Implementation and Application of Density Functional Theory based Symmetry-Adapted Perturbation Theory for Dimers, Trimers and Molecular Crystals
Loading...
Author(s)
Xie, Yi
Advisor(s)
Editor(s)
Collections
Supplementary to:
Permanent Link
Abstract
This thesis presents an implementation of the density functional theory
based symmetry-adapted perturbation theory [SAPT(DFT)], and its application
to interacting systems including dimers, trimers, and molecular crystals.
SAPT(DFT) is a computational method for computing interaction energy of noncovalent
interactions, which are central to many chemical and biochemical phenomena,
such as phase transition, protein-ligand binding and formation of the structure
of biomacromolecules. In order to study noncovalent interaction in complex systems,
one can use the many-body expansion (MBE) approach to decompose the interaction
energy of the complex system into interaction energies of dimers, trimers,
tetramers, etc. This makes studying the interaction energies for dimers and
trimers meaningful. One of the most important feature of SAPT methods is
that their results have very clear physical interpretations; each SAPT term
can be assigned to interaction of different physical nature, including
electrostatics, exchange-repulsion, induction and dispersion. This allows
the physical nature of the interaction of interest to be reflected in addition
to the ``plain'' interaction energy, allowing better understanding of noncovalent
interactions.
In Chapter 2, we implemented a variant of SAPT, SAPT(DFT), as a part of the
{\sc Psi4} quantum chemistry program package, and assessed its
performance in accuracy and efficiency. SAPT(DFT) has an advantage of
being able to capture the intramonomer electron correlation effects with
a relatively low computational cost. This feature makes SAPT(DFT) desirable
when one is interested in computing the electrostatics, exchange, induction
and dispersion contributions to the interaction energy of an interacting
system, many of which requires the intramonomer electron correlation effects
to be considered to obtain accurate results. This chapter focused on
the treatment of hybrid DFT functionals in SAPT(DFT), in particular
the computation of the dispersion energy where a hybrid exchange-correlation
kernel is required. We have developed an algorithm that efficiently solves
the coupled Kohn-Sham equation with hybrid exchange-correlation kernel,
which allows the application of SAPT(DFT) with hybrid functionals to
dimer systems with sizes comparable to the C$_{60}$--buckycatcher complex.
We have also compared the results of SAPT(DFT) and other SAPT methods
to a few benchmark results, and concluded that the accuracy of SAPT(DFT),
with a scaling of $O(N^5)$, is comparable to the many-body perturbation
theory based SAPT2+ approach, which scales as $O(N^7)$.
In Chapter 3, we attemped to generalize the algorithm developed for
the dispersion energy in SAPT(DFT) to the three-body case, and use
the many-body expansion approach to study its contribution to the
lattice energies of molecular crystals. Unfortunately, our research
shows that the SAPT(DFT) dispersion term does not seem to fully capture
the three-body dispersion effects in molecular crystals, agreeing
the conclusions in previous studies for isolated trimers and liquids,
and we attributed this unsatisfactory performance to lack of higher-order
exchange-dispersion terms. Nevertheless, we have shown that the
Axilrod--Teller--Muto dispersion correction with empirical damping
provides a relatively accurate description to the three-body
dispersion energy due to fortuitous but consistent error cancellation.
We have also analyzed the growth of three-body contribution to crystal
lattice energy with respect to the intermonomer distance cutoff of
trimers, and it appears that for the molecular crystals where dispersion
dominates the three-body contribution to the lattice energy, the error
of the computational methods studied in this chapter is mainly contributed
by trimers with $R_\textrm{min} < 4\;\textrm{\AA}$, where $R_\textrm{min}$
is the smallest value among the three pairwise intermonomer closest-contact
distances, suggesting the possibility of a drastic reduce in required
computational resource for computing the crystal lattice energies
by using approximate methods for trimers with $R_\textrm{min} > 4\;\textrm{\AA}$.
In addition to the advances made in these chapters, this thesis also
suggests a few possible future research topics, based on questions
arising from the research work related to the thesis. These include
implementation of the exchange-dispersion term in SAPT(DFT), which
is currently computed by an approximate scaling method in {\sc Psi4};
implementation of the higher-order exchange-dispersion term for
three-body SAPT(DFT) to compensate the error of three-body SAPT(DFT)
dispersion term; and an investigation of the behavior of three-body
contribution to the crystal lattice energies for crystals that are
not studied in Chapter 3 of this thesis, mainly those consisting polar molecules
with stronger dipole-dipole interactions. While we have not explored
on these questions here, we hope that further studies on these
questions can provide a better insight of understanding noncovalent
interactions, as well as allowing development of computational
methods in studying these interactions.
Sponsor
Date
2022-07-30
Extent
Resource Type
Text
Resource Subtype
Dissertation