A complementary view to the bonding pattern in the N5 +cation an electron localization function and local temperature analysis

Indexación: ScieloThe electron localization function (ELF), a local measure of the Pauli repulsion effect, and the local Kohn-Sham temperature analysis, which is defined within the framework of a local thermodynamics description of density functional theory, have been used to explore the bonding characteristics in the open chain N5+ cation. It is found that both the ELF and local temperature maps depict uniquely the regions of pair localizations, yielding a description of bonding which agrees and complements previous techniques of analysis. Particularly, the three-center four-electron interaction in the NNN terminal atoms of N5+ and the contribution of terminal triple bonds to the bonding nature of the cation have been characterized in detail from the electron fluctuation among ELF basins populations. The features of bonding in terms of the local kinetic energy analysis have been visualized directly from the analysis of local temperature map.http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0717-97072003000400010&lang=p

Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators

As approximations to the wave functions governing quantum chemical systems become more and more complex, it is becoming increasingly important to devise descriptors that help understand the practical results of those approximations by condensing information in insightful ways. Quantum chemical descriptors that are able to capture the statistical signatures of quantum chemical interactions provide such conceptual building blocks. Central to an understanding of these descriptors is the concept of a "domain occupation number operator," which allows the so-called "real space" and Hilbert space partitionings to be treated on the same footing. Many of the existing descriptors can be expressed as the (central) densities and density cumulants associated with the domain operators. These densities can be obtained by successive differentiation of generating functions, effectively structuring domain associated densities into hierarchies. Not only do the resulting hierarchies indicate how many of the previously reported descriptors are related, they also show which areas have not yet been explored. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Method

Relationships between charge density response functions, exchange holes and localized orbitals

The charge density response function and the exchange hole are closely related to each other via the fundamental fluctuation-dissipation theorem of physics. A simple approximate model of the static response function is visually compared on several examples in order to demonstrate this relationship. This study is completed by illustrating the well-known isomorphism between the exchange hole and the square of the dominant localized orbital lying in the space region of the reference point of the exchange hole function. The implications of these relationships for the interpretation of common chemical concepts, such as delocalization, are discussed.Comment: 10 two-columns pages, including 3 figure

Bonding in methylalkalimetals (CH(3)M)(n) (M = Li, Na, K; n = 1, 4). Agreement and divergences between AIM and ELF analyses

The chemical bonding in methylalkalimetals (C

Curly arrows meet electron density transfers in chemical reaction mechanisms: from electron localization function (ELF) analysis to valence-shell electron-pair repulsion (VSEPR) inspired interpretation

Probing the electron density transfers during a chemical reaction can provide important insights, making possible to understand and control chemical reactions. This aim has required extensions of the relationships between the traditional chemical concepts and the quantum mechanical ones. The present work examines the detailed chemical insights that have been generated through 100 years of work worldwide on G. N. Lewis's ground breaking paper on The Atom and the Molecule (Lewis, G. N. The Atom and the Molecule, J. Am. Chem. Soc. 1916, 38, 762–785), with a focus on how the determination of reaction mechanisms can be reached applying the bonding evolution theory (BET), emphasizing how curly arrows meet electron density transfers in chemical reaction mechanisms and how the Lewis structure can be recovered. BET that combines the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT) provides a powerful tool providing insight into molecular mechanisms of chemical rearrangements. In agreement with physical laws and quantum theoretical insights, BET can be considered as an appropriate tool to tackle chemical reactivity with a wide range of possible applications. Likewise, the present approach retrieves the classical curly arrows used to describe the rearrangements of chemical bonds for a given reaction mechanism, providing detailed physical grounds for this type of representation. The ideas underlying the valence-shell-electron pair-repulsion (VSEPR) model applied to non-equilibrium geometries provide simple chemical explanations of density transfers. For a given geometry around a central atom, the arrangement of the electronic domain may comply or not with the VSEPR rules according with the valence shell population of the considered atom. A deformation yields arrangements which are either VSEPR defective (at least a domain is missing to match the VSEPR arrangement corresponding to the geometry of the ligands), VSEPR compliant or pseudo VSEPR when the position of bonding and non-bonding domains are interchanged. VSEPR defective arrangements increase the electrophilic character of the site whereas the VSEPR compliant arrangements anticipate the formation of a new covalent bond. The frequencies of the normal modes which account for the reaction coordinate provide additional information on the succession of the density transfers. This simple model is shown to yield results in very good agreement with those obtained by BET.We wish to thank Professors R. J. Gillespie, Henry H. Rzepa and Patrick Chaquin and L. R. Domingo for stimulating discussions and the referees for their very constructive comment

A Position-Space View on Chemical Bonding in Metal Digallides with AlB2 Type of Structure and Related Compounds

The main focus of this work was to investigate substitution effects on the chemical bonding in compounds of AlB 2 -type and related structure types. Delocalization indices within the QTAIM approach and the topological analysis of the ELI functionals were used as tools to describe the bonding situation in digallides and diborides. Digallides of AlB 2 -type were found only within group I and II; for CaGa 2 (meta-stable phase), SrGa 2 , BaGa 2 , YGa 2 and LaGa 2 compounds. Within these compounds, QTAIM analysis showed similar trend as previously found in diborides. That is, along the period in the Periodic Table, metal-triel interactions increase at the expense of in-plane (triel-triel) ab interactions (Tr=triel). However, transition metal diborides adopt the AlB 2 -type up to group VI. To understand this difference, we simulated transition metal (TM) digallides and diborides up to group VI in the AlB 2 -type. Additionally, the puckered variants diborides ReB 2 and OsB 2 were also simulated in the AlB 2 -type. With filling of d shell, there is a delicate balance between increase of TM–Tr and decrease of in-plane (Tr–Tr) ab electron sharing. This balance is maintained as long as interlayer interactions in the c direction (Tr–Tr ) c and (TM–TM ) c are not relatively too high in comparison to in-plane electron sharing. In contrast to TM B 2 of AlB 2 -type, digallides in the same structure type build up strong interlayer interactions for early transition metal elements. Our results showed that within digallides, a relatively strong increase in interlayer electron sharing (Ga–Ga) c and (TM–TM ) c takes place. Such increase occurs already for ScGa 2 and TiGa 2 . On the other hand, diborides show a steady increase in electron sharing of TM –B and (TM–TM ) c , but not of (B–B) c . Therefore, it is reasonable to suggest that diborides will tend to adopt a 3D network composed of boron and transition metal atoms (ReB 2 and RuB 2 types). The additional high (Ga–Ga) c interlayer interactions indicate a tendency for digallides to form 3D networks composed only by gallium atoms, characteristic of CaGa 2 (CaIn 2 -type) and ScGa 2 (KHg 2 -type). The counterbalancing bonding effects of in-plane and out-of-plane interactions that give the chemical flexibility of the AlB 2 -type in diborides is thus disrupted in AlB 2 -type digallides by a further enhanced degree of interlayer interactions (Ga–Ga) c and (TM –TM ) c . This results in a smaller number of digallides than that of diborides in AlB 2 -type. The most conspicuous difference between diborides and digallides of AlB 2 -type is in the representation of the B – B and Ga – Ga bonds revealed by the ELI- D topology. Whereas AlB 2 -type diborides exhibit one ELI-D attractor at the B – B midpoint, AlB 2 -type digallides exhibit two ELI-D attractors symmetrically opposite around the Ga – Ga bond midpoint. We utilized the E 2 H 4 (E=triel, tetrel ) molecular series in the D 2h point group symmetry as model systems for solid state calculations. In particular, we addressed the appearance of ELI- D double maxima for Ga – Ga, by using orbital decomposition within the ELI framework. The ELI-D topology changes along the 13th group T r 2 H 4 series. Whereas B 2 H 4 and Al 2 H 4 exhibit one ELI-D attractor representing the Tr–Tr bond, Ga 2 H 4 and In 2 H 4 give rise to two ELI-D attractors. Partial ELI-D allows the orbital decomposition of the electron density. Partial ELI-q gives access to the decomposition of a two-particle property, which is given by the Fermi-hole curvature. We have found that the d-orbitals enable the formation of the two ELI-D attractors through pairing contributions. This has a net effect of lowering electron localizability at the Ga – Ga bond midpoint. Namely, the different ELI-D topology of Ga – Ga and B – B bonds stems from the contributions of d-orbitals to orbital pairing. We have also investigated the bonding situation in transition metal diborides of ReB 2 -type (MnB 2 , TcB 2 , ReB 2) and RuB 2 -type (OsB 2 , RuB 2). One can consider these two structure types as an extension of the trend found in TM B 2 of AlB 2 -type: an increase in TM –B interactions and an enhanced three-center bonding. The change in the structure type results in a puckered layer of boron atoms with electrons equally shared between B – B and TM –B. However, TM –B bonds exhibit a high three-center character. The ELI-D/QTAIM intersection technique also revealed a high participation of TM in the B – B bonding basin population. Moreover, ELI-D topology in the ReB 2 -type also discloses a seemingly important Re 3 three-center interaction along the flat layer of Re atoms. Such basin is absent in MnB 2 , which coincides with the fact that MnB 2 was only observed in the AlB 2 -type. In this regard, we concluded that the 3D network consists not only of covalent B – B bonds, but also of TM –B bonds

Una perspectiva mecánica sobre la estabilidad del enlace químico

Tesis inédita de la Universidad Complutense de Madrid. Facultad de Ciencias Químicas, leída el 16-12-2019This PhD was devoted to demonstrating that the nature and intrinsic features of a given pairwise interaction (covalent, electrostatic, van der Waals, etc.) defines a suitable framework to relate both molecular and bulk properties. To reach this goal, we have considered classical, well-established concepts from the field of condensed matter and translated them into the molecular realm, and vice versa. Pairwise interactions rest on the idea that the physical and chemical properties of a system can be accurately described considering only the potential energy curve between the neighbor atoms or, in other words, how the energy changes with the distance between the interacting particles. Several authors have demonstrated that the shape of the potential energy curve can be considered universal regardless that we consider a molecule or a crystal, implying that its general characteristics are also universally applicable and transferable from one system to the others. This procedure has been profusely applied in chemistry and physics of the solid state, but it has important the important limitation that to transfer the characteristic parameters it is required to fit specific experimental properties. In other words, the shape of the interaction potential is universal, but the characteristic parameters are not. Developing a methodology capable of providing truly universal parameters is one of the major challenges of this PhD thesis and one of its underlying motivations. . Commonly used potential functions include those classical of Lennard-Jones, Born-Mayer and Mie-Grüneisen, or others borrowed from spectroscopy, like Rydberg, Morse and Sutherland. And an example of the success of considering the universality of the potential energy curve was provided in the introduction chapter of this PhD memo with the model relating the stretching forcé constant of diatomic molecules with the bulk modulus of their ionic, metallic and covalent counterpart crystals. The key ideas to put forward such relationship were: to assume that the distance dependence of the diatomic stretching force constant can be universally described, and that they can accurately describe the interaction between the same atoms in the crystal. These two assumptions can be only fulfilled if the pairwise potential shape is universal and its parameters can be universally transferred between molecules and crystals...El objetivo central de Tesis Doctoral ha sido demostrar que las características intrínsecas de una interacción entre pares de átomos dada (covalente, electrostático, van der Waals, etc.) permite establecer un marco interpretativo excelente para relacionar las propiedades mecánicas y químicas de las moléculas y los sólidos cristalinos caracterizadas por dicho tipo de enlace. Para alcanzar este objetivo, hemos tomado como base conceptos clásicos y ampliamente aceptados en materia condensada y los hemos trasladado al campo molecular; pero en otras ocasiones hemos recorrido el camino inverso, con el objetivo de demostrar que dichos conceptos pueden ser -y lo son de hecho- intercambiables entre sistemas materiales muy dispares. Las interacciones entre pares de átomos se fundamental en la idea de que las propiedades físicas y químicas de un sistema pueden describirse con precisión considerando sólo la curva de energía potencial entre los átomos vecinos; en otras palabras, cómo cambia la energía con la distancia entre las partículas que interaccionan. Algunos autores han demostrado en las últimas décadas que la forma de la curva de energía potencial puede considerarse universal, independientemente de que consideremos una molécula o un cristal, lo que implica que las características generales del potencial de interacción son también universalmente aplicables y transferibles de un sistema a otro. A pesar de que esta metodología se ha aplicado de forma exitosa y extensa en las áreas de la Química y la Física del Estado Sólido, tiene la limitación de que para transferir los parámetros característicos entre dos sistemas es necesario ajustar los parámetros característicos del potencial de interacción a propiedades experimentales específicas. En otras palabras, la forma del potencial de interacción es universal, pero los parámetros característicos no lo son. En consecuencia, uno de los mayores retos de esta Tesis Doctoral y una de sus motivaciones originales ha sido el de desarrollar una metodología capaz de proporcionar parámetros verdaderamente universales...Fac. de Ciencias QuímicasTRUEunpu

Topological analysis of the cd → β-Sn phase transition of group 14 elements

To understand the mechanism of a pressure-induced structural phase transition, it is important to know which bonding changes lead to the stabilization of the new structure. A useful approach in this regard is the quantum chemical topology, which provides a large variety of indicators for the characterization of interatomic interactions. In this work, a number of topological indicators are used to analyze the bonding changes during the pressure-induced phase transition from the cubic diamond (cd) to the β-Sn-type structure of the elements of the 14th group of the periodic table. The ability of these indicators to reflect the presence of the cd → β-Sn transition in experiment for Si, Ge and Sn and its absence for carbon is investigated. Furthermore, the effect of pressure on the interatomic interactions in the cd- and β-Sn-type structures is examined. It is observed that the energy change along the cd → β-Sn transformation pathway correlates with the evolution of certain parameters of the electron density and the electron localizability indicator (ELI-D). Accordingly, criteria of structural stability were formulated based on characteristics of interatomic interactions. These results can serve as guidelines for the investigation of other solid-state phase transformations by the topological methods