Chemical Bonds without “Chemical Bonding”? A Combined Experimental and Theoretical Charge Density Study on an Iron Trimethylenemethane Complex

Influence of N-protonation on electronic properties of acridine derivatives by quantum crystallography

Applications of 9-aminoacridine (9aa) and its derivatives span fields such as chemistry, biology, and medicine, including anticancer and antimicrobial activities. Protonation of such molecules can alter their bioavailability as weakly basic drugs like aminoacridines exhibit reduced solubility at high pH levels potentially limiting their effectiveness in patients with elevated gastric pH. In this study, we analyse the influence of protonation on the electronic characteristics of the molecular organic crystals of 9-aminoacridine. The application of quantum crystallography, including aspherical atom refinement, has enriched the depiction of electron density in the studied systems and non-covalent interactions, providing more details than previous studies. Our experimental results, combined with a topological analysis of the electron density and its Laplacian, provided detailed descriptions of how protonation changes the electron density distribution around the amine group and water molecule, concurrently decreasing the electron density at bond critical points of N/O-H bonds. Protonation also alters the molecular architecture of the systems under investigation. This is reflected in different proportions of the N⋯H and O⋯H intermolecular contacts for the neutral and protonated forms. Periodic DFT calculations of the cohesive energies of the crystal lattice, as well as computed interaction energies between molecules in the crystal, confirm that protonation stabilises the crystal structure due to a positive synergy between strong halogen and hydrogen bonds. Our findings highlight the potential of quantum crystallography in predicting crystal structure properties and point to its possible applications in developing new formulations for poorly soluble drugs.

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

Experimental and Computational Tuning of Metalla-N-Heterocyclic Carbenes at Palladium(II) and Platinum(II) Centers

Palladium(II) and platinum(II) complexes featuring metalla-N-heterocyclic carbenes (7–12) were synthesised via metal-mediated coupling between equimolar cis-[MCl2(CNR)2] (R = 2,6-Me2C6H3 (Xyl), 2,4,6-Me3C6H3 (Mes)] and 2-aminopyridine or 2-aminopyrazine. Thiocyanate complexes 13–18 with...

Metal–ligand bonding in tricarbonyliron(0) complexes bearing thiochalcone ligands

Bonding interactions between iron and thiochalcones in a series of recently synthesized complexes were analyzed using various theoretical methods.

Azide···Oxygen Interaction: A Crystal Engineering Tool for Conformational Locking

We have designed, synthesized and crystallized 36 compounds, each containing an azide group and an oxygen atom separated by three bonds. Crystal structure analysis revealed that each of these molecules adopts a conformation in which the azide and oxygen groups orient syn to each other with a short O ··· N b  contact. Geometry-optimized structures [using  M06-2X/6-311G(d,p) level of theory ] also showed the syn conformation in all 36 of these cases, suggesting that this not merely a crystal packing effect. Quantum topological analysis using Bader's Atoms in Molecules (AIM) theory revealed bond paths and bond critical points (BCP) in these structures suggesting its nature and energetics to be similar to weak hydrogen bonding. The NCI-RDG plot clearly revealed the attractive interaction consisting of electrostatic or dispersive components in all the 36 systems. NBO analysis suggested a weak orbital-relaxation (charge-transfer) contribution of energy for a few  (sp2) O-donor systems. Natural population analysis (NPA) and molecular electrostatic potential mapping (MESP) of these crystal structures further revealed the existence of favorable azide-oxygen interaction.   A CSD search indicated the frequent and consistent occurrence of this interaction and its role dictating the syn conformation of azide and oxygen in molecules where these groups are separated by 2-4 bonds.

Orbital-Free Quantum Crystallographic View on Noncovalent Bonding: Insights into Hydrogen Bonds, π⋅⋅⋅π and Reverse Electron Lone Pair⋅⋅⋅π Interactions

A detailed analysis of a complete set of the local potentials that appear in the Euler equation for electron density is carried out for noncovalent interactions in the crystal of a uracil derivative using experimental X-ray charge density. The interplay between the quantum theory of atoms in molecules and crystals and the local potentials and corresponding inner-crystal electronic forces of electrostatic and kinetic origin is explored. Partitioning of crystal space into atomic basins and atomic-like potential basins led us to the definite description of interatomic interaction and charge transfer. Novel physically grounded bonding descriptors derived within the orbital-free quantum crystallography provided the detailed examination of π-stacking and intricate C=O⋅⋅⋅π interactions and nonclassical hydrogen bonds present in the crystal. The donor-acceptor character of these interactions is revealed by analysis of Pauli and von Weizsäcker potentials together with well-known functions, e. g., deformation electron density and electron localization function. In this way, our analysis throws light on aspects of these closed-shell interactions hitherto hidden from the description.

Application of a quantum genetic algorithm and QTAIM analysis in the study of structural and electronic properties of neutral bimetallic clusters NaxLiy (4 ≤ x + y ≤ 10)

Alloy clusters of Na_xLi_y (4 ≤ x + y ≤ 10) are studied by exploring the potential energy surface in the ab initio MP2 level with the support of a quantum genetic algorithm (QGA). In some cases, the structures have been also refined with DFT and coupled-cluster methods. The general trends of sodium-lithium structures are in line with previous studies. The ionization potentials and polarizabilities to all structures were calculated with MP2 method and the average error between these two properties compared with experimental data was 6% and 13%, respectively. The topological analysis based on quantum theory of atoms in molecules (QTAIM) showed that by increasing the cluster size of the diatomic system there was a decrease of atomic interaction energies. The degree of degeneracy from D3BIA aromaticity index and the analysis of the atomic charges showed the influence (by charge transfer) of the chemical element in lower quantity in the cluster with respect to the other atoms. Our achievements of comparing our theoretical results with available experimental data have demonstrated that our approach can also predict satisfactorily quantum atomic and alloy clusters properties, at least, for low nuclearities.

Interatomic exchange-correlation interaction energy from a measure of quantum theory of atoms in molecules topological bonding: A diatomic case

The potential relations between the measure of topological interatomic bonding-integrals of electron density with respect to internuclear axis over the corresponding quantum theory of atoms in molecules (QTAIM)-defined interatomic surface (IAS)-and interatomic exchange-correlation contributions from the interacting quantum atoms approach are discussed. The quantum chemical computations of 38 equilibrium diatomic systems at different levels of theory (HF, MP2, MP4SDQ, and CCSD) are invoked to support abstract considerations. Parameters of excellent correlations between IAS integrals and interatomic exchange-correlation energy are found by the optimization. The performance of these trends depends on the accuracy of the electronic correlation treatment. The resulting trends are a unique feature of equilibrium states, whereas more complicated dependencies are explored for several systems at non-equilibrium conditions. The relations of established trends with other IAS-based estimations of strength of bonding interactions between topological atoms and issues explored for multiatomic systems are briefly discussed.

Perfluoroolefin complexes versus perfluorometallacycles and perfluorocarbene complexes in cyclopentadienylcobalt chemistry

Fluorocarbons have been shown experimentally by Baker and coworkers to combine with the cyclopentadienylcobalt (CpCo) moiety to form fluoroolefin and fluorocarbene complexes as well as fluorinated cobaltacyclic rings. In this connection density functional theory (DFT) studies on the cyclopentadienylcobalt fluorocarbon complexes CpCo(L)(C_nF_2n) (L = CO, PMe₃; n = 3 and 4) indicate structures with perfluoroolefin ligands to be the lowest energy structures followed by perfluorometallacycle structures and finally by structures with perfluorocarbene ligands. Thus, for the CpCo(L)(C₃F₆) (L = CO, PMe₃) complexes, the perfluoropropene structure has the lowest energy, followed by the perfluorocobaltacyclobutane structure and the perfluoroisopropylidene structure less stable by 8 to 11 kcal mol^-1, and the highest energy perfluoropropylidene structure less stable by more than 12 kcal mol^-1. For the two metal carbene structures Cp(L)Co[double bond, length as m-dash]C(CF₃)₂ and Cp(L)Co[double bond, length as m-dash]CF(C₂F₅), the former is more stable than the latter, even though the latter has Fischer carbene character. For the CpCo(L)(C₄F₈) (L = CO, PMe₃) complexes, the perfluoroolefin complex structures have the lowest energies, followed by the perfluorometallacycle structures at 10 to 20 kcal mol^-1, and the structures with perfluorocarbene ligands at yet higher energies more than 20 kcal mol^-1 above the lowest energy structure. This is consistent with the experimentally observed isomerization of the perfluorinated cobaltacyclobutane complexes CpCo(PPh₂Me)(-CFR-CF₂-CF₂-) (R = F, CF₃) to the perfluoroolefin complexes CpCo(PPh₂Me)(RCF[double bond, length as m-dash]CF₂) in the presence of catalytic quantities of HN(SO₂CF₃)₂. Further refinement of the relative energies by the state-of-the-art DLPNO-CCSD(T) method gives results essentially consistent with the DFT results summarized above.

Observing the 3D Chemical Bond and its Energy Distribution in a Projected Space

Our curiosity-driven desire to "see" chemical bonds dates back at least one-hundred years, perhaps to antiquity. Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric understanding of molecules and materials, heighten this desire with means and significance. Here we present a method for analyzing chemical bonds and their energy distributions in a two-dimensional projected space called the condensed charge density. Bond "silhouettes" in the condensed charge density can be reverse-projected to reveal precise three-dimensional bonding regions we call bond bundles. We show that delocalized metallic bonds and organic covalent bonds alike can be objectively analyzed, the formation of bonds observed, and that the crystallographic structure of simple metals can be rationalized in terms of bond bundle structure. Our method also reproduces the expected results of organic chemistry, enabling the recontextualization of existing bond models from a charge density perspective.

A Neutral "Aluminocene" Sandwich Complex: η1 - versus η5 -Coordination Modes of a Pentaarylborole with ECp* (E=Al, Ga; Cp*=C5 Me5 )

The pentaaryl borole (Ph*C)₄ BXyl^F [Ph*=3,5-tBu₂ (C₆ H₃ ); Xyl^F =3,5-(CF₃ )₂ (C₆ H₃ )] reacts with low-valent Group 13 precursors AlCp* and GaCp* by two divergent routes. In the case of [AlCp*]₄ , the borole reacts as an oxidising agent and accepts two electrons. Structural, spectroscopic, and computational analysis of the resulting unprecedented neutral η⁵ -Cp*,η⁵ -[(Ph*C)₄ BXyl^F ] complex of Al^III revealed a strong, ionic bonding interaction. The formation of the heteroleptic borole-cyclopentadienyl "aluminocene" leads to significant changes in the ¹³ C NMR chemical shifts within the borole unit. In the case of the less-reductive GaCp*, borole (Ph*C)₄ BXyl^F reacts as a Lewis acid to form a dynamic adduct with a dative 2-center-2-electron Ga-B bond. The Lewis adduct was also studied structurally, spectroscopically, and computationally.

Polarization of Electron Density Databases of Transferable Multipolar Atoms

Polarizability is a key molecular property involved in either macroscopic (i.e., dielectric constant) and microscopic properties (i.e., interaction energies). In rigid molecules, this property only depends on the ability of the electron density (ED) to acquire electrostatic moments in response to applied electric fields. Databases of transferable electron density fragments are a cheap and efficient way to access molecular EDs. This approach is rooted in the relative conservation of the atomic ED between different molecules, termed transferability principle. The present work discusses the application of this transferability principle to the polarizability, an electron density-derived property, partitioned in atomic contributions using the Quantum Theory of Atoms In Molecules topology. The energetic consequences of accounting for in situ deformation (polarization) of database multipolar atoms are investigated in detail by using a high-quality quantum chemical benchmark.

Crystal structure, interaction energies and experimental electron density of the popular drug ketoprophen

The crystal and molecular structure of the pure (S)-enantiomer of the popular analgesic and anti-inflammatory drug ketoprophen (α-ket) is reported. A detailed aspherical charge-density model based on high-resolution X-ray diffraction data has been refined, yielding a high-precision geometric description and classification of the O-H⋯O interactions as medium strength hydrogen bonds. The crystal structure of the racemic form of ketoprophen (β-ket) was also redetermined at 100 K, at 0.5 Å resolution. A previously unreported disorder (10% occupancy) was discovered. In contrast to the racemic β-ket case, the (S)-enantiomer crystallizes with two independent molecules in the asymmetric unit with two distinct conformations. The major difference between the β-ket and α-ket crystal forms lies in the formation of distinct hydrogen-bonded motifs: a closed ring motif in β-ket versus infinite chains of hydrogen bonds in the chiral α-ket structure. However, the overall crystal packing of both forms is surprisingly similar, with close-packed layers of antiparallel-oriented benzo-phenone moieties bound by C-H⋯π interactions. Notably, the most important stabilizing term in the total lattice energies in both instances proved to be the dispersion related to these interactions. Both forms of the title compound (α- and β-ket) were additionally characterized by differential scanning calorimetry and thermogravimetric analysis.

FALDI-based criterion for and the origin of an electron density bridge with an associated (3,-1) critical point on Bader's molecular graph

The total electron density (ED) along the λ₂ -eigenvector is decomposed into contributions which either facilitate or hinder the presence of an electron density bridge (DB, often called an atomic interaction line or a bond path). Our FALDI-based approach explains a DB presence as a result of a dominating rate of change of facilitating factors relative to the rate of change of hindering factors; a novel and universal criterion for a DB presence is, thus, proposed. Importantly, facilitating factors show, in absolute terms, a concentration of ED in the internuclear region as commonly observed for most chemical bonds, whereas hindering factors show a depletion of ED in the internuclear region. We test our approach on four intramolecular interactions, namely (i) an attractive classical H-bond, (ii) a repulsive O⋅⋅⋅O interaction, (iii) an attractive Cl⋅⋅⋅Cl interaction, and (iv) an attractive CH⋅⋅⋅HC interaction. (Dis)appearance of a DB is (i) shown to be due to a "small" change in molecular environment and (ii) qualitatively and quantitatively linked with specific atoms and atom-pairs. The protocol described is equally applicable (a) to any internuclear region, (b) regardless of what kind of interaction (attractive/repulsive) atoms are involved in, (c) at any level of theory used to compute the molecular structure and corresponding wavefunction, and (d) equilibrium or nonequilibrium structures. Finally, we argue for a paradigm shift in the description of chemical interactions, from the ED perspective, in favor of a multicenter rather than diatomic approach in interpreting ED distributions in internuclear regions. © 2018 Wiley Periodicals, Inc.

Bond paths between distant atoms do not necessarily indicate dominant interactions

The goal of the article is to revive discussion on the interpretation of bond paths linking distant atoms, particularly tracing weak interactions in dimers. According to the Pendás' concept of privileged exchange channel, a bond path is formed between this pair of competing atoms, which is associated with larger value of the exchange energy. We point out that, due to the short-range nature of the exchange energy, bond paths linking distant atoms clearly become doubtful indicators of dominant intermolecular interactions, particularly if some other characteristics (geometric, spectroscopic, based on electrostatic parameters, etc.) indicate other intermolecular interactions as dominant. Several such cases are thoroughly investigated. We show that electrostatic parameters are much more reliable indicators of dominant intermolecular interactions than bond paths. Then, we pay attention that the presence of ("unexpected", i.e., not necessarily indicating dominant intermolecular interactions) bond paths between pairs of atoms featuring highly expanded charge distributions can be easily explained by visual exploration of isodensity contour plots. As always pointing in the direction of the steepest increase, the gradient vector of the electron density favors areas of its high values gaining higher exchange energy, yet being blind to highly electron deficient areas nearby, which, however, can quite often be involved in dominant intermolecular interactions as strongly suggested by many other bonding analysis. We also suggest that an interatomic component of Hellmann-Feynman force would most likely be the most reliable indicator of attractive or repulsive character of individual interatomic interaction. © 2018 Wiley Periodicals, Inc.

Experimental charge density study on FLPs and a FLP reaction product

The charge density distribution of the intramolecular frustrated Lewis pair (FLP) Mes2PCH2CH2B(C6F5)2 (1), the phosphinimine HNPMes2CH2CH2B(C6F5)2 (2), as well as a FLP homologue with nitrogen NEt2CHPhCH2B(C6F5)2 (3) were investigated with Bader’s quantum theory of atoms in molecules (QTAIM). The charge densities were derived from both experimental high-resolution X-ray diffraction data (2, 3) and theoretical calculations (1, 3). The QTAIM analysis for the FLPs 1 and 3 showed the prominent B-pnictogen interaction to be weak dative bonds without significant charge-transfer. This holds also true for the B–N–bond of 2. The nitrogen atom is negatively charged, due to a charge transfer from phosphorous and shows features of a sp2-hybridization. The bond is therefore best described as a non-hypervalent Pδ+–Nδ− moiety.

Revitalizing the concept of bond order through delocalization measures in real space

Ab initio quantum chemistry is an independent source of information supplying an ever widening group of experimental chemists. However, bridging the gap between these ab initio data and chemical insight remains a challenge. In particular, there is a need for a bond order index that characterizes novel bonding patterns in a reliable manner, while recovering the familiar effects occurring in well-known bonds. In this article, through a large body of calculations, we show how the delocalization index derived from Quantum Chemical Topology (QCT) serves as such a bond order. This index is defined in a parameter-free, intuitive and consistent manner, and with little qualitative dependency on the level of theory used. The delocalization index is also able to detect the subtler bonding effects that underpin most practical organic and inorganic chemistry. We explore and connect the properties of this index and open the door for its extensive usage in the understanding and discovery of novel chemistry.

Benchmarking lithium amide versus amine bonding by charge density and energy decomposition analysis arguments

We investigated [{(Me₂NCH₂)₂(C₄H₂N)}Li]₂ (1) by means of experimental charge density calculations based on the quantum theory of atoms in molecules (QTAIM) and DFT calculations using energy decomposition analysis (EDA).

Lithium amides are versatile C–H metallation reagents with vast industrial demand because of their high basicity combined with their weak nucleophilicity, and they are applied in kilotons worldwide annually. The nuclearity of lithium amides, however, modifies and steers reactivity, region- and stereo-selectivity and product diversification in organic syntheses. In this regard, it is vital to understand Li–N bonding as it causes the aggregation of lithium amides to form cubes or ladders from the polar Li–N covalent metal amide bond along the ring stacking and laddering principle. Deaggregation, however, is more governed by the Li←N donor bond to form amine adducts. The geometry of the solid state structures already suggests that there is σ- and π-contribution to the covalent bond. To quantify the mutual influence, we investigated [{(Me₂NCH₂)₂(C₄H₂N)}Li]₂ (1) by means of experimental charge density calculations based on the quantum theory of atoms in molecules (QTAIM) and DFT calculations using energy decomposition analysis (EDA). This new approach allows for the grading of electrostatic Li⁺N^–, covalent Li–N and donating Li←N bonding, and provides a way to modify traditional widely-used heuristic concepts such as the –I and +I inductive effects. The electron density ρ(r) and its second derivative, the Laplacian ∇²ρ(r), mirror the various types of bonding. Most remarkably, from the topological descriptors, there is no clear separation of the lithium amide bonds from the lithium amine donor bonds. The computed natural partial charges for lithium are only +0.58, indicating an optimal density supply from the four nitrogen atoms, while the Wiberg bond orders of about 0.14 au suggest very weak bonding. The interaction energy between the two pincer molecules, (C₄H₂N)₂^2–, with the Li₂²⁺ moiety is very strong (ca. –628 kcal mol^–1), followed by the bond dissociation energy (–420.9 kcal mol^–1). Partitioning the interaction energy into the Pauli (ΔE_Pauli), dispersion (ΔE_disp), electrostatic (ΔE_elstat) and orbital (ΔE_orb) terms gives a 71–72% ionic and 25–26% covalent character of the Li–N bond, different to the old dichotomy of 95 to 5%. In this regard, there is much more potential to steer the reactivity with various substituents and donor solvents than has been anticipated so far.

The truth is out there: the metal-π interactions in crystal of Cr(CO)3(pcp) as revealed by the study of vibrational smearing of electron density

The vibrational smearing of electron density was studied in the crystal of complex of Cr(CO)3 with [2.2]paracyclophane. The combination of theoretical and experimental methods, including periodic calculations and screening of DFT calculated and multipole-decomposed electron densities, was utilized to reveal the vibrational smearing of electron density and its influence on the multipole-constructed electron density. The multipole model, commonly used to treat the high-resolution X-ray diffraction data, was shown to be rather inaccurate in description of electron density and its vibrational smearing in metal-π complex where the interchange between diatomic interactions can occur. Namely, some bond critical points can be hidden while analyzing multipole-decomposed electron density with proved effects of vibrational smearing even if the deconvolution problem is overcome by using the invariom approach. On the contrary, the recently proposed “clouds of critical point variation” (CCPV) approach is demonstrated as the route to gather all reasonable bonding trends and to reconstruct static electron density pattern in metal-π complexes.

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 thetheoreticalspin density in azido CuIIdinuclear complexes, where the azido group, acting as a coupler between the CuIIcations, 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 ραand ρβderived from different approaches does not warrant a corresponding agreement between their associated spin densities.

The future of topological analysis in experimental charge-density research

In a recent paper, Dittrich (2017) critically discussed the benefits of analysing experimental electron density within the framework of the quantum theory of atoms in molecules, often called simply the topological analysis of the charge density. The point he raised is important because it challenges the scientific production of a very active community. The question whether this kind of investigation is still sensible is intriguing and it fosters a multifaceted answer. Granted that none can predict the future of any field of science, but an alternative point of view emerges after answering three questions: Why should we investigate the electron charge (and spin) density? Is the interpretative scheme proposed by the quantum theory of atoms in molecules useful? Is an experimental charge density necessary?

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.

Transferable Aspherical Atom Modeling of Electron Density in Highly Symmetric Crystals: A Case Study of Alkali-Metal Nitrates

A comparative electron density study (from X-ray diffraction and periodic quantum chemistry) of sodium and potassium nitrates is performed to test the performance of a transferrable aspherical atom model, which is based on the invarioms, to describe chemical bonding features of ions occurring in sites of different symmetry typical of inorganic salts and in different crystal environments. Relying on tabulated entries for the isolated ions (although tailor-made to account for different site symmetries), it takes the same time to employ as the spherical atom model routinely used in X-ray diffraction studies but provides an electron density distribution that faithfully reveals all the interionic interactions-even the weakest ones (such as between the nitrate anions or a K···N interaction found in the metastable form of KNO₃) yet important for properties of inorganic materials-as if obtained from high-resolution X-ray diffraction data.

Binuclear chromium carbonyl complexes of methylaminobis(difluorophosphine): metal–metal bonds versus four-electron donor bridging carbonyl groups

[MeN(PF₂)₂]_mCr₂(CO)_n (m = 1, n = 10, 9, 8; m = 2, n = 8, 7, 6; m = 3, n = 6, 5, 4) have been studied theoretically. Low-energy structures with four-electron donor groups and split ligands are found.

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.

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.

Unsaturation in binuclear heterometallic carbonyls: the cyclopentadienyliron manganese carbonyl CpFeMn(CO)n system as a hybrid of the Cp2Fe2(CO)n and Mn2(CO)n systems

The structures and energetics of the CpFeMn(CO)_n (n = 7, 6, 5) have been examined by density functional theory.

Actinide (An = Th-Pu) dimetallocenes: promising candidates for metal-metal multiple bonds

Synthesis of complexes with direct actinide-actinide (An-An) bonding is an experimental 'holy grail' in actinide chemistry. In this work, a series of actinide dimetallocenes An2Cp (Cp(*) = C5(CH3)5, An = Th-Pu) with An-An multiple bonds have been systematically investigated using quantum chemical calculations. The coaxial Cp(*)-An-An-Cp(*) structures are found to be the most stable species for all the dimetallocenes. A Th-Th triple bond is predicted in the Th2Cp complex, and the calculated An-An bond orders decrease across the actinide series from Pa to Pu. The covalent character of the An-An bonds is analyzed by using natural bond orbitals (NBO), molecular orbitals (MO), the quantum theory of atoms in molecules (QTAIM), and electron density difference (EDD). While Th 6d orbitals dominate the Th-Th bonds in Th2Cp, the An 6d-orbital characters decrease and 5f-orbital characters increase for complexes from Pa2Cp to Pu2Cp. All these actinide dimetallocenes are stable in the gas phase relative to the AnCp(*) reference at room temperature. Based on the reactions of AnCp and An, Th2Cp, Pa2Cp and possibly also U2Cp should be accessible as isolated molecules under suitable synthetic conditions. Our results shed light on the molecular design of ligands for stabilizing actinide-actinide multiple bonds.