Fundamental nature of chemical bonding from the novel Fragment Atom Localised Delocalised and Interatomic (FALDI) electron density decomposition scheme: A theoretical study

Abstract

The primary novel development of this work is the derivation and implementation of the Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) electron density decomposition. FALDI is a quantum chemical analytical scheme that is atom-centric and density-based. The FALDI scheme decomposes the electron density at any given coordinate into various 1- and 2-centre contributions related to the correlated probability of finding two electrons simultaneously at two coordinates – the electron pair density. At its base level, FALDI provides real-space, molecular-wide distributions of electrons localized to a single atom or electrons delocalized amongst two different atoms, thereby providing a holistic approach to a quantum mechanical definition of an atom in a molecule and extending Bader’s Quantum Theory of Atoms in Molecules (QTAIM). This thesis further provides a number of applications of the FALDI density decomposition scheme. It is shown that FALDI fully recovers general chemist’s notions of core, nonbonded and valence electrons of an atom, for the first time in topological approaches. FALDI provides real-space distributions of exclusively localized and delocalized electrons throughout the entire molecular space, and can visualize and quantify various modes of (de)localized density such as σ- or π-bonding modes or core s electrons. The local concentration or depletion of FALDI fields are also shown, and provide a measure of absolute rather than relative electron accumulation or depletion. In this regard, distributions of electron density with a bonding, nonbonding or antibonding natures are derived, and it is shown how such distributions link to similarly named concepts in Molecular Orbital (MO) bond theory. Bonding and nonbonding electron density distributions are used to (i) show the multicenter nature of various intramolecular interactions, ranging from classical covalent bonds to H-bonds to organometallic carbene bonds, and (ii) derive an in-depth analytical tool to investigate the origins and nature of Bader’s atomic interaction lines (AILs). It is shown that AILs are predominantly multicenter in nature and arise as a result of an increased rate of change of FALDI’s bonding density relative to the rate of change of nonbonding density. Using the FALDI decomposition, a scheme for calculating a change in density between two states (deformation densities) as a result of conformational transformation is developed. The resulting conformational deformation density breaks the limitation of orthodox deformation density schemes in the study of of intramolecular interactions and their formation. It is shown that such conformational deformation densities (as well as their subsequent decomposition into FALDI components) provide a very useful analytical tool for researchers to investigate the effects on the electron density distribution from the formation of any chemical bond. As a case study, the formation of intramolecular red- and blue-shifted H-bonds is investigated and it is concluded that these bonds show a fundamentally distinct nature. The FALDI density decomposition scheme provides a very strong step towards a consistent and universal interpretation of chemical bonding from an atom-centric, multi-centre and density-based approach. It recovers classical and MO-based notions of atomic structures and chemical bonding, but also reveals a number of novel insights regarding the nature of molecular electron density distributions.