Carlo Gatti

Evaluation of net atomic charges and atomic and molecular electrostatic moments through topo- logical analysis of the experimental charge density

The atoms in molecules (AIM) theory may be used to derive atomic charges, atomic volumes and molecular dipole moments from the charge density. The theory is applied to theoretical periodic Hartree-Fock (PHF), density-functional (DFT) and experimental X-ray densities of p-nitroaniline using the program TOPOND and a newly developed program, TOPXD, for topological analysis of densities described by the Coppens-Hansen multipole formalism. Results show that, like dipole moments derived directly from the multipole refinement, AIM-derived atomic and molecular moments are dependent on the multipole model used. As expected, large differences are found between charges derived from the monopole parameters and those from AIM analysis of the experimental model density. Differences between the k-restricted multipole model (KRMM) and the unrestricted multipole model (UMM) results are preserved in the AIM analysis. The enhancement of the molecular dipole moment of p-nitroaniline in the solid state is confirmed by both experiment and theory but the experimental dipole moment is in much better agreement with theoretical periodic Hartree-Fock and, especially, periodic DFT (PDFT) data when KRMM is used in the refinement. The AIM analysis allows a rigorous definition of the charges of the atoms in molecules and provides a realistic basis for comparison between molecules and between experiment and theory.

On the origin of topological differences between experimental and theoretical crystal charge densities

Topological analysis of experimental and theoretical (molecular and crystal) electron densities of p-nitroaniline and p-amino-p-nitrobiphenyl reveals considerable discrepancies between experiment and theory for the bond critical points properties. Particularly large differences occur for the positive curvature along the bond path (lambda 3). The differences become somewhat smaller when more extended basis sets and correlation effects are introduced in the theoretical calculations. The effect of the crystal matrix on the properties of bond critical points is evaluated for the p-nitroaniline molecule using the 6-21G** and 6-31G** basis sets. The differences between the isolated molecule and the molecule in the crystal are too small to explain the quantitative disagreement between the theoretical and experimental topologies reported in the literature and found in the current study. For most bonds, the observed changes in the properties of the electron density agree well for both basis sets but some discrepancies are found for changes in lambda 3 for N-H and aromatic C-C bonds. When the theoretical densities are projected into the multipole density functions through refinement of the theoretical structure factors, the topological properties change and differences between theory and experiment are reduced. The main origin of the observed discrepancies is attributed to the nature of the radial functions in the experimental multipole model.

Comparative study of X-ray charge-density data on CoSb3.

CoSb3 is an example of a highly challenging case for experimental charge-density analysis due to the heavy elements (suitability factor of ~0.01), the perfect crystallinity and the high symmetry of the compound. It is part of a family of host-guest structures that are potential candidates for use as high-performance thermoelectric materials. Obtaining and analysing accurate charge densities of the undoped host structure potentially can improve the understanding of the thermoelectric properties of this family of materials. In a previous study, analysis of the electron density gave a picture of covalent Co-Sb and Sb-Sb interactions together with relatively low atomic charges based on state-of-the-art experimental and theoretical data. In the current study, several experimental X-ray diffraction data sets collected on the empty CoSb3 framework are compared in order to probe the experimental requirements for obtaining data of high enough quality for charge-density analysis even in the case of very unsuitable crystals. Furthermore, the quality of the experimental structure factors is tested by comparison with theoretical structure factors obtained from periodic DFT calculations. The results clearly show that, in the current study, the data collected on high-intensity, high-energy synchrotron sources and very small crystals are superior to data collected at conventional sources, and in fact necessary for a meaningful charge-density study, primarily due to greatly diminished effects of extinction and absorption which are difficult to correct for with sufficient accuracy.

The electron density in flavones I. Baicalein

The experimental charge density distribution of 5,6,7-trihydroxyflavone (1), has been determined from high-resolution X-ray diffraction data collected at 100 K. Additionally, high level single-point gas-phase calculations as well as periodic calculations have been carried out for (1). To our surprise, the topological analysis of the experimental electron density revealed a cage critical point in the geometric center of the tri-hydroxy substituted aromatic ring. This feature was independently confirmed by analysis of another study of 1. However, both high-level gas-phase and periodic ab initio calculations failed to reproduce this feature. The degree of bias on the electron density by using the Hansen–Coppens multipole model was tested by a multipole refinement of generated theoretical structure factors. This clearly showed that the cage critical point is not an artefact resulting from the use of the multipole model. Compound 1 contains a large number of weak, intermolecular hydrogen bonds and these are analysed using the Atoms in Molecules (AIM) approach, which leads to quantitative measures for hydrogen bond strength. The experimentally derived lattice energy of −467 kJ mol−1 shows a rather strongly held crystal lattice.

Operational comparison of various thermodynamic treatments of organic substance adsorption at the electrode/solution interface☆

Abstract Three isotherms are considered: Frumkins Bennes and Mohilners. The relationship between the interaction parameters in the first two and the adsorbate activity coefficient in the last is discussed. The significance of various standard states for the definition of ΔG° ads is analysed. The operational derivation of ΔG°ads in the three cases and the relationship between the resulting three quantities are illustrated. The isotherms have been used to describe the adsorption of 1,4-dioxane on a polarized Hg electrode. The analysis has been carried out both at constant potential and constant charge. The picture emerging in each of the three cases is discussed in the light of the results obtained in the other two. It is concluded that the three approaches give the same qualitative information about the interfacial behaviour of dioxane, especially as far as the effect of the electric field and the particle-particle lateral interaction are concerned. The usefulness of the Frumkin isotherm for analysing promptly experimental adsorption data is thus maintained. Limitations of the present approach are discussed.

Generalized self-consistent valence bond method for ground and excited potential energy surfaces

A new method is presented for computing ground and excited states potential energy surfaces, within the context of the valence bond (VB) theory, retaining the possibility of describing electronic molecular changes in terms of valence bond structure concepts. The separated electron pair (SEP) theory in the rank two geminal approximation is reformulated and compounded with the straightforward VB formalism: the set of non-orthogonal orbitals generated by the SEP optimization is used to construct VB structures, which allow a compact and correct description of the wavefunction. The procedure is applied to the study of the ground and excited states of LiH of Σ and Π symmetry (A 1Σ+, C 1Σ+, a 3Σ, b 3Π, B 1Π). All the qualitative features of these states are reproduced, including the peculiarities of the A 1Σ+ state. Each state is described by one to four structures, from small values of the internuclear distance up to dissociation: a clear interpretation of the wavefunction is therefore provided.

Challenging Problems in Charge Density Determination: Polar Bonds and Influence of the Environment

The review focuses on the influence of environments on electron densities (ED) and their Laplacians. This is of interest for many applications which uses EDs measured at hand of crystals of a given ligand to predict its pharmaceutical properties. This comprises for example the questions if the ligand fits into the active center of an enzyme and how strong it binds to this active side. This widely used approximation strongly rely on the assumption that the active side of the enzyme influences the ED of the ligand the same way the crystal environment does. This is not obvious since enzymes represent systems made to catalyze reactions. So one could assume that the active sides influence the EDs of ligands in a special way to prepare them for a given reaction. The review shows that this is indeed the case for E64c. Its inhibition properties result since it reacts with cathepsin B and forms a covalently bonded cathepsin B–E64c complex. It clearly comes out that the reaction only takes place since the ED of the ligand is influenced in a way which is not found in the respective crystals. Nevertheless, the review also shows that the above mentioned approximation holds for AMCHA which serves as a model compound for reversible inhibitors. In the last part the review shows in detail that the source function can be used to study the influence of the environment in more detail. In the first part the review summarizes investigations on the reliability of pure theoretical approaches to ED and its Laplacians.

Modeling environmental effects on charge density distributions in polar organometallics: Validation of embedded cluster models for the methyl lithium crystal

The charge density and its Laplacian at the Liuf8ffC and Cuf8ffH bond critical points and other features of the electron density distribution of the methyl lithium crystal have been compared by density functional methods for (i) the isolated (LiCH3)4 tetramer or larger clusters, (ii) for quantum mechanically treated clusters in polarizable continuum model (PCM) surroundings, (iii) for clusters augmented by the periodic electrostatic embedded cluster model (PEECM), and for (iv) the periodic crystal. Comparisons with identical functional and basis sets indicate that both PCM and PEECM embedding of only a tetramer did not fully account for the environmental effect. In contrast, embedding of a full unit cell gave results that were essentially converged to the periodic crystal data. Effects of basis set and exchange correlation functional on the QTAIM bond descriptors are of a comparable order of magnitude as the crystal environmental effects. In this context, embedded cluster computations provide distinct advantages over explicit solid‐state calculations with respect to their freedom of the choice of computational and theoretical level. This is demonstrated by embedded MP2 calculations.

Cyclopropane ring closure in 11,11-disubstituted 1,6-methano [10] annulenes

Abstract The effect of substituents at the bridging carbon atom of 11,11-disubstituted 1,6-methano [10]annulenes is investigated by means of the topological theory of molecular structure 3-21G ab initio calculations of the potential energy hypersurface of the parent hydrocarbon, within C2v symmetry constraints, indicate three distinct stationary points, which correspond to the norcaradienic structure (1), the annulenic structure (2) and the transition state (TS) for their interconversion. Topological analysis of the charge density of the three stationary points shows that 1 is built by two 6MRs and one 3MR condensed on the C1ue5f8C6 bond, while 2 is formed by two 7MRs which share the C1ue5f8C11 and C6ue5f8C11 bonds. In TS the 3MR and C1ue5f8C6 bond critical points merge to yield a singularity in ϱ and the system goes through a catastrophe configuration of the bifurcative type. The bond equalization in 2 is far from being complete and, beside the fundamental 10π-electron aromatic system, a conjugative coupling of the bridging bonds to the [10]annulenic framework is of a clear-cut relevance.

Substituent effect on the planarization energy and the relative stability of Winstein and Möbius structures of the homotropylium cation

Abstract The substituent (OH, OC 2 H 5 , Cl, z.sbnd;CHue5fbCHue5f8CHue5fbCHue5f8) effects on the relative stabilities of Winstein and Mobius structures of the homotropylium cation, 1 , have been investigated by the MNDO model. Electron donor substituent at C 1 , C 3 , C 5 , and C 7 favor Mobius structures in the order C 1 ,C 7 >C 3 ,C 5 , whereas Winstein structures are stabilized by electron donor substituents at position C 2 , C 4 , and C 6 , and in the order C 2 ,C 6 > C 4 . Electron withdrawing substituents at C 8 enhance stability of the homoaromatic structures, in the order OH>Cl. In any case, the substituent effect is found to be nearly additive. The reaction path for the three-carbon membered ring opening the eight-carbon membered ring inversion has been derived for all the compounds investigated. The equilibrium populations of Winstein Mobius structures were then obtained from the calculated probability distribution functions along the reaction path. The unsubstituted compound 1 was found to be a non-homoaromatic cation in the gas phase, as it adopts a Mobius conformation with a large C 1 -C 7 , internuclear distance.