

In this paper, we provide general formulation of a multilayer approach, covering both additive and subtractive quantum mechanics/molecular mechanics (QM/MM) as special cases. After that, we suggest a novel definition of QM/MM total energy based on the consideration of a system divided into three layers. In a simplified form, it is , where layers 1, 2, and 3 represent inner QM, outer QM, and classical MM regions, respectively. The novel formulation is also not limited by only QM/MM combination of methods─in fact, any computational methods can be combined in a hybrid calculation. In this paper, we call the new approach seamless multilayer. Test calculations performed for silica and boric oxide show that the new approach requires no QM/MM interface parameterization as well as no or very simple correction terms for boundary atoms. This can greatly facilitate QM/MM studies of covalent inorganic solids. However, test calculations of α-Al2O3 show that for ionic compounds, the new method requires some additional development.

Partition the total energy of Al3Ti to characterize the Al3Ti/Al interface properties: a first-principles study

The geometric model of coplanar reciprocal lattice points (CRLPs) was used to predict the preferred orientation relationships (ORs) between the Al3Ti intermetallic particle and the Al matrix. The calculation result indicates that there exist two preferred ORs, i.e. (001)Al3Ti//(001)Al, [100]Al3Ti//[100]Al and (010)Al3Ti//(010)Al, [100]Al3Ti//[101¯]Al. The periodic models with a specific interface structure and surface slab models on a particular crystallographic plane were proposed to partition the total energy of the Al3Ti compound into its constituent atoms’ energies. The Ti and two kinds of Al atoms (Wyckoff notation 2b and 4d) possess the energy of -119.80325739 Ry, -5.09778518 Ry, and -5.03677683 Ry, respectively. Compared with the Al3Ti total energy of -269.94919247 Ry, the proposed energy partition scheme presents a satisfactory accuracy better than ∼10−7 Ry. Owing to the data of the atom's energy in the solid state, the definite value of surface energy can be obtained whether or not it is a stoichiometric or non-stoichiometric surface. The interface energy calculation, which was carried out on all the preferred ORs with all the possible atomic configurations, indicates that the energy-preferred interface possesses the orientation relationship of (001)Al3Ti//(001)Al, [100]Al3Ti//[100]Al. The atomic configuration is that the atoms on the surface of the Al slab face directly to atoms on the second layer of the Al3Ti slab with the Al-Ti terminated surface on account of its lowest interface energy of 0.005 J/m2. The predicted OR agrees well with the previously published experimental results, and the significantly lower interface energy explains the potency of the Al3Ti particle as a heterogeneous nucleation site in the aluminum solidification process.

Cooperativity and intermolecular hydrogen bonding in donor‐acceptor complexes of phenol and polyhydroxybenzenes

AbstractCooperativity between intermolecular and intramolecular hydrogen bonds is an important factor determining the strength of donor‐acceptor complexes. Its impact in poly‐1,2‐diols, notably polyhydroxybenzenes, is subject to debate. Density functional theory calculations have been performed on complexes of phenol, catechol, pyrogallol and 1,2,3,4‐tetrahydroxybenzene with pyridine, trimethylamine and trimethylphosphine oxide. Binding energies, proton NMR shifts, Quantum Theory of Atoms in Molecules analysis and Interacting Quantum Atoms (IQA) interaction energies reveal a positive cooperative effect of a topological intramolecular hydrogen bond (IMHB) in catechol relative to phenol, with insignificant or small negative effects of further HO groups. Except for catechol complexes, there are no topological IMHBs in any donors or their complexes, although all show Non‐Covalent Interaction isosurfaces. The absence of a topological IMBH in catechol itself is explained by electron density contour plots. Complexes of Me3N and Me3PO with catechol, pyrogallol and 1,2,3,4‐tetrahydroxybenzene display additional intermolecular hydrogen bonds, C‐H…H‐C and C‐H…O=P, respectively, with the hydrogen atom ortho to the bound HO group. The predominantly covalent or electrostatic character of the various hydrogen bond types is discussed in terms of the IQA energy partition scheme, which is also useful for characterising IMHBs in the absence of a bond critical point. These results further our understanding of the nature and the limits of cooperative hydrogen bonding in donor‐acceptor complexes.

Cooperativity and reactivity properties of medium-sized boron clusters: a combined density functional theory and information-theoretic approach study

In continuation of our previous work of small boron clusters [Phys. Chem. Chem. Phys. 23, 24118 (2021)], we systematically examined the neutral and negatively charged boron clusters B n /B − (nε{8–38}) with planar or quasi-planar conformations, whose exotic properties have aroused considerable interest in the literature. We make use of two total energy partition schemes, conceptual density functional theory, and the information-theoretic approach to appreciate the cooperativity and reactivity properties. We found that neutral boron clusters are positively cooperative, but negatively charged boron clusters are negatively cooperative. Our results show that the origin of the cooperativity effect for the negatively cooperative boron clusters is much more complicated than the neutral boron clusters. For chemical reactivity, we unveil that the reactive sites are around the cluster periphery and boron atoms can be both electrophilic and nucleophilic. Global and local aromaticity for the boron clusters can be totally different. For the first time, we have observed helical spin density distributions for negatively charged boron clusters (B16 – and B20 – ), which is reminiscent of helical molecular orbitals [Chem. Sci. 4, 4278 (2013)] in allenes, cumulenes, and oligoynes (polyalkynes). Collectively, our results should provide more insights to understand the exotic properties of boron clusters and henceforth yield novel potential applications.

A Density Functional Theory and Information-Theoretic Approach Study of Interaction Energy and Polarizability for Base Pairs and Peptides.

Using density functional theory (DFT) and the information-theoretic approach (ITA) quantities to appreciate the energetics and properties of biopolymers is still an unaccomplished and ongoing task. To this end, we studied the building blocks of nucleic acid base pairs and small peptides. For base pairs, we have dissected the relative importance of energetic components by using two energy partition schemes in DFT. Our results convincingly show that the exchange-correlation effect predominantly governs the molecular stability of base pairs while the electrostatic potential plays a minor but indispensable role, and the steric effect is trivial. Furthermore, we have revealed that simple density-based ITA functions are in good relationships with molecular polarizabilities for a series of 30 hydrogen-bonded base pairs and all 20 natural α-amino acids, 400 dipeptides, and 8000 tripeptides. Based on these lines, one can easily predict the molecular polarizabilities of larger peptides, even proteins as long as the total molecular wavefunction is available, rather than solving the computationally demanding coupled-perturbed Hartree–Fock (CPHF) equation or its DFT counterpart coupled-perturbed Kohn–Sham (CPKS) equation.

Nano-saturn and ExBox systems: Dominant role of steric, exchange-correlation, and electrostatic effects

To appreciate the origin of host-guest (HG) interactions in nano-Saturn and ExBox systems, we propose to use the density functional theory energy partitioning schemes. One approach includes the kinetic, electrostatic, and exchange-correlation energies, while the contributions of another partitioning scheme are the steric, electrostatic, and quantum effects. It is shown that the steric and exchange-correlation effects as well as the electrostatic interactions are dominant factors contributing to the total interaction energies. Furthermore, an alternative energy partitioning scheme including steric, exchange-correlation, and electrostatic energies is also proposed to accurately accounting for HG interactions in nano-Saturn and ExBox systems.

Hydrogen bonding networks and cooperativity effects in the aqueous solvation of trimethylene oxide and sulfide rings by microwave spectroscopy and computational chemistry.

The intermolecular interactions responsible for the microsolvation of the highly flexible trimethylene oxide (TMO) and trimethylene sulfide (TMS) rings with one and two water (w) molecules were investigated using rotational spectroscopy (8-22GHz) and quantum chemical calculations. The observed patterns of transitions are consistent with the most stable geometries of the TMO-w, TMO-(w)2, and TMS-w complexes at the B2PLYP-D3(BJ)/aug-cc-pVTZ level and were confirmed using spectra of the 18O isotopologue. Due to its effectively planar backbone, TMO offers one unique binding site for solvation, while water can bind to the puckered TMS ring in either an axial or equatorial site of the heteroatom. In all clusters, the first water molecule binds in the σv symmetry plane of the ring monomer and serves as a hydrogen bond donor to the heteroatom. The second water molecule is predicted to form a cooperative hydrogen bonding network between the three moieties. Secondary C-H⋯O interactions are a key stabilizing influence in trimers and also drive the preferred binding site in the TMS clusters with the axial binding site preferred in TMS-w and the equatorial form calculated to be more stable in the dihydrate. Using an energy partition scheme from the symmetry-adapted perturbation theory for the O, S, and Se containing mono- and dihydrates, the intermolecular interactions are revealed to be mainly electrostatic, but the dispersive character of the contacts is enhanced with the increasing size of the ring's heteroatom due to the key role of longer-range secondary interactions.

On the role of steric and exchange–correlation effects in halogenated complexes

Density functional theory formalisms of energy partitioning schemes are utilized to find out what energetic components govern interactions in halogenated complexes.

Beyond the Classical Electron-Sharing and Dative Bond Picture: Case of the Spin-Polarized Bond.

Chemical bonds are traditionally assigned as electron‐sharing or donor‐acceptor/dative. External criteria such as the nature of the dissociation process, energy partitioning schemes, or quantum chemical topology are invoked to assess the bonding situation. However, for systems with marked multi‐reference character, this binary categorization might not be precise enough to render the bonding properties. A third scenario can be foreseen: spin polarized bonds. To illustrate this, the case of a NaBH3 − cluster is presented. According to the analysis NaBH3 − exhibits a strong diradical character and cannot be classified as either electron‐sharing or a dative bond. Elaborated upon are the common problems of popular bonding descriptions. Additionally, a simple model, based on the bond order and local spin indicators, which discriminates between all three bonding situations, is provided.

Interacting Quantum Atoms-A Review.

The aim of this review is threefold. On the one hand, we intend it to serve as a gentle introduction to the Interacting Quantum Atoms (IQA) methodology for those unfamiliar with it. Second, we expect it to act as an up-to-date reference of recent developments related to IQA. Finally, we want it to highlight a non-exhaustive, yet representative set of showcase examples about how to use IQA to shed light in different chemical problems. To accomplish this, we start by providing a brief context to justify the development of IQA as a real space alternative to other existent energy partition schemes of the non-relativistic energy of molecules. We then introduce a self-contained algebraic derivation of the methodological IQA ecosystem as well as an overview of how these formulations vary with the level of theory employed to obtain the molecular wavefunction upon which the IQA procedure relies. Finally, we review the several applications of IQA as examined by different research groups worldwide to investigate a wide variety of chemical problems.

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

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

Nature and origin of γ-gauche effect in sulfoxides: A density functional theory and information-theoretic approach study

Bulky vicinal groups around a single bond usually prefer to be in the opposite (anti) conformation but when extra interactions come into play, more stable could be the gauche conformer, where the neighboring groups embrace a dihedral angle around 60°. This is called the gauche effect. The γ-gauche effect historically features the upfield shift of 13C NMR spectra when a carbon atom and its nonprotonic γ-substituent are in a gauche arrangement. In this work, using sulfoxides as illustrative examples, we show that the nature of the γ-gauche effect is the same as that of the gauche effect, i.e., the gauche conformation is more stable than the anti conformation. To unveil the origin of this effect, we employ two total energy partition schemes in density functional theory and four quantities from the information-theoretic approach. Our results unambiguously show that the γ-gauche effect is of the stereoelectronic origin with a multifaceted nature. Its origin can be understood from a few different perspectives including energetic contributions, dipole moment, charge distribution, hyperconjugation, and information theory. Substantially different from other stereoelectronic effects such as anomeric and generalized anomeric effects, this effect has its unique features as demonstrated from our results in the present work. Having successfully established the link of the γ-gauche with other gauche effects and unveiled its multi-faceted origin, this study should shed new light towards the comprehensive understanding about this important effect of conformational stability in sulfoxides and other systems alike.

On the theoretical rationalization of intermolecular interactions: insights from DFT energy partitioning schemes

The energy partitioning schemes are powerful tools bridging the gap between elementary quantum chemistry and conceptually interpretation of interactions. In this work, the density functional theory (DFT)-based energy partitioning schemes through conventional and modern formalisms have been utilized to find out what energetic components govern the nature and origin of different types of intermolecular interactions. To this end, diverse datasets covering wide ranges of interactions at equilibrium geometries as well as during the potential energy curves are investigated. With more or less different roles on the stabilization and destabilization, the electrostatic, exchange–correlation, and steric effects are shown to be the dominant factors contributing to the total interaction energies. Furthermore, the energy decomposition analyses have also been employed during the potential energy curve of the systems under study. The obtained profiles of the energetic components and their changing pattern ascertain that exchange–correlation effects alongside electrostatic and noninteracting kinetic energy components are determinant contributions following the variation trend of interaction energies. On the other hand, we find that for both equilibrium and nonequlibrium geometries of the formed complexes in each category there are reasonable and meaningful correlations between interaction energies and any of their components as well as energy components themselves based on one- to three-variables fittings. To wrap up, our findings unveil that the traditional and novel DFT energy partitioning schemes can pave the way to figure out the essence of intermolecular interactions, where the DFT energetic components come into play and further evidences of their quality to theoretical rationalization of intermolecular interactions are showcased.

Efficiency of electrostatic and steric forces in theoretical appreciating chemical reactivity-related phenomena

ABSTRACTRationalisation of computational results towards appreciating and predicting chemical reactivity is a topic worthy of investigation in theoretical chemistry. In this regard, a robust and generally applicable framework to comprehend the problem is still lacking. Nevertheless, on the basis of a density functional theory (DFT) energy partition scheme where the total electronic energy is decomposed into three independent effects as steric, electrostatic and the fermionic quantum, the fundamental driving forces of chemical processes to understand molecular reactivity have recently been proposed. In the present contribution, the two related descriptors, electrostatic and steric forces, are utilised to evaluate their applicability and accountability to comprehend different chemical reactivity properties. To do so, we have considered the electrophilic and nucleophilic regioselectivity, stereoselectivity and etherification reaction of phenolic derivatives as illustrative examples of reactivity-related phenomena. Highlighting the distinguished characteristics of the descriptors under study, their usefulness for analysing the chemical reactivity properties and reproducing experimental evidences is showcased. On the whole, our findings corroborate that the DFT energy partitioning scheme and the associated reactivity descriptors can pave the way towards theoretical rationalisation of chemical reactivity-related phenomena.

Chemical Pressure Maps of Molecules and Materials: Merging the Visual and Physical in Bonding Analysis.

The characterization of bonding interactions in molecules and materials is one of the major applications of quantum mechanical calculations. Numerous schemes have been devised to identify and visualize chemical bonds, including the electron localization function, quantum theory of atoms in molecules, and natural bond orbital analysis, whereas the energetics of bond formation are generally analyzed in qualitative terms through various forms of energy partitioning schemes. In this Article, we illustrate how the chemical pressure (CP) approach recently developed for analyzing atomic size effects in solid state compounds provides a basis for merging these two approaches, in which bonds are revealed through the forces of attraction and repulsion acting between the atoms. Using a series of model systems that include simple molecules (H2, CO2, and S8), extended structures (graphene and diamond), and systems exhibiting intermolecular interactions (ice and graphite), as well as simple representatives of metallic and ionic bonding (Na and NaH, respectively), we show how CP maps can differentiate a range of bonding phenomena. The approach also allows for the partitioning of the potential and kinetic contributions to the interatomic interactions, yielding schemes that capture the physical model for the chemical bond offered by Ruedenberg and co-workers.

Energy decomposition analysis

The energy decomposition analysis (EDA) is a powerful method for a quantitative interpretation of chemical bonds in terms of three major components. The instantaneous interaction energy ΔEintbetween two fragments A and B in a molecule A–B is partitioned in three terms, namely (1) the quasiclassical electrostatic interaction ΔEelstatbetween the fragments; (2) the repulsive exchange (Pauli) interaction ΔEPaulibetween electrons of the two fragments having the same spin, and (3) the orbital (covalent) interaction ΔEorbwhich comes from the orbital relaxation and the orbital mixing between the fragments. The latter term can be decomposed into contributions of orbitals with different symmetry which makes it possible to distinguish between σ, π, and δ bonding. After a short introduction into the theoretical background of the EDA we present illustrative examples of main group and transition metal chemistry. The results show that the EDA terms can be interpreted in chemically meaningful way thus providing a bridge between quantum chemical calculations and heuristic bonding models of traditional chemistry. The extension to the EDA–Natural Orbitals for Chemical Valence (NOCV) method makes it possible to breakdown the orbital term ΔEorbinto pairwise orbital contributions of the interacting fragments. The method provides a bridge between MO correlations diagrams and pairwise orbital interactions, which have been shown in the past to correlate with the structures and reactivities of molecules. There is a link between frontier orbital theory and orbital symmetry rules and the quantitative charge‐ and energy partitioning scheme that is provided by the EDA–NOCV terms. The strength of the pairwise orbital interactions can quantitatively be estimated and the associated change in the electronic structure can be visualized by plotting the deformation densities.This article is categorized under:Structure and Mechanism > Molecular StructuresElectronic Structure Theory > Density Functional TheoryComputer and Information Science > Visualization

Accurate prediction of the energetics of weakly bound complexes using the machine learning method kriging

Here, we extend the system energy prediction approach used in the force field FFLUX (Maxwell et al. Theor Chem Acc 135:195, 2016) to complexes bound by weak intermolecular interactions. The investigation features the first application of the approach to bound complex systems, additionally challenged by investigating complexes held together only weakly, through either a predominant dispersion contribution, or through mixed dispersion and hydrogen-bonding. Our approach uses the interacting quantum atoms (IQA) energy partitioning scheme to obtain the intra-atomic, {E}_{mathrm{intra}}^{mathrm{A}} , and interatomic, {V}_{mathrm{inter}}^{{mathrm{AA}}^{hbox{'}}} , energies, which when summed, compose the molecular energy, {E}_{mathrm{IQA}}^{mathrm{system}} . The {E}_{mathrm{intra}}^{mathrm{A}} and {V}_{mathrm{inter}}^{{mathrm{AA}}^{hbox{'}}} energies are mapped to the positions of the nuclear coordinates through the machine learning method kriging to build atomic energy models. A model’s quality is established through its ability to accurately predict the atomic and molecular energies of atoms in an external test set. Mean absolute error percentages (MAE%) of 1.5, 1.5, 1.6, 1.0, 2.6 and 1.7% are obtained in recovering the molecular energy for ammonia…benzene, water…benzene, HCN…benzene, methane…benzene, stacked-benzene (C2h) dimer and T-benzene (C2v) dimer complexes, respectively.

The long-range convergence of the energetic properties of the water monomer in bulk water at room temperature.

The Interacting Quantum Atoms (IQA) energy partitioning scheme has been applied to a set of liquid water largely spherical clusters (henceforth called spheres) of up to 9 Å radius, with a maximum cluster size of 113 molecules. This constitutes half of the commonly used 216 molecules in a typical simulation box of a liquid water box, and to our knowledge is the largest analysis of this kind ever undertaken. As well as demonstrating the topological analysis of large systems, which has only recently become computationally feasible, important long range properties of liquid water are obtained. The full topological partitioning of each sphere into atomic basins is used to consider the long-range convergence of the energetic and multipolar properties of the water molecule at the centre of each sphere. It is found that the total molecular energy converges to its 9 Å value after 7 Å, which corresponds to approximately the first three solvation shells, while the molecular dipole and quadrupole moments approximately converge after 5.5 Å, which corresponds to approximately the first two solvation shells. The effect of water molecule flexibility is also considered.