From bonding to molecular properties in the context of quantum chemical topology

Abstract

The chemical bond might be considered as the central pillar of chemistry. Not being a quantum mechanical observable, however, its understanding escapes a rigorous theoretical foundation. In this scenario, historic events, not scientific reasoning, have conditioned the prevailing models on chemical bonding. It is in this way that molecular orbital (MO) theory has achieved its present status, becoming so rooted in modern chemistry that much of the chemist vocabulary comes from it. Taken from a non-MO biased perspective, however, MO theory is strangely based on objects that live on a complex multidimensional space that rarely evokes the natural chemical intuition, made up of considering electrons as entities living in real space. Under this premise a theory of chemical bonding in real space has flourished that has as a clear exponent in the Quantum Theory of Atoms in Molecules (QTAIM) proposed by Richard Bader and coworkers. Based on the space partition proposed by QTAIM, we highlight in this Ph.D. thesis the possibility of performing an energy partitioning (IQA), of measuring the probabilities of the possible electron populations in the QTAIM regions (EDFs), and of exploring effective one-electron images valid for correlated systems that mimic those of the MO paradigm (NAdOs). Specifically, we have emphasized the suitability of the IQA energy partition to define a theoretically sound bond energy, called in situ bond energy. This combined with the other tools mentioned above allows us to know, under special circumstances, what the valence state of the molecular fragments are and how the binding components are formed, all this contributing to a very intimate understanding of both their electronic behavior in equilibrium as well as at the different stages of the formation of bonds. Considering the trends towards ever larger systems and the particularly expensive scaling of IQA so far, in part due to the calculation of the exchange-correlation between two different basins, we have also proposed to carry out a multipolar approximation of this term, in the same fashion as for the Coulombic interaction energy. This approach has been shown to be accurate, even with a truncation to at most charge-quadrupole interaction terms, if the interacting basins are far enough from each other. The approach has been tested with a varied selection of molecules. Also, the connection of the first term of the expansion and one of the most important descriptors in the QTAIM, the delocalization index, is also established. Bonding descriptors housed under the framework of Quantum Chemical Topology (QCT) can also be shown to be involved in the explanation of a broader class of chemical phenomena. In this thesis, it has been pointed out that a link exists between bond order indices and the localization tensor used in the modern theory of the insulating state. The last one signals insulating or conducting behavior based on its convergence or divergence properties in the thermodynamical limit. After a partitioning of space we have demonstrated that convergence/divergence of the tensor depends only on interatomic components that in turn are dominated by the delocalization index. Thus a chemically appealing notion of the localization tensor is gained in the process. Another topic of interest that we have deald with is the study of weak interactions in molecular solids. For this, we have taken advantage of the topological properties that the electrostatic potential presents. Because the previous work in the literature on the topology of the electrostatic potential in solids is scarce, we have undertaken first an exploration of its characteristincs in the charge-complex BTDMTTF-TCNQ. The interactions predicted both by the density and the electrostatic potential were searched exhaustively, being later intertwined to provide a better understanding of the crystal packaging. Also from the combined partition of space, we deciphered which are the main actors driving the charge transfer.