Implementation and Application of Density Functional Theory based Symmetry-Adapted Perturbation Theory for Dimers, Trimers and Molecular Crystals

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Xie, Yi
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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.
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2022-07-30
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