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.

Exploring the Non-Covalent Bonding in Water Clusters.

QTAIM and source function analysis were used to explore the non-covalent bonding in twelve different water clusters (H2O)n obtained by considering n = 2-7 and various geometrical arrangements. A total of seventy-seven O-H⋯O hydrogen bonds (HBs) were identified in the systems under consideration, and the examination of the electron density at the bond critical point (BCP) of these HBs revealed the existence of a great diversity of O-H⋯O interactions. Furthermore, the analysis of quantities, such as |V(r)|/G(r) and H(r), allowed a further description of the nature of analogous O-H⋯O interactions within each cluster. In the case of 2-D cyclic clusters, the HBs are nearly equivalent between them. However, significant differences among the O-H⋯O interactions were observed in 3-D clusters. The assessment of the source function (SF) confirmed these findings. Finally, the ability of SF to decompose the electron density (ρ) into atomic contributions allowed the evaluation of the localized or delocalized character of these contributions to ρ at the BCP associated to the different HBs, revealing that weak O-H⋯O interactions have a significant spread of the atomic contributions, whereas strong interactions have more localized atomic contributions. These observations suggest that the nature of the O-H⋯O hydrogen bond in water clusters is determined by the inductive effects originated by the different spatial arrangements of the water molecules in the studied clusters.

A Theoretical Study of the C-X Bond Cleavage Mediated by Cob(II)Aloxime.

The C-X bond cleavage in different methyl halides (CH3X; X = Cl, Br, I) mediated by 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(II) (CoIICbx) was theoretically investigated in the present work. An SN2-like mechanism was considered to simulate the chemical process where the cobalt atom acts as the nucleophile and the halogen as the leaving group. The reaction path was computed by means of the intrinsic reaction coordinate method and analyzed in detail through the reaction force formalism, the quantum theory of atoms in molecules (QTAIM), and the calculation of one-electron density derived quantities, such as the source function (SF) and the spin density. A thorough comparison of the results with those obtained in the same reaction occurring in presence of 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(I) (CoICbx) was conducted to reveal the main differences between the two cases. The reactions mediated by CoIICbx were observed to be endothermic and possess higher activation energies in contrast to the reactions where the CoICbx complex is present. The latter was supported by the reaction force results, which suggest a relationship between the activation energy and the ionization potentials of the different nucleophiles present in the cleavage reaction. Moreover, the SF results indicates that the lower axial ligand (i.e., 5,6-dimethylbenzimidazole) exclusively participates on the first stage of the reaction mediated by the CoIICbx complex, while for the CoICbx case, it appears to have an important role along the whole process. Finally, the QTAIM charge analysis indicates that oxidation of the cobalt atom occurs in both cases; at the same time, it suggests the formation of an uncommon two-center one-electron bond in the CoIICbx case. The latter was confirmed by means of electron localization calculations, which resulted in a larger electron count at the Co-C interatomic region for the CoICbx case upon comparison with its CoIICbx counterpart.

The explicit role of electron exchange in the hydrogen bonded molecular complexes.

We applied a set of advanced bonding descriptors to establish the hidden electron density features and binding energy characteristics of intermolecular DH∙∙∙A hydrogen bonds (OH∙∙∙O, NH∙∙∙O and SH∙∙∙O) in 150 isolated and solvated molecular complexes. The exchange-correlation and Pauli potentials as well as corresponding local one-electron forces allowed us to explicitly ascertain how electron exchange defines the bonding picture in the proximity of the H-bond critical point. The electron density features of DH∙∙∙A interaction are governed by alterations in the electron localization in the H-bond region displaying itself in the exchange hole. At that, they do not depend on the variations in the exchange hole mobility. The electrostatic interaction mainly defines the energy of H-bonds of different types, whereas the strengthening/weakening of H-bonds in complexes with varying substituents depends on the barrier height of the exchange potential near the bond critical point. Energy variations between H-bonds in isolated and solvated systems are also caused the electron exchange peculiarities as follows from the corresponding potential and the interacting quantum atom analyses complemented by electron delocalization index calculations. Our approach is based on the bonding descriptors associated with the characteristics of the observable electron density and can be recommended for in-depth studies of non-covalent bonding.

Factors Impacting σ- and π-Hole Regions as Revealed by the Electrostatic Potential and Its Source Function Reconstruction: The Case of 4,4'-Bipyridine Derivatives.

Positive electrostatic potential (V) values are often associated with σ- and π-holes, regions of lower electron density which can interact with electron-rich sites to form noncovalent interactions. Factors impacting σ- and π-holes may thus be monitored in terms of the shape and values of the resulting V. Further precious insights into such factors are obtained through a rigorous decomposition of the V values in atomic or atomic group contributions, a task here achieved by extending the Bader-Gatti source function (SF) for the electron density to V. In this article, this general methodology is applied to a series of 4,4'-bipyridine derivatives containing atoms from Groups VI (S, Se) and VII (Cl, Br), and the pentafluorophenyl group acting as a π-hole. As these molecules are characterized by a certain degree of conformational freedom due to the possibility of rotation around the two C-Ch bonds, from two to four conformational motifs could be identified for each structure through conformational search. On this basis, the impact of chemical and conformational features on σ- and π-hole regions could be systematically evaluated by computing the V values on electron density isosurfaces (VS) and by comparing and dissecting in atomic/atomic group contributions the VS maxima (VS,max) values calculated for different molecular patterns. The results of this study confirm that both chemical and conformational features may seriously impact σ- and π-hole regions and provide a clear analysis and a rationale of why and how this influence is realized. Hence, the proposed methodology might offer precious clues for designing changes in the σ- and π-hole regions, aimed at affecting their potential involvement in noncovalent interactions in a desired way.

Spin Density Topology.

Despite its role in spin density functional theory and it being the basic observable for describing and understanding magnetic phenomena, few studies have appeared on the electron spin density subtleties thus far. A systematic full topological analysis of this function is lacking, seemingly in contrast to the blossoming in the last 20 years of many studies on the topological features of other scalar fields of chemical interest. We aim to fill this gap by unveiling the kind of information hidden in the spin density distribution that only its topology can disclose. The significance of the spin density critical points, the 18 different ways in which they can be realized and the peculiar topological constraints on their number and kind, arising from the presence of positive and negative spin density regions, is addressed. The notion of molecular spin graphs, spin maxima (minima) joining paths, spin basins and of their valence is introduced. We show that two kinds of structures are associated with a spin-polarized molecule: the usual one, defined through the electron density gradient, and the magnetic structure, defined through the spin density gradient and composed in general by at least two independent spin graphs, related to spin density maxima and minima. Several descriptors, such as the spin polarization index, are introduced to characterize the properties of spin density critical points and basins. The study on the general features of the spin density topology is followed by the specific example of the water molecule in the 3B1 triplet state, using spin density distributions of increasing accuracy.

When does a hydrogen bond become a van der Waals interaction? a topological answer.

The hydrogen bond (H-bond) is among the most important noncovalent interaction (NCI) for bioorganic compounds. However, no "energy border" has yet been identified to distinguish it from van der Waals (vdW) interaction. Thus, classifying NCIs and interpreting their physical and chemical importance remain open to great subjectivity. In this work, the "energy border" between vdW and H-bonding interactions was identified using a dimer of water, as well as for a series of classical and nonclassical H-bonding systems. Through means of the quantum theory of atoms in molecules and in particular the source function, it was possible to clearly identify the transition from H-bonding to vdW bonding via analysis of the electronic structure. This "energy border" was identified both on elongating the interatomic interaction and by varying the contact angle. Hence, this study also redefines the "critic angle" previously proposed by Galvão et al. (J. Phys. Chem. A 2013, 117, 12668). Consequently, such "energy border" through an analysis of atomic basins volume variation was possible to identify the end of long-range interactions. © 2019 Wiley Periodicals, Inc.

Spin density accuracy and distribution in azido Cu(II) complexes: A source function analysis.

Magnetic properties of open-shell systems depend on their unpaired electron density distribution. Accurate spin density (SD) is difficult to retrieve, both from polarized neutron diffraction (PND) data and from quantum approaches, and its interpretation is not trivial. The Source Function is a useful tool to interpret SD distributions and their accuracy. It is here applied to analyze and compare the theoretical SD in a weakly ferromagnetically coupled end-end azido dicopper complex with that in a strongly-coupled end-on complex. The Source Function enables to highlight the origin of the SD differences between the two dicopper complexes and among adopted computational approaches (CASSCF, DFT, UHF). Further insight is provided by partial Source Function SD reconstructions using given subsets of atoms. DFT methods exaggerate electron sharing between copper and the ligands, causing spin delocalization toward them and overestimating metal-ligand spin polarization, while underestimating CASSCF spin information transmission between atoms. CAS(10,10) SD is closer to the PND SD than other adopted methods © 2018 Wiley Periodicals, Inc.

An Electron Density Source-Function Study of DNA Base Pairs in Their Neutral and Ionized Ground States†.

The source function (SF) decomposes the electron density at any point into contributions from all other points in the molecule, complex, or crystal. The SF "illuminates" those regions in a molecule that most contribute to the electron density at a point of reference. When this point of reference is the bond critical point (BCP), a commonly used surrogate of chemical bonding, then the SF analysis at an atomic resolution within the framework of Bader's Quantum Theory of Atoms in Molecules returns the contribution of each atom in the system to the electron density at that BCP. The SF is used to locate the important regions that control the hydrogen bonds in both Watson-Crick (WC) DNA dimers (adenine:thymine (AT) and guanine:cytosine (GC)) which are studied in their neutral and their singly ionized (radical cationic and anionic) ground states. The atomic contributions to the electron density at the BCPs of the hydrogen bonds in the two dimers are found to be delocalized to various extents. Surprisingly, gaining or loosing an electron has similar net effects on some hydrogen bonds concealing subtle compensations traced to atomic sources contributions. Coarser levels of resolutions (groups, rings, and/or monomers-in-dimers) reveal that distant groups and rings often have non-negligible effects especially on the weaker hydrogen bonds such as the third weak CH⋅⋅⋅O hydrogen bond in AT. Interestingly, neither the purine nor the pyrimidine in the neutral or ionized forms dominate any given hydrogen bond despite that the former has more atoms that can act as source or sink for the density at its BCP. © 2018 Wiley Periodicals, Inc.

Probing Cyclic π-Electron Delocalization in an Imidazol-2-ylidene and a Corresponding Imidazolium Salt.

The extent of cyclic π-electron delocalization in the N-heterocyclic ring of an imidazol-2-ylidene (i.e., 1,3,4,5-tetramethylimidazol-2-ylidene) and its corresponding imidazolium salt (i.e., 1,3,4,5-tetramethylimidazolium chloride) has been investigated theoretically by using Bader's quantum theory of atoms in molecules (QTAIM) descriptors, delocalization indices, electron localizability indicators (ELI-Ds), and the source function tool. In addition, the experimental electron density distribution for the imidazolium salt has been obtained and analyzed from 100 K X-ray diffraction data. A significant drop is found in the ellipticity of the electron density along the Ccarbene -N bond path in the imidazol-2-ylidene. This is shown to be a natural consequence of the σ lone pair of the Ccarbene atom, which overwhelms the π-electron density, rather than a sign of a significantly diminished degree of π-electron delocalization in the imidazol-2-ylidene compared to its imidazolium salt. In fact, the source functions, the ELI-Ds, and the delocalization indices all probe a quite similar extent of cyclic π-electron delocalization in the N-heterocyclic rings of the two compounds.

Source function and plane waves: Toward complete bader analysis.

The source function (SF) is a topological descriptor that was introduced and developed by C. Gatti and R.W. Bader in 1998. The SF describes the contribution of each atom to the total electron density at a given point. To date, this descriptor has only been calculable from electron densities generated by all-electron (AE) methods for the investigation of single molecules or periodic systems. This study broadens the accessibility of the SF, offering its calculation from electron densities generated by plane wave (PW) methods. The new algorithm has been implemented in the open source code, CRITIC2. Our novel approach has been validated on a series of test systems, comparing the results obtained at PW level with those previously obtained through AE methods. © 2016 Wiley Periodicals, Inc.

QTAIM analysis of the bonding in anionic group 6 carbonyl selenide clusters: [Se2M3(CO)10]2- (M=Cr, Mo, W).

CONTEXT: This research aims to offer a deeper understanding of the bonding interactions between M-Se and M-CO and how these interactions change across the group 6 transition metal series: [Se2M3(CO)10]2- (M = Cr, Mo, W). It also seeks to explore the impact of carbonyl groups on M-M interactions within the clusters. Seven criteria, which are based on QTAIM properties, have been considered and compared with the corresponding criteria in other transition metal clusters. The results confirm that no such bond critical points or bond baths occur between transition metals, which instead have 5c-7e bonding interactions delocalized over their five-membered M3(µ-Se)2 ring, as evidenced by the non-negligible nonbonding delocalization indices. The topological properties of three bond clusters, Cr-Se, Mo-Se, and W-Se, resemble those of "intermediate closed shell characters," which combine covalent and electrostatic properties. Source function calculations indicated that the bonded Se atom contributed the most to each Cr-Se and Mo-Se bcp. The OCO atoms and nonbonded Se atoms also contributed to some extent. However, metal atoms act as sinks rather than as sources of electron density. In contrast, the majority of the metal atoms, both bonded and nonbonded, contribute to Cr-W bcps. Analysis of the delocalization indices δ(M…O) in the three clusters indicates that CO significantly contributes to Cr π-back donation in cluster 1. In contrast, no π-back donation occurs from CO to Mo or W in clusters 2 or 3, respectively. METHODS: The B3P86 hybrid functional was used for computations in the Gaussian 09 software. The LanL2DZ basis set was employed for Cr, Mo, and W, while the 6-31G (d, p) basis set was used for C, O, and Se atoms. We performed QTAIM analysis using the AIM2000 and Multiwfn packages, incorporating B3P86/WTBS for Cr, Mo, and W atoms. The 6-311++G(3df,3pd) basis set was used for C, O, and Se atoms. Additionally, we utilized the ELF and SF.

A multi-objective framework to select numerical options in air quality prediction models: A case study on dust storm modeling.

Numerical weather prediction models are very important tools in predicting severe weather phenomena such as dust storms. However, the prediction accuracy in these models depends on the options considered in the modeling. In this study, a multi-objective framework is presented to determine the optimal options of the weather research forecasting with chemistry (WRF-Chem) model. For this purpose, a severe dust storm that occurred in the center of Iran is considered and the effect of 10 options including grid (computational domain size, modeling start time, horizontal, vertical and temporal resolution), physical (initial conditions, boundary layer and land surface schemes) and chemical options (dust emission schemes and dust source functions) are investigated. In general, the results showed that the WRF-Chem model has a high ability to model dust storms, but its results depend on the options considered in the modeling. Evaluation of grid options showed that inappropriate selection of domain size and modeling start time can lead to the failure in dust storm forecasting. Also, the land surface scheme has the greatest impact on dust concentration among the physical options. In addition, chemical options have the greatest impact on the dust storm forecasting as well. Based on the proposed multi-objective framework, the optimal options for dust storm modeling were determined. The proposed approach is comprehensive and can be used for other atmospheric/air quality modeling.

Unravelling functions of halogen substituents in the enantioseparation of halogenated planar chiral ferrocenes on polysaccharide-based chiral stationary phases: experimental and electrostatic potential analyses.

Planar chiral halogenated ferrocenes have come in useful as synthetic intermediates over the years, allowing for the preparation of functionalized derivatives for catalysis, material science, optoelectronics, and medicinal chemistry. Despite their chemical interest, few halogenated planar chiral ferrocenes have been prepared in enantiopure form by asymmetric synthesis so far. Enantioselective HPLC on polysaccharide-based chiral stationary phases (CSPs) has been used for resolving planar chiral ferrocenes making both enantiomers available. However, the enantioseparation of derivatives containing halogens or alkyl groups exclusively remains rather challenging. Given this context, in this study the enantioseparation of eleven dihalogenated planar chiral ferrocenes was systematically explored by using five polysaccharide-based CSPs under multimodal elution conditions. Baseline enantioseparations were achieved for nine analytes with separation factors (α) ranging from 1.15 to 1.66. Thermodynamic quantities associated with the enantioseparations were derived from van't Hoff plots, and for 1-halo-2-(iodoethynyl)ferrocenes (1-halogen = F, Cl, Br) halogen-dependent thermodynamic profiles were identified on a cellulose tris(3,5-dimethylphenylcarbamate)-based column. The impact of CSP structure and mobile phase (MP) polarity on the enantioseparation was evaluated. In addition, with the aim to unravel the functions of halogen substituents in mechanisms and noncovalent interactions underlying selector-selectand complex formation at molecular level, local electron charge density of specific molecular regions of the interacting partners were evaluated in terms of calculated electrostatic potential (V) and related source function (SF) contributions. On this basis, the impact of halogen type and position on the enantioseparation was investigated by correlating theoretical and experimental data.

Aerosols chemical composition, light extinction, and source apportionment near a desert margin city, Yulin, China.

Daily PM10and PM2.5 sampling was conducted during four seasons from December 2013 to October 2014 at three monitoring sites over Yulin, a desert margin city. PM10 and PM2.5 levels, water soluble ions, organic carbon (OC), and elemental carbon (EC) were also analyzed to characterize their chemical profiles. b ext (light extinction coefficient) was calculated, which showed the highest in winter with an average of 232.95 ± 154.88 Mm-1, followed by autumn, summer, spring. Light extinction source apportionment results investigated (NH4)2SO4 and NH4NO3 played key roles in the light extinction under high RH conditions during summer and winter. Sulfate, nitrate and Ca2 + dominated in PM10/PM2.5 ions. Ion balance results illustrated that PM samples were alkaline, and PM10 samples were more alkaline than PM2.5. High SO4 2-/K+ and Cl-/K+ ratio indicated the important contribution of coal combustion, which was consistent with the OC/EC regression equation intercepts results. Principal component analysis (PCA) analyses results showed that the fugitive dust was the most major source of PM, followed by coal combustion & gasoline vehicle emissions, secondary formation and diesel vehicle emissions. Potential contribution source function (PSCF) results suggested that local emissions, as well as certain regional transport from northwesterly and southerly areas contributed to PM2.5 loadings during the whole year. Local government should take some measures to reduce the PM levels.

Enantioseparation of fluorinated 3-arylthio-4,4'-bipyridines: Insights into chalcogen and π-hole bonds in high-performance liquid chromatography.

A chalcogen bond (ChB) is a σ-hole-based noncovalent interaction between a Lewis base and an electrophilic element of Group VI (O, S, Se, Te), which behaves as a Lewis acid. Recently, we demonstrated that halogen bond, the more familiar σ-hole-based interaction, is able to promote the enantioseparation of chiral compounds in HPLC environment. On this basis, an investigation to detect ChBs, functioning as stereoselective secondary interactions for HPLC enantioseparations, was started off and the results of this study are described herein. Our investigation also focused on the impact of the perfluorinated aromatic ring as a π-hole donor recognition site. For these purposes, seven atropisomeric fluorinated 3-arylthio-4,4'-bipyridines were designed, synthesized and used as potential ChB donors (ChBDs) with two cellulose-based chiral stationary phases (CSPs) containing carbonyl groups as ChB acceptors (ChBAs). In addition, one and two analogues lacking fluorine and sulphur, respectively, were prepared as terms of comparison. The design of the test analytes was computationally guided. In this regard, electrostatic potentials (EPs) associated with σ- and π-holes were computed and the atomic contributions to the sulphur EP maxima were derived using a molecular space partitioning in terms of Bader's atomic basins. This procedure is akin to the Bader-Gatti electron density source function (SF) decomposition, yet suitably extended to the EP field. For five 3-substituted-4,4'-bipyridines, thermodynamic parameters were derived from van't Hoff plots. Finally, the use of molecular dynamic (MD) simulation to model ChB in cellulose-analyte complexes was explored. Evidences that σ-hole and π-hole interactions can jointly drive HPLC enantioseparations through recognition sites generated by electronic charge depletion emerged from both experimental results and theoretical data.

Insights on spin delocalization and spin polarization mechanisms in crystals of azido copper(II) dinuclear complexes through the electron spin density Source Function.

The Source Function (SF) tool was applied to the analysis of the theoretical spin density in azido CuII dinuclear complexes, where the azido group, acting as a coupler between the CuII cations, is linked to the metal centres either in an end-on or in an end-end fashion. Results for only the former structural arrangement are reported in the present paper. The SF highlights to which extent the magnetic centres contribute to determine the local spin delocalization and polarization at any point in the dimetallic complex and whether an atom or group of atoms of the ligands act in favour or against a given local spin delocalization/polarization. Ball-and-stick atomic SF percentage representations allow for a visualization of the magnetic pathways and of the specific role played by each atom along these paths, at given reference points. Decomposition of SF contributions in terms of a magnetic and of a relaxation component provides further insight. Reconstruction of partial spin densities by means of the Source Function has for the first time been introduced. At variance with the standard SF percentage representations, such reconstructions offer a simultaneous view of the sources originating from specific subsets of contributing atoms, in a selected molecular plane or in the whole space, and are therefore particularly informative. The SF tool is also used to evaluate the accuracy of the analysed spin densities. It is found that those obtained at the unrestricted B3LYP DFT level, relative to those computed at the CASSCF(6,6) level, greatly overestimate spin delocalization to the ligands, but comparatively underestimate magnetic connection (spin transmission) among atoms, along the magnetic pathways. As a consequence of its excessive spin delocalization, the UB3LYP method also overestimates spin polarization mechanisms between the paramagnetic centres and the ligands. Spin delocalization measures derived from the refinement of Polarized Neutron Diffraction data seem in general superior to those obtained through the DFT UB3LYP approach and closer to the far more accurate CASSCF results. It is also shown that a visual agreement on the spin-resolved electron densities ρα and ρß derived from different approaches does not warrant a corresponding agreement between their associated spin densities.

Expanding the usage of the Source Function to experimental electron densities.

The Source Function provides unique information about chemical bonding in the solid state, from theory as well as from experiment. It is now established that the concept of electronic delocalization in aromatic systems can be accurately studied using X-ray derived electron densities, and even more importantly the contributions are transferable between similar systems.

Source Function applied to experimental densities reveals subtle electron-delocalization effects and appraises their transferability properties in crystals.

The Source Function (SF), introduced in 1998 by Richard Bader and Carlo Gatti, is succinctly reviewed and a number of paradigmatic applications to in vacuo and crystal systems are illustrated to exemplify how the SF may be used to discuss chemical bonding in both conventional and highly challenging cases. The SF enables the electron density to be seen at a point determined by source contributions from the atoms or a group of atoms of a system, and it is therefore well linked to the chemist's awareness that any local property and chemical behaviour is to some degree influenced by all the remaining parts of a system. The key and captivating feature of the SF is that its evaluation requires only knowledge of the electron density (ED) of a system, thereby enabling a comparison of ab initio and X-ray diffraction derived electron density properties on a common and rigorous basis. The capability of the SF to detect electron-delocalization effects and to quantify their degree of transferability is systematically explored in this paper through the analysis and comparison of experimentally X-ray derived Source Function patterns in benzene, naphthalene and (±)-8'-benzhydrylideneamino-1,1'-binaphthyl-2-ol (BAB) molecular crystals. It is shown that the SF tool recovers the characteristic SF percentage patterns caused by π-electron conjugation in the first two paradigmatic aromatic molecules in almost perfect quantitative agreement with those obtained from ab initio periodic calculations. Moreover, the effect of chemical substitution on the degree of transferability of such patterns to the benzene- and naphthalene-like moieties of BAB is neatly shown and quantified by the observed systematic deviations, relative to benzene and naphthalene, of only those SF contributions from the substituted C atoms. Finally, the capability of the SF to reveal electron-delocalization effects is challenged by using a promolecule density, rather than the proper quantum mechanical density, to determine the changes in SF patterns along the cyclohexene, 1,3-cyclohexadiene and benzene molecule series. It is shown that, differently from the proper quantum density, the promolecular density is unable to reproduce the SF trends anticipated by the increase of electron delocalization along the series, therefore ruling out the geometrical effect as being the only cause for the observed SF patterns changes.