Quantum Theory Of Atoms In Molecules Parameters Research Articles

Understanding the hydrogen bonding preferences and dynamics of prontosil in water and methanol

Solvation energy, defined as the Gibbs energy change accompanying the transfer of a molecule or an atom from vacuum to the solution, plays a crucial role in understanding molecular interactions. In this study, we explore the interaction of prontosil, an important sulfa drug and the first developed antibiotic capable of combating gram-positive cocci bacteria with two common solvents, methanol and water. To investigate these interactions, we employed the DFT/M06–2X/cc-pVDZ level of theory for the geometry optimization of each system. Considering prontosil's six electronegative sites that offers numerous possibilities for interactions, we observed prominent interactions between the drug prontosil and the solvents water and methanol at various sites. The prontosil-water and prontosil-methanol complexes most stable sites were used for additional research. The NBO analysis provided insights into the delocalization phenomena present in prontosil under vacuum and in the presence of solvents. The non-covalent interactions (NCI) and reduced density gradient (RDG) plot aided in the interpretation of the steric interactions, strong and weak hydrogen bonds, as well as intra and intermolecular interactions within prontosil and its complexes. In the NBO analysis, the hydrogen and electronegative atoms of the most stable site of the prontosil-methanol complex showed the highest transmittance energy and in the case of the NCI plot, the same region displayed a blue colour which denotes a strong hydrogen bond. After calculating the quantum chemical parameters of reactivity, it was observed that the prontosil-methanol complex had a lower electrophilicity and is hence more stable. Quantum theory of atoms in molecules (QTAIM) analysis revealed the existence of non-covalent interactions at all the bond critical points (BCP) under consideration in the prontosil molecule and its complexes formed with the solvents. Further investigation of several QTAIM parameters revealed that the prontosil-methanol complex exhibited the lowest binding energy, indicating the most stable interactions among the investigated bond critical points. Additionally, we employed local energy decomposition (LED) and ab initio molecular dynamics (AIMD) simulations based on the M06–2X/cc-pVDZ method, with LED analysis performed using DLPNOCCSD(T). The LED analysis demonstrated that prontosil exhibits more pronounced interactions with methanol than water, and we explored how energy distributions contribute to the total binding energy. Prontosil-methanol complex showed the lowest energy (-14.50 kcal/mol) than the prontosil-water complex (-14.32 kcal/mol). The LED analysis provided insights into why the total binding energy is attractive and predominates the repulsive nature. AIMD simulations of prontosil-methanol complexes yielded favourable results when compared to prontosil-water complexes.

A novel approach for estimating the strength of argentophilic and aurophilic interactions using QTAIM parameters.

Metallophilic interactions, specifically argentophilic (Ag⋯Ag) and aurophilic (Au⋯Au) interactions, play a crucial role in stabilizing various molecular and solid-state structures. In this manuscript, we present a convenient method to estimate the strength of argentophilic and aurophilic interactions based on quantum theory of atoms in molecules (QTAIM) parameters evaluated at the bond critical points connecting the metal centres. We employ density functional theory (DFT) calculations and the QTAIM parameters to develop this energy predictor. To validate the reliability and applicability of our method, we test it using a selection of X-ray crystal structures extracted from the cambridge structural database (CSD), where argentophilic and aurophilic interactions are known to be significant in their solid-state arrangements. This method offers a distinct advantage in systems where multiple interactions, beyond metallophilic interactions, contribute to the overall stability of the structure. By employing our approach, researchers can distinctly quantify the strength of argentophilic and aurophilic interactions, facilitating a deeper understanding of their impact on molecular and solid-state properties. This method fills a critical gap in the existing literature, offering a valuable tool to researchers seeking to unravel the intricate interactions in metal-containing compounds.

Halide‐Triel Bonds between R3SiX (X=F, Cl and Br) and TrY3 (Tr=Al, B and Ga)

AbstractHalide‐triel bonds between halosilane donors and alane/borane/gallane acceptors are investigated considering 24 model complexes using quantum chemical calculations. Nature and strength of Si−X….Tr interactions (X=F, Cl, Br and Tr=Al, B, Ga) binding these complexes has been studied using Electrostatic Potential (ESP), Quantum Theory of Atoms in Molecules (QTAIM), Natural Bond Orbital (NBO), and Energy Decomposition Analysis (EDA) techniques. Basis Set Superposition Error (BSSE) corrected binding energy of the complexes ranges from −3.19 to −29.40 kcal mol−1. QTAIM parameters Laplacian and the total electron density at the Bond Critical Points (BCPs) indicate that the halide‐triel bonds studied here are largely electrostatic in nature (closed‐shell interactions); this has also been revealed through ESP analysis and EDA scheme. In addition, role of charge transfer in these halide‐triel bonds has also been established through NBO analysis. Two charge transfer orbital interactions are responsible for the primary interaction Si−X….Tr: and σ(Si−X) . EDA analysis identifies electrostatic term as the biggest contributor towards the binding of the complexes followed by the polarisation and dispersion terms in most of the complexes. Results of this study have relevance in the Si−F bond activation methodology in organic synthesis.

Atoms in Highly Symmetric Environments: H in Rhodium and Cobalt Cages, H in an Octahedral Hole in MgO, and Metal Atoms Ca-Zn in C20 Fullerenes

An atom trapped in a crystal vacancy, a metal cage, or a fullerene might have many immediate neighbors. Then, the familiar concept of valency or even coordination number seems inadequate to describe the environment of that atom. This difficulty in terminology is illustrated here by four systems: H atoms in tetragonal-pyramidal rhodium cages, H atom in an octahedral cobalt cage, H atom in a MgO octahedral hole, and metal atoms in C20 fullerenes. Density functional theory defines structure and energetics for the systems. Interactions of the atom with its container are characterized by the quantum theory of atoms in molecules (QTAIM) and the theory of non-covalent interactions (NCI). We establish that H atoms in H2Rh13(CO)243− trianion cannot be considered pentavalent, H atom in HCo6(CO)151− anion cannot be considered hexavalent, and H atom in MgO cannot be considered hexavalent. Instead, one should consider the H atom to be set in an environmental field defined by its 5, 6, and 6 neighbors; with interactions described by QTAIM. This point is further illustrated by the electronic structures and QTAIM parameters of M@C20, M=Ca to Zn. The analysis describes the systematic deformation and restoration of the symmetric fullerene in that series.

Molybdenum disulfide monolayer electronic structure information as explored using density functional theory and quantum theory of atoms in molecules

We use density functional theory (DFT) and quantum theory of atoms in molecules (QTAIM) to study the electronic structure of pristine and defect molybdenum disulfide (MoS2) monolayers, at dry and hydrated conditions. We study various defect MoS2 configurations, which are described by the presence of one or more sulfur (S) vacancies, including voids. Structural defects introduce deep and shallow defect states in the electronic band structure in the vicinity of the Fermi energy, which affect the bandgap and introduce mid-gap states. Hydration also affects the bandgap and the mid-gaps of defect MoS2. We use QTAIM parameters at bond critical points to identify the MoS2 bond types and their strength. QTAIM shows the presence of MoS and SS bonding, the former being weakly covalent, and the latter refers to a closed shell interaction. Water and its dissociated products are strongly adsorbed on Mo atoms due to the presence of low electron density areas in the vicinity of these atoms. We finally provide a correlation between changes in the electron density at the Mo-S bond critical points around the structural defect and the mid-gap around the Fermi energy. These findings become relevant for designing electrocatalysts based on MoS2 and two-dimensional layered systems.

Multicenter (FX)n/NH₃ Halogen Bonds (X = Cl, Br and n = 1-5). QTAIM Descriptors of the Strength of the X∙∙∙N Interaction.

In the present work an in depth deep electronic study of multicenter XBs (FX)n/NH3 (X = Cl, Br and n = 1–5) is conducted. The ways in which X∙∙∙X lateral contacts affect the electrostatic or covalent nature of the X∙∙∙N interactions are explored at the CCSD(T)/aug-cc-pVTZ level and in the framework of the quantum theory of atoms in molecules (QTAIM). Calculations show that relatively strong XBs have been found with interaction energies lying between −41 and −90 kJ mol−1 for chlorine complexes, and between −56 and −113 kJ mol−1 for bromine complexes. QTAIM parameters reveal that in these complexes: (i) local (kinetics and potential) energy densities measure the ability that the system has to concentrate electron charge density at the intermolecular X∙∙∙N region; (ii) the delocalization indices [δ(A,B)] and the exchange contribution [VEX(X,N)] of the interacting quantum atoms (IQA) scheme, could constitute a quantitative measure of the covalence of these molecular interactions; (iii) both classical electrostatic and quantum exchange show high values, indicating that strong ionic and covalent contributions are not mutually exclusive.

Real space atomic decomposition of fundamental properties of carbon monoxide in the ground and the two lowest lying excited electronic states

ABSTRACTThe properties of carbon monoxide in its ground and two lowest lying excited states are investigated by conventional and time-dependent (TD) density functional theory (DFT). The dipole moment is decomposed into atomic polarisation (AP) and inter-atomic charge transfer (CT) contributions according to the quantum theory of atoms in molecules (QTAIM). Considerable AP and CT contributions cancel in the ground state (S0) resulting in its known negligible dipole moment. This balance is disturbed in the lowest triplet (T1) and singlet (S1) excited states, resulting in dipole moments of 1.57 D for T1 and 0.49 D for S1 . The AP decreases by 2.5 D on excitation to either state but the opposing CT is reduced by 0.8 D for T1 and by 1.8 D for S1, insufficient for cancellation. These excitations induce charge transfer from O to C which drives dipole changes accompanied by a weakening of the C–O bond, more pronounced in the S1 state, as trends in bond lengths, vibrational frequencies, and QTAIM properties suggest. The charge–charge flux–dipole flux (CCFDF) model in terms of QTAIM parameters reveals that the vibrational stretching band weakening on excitation is predominantly due to changes in atomic charges.

Atomic polarizations necessary for coherent infrared intensity modeling with theoretical calculations.

The inclusion of atomic polarizations for describing molecular electronic structure changes on vibration is shown to be necessary for coherent infrared intensity modeling. Atomic charges from the ChelpG partition scheme and atomic charges and dipoles from Quantum Theory of Atoms in Molecules (QTAIM) were employed within two different models to describe the stretching and bending vibrational intensities of the C-H, C-F, and C=O groups. The model employing the QTAIM parameters was the Charge-Charge Transfer and Dipolar Polarization model (QTAIM/CCTDP), and the model employing the ChelpG charges was the Equilibrium Charge-Charge Flux (ChelpG/ECCF). The QTAIM/CCTDP models result in characteristic proportions of the charge-charge transfer-dipolar polarization contributions even though their sums giving the total intensities do not discriminate between these vibrations. According to the QTAIM/CCTDP model, the carbon monoxide intensity has electronic structure changes similar to those of the carbonyl stretches whereas they resemble those of the CH stretches for the ChelpG/ECCF model.

NATURE OF Mδ+···δ+C-Oδ-INTERACTIONS IN METAL CARBONYLS. AN ELECTRONIC STUDY BASED ON THE TOPOLOGY OF THE ELECTRON CHARGE DENSITY DISTRIBUTION AND ITS LAPLACIAN FUNCTION

Fil: Buralli, Gabriel Jesus. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Ecologia de Anfibios; Argentina

Quantum chemical topological analysis of hydrogen bonding in HX…HX and CH3X…HX dimers (X = Br, Cl, F)

We present a systematic investigation of the nature and strength of the hydrogen bonding in HX···HX and CH3X…HX (X = Br, Cl and F) dimers using ab initio MP2/aug-cc-pVTZ calculations in the framework of the quantum theory of atoms in molecules (QTAIM) and electron localisation functions (ELFs) methods. The electron density of the complexes has been characterised, and the hydrogen bonding energy, as well as the QTAIM and ELF parameters, is consistent, providing deep insight into the origin of the hydrogen bonding in these complexes. It was found that in both linear and angular HX…HX and CH3X…HX dimers, F atoms form stronger HB than Br and Cl, but they need short (∼2 Å) X…HX contacts.

Do QTAIM metrics correlate with the strength of heavy element–ligand bonds?

The bonding in monomeric and dimeric molecular compounds of Cr, Mo, W and U is explored using the Quantum Theory of Atoms-in-Molecules (QTAIM). The metal-ligand and metal-metal bond critical point properties ρb, ∇(2)ρb and Hb, and also the bond delocalisation indices δ(A, B), are correlated with the data from previous Ziegler-Rauk energy decomposition studies of the same systems. For M2X6 (M = Mo, W, U; X = Cl, F, OH, NH2, CH3), ρb, Hb and δ(A, B) display anticorrelations with the total interaction energy of the two MX3 fragments, implying that the weaker metal-metal bonds (those between two uranium atoms) are the more covalent ones. By contrast, strongly positive correlations are observed between the QTAIM parameters and the energy decomposition orbital mixing energies. This is also the case for metal-carbon, metal-nitrogen and metal-oxygen bonds in (CO)5M-imidazole tautomers (M = Cr, Mo, W) and uranyl phosphinimine and phosphine oxide compounds. These targets were chosen specifically because their energy decompositions feature negligible net electrostatic + Pauli "pre-relaxation" effects, and the QTAIM parameters correlate strongly with the orbital mixing-dominated total interaction energies. The metal-metal bonds in M2X6 are found to have significantly positive ∇(2)ρb (in agreement with many previous QTAIM studies of metal-metal bonding), and an anticorrelation is found between the total X3M-MX3 interaction energies and ∇(2)ρb. The positive ∇(2)ρb are traced to the dominant λ3 principal curvature, which correlates well with the destabilising electronic kinetic energy density at the bond critical points, providing a rationalisation of the anticorrelation between the total X3M-MX3 interaction energies and ∇(2)ρb.

Experimental and theoretical charge density of hydrated cupric acetate

The charge density of the hydrated cupric acetate Cu2(μ-OOCCH3)4·2H2O has been studied experimentally at 100K and by DFT calculations on the isolated molecule using the Quantum Theory of Atoms In Molecules (QTAIMs). The bimetallic moiety is bridged by four equivalent acetate groups each other perpendicular and forming penta-atomic rings. The QTAIM parameters of charge density, its Laplacian, potential and kinetic energy density, delocalization indexes, static deformation density have been used to describe all intra- and intermolecular interactions. The topological analysis of the charge density maps shows the expected bond critical points with the corresponding bond paths, Cu–Cu bonding included. The data obtained using the different parameters and functions are consistent for all types of interatomic interactions, i.e. covalent, dative and intermetallic. The unpaired electrons responsible of the magnetic properties of d9 Cu(II) ions occupy the orbitals pointing towards the acetate groups. The valence shell orbital populations of Cu(II) are consistent with the distortion of the octahedral coordination due to the Jahn–Teller effect.

QTAIM Characteristics of Halogen Bond and Related Interactions

Different types of noncovalent interactions such as, for example, halogen bond, hydrogen bond, and dihalogen bond are analyzed. The analysis is based on ab initio calculations which were performed on complexes of the F(3)CCl molecule. This choice is connected with the features of the Cl atom which may act as the Lewis acid and also as the Lewis base center. Such a dual role is a consequence of the existence of negative and positive regions of the electrostatic potential of the Cl center. Hence, the F(3)CCl molecule forms complexes linked by various interactions. The formation of the complexes leads to the electron charge redistribution which is reflected in the quantum theory of atoms in molecules (QTAIM) characteristics. Numerous correlations and tendencies were found here between QTAIM, geometrical and energetic parameters. It was found that the mechanism of the formation of complexes linked through various interactions is generally the same as that known for the hydrogen bond formation. The dependencies and QTAIM characteristics considered here are in agreement with Bent's rule.

Electron Density Characteristics in Bond Critical Point (QTAIM) versus Interaction Energy Components (SAPT): The Case of Charge-Assisted Hydrogen Bonding

Charge-assisted hydrogen bonds (CAHBs) of N-H···Cl, N-H···Br, and P-H···Cl type were investigated using advanced computational approach (MP2/aug-cc-pVTZ level of theory). The properties of electron density function defined in the framework of Quantum Theory of Atoms in Molecules (QTAIM) were estimated as a function of distance in H-bridges. Additionally, the interaction energy decomposition was performed for H-bonded complexes with different H-bond lengths using the Symmetry-Adapted Perturbation Theory (SAPT). In this way both QTAIM parameters and SAPT energy components could be expressed as a function of the same variable, that is, the distance in H-bridge. A detailed analysis of the changes in QTAIM and SAPT parameters due to the changes in H···A distance revealed that, over some ranges of H···A distances, electrostatic, inductive and dispersive components of the SAPT interaction energy show a linear correlation with the value of the electron density at H-BCP ρ(BCP). The linear relation between the induction component, E(ind), and ρ(BCP) confirms numerically the intuitive expectation that the ρ(BCP) reflects directly the effects connected with the sharing of electron density between interacting centers. These conclusions are important in view of charge density studies performed for crystals in which the distance between atoms results not only from effects connected with the interaction between atomic centers directly involved in bonding, but also from packing effects which may strongly influence the length of the H-bond.

Intramolecular Hydrogen Bonds: the QTAIM and ELF Characteristics

B3LYP/aug-cc-pVTZ calculations were performed on the species with intramolecular O-H···O hydrogen bonds. The Quantum Theory of Atoms in Molecules (QTAIM) and the Electron Localization Function (ELF) method were applied to analyze these interactions. Numerous relationships between ELF and QTAIM parameters were found. It is interesting that the CVB index based on the ELF method as well as the total electron energy density at the bond critical point of the proton-acceptor distance (H(bcp)) may be treated as universal descriptors of the hydrogen bond strength, they are also useful to estimate the covalent character of this interaction. There are so-called resonance-assisted hydrogen bonds (RAHBs) among the species analyzed here. It was found that there are not any distinct differences between RAHBs and the other intramolecular hydrogen bonds.

Hydrogen bonds determine the structures of the ternary heterocyclic complexes C2H4O···2HF, C2H5N···2HF and C2H4S···2HF: density functional theory and topological calculations

A theoretical study of structural, electronic, topological and vibrational parameters of the ternary hydrogen-bonded complexes C(2)H(4)O···2HF, C(2)H(5)N···2HF and C(2)H(4)S···2HF is presented here. Different from binary systems with a single proton donor, the tricomplexes have the property of forming multiple hydrogen bonds, which are analyzed from a structural and vibrational point of view, but verified only by means of the quantum theory of atoms in molecules (QTAIM). As traditionally done in the hydrogen bond theory, the charge transfer between proton donors and acceptors was computed using the CHELPG calculations, which also revealed agreement with dipole moment variation and a cooperative effect on the tricomplexes. Furthermore, redshift events on proton donor bonds were satisfactorily identified, although, in this case, an absence of experimental data led to the use of a theoretical argument to interpret these spectroscopic shifts. It was therefore the use of the QTAIM parameters that enabled all intermolecular vibrational modes to be validated. The most stable tricomplex in terms of energy was identified via the strength of the hydrogen bonds, which were modeled as directional and bifurcated.

ChelpG and QTAIM atomic charge and dipole models for the infrared fundamental intensities of the fluorochloromethanes

ChelpG atomic charges and dipoles and the charge–charge flux–dipole flux (CCFDF) model have been used to quantitatively estimate the fundamental infrared intensities of the fluorochloromethanes. Since the ChelpG calculational procedure includes the constraint that the atomic charges and dipoles reproduce the equilibrium dipole moments the model results in accurate intensity values that have a root mean square error of 0.7 km mol−1 compared to those determined directly from the MP2/6-311G++(3d,3p) electronic density and 23.1 km mol−1 relative to the experimental intensities. Although these ChelpG results for total dipole moment derivatives are almost the same as those obtained previously using QTAIM (Quantum Theory of Atoms in Molecules) atomic charges and dipoles in the CCFDF model, their charge, charge flux and dipole flux contributions are completely different. Whereas the contributions calculated using the QTAIM parameters have values following expectations based on electronegativity concepts this is not true for those obtained from the ChelpG parameters. Mean dipole moment derivatives determined from experimental fundamental infrared intensities are compared with the ChelpG and QTAIM atomic charges. Furthermore, Generalized Atomic Polar Tensor Charges (GAPT) are found to need correction for their dynamic contributions if they are to be used as static atomic charges.

Transition from Moderate to Strong Hydrogen Bonds: Its Identification and Physical Bases in the Case of O−H···O Intramolecular Hydrogen Bonds

A systematic investigation aimed at identifying the transition from moderate (M) to strong (S) hydrogen bonds (HBs) and the physical bases of the main geometry-based HB strength classifications reported in the literature has been undertaken using the quantum theory of atoms in molecules (QTAIM). Correlations between the Laplacian of the electron density (rho) at the O...H hydrogen bond critical points (HBCPs), nabla2rhohb, specifically between the more intuitive parameter Lhb = -nabla2rhohb and other QTAIM parameters, have also been explored. The transition from MHBs to SHBs has been identified as the minimum (maximum) in the geometric dependence of Lhb (nabla2rhohb). For O-H...O intramolecular (IM) HBs (including resonance-assisted HBs), the transition is obtained, in a truly remarkable agreement with the existing geometry-based HB strength classifications, when the O...O (O...H) distance is approximately 2.51 ( approximately 1.55) A and when the ratio of the potential energy density (|Vhb|) to the kinetic energy density (Ghb) approximately 1.3. Accordingly, the ranges of the |Vhb|/Ghb ratios are >2-1.3 and 1.3-1 for, respectively, SHBs and MHBs. When the O...O distance is not a genuine indicator of HB strength, the |Vhb|/Ghb ratio and other parameters should be considered to characterize the strength of the HBs. Rationalizations have been provided by way of decoding the physical bases of the transition in terms of the properties of rho and the mechanical characteristics of the interactions that created the HBCPs. Lhb was found to correlate, with a very high degree of fidelity, with at least three parameters (in addition to O...O and O...H distances and the IMHB energy), Vhb/Ghb, Hhb/rhohb (the ratio of the total energy density, Hhb, to the electron density, rhohb (the so-called bond degree parameter)), and deltahb(O,H) (the delocalization index), demonstrating the importance and utility of Lhb (nabla2rhohb) for the study of HB interactions. A new refined energetics-based classification of O-H...O IMHB strengths has been advanced. The approach taken in this investigation can be extended to other HB systems.

Wide spectrum of H⋯H interactions: van der Waals contacts, dihydrogen bonds and covalency

Dihydrogen bonds (DHBs) as a sub-class of H-bond interactions are analyzed in this paper. The results of studies on numerous DHBs obtained at the MP2/6-311++G(d,p) level of approximation are revealed. Different kinds of DHBs are investigated, from weak H⋯H interactions attributed to van der Waals interactions with binding energies amounting to less than 1 kcal/mol, through DHBs of medium strength, to strong interactions possessing characteristics of covalent bonds. The Bader theory as well as the interaction energy components defined within the variation-perturbation method have been applied here to understand the nature of these interactions. Different relationships between the energetic and QTAIM (Quantum Theory of “Atoms in Molecules”) parameters are also analyzed.

Closed shell oxygen–oxygen bonding interaction based on electron density analysis

Electron density analysis within the framework of Quantum Theory of Atoms in Molecules (QTAIM) indicates bond paths between oxygen atoms in open conformers of enol forms of cis-β-diketones. The calculation of atomic energies shows that such a O O interaction in 1,8-naphthalenediol rather than denoting the presence of “non-bonded steric repulsion” can impart as much as 11 kcal/mol (in B3LYP) and 16 kcal/mol (in MP2) of local stabilization to the total energy of the molecule. In addition, QTAIM is also used to characterize these O O interactions. In the studied cases, QTAIM parameters at the BCP of O O bond, including electron density, the Laplacian of the electron density, the energy density and the ellipticity, exhibit the characteristics of closed shell interactions. Delocalization indices between oxygen atoms indicate very little sharing between oxygen atomic basins, which can be interpreted as small O O bond orders.