Weak interactions and excited states from Coulomb-attenuated DFT

Abstract

Density functional theory (DFT) is currently the most widely applied electronic structure theory in Chemistry. It is favoured for its computational efficiency, coupled with good accuracy. Although formally exact, approximations are required when practically applied. In the Kohn-Sham formalism, these approximations are contained within the exchange-correlation functional. Well established exchange-correlation functionals, such as the ubiquitous B3LYP, provide reasonable accuracy, but their continued use is increasingly based on the collective experience with the functional that has been accumulated, rather than the results that can be achieved. This thesis considers the circumstances under which conventional functionals fail and how a recent modification— coulomb attenuation—can resolve such issues.
An outline of basic electronic structure theory is provided in chapter 1, particularly the formulation of the Hartree-Fock approach. This is extended to more sophisticated wavefunction based methods. Chapter 2 provides a formal proof for the validity of DFT as well as a framework for its implementation. A recently developed exchange-correlation functional (CAM-B3LYP) based on a varying quantity of exact exchange is outlined. Also discussed is the time-dependent DFT (TDDFT) approach to the determination of excitation energies, its failures and how such failures can be predicted and eliminated. The subsequent chapters consider the application of CAM-B3LYP to the description of weak interactions and excited states.
Chapter 3 considers some key problems facing modern DFT—dispersion, fractional spins and fractional charges—in terms of the force and the Feynman electron density distortion, in addition to the conventional viewpoint of the energy. Two model systems, H2 and H+2 are employed to illustrate how increasing quantities of exact exchange can increase the fractional spin error while decreasing the fractional charge error, respectively. This is reflected in the improved description offered by CAM-B3LYP for H2 and the corresponding poor performance for H+2 .
Chapter 4 takes a more detailed look at the dispersion interaction. C6 dispersion coefficients are calculated using a range of functionals—CAM-B3LYP showing a clear improvement over GGA and hybrid functionals. Dispersion corrected potential energy surfaces and interaction energies are determined with CAM-B3LYP providing comparable accuracy to other, existing long-range corrected functionals.
Chapters 5 and 6 consider the application of CAM-B3LYP to the excited states of large systems of chemical and biological importance, respectively. In the former, the difficulty of comparing theoretically determined excitation energies with experimentally observed absorption spectra is of particular focus. In the latter, the failure of conventional functionals to correctly predict the energy and character of charge-transfer excitations is highlighted. For both cases, it is shown that CAM-B3LYP can provide a significant improvement over conventional functionals, all but eradicating the charge- transfer issue in the latter case.
Chapter 7 further investigates the charge-transfer issue experienced by conventional functionals and illustrates how the error can manifest itself as an inaccuracy in the character of an excited state rather than the energy. CAM-B3LYP provides an accurate description of both aspects. Triplet excitation energies are determined from TDDFT and the ∆SCF approach—the latter providing improved results for conventional functionals.