Implementation and applications of density-fitted symmetry-adapted perturbation theory

Noncovalent interactions play a vital role throughout much of chemistry. The understanding and characterization of these interactions is an area where theoretical chemistry can provide unique insight. While many methods have been developed to study noncovalent interactions, symmetry-adapted perturbation theory (SAPT) stands out as one of the most robust. In addition to providing energetic information about an interaction, it provides insight into the underlying physics of the interaction by decomposing the interaction energy into contributions from electrostatics, induction, exchange-repulsion, and dispersion. Therefore, SAPT is capable of not only answering questions about how strongly a complex is bound, but also why it is bound. This proves to be an invaluable tool for the understanding of noncovalent interactions in complex systems.;The wavefunction-based formulation of SAPT can provide qualitative results for large systems as well as quantitative results for smaller systems. In order to extend the applicability of this method, approximations to the two-electron integrals must be introduced. At low-order, the introduction of density fitting approximations allows SAPT computations to be performed on systems with up to 220 atoms and 2850 basis functions. Higher-orders of SAPT, which boast accuracy rivaling the best conventional theoretical methods, can be applied to systems with over 40 atoms. Additionally, higher-order SAPT benefits from approximations that attempt to truncate unnecessary unoccupied orbitals.;SAPT has proven especially useful in the study of heteroatom effects on π-π interactions. Here, benzene-pyridine and pyridine dimer complexes were used as a model for understanding the effect of nitrogen substitutions. SAPT computations implicate the introduction of a dipole, a reduction in polarizability, and a reduction in the spatial extent of the π orbitals for the changes in interaction energy. The indole-benzene complex contains many possible T-shaped configurations as well as several local minima on the π stacked potential energy surface. SAPT computations illustrate the origin of the energetic differences between all of these geometries. Acene dimers are prototypes for π-π interactions in extended systems. The changes in these interactions with increasing linear acene length provide a glimpse into the nature of π-π interactions. Highly polarizable molecules and those containing high degrees of delocalization are often problematic for many theoretical methods; molecules that are both highly polarizable and delocalized can cause catastrophic failures in those methods. Different levels of SAPT are used to probe the problematic dispersion interactions in these types of complexes and locate the origin of some of these failures. Finally, the question of how substituents tune π-π interactions has been hotly contested amongst theoretical chemists for the last ten years. The most recent development has been the finding that both electron donating and electron withdrawing substituents increase the strength of the electrostatic interaction, which contradicts conventional wisdom. The application of SAPT clearly explains the origin of this surprising effect.