Atomic Charges Are Measurable Quantum Expectation Values: A Rebuttal of Criticisms of QTAIM Charges

Electronic Force Density Fields: Insights into Partial Bonds, Transition States, and Chemical Structure Evolution

This paper presents the quantum-topological binding approach, in which the electrostatic and total static force density fields, Fes(r) and F ( r ) , together with the electron density gradient field ∇ρ(r), are simultaneously analyzed to elucidate the chemical structure of transition states and the nature of interatomic interactions for semibroken semiformed partial chemical bonds. The approach attributes the discrepancies between the force fields F ( r ) and Fes(r) to the nonclassical electron-electron interaction effects. The internuclear gap between the zero-flux boundaries of Fes(r) and ∇ρ(r) indicates the interatomic charge transfer phenomenon (ICT) that occurs upon the formation of a system from free atoms. Concomitantly, the mismatch of the zero-flux surfaces defined in - F ( r ) and ∇ρ(r) can be interpreted as a phenomenon of the electron-transfer-induced quantum chemical response (QCR), which originates from the electron exchange correlation. Our study permits the assertion of parallels between partial bonds and noncovalent interactions, as both typically exhibit incomplete QCRs, indicating the partial electron sharing of the transferred density. The changes in atomic and pseudoatomic charges are employed to describe the evolution of the chemical structure upon the substitution reaction. It is observed that the acquired difference in the actual atomic electronegativity causes polarization upon the heterolytic breaking of virtually nonpolar bonds. It is further proposed that the proximity of closely related stationary states along the reaction path on a potential energy hypersurface implies their similarity in the manifestation of the ICT and sympathetic QCR. Furthermore, the involvement of an electron pair in a partial bond facilitates its delocalization through the attraction by the static forces F ( r ) and Fes(r) to a neighboring nucleus and through the smearing by the Pauli kinetic force FP(r).

Toward the Chemical Structure of Diborane: Electronic Force Density Fields, Effective Electronegativity, and Internuclear Turning Surface Properties

The chemical structure of diborane was elucidated through the superposition of the vector fields of the electron density gradient ∇ρ(r), the electrostatic force Fes(r), and the kinetic force Fk(r), together with the analysis of the cumulative charges of the atoms and pseudoatoms delimited in the aforementioned fields. It was proposed that the Fk-pseudoatomic charge could be employed as a metric for quantifying the ionic component of a related atomic charge. The electron permeability across an internuclear turning surface─specifically, the zero-flux surface in Fk(r)─was characterized by probing it through mapping the total static potential φem(r). The conceptualization of post hoc electronegativity was presented for consideration. Our analysis revealed that the ordinary B-H and bent B-μ-H bonds in diborane demonstrate the polar covalent character with minor contributions of the ionic component. The former bond exhibits a greater electron permeability through the internuclear turning surface, indicating a stronger tendency for electron sharing between the corresponding nucleus-dominated regions. The electron density accumulation along the bent B-μ-H bond path diverges from the minimum action trajectories of the forces Fes(r) and Fk(r). This phenomenon can be associated with the structural strain within the angled, three-center two-electron bonding B-μ-H-B. The internuclear B···B paths were identified in Fes(r) and Fk(r), in contrast to ∇ρ(r). This fact, in conjunction with a pronounced electron permeability through the mutual turning surface between the two boron nuclei, implies a certain degree of electron exchange between the boron-dominated pseudoatomic regions. Furthermore, the anomalous [B-]H···μ-H intermolecular polar interactions were described between the strongly negatively charged hydrogen atoms in the monoclinic crystalline β-phase of diborane. In fact, the ionic contributions to the charges of the hydrogen atoms are shown to be relatively small.

PACMAN: A Robust Partial Atomic Charge Predicter for Nanoporous Materials Based on Crystal Graph Convolution Networks

We report a fast and easy method (PACMAN) to assign partial atomic charges on metal-organic framework (MOF) and covalent-organic framework (COF) crystal structures based on graph convolution networks (GCNs) trained on >1.8 million high-fidelity partial atomic charge data obtained from the Quantum Metal-Organic Framework (QMOF) database. The developed model shows outstanding performance, achieving a mean absolute error (MAE) of 0.0055 e (test set performance) while maintaining consistency with DDEC6, Bader, and CM5 charges across diverse chemistry and topologies of MOFs and COFs. We find that the new method accurately assigns partial atomic charges for ion-containing nanoporous materials, which has not been possible in previous machine learning (ML) models. Grand canonical Monte Carlo (GCMC) simulation results for CO2 and N2 uptakes and the Widom particle insertion calculation for Henry's law constant of water results based on PACMAN and the original DDEC6 charges show excellent agreements compared to other ML models reported in the literature. The runtime analysis of the new method demonstrates that the partial atomic charges of MOF and COF structures with up to 500 atoms can be obtained in less than 10 s. An easy-to-use web interface has been developed to facilitate the adoption of the developed model.

Chemical bonding in Uranium-based materials: A local vibrational mode case study of Cs 2 UO 2 Cl 4 and UCl 4 crystals

The Local Vibrational Mode Analysis, initially applied to diverse molecular systems, was extended to periodic systems in 2019. This work introduces an enhanced version of the LModeA software, specifically designed for the comprehensive analysis of two and three-dimensional periodic structures. Notably, a novel interface with the Crystal package was established, enabling a seamless transition from molecules to periodic systems using a unified methodology. Two distinct sets of uranium-based systems were investigated: (i) the evolution of the Uranyl ion (UO  2 2 + ) traced from its molecular configurations to the solid state, exemplified by Cs  2 UO  2 Cl  4 and (ii) Uranium tetrachloride (UCl  4 ) in both its molecular and crystalline forms. The primary focus was on exploring the impact of crystal packing on key properties, including IR and Raman spectra, structural parameters, and an in-depth assessment of bond strength utilizing local mode perspectives. This work not only demonstrates the adaptability and versatility of LModeA for periodic systems but also highlights its potential for gaining insights into complex materials and aiding in the design of new materials through fine-tuning.

Symmetry-Constrained Properties Behave Differently for 2D or 3D Structures under the Same Point Group

In chemistry and physics, two molecules belonging to the same point group are expected to behave similarly regarding various properties, following their character tables. Here, we show that the derivative of the dipole moment with respect to the normal coordinate of vibration might show different symmetry constraints if the molecule is planar, even if these molecules belong to the same point group. Examples of pairs of molecules featuring these conditions are presented. These findings open a new path toward a much deeper understanding of how 2D materials behave so differently compared to 3D materials featuring the very same atoms and arrangements (graphene and graphite, for example); chemists and physicists dealing with 2D materials could benefit from looking more deeply into pure mathematical relations that might be governing 2D systems in a different way when compared to 3D systems. The aid from mathematicians is welcomed.

Does the radical GPRI strongly depend on the population scheme? A comparative study to predict radical attack on unsaturated molecules with the radical general-purpose reactivity indicator

The reactivity of 22 unsaturated molecules undergoing attack by a methyl radical (⋅CH3) have been elucidated using the condensed radical general-purpose reactivity indicator (condensed radical GPRI) appropriate for relatively nucleophilic or electrophilic molecules. Using the appropriate radical GPRI equation for electrophilic attack or nucleophilic radical attack, seven different population schemes were used to assign the most reactive atoms in each of the 22 molecules. The results show that the condensed radical GPRI is sensitive to the population scheme chosen, but less sensitive than the radical Fukui function. Therefore, the reliability of these methods depends on the population scheme. Our investigation indicates that the condensed radical GPRI is most accurate in predicting the dominant products of the methyl radical addition reactions on a variety of unsaturated molecules when the Hirshfeld, Merz-Singh-Kollman, or Voronoi deformation density population schemes are used. Furthermore, for all populations schemes in the majority of instances where the radical Fukui function failed the radical GPRI was able to identify the most reactive atom under certain reactivity conditions.

On the sensitivity of computed partial charges toward basis set and (exchange-)correlation treatment

Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [Cho et al., ChemPhysChem 21, 688-696 (2020)], we showed that these can be reduced to at most three 'principal components of ionicity'. The present study addressed the dependence of computed partial charges q on 1-particle basis set and (for WFT methods) n -particle correlation treatment or (for DFT methods) exchange-correlation functional, for several representative partial charge definitions such as QTAIM, Hirshfeld, Hirshfeld-I, HLY (electrostatic), NPA, and GAPT. Our findings show that semi-empirical double hybrids can closely approach the CCSD(T) 'gold standard' for this property. In fact, owing to an error compensation in MP2, CCSD partial charges are further away from CCSD(T) than is MP2. The nonlocal correlation is important, especially when there is a substantial amount of nonlocal exchange. Employing range separation proves to be "mostly" not advantageous, while global hybrids perform optimally for 20%-30% Hartree-Fock exchange across all charge types. Basis set convergence analysis shows that an augmented triple-zeta heavy-aug-cc-pV(T+d)Z basis set or a partially augmented jun-cc-pV(T+d)Z basis set is sufficient for Hirshfeld, Hirshfeld-I, HLY, and GAPT charges. In contrast, QTAIM and NPA display slower basis set convergence. It is noteworthy that for both NPA and QTAIM, HF exhibits markedly slower basis set convergence than the correlation components of MP2 and CCSD. Triples corrections in CCSD(T), denoted as CCSD(T)-CCSD, exhibit even faster basis set convergence.

Outstanding Properties of the Hydration Shell around β-d-Glucose: A Computational Study

Ab initio molecular dynamics (AIMD) simulations have been performed on aqueous solutions of four simple sugars, α-d-glucose, β-d-glucose, α-d-mannose, and α-d-galactose. Hydrogen-bonding (HB) properties, such as the number of donor- and acceptor-type HB-s, and the lengths and strengths of hydrogen bonds between sugar and water molecules, have been determined. Related electronic properties, such as the dipole moments of water molecules and partial charges of the sugar O atoms, have also been calculated. The hydrophilic and hydrophobic shells were characterized by means of spatial distribution functions. β-d-Glucose was found to form the highest number of hydrophilic and the smallest number of hydrophobic connections to neighboring water molecules. The average sugar-water H-bond length was the shortest for β-d-glucose, which suggests that these are the strongest such H-bonds. Furthermore, β-d-glucose appears to stand out in terms of the symmetry properties of both its hydrophilic and hydrophobic hydration shells. In summary, in all aspects considered here, there seems to be a correlation between the distinct characteristics of β-d-glucose reported here and its outstanding solubility in water. Admittedly, our findings represent only some of the important factors that influence the solubility.

An Unsupervised Machine Learning Approach for the Automatic Construction of Local Chemical Descriptors

Condensing the many physical variables defining a chemical system into a fixed-size array poses a significant challenge in the development of chemical Machine Learning (ML). Atom Centered Symmetry Functions (ACSFs) offer an intuitive featurization approach by means of a tedious and labor-intensive selection of tunable parameters. In this work, we implement an unsupervised ML strategy relying on a Gaussian Mixture Model (GMM) to automatically optimize the ACSF parameters. GMMs effortlessly decompose the vastness of the chemical and conformational spaces into well-defined radial and angular clusters, which are then used to build tailor-made ACSFs. The unsupervised exploration of the space has demonstrated general applicability across a diverse range of systems, spanning from various unimolecular landscapes to heterogeneous databases. The impact of the sampling technique and temperature on space exploration is also addressed, highlighting the particularly advantageous role of high-temperature Molecular Dynamics (MD) simulations. The reliability of the resulting features is assessed through the estimation of the atomic charges of a prototypical capped amino acid and a heterogeneous collection of CHON molecules. The automatically constructed ACSFs serve as high-quality descriptors, consistently yielding typical prediction errors below 0.010 electrons bound for the reported atomic charges. Altering the spatial distribution of the functions with respect to the cluster highlights the critical role of symmetry rupture in achieving significantly improved features. More specifically, using two separate functions to describe the lower and upper tails of the cluster results in the best performing models with errors as low as 0.006 electrons. Finally, the effectiveness of finely tuned features was checked across different architectures, unveiling the superior performance of Gaussian Process (GP) models over Feed Forward Neural Networks (FFNNs), particularly in low-data regimes, with nearly a 2-fold increase in prediction quality. Altogether, this approach paves the way toward an easier construction of local chemical descriptors, while providing valuable insights into how radial and angular spaces should be mapped. Finally, this work opens the possibility of encoding many-body information beyond angular terms into upcoming ML features.

First-principles study of multifunctional Mn2B3 materials with high hardness and ferromagnetism

Transition metal boride TM2B3 is widely studied in the field of physics and materials science. However, Mn2B3 has not been found in Mn-B systems so far. Mn2B3 undergoes phase transitions from Cmcm (0-28 GPa) to C2/m (28-80 GPa) and finally to C2/c (80-200 GPa) under pressure. Among these stable phases, Cmcm- and C2/m-Mn2B3s comprise six-membered boron rings and C2/c-Mn2B3 has wavy boron chains. They all have good mechanical properties and can become potential multifunctional materials. The strong B-B covalent bonding is mainly responsible for the structural stability and hardness. Comparison of the hardness of the five TM2B3s with different bonding strengths of TM-B and B-B bonds reveals a nonlinear change in the hardness. According to the Stoner model, these structures possess ferromagnetism, and the corresponding magnetic moments are almost the same as those of GGA and GGA + U (U = 3.9 eV, J = 1 eV).

A Charge-Charge Flux-Dipole Flux Analysis of Simple Molecular Systems with Halogen Bonds

The presence of halogen bonds (R-X···B; R = substituent group, X = halogen, and B = Lewis base) provides quite amazing molecular systems for electronic structure investigations, presenting unique characteristics of fundamental relevance to supramolecular chemistry among other areas. Here, we use a double-hybrid approach from Density Functional Theory and triple-ζ basis sets augmented with diffuse functions (B2PLYP/def2-TZVPD) to deal with a large group of simple molecular systems containing halogen bonds (XBs), focusing on geometrical structures, binding energies, harmonic vibrational frequencies, and fundamental infrared intensities. Next, the electron densities and their variations on vibrations are carefully studied with the Quantum Theory of Atoms in Molecules (QTAIM) formalism and the charge-charge flux-dipole flux (CCFDF) model. We notice that the R-X stretching mode usually shows vibrational frequency decrements and infrared intensifications during the XB formation. Such features were also observed in hydrogen bonds, although the explanation for the band strengthening is different. Surprisingly, the most important contribution to these intensity increments due to complexation is now the interaction term between the charge flux and dipole flux (CF × DF). Thus, the use of atomic dipoles is mandatory to fully understand this phenomenon. In fact, the huge charge flux contributions to changes in dipole moment derivatives of R-X stretchings on halogen bonding are no longer accompanied by opposite variations of similar magnitudes in polarizations described by atomic dipole fluxes, which provided nearly unaltered values during the XB formation. Thus, the electronic charge flux direction change that takes place in complexes (from B to R) now reinforces dipole moment derivative terms from such atomic polarizations (mainly from the X atom). This intermolecular charge flux seems to be responsible for the unusual features noticed in the R-X stretching mode with the CCDDF/QTAIM model.

Synergistic Charge Transfer Effect in Ferrous Heme-CO Bonding within Cytochrome P450

We conducted ab initio valence bond (VB) calculations employing the valence bond self-consistent field (VBSCF) and breathing orbital valence bond (BOVB) methods to investigate the nature of the coordination bonding between ferrous heme and carbon monoxide (CO) within cytochrome P450. These calculations revealed the significant influence exerted by both proximal and equatorial ligands on the π-backdonation effect from the heme to the CO. Moreover, our VB calculations unveiled a phenomenon of synergistic charge transfer (sCT). In the case of ferrous heme-CO bonding, the significant stabilization in this sCT arises from cooperative resonance between the VB structures associated with σ donation and π backdonation. Unlike many other ligands, CO possesses the unique ability to establish two mutually perpendicular π-backdonation orbital interaction pairs, leading to an intensified stabilization attributed to σ-π resonance. Furthermore, while of a smaller energy magnitude, sCT due to one π-π pair is also present, contributing to the differential stabilization of ferrous heme-CO bonding.

H2O2(s) and H2O2·2H2O(s) crystals compared with ices: DFT functional assessment and D3 analysis

The H2O and H2O2 molecules resemble each other in a multitude of ways as has been noted in the literature. Here, we present density functional theory (DFT) calculations for the H2O2(s) and H2O2·2H2O(s) crystals and make selected comparisons with ice polymorphs. The performance of a number of dispersion-corrected density functionals-both self-consistent and a posteriori ones-are assessed, and we give special attention to the D3 correction and its effects. The D3 correction to the lattice energies is large: for H2O2(s) the D3 correction constitutes about 25% of the lattice energy using PBE, much more for RPBE, much less for SCAN, and it primarily arises from non-H-bonded interactions out to about 5 Å.The large D3 corrections to the lattice energies are likely a consequence of several effects: correction for missing dispersion interaction, the ability of D3 to capture and correct various other kinds of limitations built into the underlying DFT functionals, and finally some degree of cell-contraction-induced polarization enhancement. We find that the overall best-performing functionals of the twelve examined are optPBEvdW and RPBE-D3. Comparisons with DFT assessments for ices in the literature show that where the same methods have been used, the assessments largely agree.

Exploring adsorption behavior of sulfur and nitrogen compounds on transition metal-doped Cu(100) surfaces: insights from DFT and MD simulations

We conducted an extensive investigation using density functional theory (DFT) calculations and ReaxFF molecular dynamics (MD) simulations to elucidate the mechanisms of desulfurization and denitrogenation on Cu(100) surfaces. This study encompassed both pristine surfaces and those modified with Pt or Rh transition metals. Our primary objective was to gain a deep understanding of the adsorption behavior of thiophene (C4H4S) and pyridine (C5H5N) molecules on stepped Cu(100) surfaces, which serve as models for sulfur and nitrogen compounds. We systematically explored the interplay among water, adsorption efficiency, and surface regeneration capabilities. Using DFT, we thoroughly examined various aspects, including interaction energies, charge transfers, changes in electron density, and alterations in work function upon molecule adsorption. Notably, we observed a decrease in the interaction energy of thiophene, whereas that of pyridine increased when adsorbed on Pt/Rh-doped surfaces compared to pristine ones. Thiophene adsorption reduced the work function, potentially enhancing detectability, without causing inhibitory effects on any surface. Stepped Cu(100) surfaces demonstrated a strong affinity for thiophene, exhibiting an energy difference of approximately 86 kJ mol-1. However, this trend reversed on doped surfaces, where pyridine displayed stronger adsorption than thiophene, resulting in energy differences of around 123 kJ mol-1 and 62 kJ mol-1 on Pt-Cu and Rh-Cu surfaces, respectively. Moreover, our investigation highlighted the regeneration capacity of these surfaces, indicating that all surfaces can be considered promising candidates for desulfurization, while only Cu and Pt-Cu surfaces were found to be suitable for denitrogenation. Furthermore, results from MD simulations in combination with potential of mean force (PMF) simulations at 300 K, aligned with DFT calculations, confirmed the adsorption configurations of pyridine and thiophene. This analysis demonstrated the competitive advantage of thiophene over pyridine in adsorption and highlighted the inhibitory effect of water on pyridine adsorption on the Cu(100) surface.

Bidirectional Charge Transfer at the Heme Iron in Reversible and Quasi-irreversible Cytochrome P450 Inhibition

The coordination bonding between inhibitor ligands and heme iron plays a critical role in disrupting the essential catalytic functions of cytochrome P450 enzymes (P450s). Despite its intrinsic importance and consequential implications for human health, our current understanding of coordination bonding in P450 inhibition remains limited. To address this knowledge gap, we conducted a systematic theoretical analysis of the complexes between a ferric or a ferrous heme model and representative inhibitor ligands. Specifically, we evaluated the charge-transfer (CT) effect within these complexes by employing a series of theoretical methods based on density functional theory (DFT). Through a comprehensive analysis, we unveiled the relative significance of ligand-to-heme forward CT in the ferric and ferrous complexes of reversible inhibitors. In contrast, backward CT dominates over forward CT in the ferrous heme complexes of quasi-irreversible inhibitors. Further analysis using the compact frontier orbital method underscores the elevated electron-accepting abilities of quasi-irreversible inhibitors for π backdonation, which greatly amplifies their binding affinity for the ferrous heme. This study sheds light on the intricate mechanisms underlying P450 inhibition and provides valuable insights for future inhibitor design and development.

Streamlining and Optimizing Strategies of Electrostatic Parameterization

Accurate characterization of electrostatic interactions is crucial in molecular simulation. Various methods and programs have been developed to obtain electrostatic parameters for additive or polarizable models to replicate electrostatic properties obtained from experimental measurements or theoretical calculations. Electrostatic potentials (ESPs), a set of physically well-defined observables from quantum mechanical (QM) calculations, are well suited for optimization efforts due to the ease of collecting a large amount of conformation-dependent data. However, a reliable set of QM ESP computed at an appropriate level of theory and atomic basis set is necessary. In addition, despite the recent development of the PyRESP program for electrostatic parameterizations of induced dipole-polarizable models, the time-consuming and error-prone input file preparation process has limited the widespread use of these protocols. This work aims to comprehensively evaluate the quality of QM ESPs derived by eight methods, including wave function methods such as Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled cluster-singles and doubles (CCSD), as well as five hybrid density functional theory (DFT) methods, used in conjunction with 13 different basis sets. The highest theory levels CCSD/aug-cc-pV5Z (a5z) and MP2/aug-cc-pV5Z (a5z) were selected as benchmark data over two homemade data sets. The results show that the hybrid DFT method, ωB97X-D, combined with the aug-cc-pVTZ (a3z) basis set, performs well in reproducing ESPs while taking both accuracy and efficiency into consideration. Moreover, a flexible and user-friendly program called PyRESP_GEN was developed to streamline input file preparation. The restraining strengths, along with strategies for polarizable Gaussian multipole (pGM) model parameterizations, were also optimized. These findings and the program presented in this work facilitate the development and application of induced dipole-polarizable models, such as pGM models, for molecular simulations of both chemical and biological significance.

Anomalous π-backbonding in complexes between B(SiR3)3 and N2: catalytic activation and breaking of scaling relations

Chemical transformations of molecular nitrogen (N2), including the nitrogen reduction reaction (NRR), are difficult to catalyze because of the weak Lewis basicity of N2. In this study, it is shown that Lewis acids of the types B(SiR3)3 and B(GeR3)3 bind N2 and CO with anomalously short and strong B-N or B-C bonds. B(SiH3)3·N2 has a B-N bond length of 1.48 Å and a complexation enthalpy of -15.9 kcal mol-1 at the M06-2X/jun-cc-pVTZ level. The selective binding enhancement of N2 and CO is due to π-backbonding from Lewis acid to Lewis base, as demonstrated by orbital analysis and density difference plots. The π-backbonding is found to be a consequence of constructive orbital interactions between the diffuse and highly polarizable B-Si and B-Ge bond regions and the π and π* orbitals of N2. This interaction is strengthened by electron donating substituents on Si or Ge. The π-backbonding interaction is predicted to activate N2 for chemical transformation and reduction, as it decreases the electron density and increases the length of the N-N bond. The binding of N2 and CO by the B(SiR3)3 and B(GeR3)3 types of Lewis acids also has a strong σ-bonding contribution. The relatively high σ-bond strength is connected to the highly positive surface electrostatic potential [VS(r)] above the B atom in the tetragonal binding conformation, but the σ-bonding also has a significant coordinate covalent (dative) contribution. Electron withdrawing substituents increase the potential and the σ-bond strength, but favor the binding of regular Lewis acids, such as NH3 and F-, more strongly than binding of N2 and CO. Molecules of the types B(SiR3)3 and B(GeR3)3 are chemically labile and difficult to synthesize. Heterogenous catalysts with the wanted B(Si-)3 or B(Ge-)3 bonding motif may be prepared by boron doping of nanostructured silicon or germanium compounds. B-doped and hydrogenated silicene is found to have promising properties as catalyst for the electrochemical NRR.

In silico characterization of nanoparticles

Nanoparticles (NPs) make for intriguing heterogeneous catalysts due to their large active surface area and excellent and often size-dependent catalytic properties that emerge from a multitude of chemically different surface reaction sites. NP catalysts are, in principle, also highly tunable: even small changes to the NP size or surface facet composition, doping with heteroatoms, or changes of the supporting material can significantly alter their physicochemical properties. Because synthesis of size- and shape-controlled NP catalysts is challenging, the ability to computationally predict the most favorable NP structures for a catalytic reaction of interest is an in-demand skill that can help accelerate and streamline the material optimization process. Fundamentally, simulations of NP model systems present unique challenges to computational scientists. Not only must considerable methodological hurdles be overcome in performing calculations with hundreds to thousands of atoms while retaining appropriate accuracy to be able to probe the desired properties. Also, the data generated by simulations of NPs are typically more complex than data from simulations of, for example, single crystal surface models, and therefore often require different data analysis strategies. To this end, the present work aims to review analytical methods and data analysis strategies that have proven useful in extracting thermodynamic trends from NP simulations.

The inorganic chemistry of the cobalt corrinoids - an update

The inorganic chemistry of the cobalt corrinoids, derivatives of vitamin B₁₂, is reviewed, with particular emphasis on equilibrium constants for, and kinetics of, their axial ligand substitution reactions. The role the corrin ligand plays in controlling and modifying the properties of the metal ion is emphasised. Other aspects of the chemistry of these compounds, including their structure, corrinoid complexes with metals other than cobalt, the redox chemistry of the cobalt corrinoids and their chemical redox reactions, and their photochemistry are discussed. Their role as catalysts in non-biological reactions and aspects of their organometallic chemistry are briefly mentioned. Particular mention is made of the role that computational methods - and especially DFT calculations - have played in developing our understanding of the inorganic chemistry of these compounds. A brief overview of the biological chemistry of the B₁₂-dependent enzymes is also given for the reader's convenience.

On the quest for a molecular vibration whose absolute intensity is described solely by fluctuations of atomic dipoles: Can we find it?

The conditions for a molecular vibration to be active in the infrared spectrum while its absolute intensity is described solely by fluctuations of atomic dipoles are presented. A quick recipe of features of such a system is presented, to guide the seek for it. If such a system can be found, it will then be proved that population analyses based solely on a point-charge approximation are unrealistic as they cannot properly describe this intensity, a real, measurable, unambiguous property.

Infrared intensities of [Formula: see text]: a true challenge for DFT methods

Absolute infrared intensities of [Formula: see text] were evaluated with a great variety of DFT and ab initio methods and basis sets. It is shown that the intensities calculated by different levels of theory may not agree with each other even in the qualitative (weak/strong) sense. Geometrical parameters, as well as net atomic charges evaluated from multiple partition schemes, did not vary as much as the intensities and thus cannot explain the tremendous differences found for the latter. As there are no experimental estimates for the intensities to guide the theoretical evaluation, deciding on the best level of theory is reduced to comparisons between the different DFT methods and QCISD or CCSD, believed to be the best theoretical estimates in the set. The differences found among the various DFT methods suggest the development of new methods, instead of converging to a focal point, is rather diverging.

Unavoidable failure of point charge descriptions of electronic density changes for out-of-plane distortions

Population analyses based on point charge approximations accurately estimating the equilibrium dipole moment will systematically fail when predicting infrared intensities of out-of-plane vibrations of planar molecules, whereas models based on both charges and dipoles will always succeed. It is not a matter of how the model is devised but rather how many degrees of freedom are available for the calculation. Population analyses based on point charges are very limited in terms of the amount of meaningful chemical information they provide, whereas models employing both atomic charges and atomic dipoles should be preferred for molecular distortions. A good model should be able to correctly describe not only static, equilibrium structures but also distorted geometries in order to correctly assess information from vibrating molecules. The limitations of point charge models also hold for distortions much larger than those encountered vibrationally.

NNAIMQ: A neural network model for predicting QTAIM charges

Atomic charges provide crucial information about the electronic structure of a molecular system. Among the different definitions of these descriptors, the one proposed by the Quantum Theory of Atoms in Molecules (QTAIM) is particularly attractive given its invariance against orbital transformations although the computational cost associated with their calculation limits its applicability. Given that Machine Learning (ML) techniques have been shown to accelerate orders of magnitude the computation of a number of quantum mechanical observables, in this work, we take advantage of ML knowledge to develop an intuitive and fast neural network model (NNAIMQ) for the computation of QTAIM charges for C, H, O, and N atoms with high accuracy. Our model has been trained and tested using data from quantum chemical calculations in more than 45 000 molecular environments of the near-equilibrium CHON chemical space. The reliability and performance of NNAIMQ have been analyzed in a variety of scenarios, from equilibrium geometries to molecular dynamics simulations. Altogether, NNAIMQ yields remarkably small prediction errors, well below the 0.03 electron limit in the general case, while accelerating the calculation of QTAIM charges by several orders of magnitude.

Interaction-determined extraction capacity between rare earth ions and extractants: taking lanthanum and lutetium as models through theoretical calculations

Extractant plays an important role in the separation and purification of rare earth elements (REEs), whereas, extraction performance is the most effective tactic to evaluate whether an extractant is complete...

High electron affinity triggered by lithium coordination: quasi-chalcogen properties of Li2Sn8Be

This work puts forward an unusual but rational strategy to design superatoms mimicking the properties of group VIA elements. A stable dianion with closo-configuration, namely Li2Sn8Be2−, has been obtained by...

Attosecond charge migration following oxygen K-shell ionization in DNA bases and base pairs

Core ionization of DNA begins a cascade of events which could lead to cellular inactivation or death. The created core-hole following an impulse inner-shell ionization of molecules naturally decays in the auger timescale. We simulated charge migration (CM) phenomena following an impulsive core ionization of individual DNA bases at the oxygen K-edge which occurs before Auger decay of the oxygen. Our approach is based on real-time time dependent density functional theory (RT-TDDFT). It is shown that the pronounced hole fluctuation observed around bonds of the initial core-hole results in various valence orbital migrations. Also, the same photo-core-ionized dynamics is studied for the related base pairs. We investigate the role of base pairing and H-bonding interactions in the attosecond CM dynamics. In particular, the creation of a core-hole in the oxygen involved in H-bonding leads to an enhancement of charge migration relative to the respective single bases. Importantly, the hole oscillation of the adenine-thymine base pair upon creation of a core-hole at the oxygen, which does not contribute to the donor-acceptor interactions (not H-bonded), decreases compared to the single thymine base. Understanding the detailed dynamics of the localized core-hole initiating CM process would open the way for chemically controlling DNA damage/repair in the future.

Are "GAPT Charges" Really Just Charges?

Generalized atomic polar tensor (GAPT) has turned into a very popular charge model since it was proposed three decades ago. During this period, several works aiming to compare different partition schemes have included it among their tested models. Nonetheless, GAPT exhibits a set of unique features that prevent it from being directly comparable to "standard" partition schemes. We take this opportunity to explore some of these features, mainly related to the need of evaluating multiple geometries and the dynamic character of GAPT, and show how to obtain the static and dynamic parts of GAPT from any static charge model in the literature. We also present a conceptual evaluation of charge models that aims to explain, at least partially, why GAPT and quantum theory of atoms in molecules (QTAIM) charges are strongly correlated with one another, even though they seem to be constructed under very different frameworks. Similar to GAPT, infrared charges (also derived from atomic polar tensors of planar molecules) are also shown to provide an improved interpretation if they are described as a combination of static charges and changing atomic dipoles rather than just experimental static atomic charges.

Cooperativity and Anticooperativity in Ion-Water Interactions: Implications for the Aqueous Solvation of Ions

Non-additive effects in hydrogen bonds (HB) take place as a consequence of electronic charge transfers. Therefore, it is natural to expect cooperativity and anticooperativity in ion-water interactions. Nevertheless, investigations on this matter are scarce. This paper addresses the interactions of (i) the cations Li⁺ , Na⁺ , K⁺ , Be²⁺ , Mg²⁺ , and Ca²⁺ together with (ii) the anions F^- , Cl^- , Br^- , NO₃ ^- and SO₄ ^2- with water clusters (H₂ O)_n , n=1-8, and the effects of these ions on the HBs within the complete molecular adducts. We used quantum chemical topology tools, specifically the quantum theory of atoms in molecules and the interacting quantum atoms energy partition to investigate non-additive effects among the interactions studied herein. Our results show a decrease on the interaction energy between ions and the first neighbouring water molecules with an increment of the coordination number. We also found strong cooperative effects in the interplay between HBs and ion-dipole interactions within the studied systems. Such cooperativity affects considerably the interactions among ions with their first and second solvation shells in aqueous environments. Overall, we believe this article provides valuable information about how ion-dipole contacts interact with each other and how they relate to other interactions, such as HBs, in the framework of non-additive effects in aqueous media.

W-RESP: Well-Restrained Electrostatic Potential-Derived Charges. Revisiting the Charge Derivation Model

Representation of electrostatic interactions by a Coulombic pairwise potential between atom-centered partial charges is a fundamental and crucial part of empirical force fields used in classical molecular dynamics simulations. The broad success of the AMBER force-field family originates mainly from the restrained electrostatic potential (RESP) charge model, which derives partial charges to reproduce the electrostatic field around the molecules. However, the description of the electrostatic potential around molecules by standard RESP may be biased for some types of molecules. In this study, we modified the RESP charge derivation model to improve its description of the electrostatic potential around molecules and thus electrostatic interactions in the force field. In particular, we reoptimized the atomic radii for definition of the grid points around the molecule, redesigned the restraining scheme, and included extra point (EP) charges. The RESP fitting was significantly improved for aromatic heterocyclic molecules. Thus, the suggested W-RESP(-EP) charge derivation model shows some potential for improving the performance of the nucleic acid force fields, for which the poor description of nonbonded interactions, such as the underestimated stability of base pairing, is well-established. We also report some preliminary simulation tests (around 1 ms of simulation data) on A-RNA duplexes, tetranucleotides, and tetraloops. The simulations reveal no adverse effects, while the description of base-pairing interactions might be improved. The new charges can thus be used in future attempts to improve the nucleic acid simulation force fields, in combination with reparametrization of the other terms.

A New Candidate in Polyanionic Compounds for a Potassium-Ion Battery Cathode: KTiOPO4

First-principles computations were performed to investigate the performance of KTiOPO₄ (KTP) as a cathode material for potassium-ion batteries (PIBs), including the stability and electronic properties of depotassiated structures and mechanisms of K deintercalation and diffusion. As depotassiation proceeds, oxygen hole polarons are produced, and there are not peroxides or superoxides formed after deep depotassiation. The anionic oxygen redox in KTP provides a voltage vs K/K⁺ over 4 V by the PBE+U method and over 5 V with the more reliable HSE06 hybrid functional. When all K in KTP is removed, the calculated volume compression is only 1.528%. The AIMD simulations at 300 K for TiOPO₄ verify its thermal stability. The PBE+U calculations predict a low ion diffusion barrier of 0.29 eV in bulk KTP, indicating a good charge-discharge rate for KTP as a cathode for PIBs. All of the calculated results indicate that KTP can be a promising cathode material for PIBs.

Fast and Accurate Machine Learning Strategy for Calculating Partial Atomic Charges in Metal-Organic Frameworks

Computational high-throughput screening using molecular simulations is a powerful tool for identifying top-performing metal-organic frameworks (MOFs) for gas storage and separation applications. Accurate partial atomic charges are often required to model the electrostatic interactions between the MOF and the adsorbate, especially when the adsorption involves molecules with dipole or quadrupole moments such as water and CO₂. Although ab initio methods can be used to calculate accurate partial atomic charges, these methods are impractical for screening large material databases because of the high computational cost. We developed a random forest machine learning model to predict the partial atomic charges in MOFs using a small yet meaningful set of features that represent both the elemental properties and the local environment of each atom. The model was trained and tested on a collection of about 320 000 density-derived electrostatic and chemical (DDEC) atomic charges calculated on a subset of the Computation-Ready Experimental Metal-Organic Framework (CoRE MOF-2019) database and separately on charge model 5 (CM5) charges. The model predicts accurate atomic charges for MOFs at a fraction of the computational cost of periodic density functional theory (DFT) and is found to be transferable to other porous molecular crystals and zeolites. A strong correlation is observed between the partial atomic charge and the average electronegativity difference between the central atom and its bonded neighbors.

Analysis and visualization of energy densities. II. Insights from linear-response time-dependent density functional theory calculations

Inspired by the analysis of Kohn-Sham energy densities by Nakai and coworkers, we extended the energy density analysis to linear-response time-dependent density functional theory (LR-TDDFT) calculations. Using ethylene-tetrafluoroethylene and oxyluciferin-water complexes as examples, distinctive distribution patterns were demonstrated for the excitation energy densities of local excitations (within a molecular fragment) and charge-transfer excitations (between molecular fragments). It also provided a simple way to compute the effective energy of both hot carriers (particle and hole) from charge-transfer excitations via an integration of the excitation energy density over the donor and acceptor grid points.

Unveiling the potential of superalkali cation Li3+ for capturing nitrogen

The potential of the superalkali cation Li3+ for capturing N2 and its behavior in gaseous nitrogen have been theoretically studied at the MP2/6-311+G(d) level. The evolution of structures and stability of the Li3+(N2)n (n = 1-7) complexes shows that the N2 molecules tend to bind to different vertices of the Li3+ core, and that Li3+ might have the capacity to capture up to twelve nitrogen molecules in the first coordination shell. Based on natural population and molecular orbital analyses, Li3+ keeps its superatom identity in the lowest-lying Li3+(N2)n (n = 1-4) complexes. The change in the Gibbs free energies of possible fragmentation channels also indicates the thermodynamic stability of Li3+ in the (N2)n clusters when n ≤ 4. Different from the case of Li3+(H2O)n, where the electrostatic interaction is dominant, the electrostatic and polarization components are found to make nearly equal contributions to Li3+(N2)n complex formation. In addition, it can be concluded that the superalkali cation Li3+ surpasses heavy alkali metal cations in capturing N2 molecules, since it has a larger binding energy with N2 than Na+ and K+ ions.

On single-electron magnesium bonding formation and the effect of methyl substitution

The complexes formed between MgX₂ (X = F, H) molecules and alkyl radicals Y [Y = CH₃, CH₂CH₃, CH(CH₃)₂, and C(CH₃)₃] have been characterized by using quantum chemical methods. The binding distance in all cases is less than the sum of vdW radii of Mg and C, indicating the formation of a non-covalent interaction, namely single-electron magnesium bond. Energy decomposition analysis reveals that electrostatic and polarization contributions are the major components responsible for the stability of the studied complexes. According to interaction energy, atoms in molecules, and independent gradient model analyses, methyl substitution on electron donor Y imposes a positive effect on its complexation with MgX₂. When compared with other nonbonded interactions, the single-electron magnesium bond is found to have strength comparable to those of the single-electron beryllium bond and π-magnesium bond.

The complexes formed between MgX₂ (X = F, H) molecules and alkyl radicals Y [Y = CH₃, CH₂CH₃, CH(CH₃)₂, and C(CH₃)₃] have been characterized by using quantum chemical methods.

Rate-Limiting Steps in the Intramolecular C-H Activation of Ruthenium N-Heterocyclic Carbene Complexes

Ruthenium (II) complexes with N-heterocyclic carbenes (NHC) are commonly used as efficient catalysts in hydrogenation of olefins with simultaneous intramolecular C-H activation. Using the DFT approach, we have investigated the entire hydrogenation reaction pathway for four new potential catalysts and ethylene, a model substrate. Our calculations imply that the dissociation of phosphine is the rate-limiting step of hydrogenation, contrary to recent computational results. We also found that catalysts bearing NHCs with aliphatic and aromatic side groups are energetically favorable over other aliphatic cyclohexyl-substituted NHC. To examine how electronic properties of various catalysts influence the energetic barrier in the crucial steps of the reaction, we applied the Noncovalent Interaction analysis, which allowed us to reveal crucial interactions which stabilize/destabilize important intermediates and transition states in the hydrogenation reaction.

A Quantum Theory Atoms in Molecules Study about the Inductive Effect of Substituents in Methane Derivatives

The substituent effect on the covalent character of C-H bonds in methane derivatives is evaluated by means of local descriptors based on the topology of the electron density. Halogens, -OH, -SH, =O, =S, -NO₂, -NH₂, and -OCH₃ increase the covalent character of the remaining C-H bonds, while alkaline metals (-Li and -Na) result in the opposite trend. This study proposes that the inductive effect is due to polarization changes driven by substituent charges.

The Atomic Partial Charges Arboretum: Trying to See the Forest for the Trees

Atomic partial charges are among the most commonly used interpretive tools in quantum chemistry. Dozens of different 'population analyses' are in use, which are best seen as proxies (indirect gauges) rather than measurements of a 'general ionicity'. For the GMTKN55 benchmark of nearly 2,500 main-group molecules, which span a broad swathe of chemical space, some two dozen different charge distributions were evaluated at the PBE0 level near the 1-particle basis set limit. The correlation matrix between the different charge distributions exhibits a block structure; blocking is, broadly speaking, by charge distribution class. A principal component analysis on the entire dataset suggests that nearly all variation can be accounted for by just two 'principal components of ionicity': one has all the distributions going in sync, while the second corresponds mainly to Bader QTAIM vs. all others. A weaker third component corresponds to electrostatic charge models in opposition to the orbital-based ones. The single charge distributions that have the greatest statistical similarity to the first principal component are iterated Hirshfeld (Hirshfeld-I) and a minimal-basis projected modification of Bickelhaupt charges. If three individual variables, rather than three principal components, are to be identified that contain most of the information in the whole dataset, one representative for each of the three classes of Corminboeuf et al. is needed: one based on partitioning of the density (such as QTAIM), a second based on orbital partitioning (such as NPA), and a third based on the molecular electrostatic potential (such as HLY or CHELPG).

A sixteen-valence-electron carbon-group 13 family with global penta-atomic planar tetracoordinate carbon: an ionic strategy

The design of planar tetracoordinate carbon (ptC) has always been a challenge due to its unique bonding mode that necessitates the perfect balance between the carbon center and surrounding ligands both electronically and mechanically. A unique type of 18-valence-electron (18ve) template, i.e., CAl42-, has been found to be very effective in designing various novel 18ve-species upon skeletal substitution. In this work, we showed that though ptC is not the global structure for the parent 16ve-CAl4, suitable skeletal substitution can allow for a series of global minimum ptC species. Theoretical calculations at the level of CCSD(T)/def2-QZVP//B3LYP/def2-QZVP for 35 carbon-group 13 systems with 16-ve, i.e., CXaYbZcKd (X, Y, Z, K = Al/Ga/In/Tl; 0 ≤ a, b, c, d ≤ 4, a + b + c + d = 4), showed that 9 systems (CAl3Tl, CGa3Tl, CGa2Tl2, CAl2GaTl, CAl2InTl, CGa2InTl, CAlGa2Tl, CGa2InTl and CAlGaInTl) possess global minimum ptC and 2 systems (CAl3In and CAl2Tl2) have quasi-GM ptC. Except for CAl3Tl and CAl3In, all the ptCs were predicted for the first time. All these stable ptC structures have the same skeleton and can be described as the same ionic sub-structure, i.e., [A-]B+. This study not only enriches 16ve-ptC, but also directly demonstrates that utilizing an ionic strategy, non-ptC CAl4 also can be used as a template to extend the ptC family.

Mono-silicon isoelectronic replacement in CAl4 : van't hoff/le bel carbon or not?

In cluster studies, the isoelectronic replacement strategy has been successfully used to introduce new elements into a known structure while maintaining the desired topology. The well-known penta-atomic 18 valence electron (ve) species C Al 4 2 - and its Al^- /Si or Al/Si⁺ isoelectronically replaced clusters CAl₃ Si^- , CAl₂ Si₂ , C AlSi 3 - , and C Si 4 2 + , all possess the same anti-van't Hoff/Le Bel skeletons, that is, nontraditional planar tetracoordinate carbon (ptC) structure. In this article, however, we found that such isoelectronic replacement between Si and Al does not work for the 16ve-CAl₄ with the traditional van't Hoff/Le Bel tetrahedral carbon (thC) and its isoelectronic derivatives CAl₃ X (X = Ga/In/Tl). At the level of CCSD(T)/def2-QZVP//B3LYP/def2-QZVP, none of the global minima of the 16ve mono-Si-containing clusters CAl₂ SiX⁺ (X = Al/Ga/In/Tl) maintains thC as the parent CAl₄ does. Instead, X = Al/Ga globally favors an unusual ptC structure that has one long C─X distance yet with significant bond index value, and X = In/Tl prefers the planar tricoordinate carbon. The frustrated formation of thC in these clusters is ascribed to the CSi bonding that prefers a planar fashion. Inclusion of chloride ion would further stabilize the ptC of CAl₂ SiAl⁺ and CAl₂ SiGa⁺ . The unexpectedly disclosed CAl₂ SiAl⁺ and CAl₂ SiGa⁺ represent the first type of 16ve-cationic ptCs with multiple bonds. © 2019 Wiley Periodicals, Inc.

Predicting reactive sites with quantum chemical topology: carbonyl additions in multicomponent reactions

The reactivity of an atom within a molecule depends mostly on the way the electron density polarizes reflected in the quadrupole moment of the reactive atom.

Quantum chemical studies of selective back-extraction of Am(III) from Eu(III) and Cm(III) with two hydrophilic 1,10-phenanthroline-2,9-bis-triazolyl ligands

We theoretically investigated the selective back-extraction towards Am(III) over Eu(III) and Cm(III) with two water-soluble 2,9-bis-triazolyl-1,10-phenanthroline derivatives BTrzPhen1 (with two ethanol side chains) and BTrz-Phen2 (with two 1,2-butanediol side chains) by density functional theory (DFT). The molecular geometries and formation reactions of the metal-ligand complexes were modeled by using M(BTrzPhen)(NO3)3 and [M(BTrzPhen)2(NO3)]2+. Am(III) selectivity over Eu(III) and Cm(III) with BTrzPhen2 was successfully reproduced by back-extraction reaction free energy analysis. Moreover, bonding properties between the metal cations and coordinated ligands (model complexes) were studied in terms of Mayer bond order and quantum theory of atoms in molecule (QTAIM). The difference in covalency between An–N and Eu–N bonds were found to be the key factors for Am(III)/Eu(III) separation, while the Am(III) selectivity over Cm(III) of BTrzPhen2 might be attributed to the competition of donor atoms for cation binding preference toward Am(III) and Cm(III).

Noble gas insertion compounds of hydrogenated and lithiated hyperhalogens

Based on density functional theory (DFT) calculations, hydrogenated hyperhalogen HM(BO2)2, lithiated hyperhalogen LiM(BO2)2 (M = Cu, Ag, Au), and their compounds with xenon were studied. Different insertion sites of Xe resulted in various isomers. According to the natural population analysis, the Xe atom donated 0.12-0.77 electrons to HM(BO2)2 and 0.14-0.41 electrons to LiM(BO2)2 when they combined, leading to metastable charge-transfer compounds in most cases. The nature of bonding between xenon and HM(BO2)2/LiM(BO2)2 was found to be related to its location. Covalent bonds were formed when Xe bound with hydrogen atoms, as indicated by the large Wiberg bond indices of the Xe-H bonds. The same was true for most Xe-M bondings. When an Xe-O connection was formed, it was either an ionic or van der Waals force in nature depending on the specific structural feature of the isomer. A parallel study on hyperhalogen-supported Ar and Kr compounds indicated that they were not very stable and were less likely to exist at room temperature, which was in accordance with the high inertness of both Ar and Kr atoms.