Quantum Atoms Research Articles

Quantum Information Patterns Between Atoms in a Molecule.

Quantum information theory provides a powerful toolbox of descriptors that characterize many-electron systems based on quantum information patterns between open quantum systems. Despite the wealth of insights gained in the condensed matter community, the use of these descriptors to study interactions between atoms in a molecule remains limited. In this study, we develop a quantum information framework for molecules that characterizes the quantum information patterns between quantum atoms as defined in the Quantum Theory of Atoms in Molecules. We show that quantum information analyses capture key properties of quantum atoms and how they interact with their molecular environment. Additionally, we show that the presence of bond critical points can remain invariant despite large changes in the quantum information patterns between the quantum atoms. Our findings indicate that quantum information theory can shed a new light on molecular electronic structure.

Theoretical description of hydride-hydride interactions in selected hydrogen storage materials.

The high content of hydride-hydride contacts Hδ-···δ-H in hydrogen storage materials appears to be relevant for hydrogen formation. At present time there is no consensus whether these contacts are attractive or repulsive. Accordingly, the main goal of this article is to shed light on physical factors which constitute homopolar hydride-hydride interactions Hδ-···δ-H in selected transition metal complexes i.e. HCoL4, L = CO,PPh3,PH3. In order to achieve this goal, the charge and energy decomposition ETS-NOCV approach along with the Interacting Quantum Atoms (IQA) and reduced density gradient (NCI) are applied for the bonded adducts L4CoH···HCoL4. Based on DFT and correlated methods it has been shown, that hydride-hydride interactions might be attractive and even far stronger than classical hydrogen bonds. The stability of the adducts is increased by phosphine ligand installation: overall Hδ-···δ-H bonding energy changes in the order: CO << PPh3 ~ PH3. It has been revealed that depending on monomer's conformations Hδ-···δ-H bonds are dominated by charge delocalization or London dispersion forces and the electrostatic term is also relevant. It is finally determined by IQA energy decomposition, that diatomic hydride-hydride interaction CoH···HCo is chameleon-like, namely, it is attractive in CO4CoH···HCoCO4, whereas the repulsion is unveiled in (CO)3(PPh3)CoH···HCo(CO)3(PPh3).

Experimental molecular structures in the gas phase at the upper size limit: The case of Si6Tip6.

Currently, the largest (ramax = 19.9Å) and by far the most complicated (234 atoms, C1 symmetry, 696 independent geometrical parameters, and 27 261 interatomic terms) experimental molecular structure of a cage-type Si6Tip6 (Tip = 2,4,6-iPr3C6H2) isomer has been investigated in the gas phase by the electron diffraction method (Tav = 645K) supplemented with theoretical simulations. A detailed analysis of the current possibilities for experimentally investigating large molecular structures is performed. A series of density functional theory approximations and the role of dispersion interactions have been benchmarked using the obtained data. Based on the refined geometry of Si6Tip6, various quantum-chemical methods have been applied for the investigation of the electronic structure of its Si6 core. In particular, natural bond orbital, quantum theory of atoms in molecules, interacting quantum atoms, fractional occupation number weighted density, and complete active space self-consistent field (CASSCF) methods were utilized. The diradical character of the molecule has been assessed by the UHF and CASSCF approximations. The problem of bonding between the hemispheroidal silicon atoms has been investigated.

Deciphering Pyramidanes: A Quantum Chemical Topology Approach.

C[C4H4], the simplest compound of the [4]-pyramidane family, has so far eluded experimental characterization, although several of its analogs, E[C4(SiMe3)4] in which the E apex atom is a tetrel group element, have been successfully prepared. The non-classical bonding mode of E, similar to that found in propellanes, has prompted a considerable number of theoretical studies to unravel the nature of the apex-base interaction. Here, we contribute to this knowledge by analyzing the electron localization function (ELF) and classical QTAIM descriptors; as well the statistical distribution of electrons in atomic regions by means of the so-called electron distribution functions (EDFs), calculation of multicenter indices (MCI) as aromaticity descriptors and by performing orbital invariant energy decompositions with the interacting quantum atoms (IQA) approach on a series of E[C4(SiMe3)4] compounds. We find that the bonding evolves from covalent to electrostatic as E changes from C to Pb, with an anomaly when E=Si, which is shown to be the most charged moiety, compatible with an aromatic [C4(SiMe3)4]2- scaffold in the pyramidane base.

Determining the Factors Accounting for Reaction Selectivity: A Relative Energy Gradient - Interacting Quantum Atoms and Natural Bonding Orbitals Study.

Identifying the main physicochemical properties accounting for the course of a reaction is of utmost importance to rationalize chemical syntheses. To this aim, the relative energy gradient (REG) method is an appealing approach because it is an unbiased and automatic process to extract the most relevant pieces of energy information. Initially formulated within the interacting quantum atoms (IQA) framework for a single reaction, here we extend the REG method to natural bond orbitals (NBO) analysis and to the case of two competitive processes. This development enables the determination of the driving forces of any chemical selectivity. We illustrate the extended REG method on the case study of ring opening in cyclobutenes, which is an important instance of the so-called torquoselectivity.

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

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

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.

Classical versus Collective Interactions in Asymmetric Trigonal Bipyramidal Alkaline Metal-Boron Halide Complexes.

Collective interactions are a novel type of chemical bond formed between metals and electron-rich substituents around an electron-poor central atom. So far only a limited number of candidates for having collective interactions are reported. In this work, we extend the newly introduced concept of collective bonding to a series of neutral boron complexes with the general formula M2BX3 (M=Li, Na, and K; X=F, Cl, and Br). Our state-of-the-art ab initio computations suggest that these complexes form trigonal bipyramidal structures with a D3h to C3v distortion along the C3 axis of symmetry. The BX3 unit in the complexes distorts from planar to pyramidal akin to a sp3 hybridized atom. Interestingly, the interaction of the metals with the pyramidal side of BX3, where the lone pair in a hypothetical [BX3]2- should be located, is weaker than the interactions of metals with the inverted side, i. e., the middle of three halogen atoms. The origin of this stronger interaction can be explained by the formation of collective interactions between metals and halogen atoms as we explored via energy decomposition within the context of the theory of interacting quantum atoms, IQA.

Revealing the Critical Role of Global Electron Density Transfer in the Reaction Rate of Polar Organic Reactions within Molecular Electron Density Theory.

The critical role of global electron density transfer (GEDT) in increasing the reaction rate of polar organic reactions has been studied within the framework of Molecular Electron Density Theory (MEDT). To this end, the series of the polar Diels-Alder (P-DA) reactions of cyclopentadiene with cyanoethylene derivatives, for which experimental kinetic data are available, have been chosen. A complete linear correlation between the computed activation Gibbs free energies and the GEDT taking place at the polar transition state structures (TSs) is found; the higher the GEDT at the TS, the lower the activation Gibbs free energy. An interacting quantum atoms energy partitioning analysis allows for establishing a complete linear correlation between the electronic stabilization of the electrophilic ethylene frameworks and the GEDT taking place at the polar TSs. This finding supports Parr's proposal for the definition of the electrophilicity ω index. The present MEDT study establishes the critical role of the GEDT in the acceleration of polar reactions, since the electronic stabilization of the electrophilic framework with the electron density gain is greater than the destabilization of the nucleophilic one, making a net favorable electronic contribution to the decrease in the activation energy.

A molecular electron density theory study of hydrogen bond catalysed polar Diels–Alder reactions of α,β-unsaturated carbonyl compounds

The hydrogen bond (HB) catalysed Diels-Alder (DA) reactions of acrolein with cyclopentadiene have been investigated within the Molecular Electron Density Theory (MEDT) at the ωB97X-D/6-311G(d,p) computational level. The formation of HBs increases the electrophilicity of these species, suggesting an acceleration of these polar Diels-Alder (P-DA) reactions with forward electron density flux. Formation of one or two HBs with acrolein decreases the activation energies of the HB-catalysed P-DA reactions by 1.7 (methanol) and 4.0 (squaramide) kcal·mol−1, with the corresponding DA reactions exhibiting low endo stereoselectivity. These HB-catalysed DA reactions proceed through non-concerted one-step mechanisms via asynchronous transition state structures (TSs). An Interacting Quantum Atoms (IQA) energy partitioning analysis of the TSs indicates that the intra-atomic stabilization of the acrolein framework, coupled with the increase of the global electron density transfer, plays a crucial role in reducing the activation energies of these HB-catalysed DA reactions.

Planar tetracoordinate beryllium compounds with a partially covalent Be-Ng bond.

An analysis of the thermodynamic and kinetic stability and the nature of the chemical bond in hypercoordinated compounds with the formula BeH3Ng+ (Ng = He-Rn) through high-level calculations is presented in this work. Thermochemical calculations show that, for the heavier noble gases (Ar-Rn), these systems are thermodynamically stable at room temperature; however, this stability decreases due to a weakening of the Be-H2 interaction, while the Be-Ng bond strengthens going down the periodic table. These results are complemented by Born Oppenheimer molecular dynamics simulations, in which the increasing tendency to dissociate the Be-H2 bond is evidenced. The nature of the chemical bonding depends on the analysis performed. On the one hand, the interacting quantum atoms method indicates that the covalent contribution is around 25 to 30%. On the other hand, the electron density topology indicates a covalent nature for compounds with Kr-Rn, while Hirshfeld population analysis in conjunction with Mayer's bond order establishes polar covalent behavior. The geometrical parameters and natural energy decomposition analysis (NEDA) indicate a covalent nature, allowing us to consider that the Be-Ng bond has a partially covalent character.

Questing for homoleptic mononuclear manganese complexes with monodentate O-donor ligands.

Compounds containing Mn-O bonds are of utmost importance in biological systems and catalytic processes. Nevertheless, mononuclear manganese complexes containing all O-donor ligands are still rare. Taking advantage of the low tendency of the pentafluoroorthotellurate ligand (teflate, OTeF5) to bridge metal centers, we have synthesized two homoleptic manganese complexes with monomeric structures and an all O-donor coordination sphere. The tetrahedrally distorted MnII anion, [Mn(OTeF5)4]2-, can be described as a high spin d5 complex (S = 5/2), as found experimentally (magnetic susceptibility measurements and EPR spectroscopy) and using theoretical calculations (DFT and CASSCF/NEVPT2). The high spin d4 electronic configuration (S = 2) of the MnIII anion, [Mn(OTeF5)5]2-, was also determined experimentally and theoretically, and a square pyramidal geometry was found to be the most stable one for this complex. Finally, the bonding situation in both complexes was investigated by means of the Interacting Quantum Atoms (IQA) methodology and compared to that of hypothetical mononuclear fluoromanganates. Within each pair of [MnXn]2- (n = 4, 5) species (X = OTeF5, F), the Mn-X interaction is found to be comparable, therefore proving that the similar electronic properties of the teflate and the fluoride are also responsible for the stabilization of these unique species.

Aza-Michael Addition in Explicit Solvent: A Relative Energy Gradient - Interacting Quantum Atoms Study.

Aza-Michael additions are key reactions in organic synthesis. We investigate, from a theoretical and computational point of view, several examples ranging from weak to strong electrophiles in dimethylsulfoxide treated as explicit solvent. We use the REG-IQA method, which is a quantum topological energy decomposition (Interacting Quantum Atoms, IQA) coupled to a chemical-interpretation calculator (Relative Energy Gradient, REG). We focus on the rate-limiting addition step in order to unravel the different events taking place in this step, and understand the influence of solvent on the reaction, with an eye on predicting the Mayr electrophilicity. For the first time a link is established between an REG-IQA analysis and experimental values.

Cooperativity and topological hydrogen bonding in aromatic diol complexes

AbstractComplexes of three aromatic diols, catechol, naphthalene‐1,8‐diol, and fluorene‐4,5‐diol, with a series of hydrogen bond acceptors (HBAs) that have oxygen, nitrogen, and sulfur acceptor atoms, have been studied by density functional theory (DFT) at the B3LYP/6‐311+G(d,p) level. Binding energies, geometries, infrared spectroscopic (IR) frequencies, nuclear magnetic resonance (NMR) shifts, and measures of the electron density distribution from the Quantum Theory of Atoms in Molecules (QTAIM) are evaluated and compared with data for the corresponding monohydroxy compounds (monols), phenol, naphth‐1‐ol, and fluorene‐4‐ol, in order to assess the importance of cooperativity between intramolecular and intermolecular hydrogen bonding. All measures for all complexes show positive cooperativity whereby both the intermolecular and intramolecular hydrogen bonds are strengthened upon complexation. Cooperativity is weak for catechol and strong for the other two diols and, for all diols, increases with the hydrogen bond basicity of the acceptor. Correlations of IR and NMR metrics against binding energies for a single HBA and all six monols and diols are excellent, but attempts to correlate the same metrics for all HBAs and a single donor are frustrated by differences in intermolecular hydrogen bonding, depending notably on the identity of the acceptor atom in the HBA. Atom–atom interaction energies, calculated by the Interacting Quantum Atoms approach, are used to discuss the covalency of both types of hydrogen bond.

IQA analysis of the two-particle density matrix: chemical insight and computational efficiency

The interacting quantum atoms (IQA) method offers a rigorous and minimal route to calculate atomic electron correlation energies from the two-particle density matrix (2PDM). The price paid is that this method is very time-consuming. However, employing CCSD and CCSD(T), we explore several approaches to speed up such calculations. We make the pivotal observation that the removal, from the true 2PDM, of both the Hartree–Fock part of the 2PDM and an approximate 2PDM (Müller) dramatically reduces the size of the quadrature grid needed to obtain accurate energies.

B-carboranyl methyl thioether ligands in coordination with the W(CO)5 fragment

Complexation of B-closo- and nido-carboranyl methyl thioethers with the pentacarbonyltungsten fragment was studied. An unusual instability of the nido-derivative is detected and rationalized by means of the quantum chemical calculations followed by the topological analysis of electron density and the Interacting Quantum Atoms analysis. The structure of {(CO)5W[9-MeS-1,2-C2B10H11-κ1-S(1)]} was determined by single crystal X-ray diffraction.

Electron density-based protocol to recover the interacting quantum atoms components of intermolecular binding energy.

A new approach for obtaining interacting quantum atoms-defined components of binding energy of intermolecular interactions, which bypasses the use of standard six-dimensional integrals and two-particle reduced density matrix (2-RDM) reconstruction, is proposed. To examine this approach, three datasets calculated within the density functional theory framework using the def2-TZVP basis have been explored. The first two, containing 53 weakly bound bimolecular associates and 13 molecular clusters taken from the crystal, were used in protocol refinement, and the third one containing other 20 bimolecular and three cluster systems served as a validation reference. In addition, to verify the performance of the proposed approach on an exact 2-RDM, calculations within the coupled cluster formalism were performed for part of the first set systems using the cc-pVTZ basis set. The process of optimization of the proposed parametric model is considered, and the role of various energy contributions in the formation of non-covalent interactions is discussed with regard to the obtained trends.

Interacting Quantum Atoms and Multipolar Electrostatic Study of XH···π Interactions.

The interaction energies of nine XH···π (X = C, N, and O) benzene-containing van der Waals complexes were analyzed, at the atomic and fragment levels, using QTAIM multipolar electrostatics and the energy partitioning method interacting quantum atoms/fragment (IQA/IQF). These descriptors were paired with the relative energy gradient method, which solidifies the connection between quantum mechanical properties and chemical interpretation. This combination provides a precise understanding, both qualitative and quantitative, of the nature of these interactions, which are ubiquitous in biochemical systems. The formation of the OH···π and NH···π systems is electrostatically driven, with the Qzz component of the quadrupole moment of the benzene carbons interacting with the charges of X and H in XH. There is the unexpectedly intramonomeric role of X-H (X = O, N) where its electrostatic energy helps the formation of the complex and its covalent energy thwarts it. However, the CH···π interaction is governed by exchange-correlation energies, thereby establishing a covalent character, as opposed to the literature's designation as a noncovalent interaction. Moreover, dispersion energy is relevant, statically and in absolute terms, but less relevant compared to other energy components in terms of the formation of the complex. Multipolar electrostatics are similar across all systems.

Borotropy: The Mechanism of Boron Transfer Between Adjacent N‐Atoms of Pyrazol‐1‐yl Rings

AbstractThis work examines theoretically the problem of the migration of borane groups between the nitrogen atoms of pyrazolyl rings. We have studied as a model the BH2 pyrazol‐1‐yl derivatives to determine the effects of substituents on the pyrazole ring; also 1‐(9‐borabicyclo[3.3.1]nonan‐9‐yl)‐1H‐pyrazoles to compare the calculated barriers with the experimental ones as well as to determine steric effects, i. e., how the buttressing effect increases the rate. The interacting quantum atoms methodology has been used for partitioning the energy of the systems in their stationary points into the contribution of pyrazole and BH2 group and their mutual interaction.

Toward a simple yet efficient cost function for the optimization of Gaussian process regression model hyperparameters

FFLUX is a novel machine-learnt force field using pre-trained Gaussian process regression (GPR) models to predict energies and multipole moments of quantum atoms in molecular dynamic simulations. At the heart of FFLUX lies the program FEREBUS, a Fortran90 and OpenMP-parallelized regression engine, which trains and validates GPR models of chemical accuracy. Training a GPR model is about finding an optimal set of model hyperparameters (θ). This time-consuming task is usually accomplished by maximizing the marginal/concentrated log-likelihood function LLy|x,θ, known as the type-II maximum likelihood approach. Unfortunately, this widespread approach can suffer from the propagation of numerical errors, especially in the noise-free regime, where the expected correlation betweenLLy|x,θ̂ [maximized value of theLLy|x,θfunction] and the models’ performance may no longer be valid. In this scenario, the LLy|x,θ function is no longer a reliable guide for model selection. While one could still rely on a pre-conditioner to improve the condition number of the covariance matrix, this choice is never unique and often comes with increased computational cost. Therefore, we have equipped FEREBUS with an alternatively simple, intuitive, viable, and less error-prone protocol called “iterative hold-out cross-validation” for the optimization of θ values. This protocol involves (1) a stratified random sampling of both training and validation sets, followed by (2) an iterative minimization of the predictive RMSE(θ) of intermediary models over a sufficiently large validation set. Its greatest asset is the assurance that the optimization process keeps reducing the generalization error of intermediary GPR models on unseen datasets, something that maximizing LLy|x,θ does not guarantee.