Understanding and Minimizing Density Functional Failures Using Dispersion Corrections

This thesis introduces original formalisms to achieve an accurate description of dispersion interactions within the framework of density functional theory. The presented research focuses on two specific objectives related to density functional approximations: (1) the development and implementation of dispersion corrections that dramatically reduce the failures for both inter- and intramolecular interaction energies and (2) the identification of the key factors at the origin of the errors in thermochemistry. Kohn-Sham density functional theory has become the preferred methodology for modeling the energy and structural properties of large molecules, yet common semilocal and hybrid approximations are affected by well-known deficiencies as illustrated by both the delocalization error and their inability to accurately describe omnipresent long-range (van der Waals) interactions. After proposing an improved variant of “classical” atom pairwise dispersion correction, we formulate an efficient dispersion correction that is dependent upon the electron density. In contrast to the schemes that are typically applied, these dispersion coefficients reflect the charge-distribution within a molecule. Additionally, the use of density overlaps allows for distinguishing of non-bonded regions from bonded atom pairs, which eliminates the correction at covalent distances. A clear advantage of the proposed dDsC scheme is its ability to improve the performance of a variety of standard density functionals for both hydrocarbon reaction energies and typical weak interaction energies simultaneously. The density dependence also offers advantages for highly polarized and charged systems. Interaction energies of ground-state charge-transfer complexes and π-dimer radical cations are illustrative examples for which the delocalization error partially counterbalances the missing dispersion. We demonstrate, however, that, in practical situations, dispersion energy corrections are mandatory. Following van der Waals interactions, (long-range) “exact” exchange has been identified as the second most important ingredient for obtaining robust results. The versatile methodology devised herein reveals the “true” performance of standard approximations and promises many fruitful applications from metal-organic catalysis to organic-electronics.