On the Influence of Density Functional Approximations on Some Local Bader’s Atoms-in-Molecules Properties

Decoding Chemical Bonds: Assessment of the Basis Set Effect on Overlap Electron Density Descriptors and Topological Properties in Comparison to QTAIM

Quantum chemical bonding descriptors based on the total and overlap density can provide valuable information about chemical interactions in different systems. However, these descriptors can be sensitive to the basis set used. To address this, different numerical treatments of electron density have been proposed to reduce the basis set dependency. In this work, we introduce overlap properties (OPs) obtained through numerical treatment of the electron density and present the topology of overlap density (TOP) for the first time. We compare the basis set dependency of numerical OP and TOP descriptors with their quantum theory of atoms in molecules (QTAIM) counterparts, considering the total electron density. Three single (C-C, C-O, and C-F) bonds in ethane, methanol, and fluoromethane and two double (C═C and C═O) bonds in ethene and formaldehyde were analyzed. Diatomic molecules Li-X with X = F, Cl, and Br were also analyzed. Eight parameters, including QTAIM descriptors and OP/TOP descriptors, are used to assess the basis dependency at the ωB97X-D level of theory using 28 basis sets from three classes: Pople, Ahlrichs, and Dunning. The study revealed that the topological overlap electron density properties exhibit comparatively lesser dependence on the basis set compared to their total electron density counterparts. Remarkably, these properties retain their chemical significance even with reduced basis set dependency. Similarly, numerical OP descriptors show less basis set dependency than their QTAIM counterparts. The excess of polarization functions increases charge concentration in the interatomic region and influences both QTAIM and OP descriptors. The basis sets Def2TZVP, 6-31++G(d,p), 6-311++G(d,p), cc-pVDZ, cc-pVTZ, and cc-pVQZ demonstrate reduced variability for the tested bond classes in this study, with particular emphasis on the triple-ζ quality Ahlrichs' basis set. We recommend against using basis sets with numerous polarization functions, such as augmented Dunning's and Ahlrichs' quadruple-ζ.

Comparative study of the antioxidant capability of EDTA and Irganox

Oxidative stress makes it difficult to preserve food and negatively affect the applicability of polymeric packaging. It is typically caused by an excess of free radicals, and it is dangerous to human health, resulting in the onset and development of diseases. The antioxidant ability and activity of ethylenediaminetetraacetic acid (EDTA) and Irganox (Irg) as synthetic antioxidant additives were studied. Three different antioxidant mechanisms were considered and compared by calculating bond dissociation enthalpy (BDE), ionization potential (IP), proton dissociation enthalpy (PDE), proton affinity (PA), and electron transfer enthalpy (ETE) values. Two density functional theory (DFT) methods were used, M05-2X and M06-2X with the 6-311++G(2d,2p) basis set in gas phase. Both additives can be used to protect pre-processed food products and polymeric packaging from oxidative stress related material deterioration. By comparing the two studied compounds, it was found that EDTA has a higher antioxidant potential than Irganox. To the best of our knowledge several studies have been carried out to understand the antioxidant potential of various natural and synthetic species, but EDTA and Irganox were not compared and investigated before. These additives can be used to protect pre-processed food products and polymeric packaging and prevent material deterioration caused by oxidative stress.

Testing of Exchange-Correlation Functionals of DFT for a Reliable Description of the Electron Density Distribution in Organic Molecules

Researchers carrying out calculations using the DFT method face the problem of the correct choice of the exchange-correlation functional to describe the quantities they are interested in. This article deals with benchmark calculations aimed at testing various exchange-correlation functionals in terms of a reliable description of the electron density distribution in molecules. For this purpose, 30 functionals representing all rungs of Jacob's Ladder are selected and then the values of some QTAIM-based parameters are compared with their reference equivalents obtained at the CCSD/aug-cc-pVTZ level of theory. The presented results show that the DFT method undoubtedly has the greatest problems with a reliable description of the electron density distribution in multiple strongly polar bonds, such as C=O, and bonds associated with large electron charge delocalization. The performance of the tested functionals turned out to be unsystematic. Nevertheless, in terms of a reliable general description of QTAIM-based parameters, the M11, SVWN, BHHLYP, M06-HF, and, to a slightly lesser extent, also BLYP, B3LYP, and X3LYP functionals turned out to be the worst. It is alarming to find the most popular B3LYP functional in this group. On the other hand, in the case of the electron density at the bond critical point, being the most important QTAIM-based parameter, the M06-HF functional is especially discouraged due to the very poor description of the C=O bond. On the contrary, the VSXC, M06-L, SOGGA11-X, M06-2X, MN12-SX, and, to a slightly lesser extent, also TPSS, TPSSh, and B1B95 perform well in this respect. Particularly noteworthy is the overwhelming performance of double hybrids in terms of reliable values of bond delocalization indices. The results show that there is no clear improvement in the reliability of describing the electron density distribution with climbing Jacob's Ladder, as top-ranked double hybrids are also, in some cases, able to produce poor values compared to CCSD.

Current Trends in Computational Quantum Chemistry Studies on Antioxidant Radical Scavenging Activity

The antioxidative nature of chemicals is now routinely studied using computational quantum chemistry. Scientists are constantly proposing new approaches to investigate those methods, and the subject is evolving at a rapid pace. The goal of this review is to collect, consolidate, and present current trends in a clear, methodical, and reference-rich manner. This paper is divided into several sections, each of which corresponds to a different stage of elaborations: preliminary concerns, electronic structure analysis, and general reactivity (thermochemistry and kinetics). The sections are further subdivided based on methodologies used. Concluding remarks and future perspectives are presented based on the remaining elements.

Structural study of 1- and 2-naphthol: new insights into the non-covalent H-H interaction in cis-1-naphthol

Previous microwave studies of naphthol monomers were supplemented by measuring spectra of all ¹³C mono-substituted isotopologues of the cis- and trans-conformers of 1-naphthol and 2-naphthol in their natural abundances. The resulting data were utilized to determine substitution structures and so-called semi-experimental effective structures. Results from electronic structure calculations show that the OH group of cis-1-naphthol points ≈6° out of plane, which is consistent with the inertial defect data of cis- and trans-1-naphthol. The non-planarity of cis-1-naphthol is a result of a close-contact H-atom-H-atom interaction. This type of H-H interaction has been the subject of much controversy in the past and we provide here an in-depth theoretical analysis of it. The naphthol system is particularly well-suited for such analysis as it provides internal standards with its four different isomers. The methods used include quantum theory of atoms in molecules, non-covalent interactions, independent gradient model, local vibrational mode, charge model 5, and natural bond orbital analyses. We demonstrate that the close-contact H-H interaction is neither a purely attractive nor repulsive interaction, but rather a mixture of the two.

Electronic Energy and Local Property Errors at QTAIM Critical Points while Climbing Perdew's Ladder of Density-Functional Approximations

We investigate the relationships between electron-density and electronic-energy errors produced by modern exchange-correlation density-functional approximations belonging to all of the rungs of Perdew's ladder. To this aim, a panel of relevant (semi)local properties evaluated at critical points of the electron-density field (as defined within the framework of Bader's atoms-in-molecules theory) are computed on a large selection of molecular systems involved in thermodynamic, kinetic, and noncovalent interaction chemical databases using density functionals developed in a nonempirical and minimally and highly parametrized fashion. The comparison of their density- and energy-based performance, also discussed in terms of density-driven errors, casts light on the strengths and weaknesses of the most recent and efficient density-functional approximations.

Toward universal substituent constants: Model chemistry sensitivity of descriptors from the quantum theory of atoms in molecules

The quantum theory of atoms in molecules (QTAIM) provides a theoretical foundation to determine the properties of functional groups through additive atomic contributions. Many studies have used QTAIM in their analyses with a variety of electronic structure methods, but it is unknown if the properties measured using one model chemistry, the combination of the electronic structure method and basis set, can be compared to those measured by another. Here, we evaluate the sensitivity of QTAIM functional group and bond critical point properties using six functionals and seven basis sets. High-level B2PLYPD3-BJ/aug-cc-pV5Z reference values are provided for 116 functional groups and the property sensitivity with respect to these values are evaluated based on absolute deviations and by assessing linear relationships. Functional group properties, including charges, dipoles, quadrupoles and volumes, were found to be mostly insensitive to choice of computational model chemistry. However, due to structural and topological inconsistencies, the 6-31G(d) basis set is not recommended for use. Bond critical point properties varied with choice of model chemistry, but models incorporating hybrid functionals and triple-ζ basis sets provided values suitable for use in regression studies.

Is the Fluorine in Molecules Dispersive? Is Molecular Electrostatic Potential a Valid Property to Explore Fluorine-Centered Non-Covalent Interactions?

Can two sites of positive electrostatic potential localized on the outer surfaces of two halogen atoms (and especially fluorine) in different molecular domains attract each other to form a non-covalent engagement? The answer, perhaps counterintuitive, is yes as shown here using the electronic structures and binding energies of the interactions for a series of 22 binary complexes formed between identical or different atomic domains in similar or related halogen-substituted molecules containing fluorine. These were obtained using various computational approaches, including density functional and ab initio first-principles theories with M06-2X, RHF, MP2 and CCSD(T). The physical chemistry of non-covalent bonding interactions in these complexes was explored using both Quantum Theory of Atoms in Molecules and Symmetry Adapted Perturbation Theories. The surface reactivity of the 17 monomers was examined using the Molecular Electrostatic Surface Potential approach. We have demonstrated inter alia that the dispersion term, the significance of which is not always appreciated, which emerges either from an energy decomposition analysis, or from a correlated calculation, plays a structure-determining role, although other contributions arising from electrostatic, exchange-repulsion and polarization effects are also important. The 0.0010 a.u. isodensity envelope, often used for mapping the electrostatic potential is found to provide incorrect information about the complete nature of the surface reactive sites on some of the isolated monomers, and can lead to a misinterpretation of the results obtained.

Non-nuclear attractors in small charged lithium clusters, Limq (m = 2-5, q = ±1), with QTAIM and the Ehrenfest force partitioning

In this investigation we explore the function and existence of the non-nuclear attractor (NNA) for a series of small charged lithium clusters Limq (m = 2-5, q = ±1) using QTAIM and the Ehrenfest force F(r) partitioning schemes. The NNAs were found to be present in all of the Limq (m = 2-5, q = ±1) clusters for QTAIM, in contrast none were found for F(r). We discovered that the anionic and cationic lithium dimers are limiting cases for minimal and maximal impact of the NNA related to the relative sparseness of total charge density ρ(r) distributions respectively. Evidence is found that the NNA in the anionic dimer is in the process of being annihilated by two neighboring BCPs. We provide a measure of the size of the NNA and find for Limq (m = 2-5, q = ±1) that larger NNAs correlate with increased Li-Li separations. The NNA was determined to be a persistent feature by varying the Li separations for the cationic and anionic dimers. Very large Li separations failed to induce an NNA in the F(r) anionic dimer and therefore we conclude that F(r) is unable to detect NNAs. The metallicity ξ(rb) was also used to measure the sparseness of the distribution of ρ(r) and significant metallic character, on the basis of ξ(rb) > 1, was present for QTAIM but not for F(r), providing further evidence that F(r) cannot detect NNAs. Advantages of the use of Ehrenfest force F(r) partitioning scheme are discussed that include the design of nano-devices through tuning of the Ehrenfest potential VF(b) by the application of external forces such as a constant electric or strain field.

Estimations of energy of noncovalent bonding from integrals over interatomic zero-flux surfaces: Correlation trends and beyond

Bonding energies of 50 associates composed by neutral molecules (atoms) and bounded by various weak noncovalent interactions are calculated within the DFT framework using the PBE0/aug-cc-pVTZ combination. The electronic virial and electron density values at bond critical points together with their integrals over interatomic surfaces are tested to check their ability to estimate bonding energies. Two correlations schemes dealing with integrals over interatomic surface are suggested to estimate bonding energy of any noncovalent interaction. The physical meaning of explored and several known correlations is discussed. Methods to estimate interatomic surface integrals of electronic virial and electron density are proposed. © 2018 Wiley Periodicals, Inc.

Revealing Factors Influencing the Fluorine-Centered Non-Covalent Interactions in Some Fluorine-Substituted Molecular Complexes: Insights from First-Principles Studies

We examine the equilibrium structure and properties of six fully or partially fluorinated hydrocarbons and several of their binary complexes using computational methods. In the monomers, the electrostatic surface of the fluorine is predicted to be either entirely negative or weakly positive. However, its lateral sites are always negative. This enables the fluorine to display an anisotropic distribution of charge density on its electrostatic surface. While this is the electrostatic surface scenario of the fluorine atom, its negative sites in some of these monomers are shown to have the potential to engage in attractive engagements with the negative site(s) on the same atom in another molecule of the same type, or a molecule of a different type, to form bimolecular complexes. This is revealed by analyzing the results of current state-of-the-art computational approaches such as DFT, together with those obtained from the quantum theory of atoms in molecules, molecular electrostatic surface potential and symmetry adapted perturbation theories. We demonstrate that the intermolecular interaction energy arising in part from the universal London dispersion, which has been underappreciated for decades, is an essential factor in explaining the attraction between the negative sites, although energy arising from polarization strengthens the extent of the intermolecular interactions in these complexes.

Density functional theory is straying from the path toward the exact functional

The theorems at the core of density functional theory (DFT) state that the energy of a many-electron system in its ground state is fully defined by its electron density distribution. This connection is made via the exact functional for the energy, which minimizes at the exact density. For years, DFT development focused on energies, implicitly assuming that functionals producing better energies become better approximations of the exact functional. We examined the other side of the coin: the energy-minimizing electron densities for atomic species, as produced by 128 historical and modern DFT functionals. We found that these densities became closer to the exact ones, reflecting theoretical advances, until the early 2000s, when this trend was reversed by unconstrained functionals sacrificing physical rigor for the flexibility of empirical fitting.

Toward a Rigorous Definition of a Strength of Any Interaction Between Bader's Atomic Basins

Strength of interaction between Bader's atomic basins, enclosed by zero-flux surfaces of electron distribution, was proposed to be a measure of elastic deformation of an interaction. The set containing 53 atomic aggregate and covering all range of interaction strength (from van der Waals interactions to triple covalent bonds) was calculated by DFT and perturbation theory methods. Further analysis was performed to seek correlations between various local quantities based on electron density and effective force constants of stretching diatomic vibrations. The linear trend between effective force constants and the potential energy density at the (3, -1) critical point of electron distribution was found. This correlation was improved by the integration of the potential energy density over an interbasin zero-flux surface of electron density. Simple mechanical explanation of established trends is presented. The correlations can be further used to at least semiquantitatively compare any pair of interactions between Bader's atomic basins.

Is the Accuracy of Density Functional Theory for Atomization Energies and Densities in Bonding Regions Correlated?

The development of approximate exchange-correlation functionals is critical for modern density functional theory. A recent analysis of atomic systems suggested that some modern functionals are straying from the path toward the exact functional because electron densities are becoming less accurate while energies are becoming more accurate since the year 2000. To investigate this trend for more chemically relevant systems, the electron densities in the bonding regions and the atomization energies are analyzed for a series of diatomic molecules with 90 different functionals. For hybrid generalized gradient approximation functionals developed since the year 2000, the errors in densities and atomization energies are decoupled; the accuracy of the energies remains relatively consistent while the accuracy of the densities varies significantly. Such decoupling is not observed for generalized gradient and meta-generalized gradient approximation functionals. Analysis of electron densities in bonding regions is found to be important for the evaluation of functionals for chemical systems.

Characterization of B-H agostic compounds involved in the dehydrogenation of amine-boranes by group 4 metallocenes

For over a decade, amine-borane has been considered as a potential chemical hydrogen vector in the context of a search for cleaner energy sources. When catalyzed by organometallic complexes, the reaction mechanisms currently considered involve the formation of β-BH agostic intermediates. A thorough understanding of these intermediates may constitute a crucial step toward the identification of ideal catalysts. Topological approaches such as QTAIM and ELF revealed to be particularly suitable for the description of β-agostic interactions. When studying model catalysts, accurate theoretical calculations may be carried out. However, for a comparison with experimental data, calculations should also be carried out on large organo-metallic species, often including transition metals belonging to the second or the third row. In such a case, DFT methods are particularly attractive. Unfortunately, triple-ζ all electrons basis sets are not easily available for heavy transition metal elements. Thus, a subtle balance should be reached between the affordable level of calculations and the required accuracy of the electronic description of the systems. Herein we propose the use of B3LYP functional in combination with the LanL2DZ pseudopotential for the metal atom and 6-311++G(2d,2p) basis set for the other atoms, followed by a single point using the DKH2 relativistic Hamiltonian in combination with the B3LYP/DZP-DKH level, as a "minimum level of theory" leading to a consistent topological description of the interaction within the ELF and QTAIM framework, in the context of isolated (gas-phase) group 4 metallocene catalysts.

Assessment of DFT Functionals for QTAIM Topological Analysis of Halogen Bonds with Benzene

Halogen bonding, a noncovalent interaction between a halogen atom and a nucleophilic site, is receiving a growing attention in the chemical community stimulating a large number of theoretical investigations. The density functional theory (DFT) approach revealed to be one of the most suitable methods owing to its accuracy and low computational cost. We report here a detailed analysis of the performance of an extensive set of DFT functionals in reproducing accurate binding energies and topological properties for the halogen-bonding interaction of either NCX or PhX molecules (X = F, Cl, Br, I) with the aromatic system of benzene in the T-shaped configuration. It was found that the better performance for both sets of properties is provided by a small subset of functionals able to take into account, implicitly or explicitly (by inclusion of an additive pairwise potential), the dispersion contribution, that is, ωB97X, M06-2X, M11, mPW2PLYP-D, and B2PLYP-D3.

GenLocDip: A Generalized Program to Calculate and Visualize Local Electric Dipole Moments

Local dipole moments (i.e., dipole moments of atomic or molecular subsystems) are essential for understanding various phenomena in nanoscience, such as solvent effects on the conductance of single molecules in break junctions or the interaction between the tip and the adsorbate in atomic force microscopy. We introduce GenLocDip, a program for calculating and visualizing local dipole moments of molecular subsystems. GenLocDip currently uses the Atoms-In-Molecules (AIM) partitioning scheme and is interfaced to various AIM programs. This enables postprocessing of a variety of electronic structure output formats including cube and wavefunction files, and, in general, output from any other code capable of writing the electron density on a three-dimensional grid. It uses a modified version of Bader's and Laidig's approach for achieving origin-independence of local dipoles by referring to internal reference points which can (but do not need to be) bond critical points (BCPs). Furthermore, the code allows the export of critical points and local dipole moments into a POVray readable input format. It is particularly designed for fragments of large systems, for which no BCPs have been calculated for computational efficiency reasons, because large interfragment distances prevent their identification, or because a local partitioning scheme different from AIM was used. The program requires only minimal user input and is written in the Fortran90 programming language. To demonstrate the capabilities of the program, examples are given for covalently and non-covalently bound systems, in particular molecular adsorbates. © 2016 Wiley Periodicals, Inc.

Conciliatory Inductive Model Explaining the Origin of Changes in the η(2)-SiH Bond Length Caused by Presence of Strongly Electronegative Atoms X (X = F, Cl) in Cp(OC)2Mn[η(2)-H(SiH3-nXn)] (n = 0-3) Complexes

Using three theoretical methods, QTAIM, IQA, and NCI, we analyze an influence of halogen atoms X (X = F, Cl) substituted at various positions in the -SiH3-nXn group on the charge density distribution within the η(2)-SiH bond and on the SiH bond energies in Cp(OC)2Mn[η(2)-H(SiH3-nXn)] complexes and isolated HSiH3-nXn molecules. It is shown that shortening of the η(2)-SiH bond in Cp(OC)2Mn[η(2)-H(SiH3-nXn)] complexes should be considered as a normal inductive result of halogenation. This η(2)-SiH bond's compression may, however, be overcome by a predominant elongation resulting from a contingent presence of a halogen atom at position trans to the η(2)-SiH bond. This trans effect is particularly large for bulky and highly polarizable chlorine. Moreover, peculiar properties of the trans chlorine atom are manifested in several ways. To explain the origin of all the observed changes in both the length and the electron charge distribution of the η(2)-SiH bond in investigated Cp(OC)2Mn[η(2)-H(SiH3-nXn)] complexes a new model, called the Conciliatory Inductive Model, is being proposed.

Atomic charge transfer-counter polarization effects determine infrared CH intensities of hydrocarbons: a quantum theory of atoms in molecules model

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

QTAIM-based comparison of agostic bonds and intramolecular charge-inverted hydrogen bonds

Using DFT-based calculations with seven exchange-correlation functionals (BP86, B3LYP, B3PW91, PBE0, TPSSh, M06-L, M06) we have performed comparative studies on α-, β-, γ-, and δ-agostic bonds (ABs) and intramolecular charge-inverted hydrogen bonds (IMCIHBs). Our detailed analysis of values of QTAIM parameters computed at bond (BCP) and ring critical points (RCP) as well as of the curvatures of bond paths tracing agostic bonds and intramolecular charge-inverted hydrogen bonds gives the opportunity to distinguish between both these types of interactions. In the case of molecules with agostic bonds, the BCP is significantly closer to the agostic hydrogen, whereas in systems with IMCIHB the BCP is, instead, somewhat closer to the metal atom. Agostic bonds are characterized by H···M bond paths being straight in the BCP···M section and then highly curved near the agostic hydrogen, whereas in the case of IMCIHB any substantial curvature of BP in the vicinity of hydrogen is not present. Quite the contrary, the significant curvature of BP near the metal atom can be obtained, instead. One can also distinguish IMCIHBs and ABs on the basis of values of bond ellipticity at BCP and the electron density at RCP which are either somewhat (PBE0) or considerably (M06) greater for the latter type of interaction. It has also been shown that, in general, the exchange-correlation functional has small influences on most of QTAIM parameters computed at BCP and RCP. More significant influences have only been obtained for Laplacian of the electron density, some its components, and the bond ellipticity.

The structures of heterocyclic complexes ruled by hydrogen bonds and halogen interactions: interaction strength and IR modes

In this work, the existence of multiple interactions in heterocyclic complexes of C2H4O⋯nHCCl3 and C2H4S⋯nHCCl3 with n=2 and 3 was unveiled at the B3LYP/6-311++G(d,p) level of theory. The forward analyses of the vibrational spectra revealed the appearing of red-shifts in the H-C bond. In agreement with this and through the optimized geometries of these systems, an increase in the H-C bond length was also observed. Besides O⋯H and S⋯H, other hydrogen bonds formed between chlorine⋯hydrogen and mainly the halogen interactions formed by chlorine⋯chlorine were identified. Thereby, the vibration spectra of the heterocyclic complexes were reanalyzed with the purpose to locate new red-shifts, although only those characterized in H-C have been detected up to then. In addition to the correlation between the frequencies shifted to downward values followed by increases in the bond lengths, the interpretation of the red-shifts was conducted by means of the Bent rule of the hybridization theory. The interaction strength was examined in several viewpoints, and one of them was the relationship between the H-bond energies and the intermolecular electronic density computed by means of the Quantum Theory of Atoms in Molecules (QTAIM). Moreover, the prediction of the interaction strength was also made through the combination between vibration modes (red-shifts) and variation of topological parameters, such as the electronic density and Laplacian of the proton donor bond (C-H).

A theoretical analysis of atomic charge fluxes in chlorofluoromethanes and relationship with bonding character descriptors

Atomic substitutions in chlorofluoromethanes were analyzed through changes in the bond character descriptors and the related effect on electronic charge fluxes, given by the QTAIM model, which occur during atomic stretching displacements. Such interpretation of halogenation may provide new insights on reaction coordinate and halogen-bonding studies.

Topology of the electron density of d0 transition metal compounds at subatomic resolution

Accurate X-ray diffraction experiments allow for a reconstruction of the electron density distribution of solids and molecules in a crystal. The basis for the reconstruction of the electron density is in many cases a multipolar expansion of the X-ray scattering factors in terms of spherical harmonics, a so-called multipolar model. This commonly used ansatz splits the total electron density of each pseudoatom in the crystal into (i) a spherical core, (ii) a spherical valence, and (iii) a nonspherical valence contribution. Previous studies, for example, on diamond and α-silicon have already shown that this approximation is no longer valid when ultrahigh-resolution diffraction data is taken into account. We report here the results of an analysis of the calculated electron density distribution in the d(0) transition metal compounds [TMCH3](2+) (TM = Sc, Y, and La) at subatomic resolution. By a detailed molecular orbital analysis, it is demonstrated that due to the radial nodal structure of the 3d, 4d, and 5d orbitals involved in the TM-C bond formation a significant polarization of the electron density in the inner electronic shells of the TM atoms is observed. We further show that these polarizations have to be taken into account by an extended multipolar model in order to recover accurate electron density distributions from high-resolution structure factors calculated for the title compounds.