## Non-covalent interactions and their role in biological and catalytic chemistry

##### Abstract

The focus of this thesis is the question of how non-covalent
interactions affect chemical systems' electronic and structural properties.
Non-covalent interactions can exhibit a range of binding strengths,
from strong electrostatically-bound salt bridges or multiple hydrogen
bonds to weak dispersion-bound complexes such as rare gas dimers
or the benzene dimer. To determine the interaction energies (IE)
of non-covalent interactions one generally takes the supermolecular
approach as described by the equation
\begin{equation}
E_{IE} = E_{AB} - E_{A} - E_{B},
\end{equation}
where subscripts A and B refer to
two monomers and AB indicates the dimer. This interaction energy is
the difference in energy between two monomers interacting at a single
configuration compared to the completely non-interacting monomers at
infinite separation. In this framework, positive interaction energies are
repulsive or unfavorable while negative interaction energies signify
a favorable interaction. We use prototype systems to understand systems
with complex interactions such as π-π stacking in curved aromatic systems,
three-body dispersion contributions to lattice energies and transition metal catalysts
affect on transition state barrier heights. The current "gold standard" of computational chemistry is coupled-cluster theory with iterative single and double excitation and perturbative triple
excitations [CCSD(T)].\cite{Lee:1995:47} Using CCSD(T) with large basis sets usually yields results that are in good agreement with experimental data.\cite{Shibasaki:2006:4397}
CCSD(T) being
very computational expensive forces us to use methods of a lower overall
quality, but also much more tractable for some interesting problems.
We must use the available CCSD(T) or experimental data available
to benchmark lower quality methods in order to ensure that the low
quality methods are providing and accurate description of the problem
of interest. To investigate the effect of curvature on the nature of π-π interactions, we studied concave-convex dimers of corannulene and coronene in nested configurations. By imposing artificial
curvature/planarity we were able to learn about the fundamental
physics of π-π stacking in curved systems. To investigate these effects, it was necessary to benchmark low level methods
for the interaction of large aromatic hydrocarbons. With the coronene and corannulene dimers being 60 and 72 atoms, respectively, they are outside the limits of tractability for a large number of
computations at the level of CCSD(T). Therefore we must determine the most efficient and accurate method of describing the physics of these systems with a few benchmark computations. Using a few benchmark computations published by Janowski et al. (Ref. \cite{Janowski:2011:155})
we were able to benchmark four functionals (B3LYP, B97, M05-2X and M06-2X) as
well as four dispersion corrections (-D2, -D3, -D3(BJ), and -XDM) and we
found that B3LYP-D3(BJ) performed best. Using B3LYP-D3(BJ) we found that both corannulene and coronene exhibit stronger interaction energies as more curvature is
introduced, except at unnaturally close intermolecular distances or high degrees
of curvature. Using symmetry adapted perturbation theory (SAPT)\cite{Jeziorski:1994:1887, Szalewicz:2012:254}, we were able to determine that this stronger interaction comes from stabilizing dispersion, induction and charge penetration interactions with smaller destabilizing interactions from exchange interactions. For accurate computations on lattice energies one needs to go beyond two-body effects to three-body effects if the cluster expansion is being used. Three-body dispersion is normally a smaller fraction of the lattice
energy of a crystal when compared to three-body induction. We investigated
the three-body contribution using the counterpoise corrected
formula of Hankins \textit{et al.}.\cite{Hankins:1970:4544}
\begin{equation}
\Delta ^{3} E^{ABC}_{ABC} = E^{ABC}_{ABC} - \sum_{i} E^{ABC}_{i} -
\sum_{ij} \Delta ^{2} E^{ABC}_{ij},
\end{equation}
where the superscript ABC represents the trimer basis and the E(subscript i) denotes the energy of each monomer, where {\em i} counts
over the individual molecule of the trimer. The last term is defined as \begin{equation}
\Delta ^{2} E^{ABC}_{ij} = E^{ABC}_{ij} - E^{ABC}_{i} - E^{ABC}_{j},
\end{equation}
where the energies of all dimers and monomers are determined in the
trimer basis. Using these formulae we investigated the three-body
contribution to the lattice energy of
crystalline benzene with CCSD(T). By using CCSD(T) computations we resolved a debate in the literature about the
magnitude of the non-additive three-body dispersion contribution
to the lattice energy of the benzene crystal. Based on CCSD(T)
computations, we report a three-body dispersion contribution of
0.89 kcal mol⁻¹, or 7.2\% of the total lattice energy. This estimate is smaller than many previous computational estimates\cite{Tkatchenko:2012:236402,Grimme:2010:154104,Wen:2011:3733,vonlilienfeld:2010:234109} of the three-body dispersion contribution, which fell
between 0.92 and 1.67 kcal mol⁻¹. The benchmark data we provide confirm that three-body dispersion effects cannot be
neglected in accurate computations of the lattice energy of benzene.
Although this study focused on benzene, three-body dispersion effects
may also contribute substantially to the lattice energy of other
aromatic hydrocarbon materials. Finally, density functional theory (DFT) was applied to the rate-limiting step of the hydrolytic kinetic resolution (HKR) of terminal
epoxides to resolve questions surrounding the mechanism. We find that the catalytic mechanism is cooperative because
the barrier height reduction for the bimetallic reaction is greater than the sum of the barrier height reductions for
the two monometallic reactions.
We were also able to compute barrier heights for multiple counter-ions which react at different rates. Based on
experimental reaction profiles, we saw a good correlation between our barrier heights for chloride, acetate, and tosylate with
the peak reaction rates reported. We also saw that hydroxide, which is inactive experimentally is inactve because when hydroxide is the only counter-ion
present in the system it has a barrier height that is 11-14 kJ mol⁻¹ higher than the other three counter-ions which are extremely
active.