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.