Bhaarathi Natarajan's Thesis Defense : " Implementation, Testing, and Application of Time-Dependent Density-Functional Theory Algorithms for Gaussian- and Wavelet-based Programs"

Thursday 19 January 2012 at 2pm

Amphithéâtre P014 - Ecole PHELMA POLYGONE
23 avenue des Martyrs - 38000 Grenoble

Bhaarathi NATARAJAN (INAC)  

Thesis supervisor: Mark E. CASIDA 

The interaction of light with matter is a well-established domain of physical science. For a chemical physicist, this interaction may be used as a probe (spectroscopy) or to induce chemical reactions (photochemistry.) Photochemical reaction mechanisms are difficult to study experimentally and even the most sophisticated modern femto-second spectroscopic studies can benefit enormously from the light of theoretical simulations. Spectroscopic assignments often also require theoretical calculations. Theoretical methods for describing photo-processes have been developed based upon wave-function theory and show remarkable success when going to sophisticated higher-order approximations. However such approaches are typically limited to small or at best medium-sized molecules. Fortunately time-dependent density-functional theory (TD-DFT) has emerged as a computationally-simpler method which can be applied to larger molecules with an accuracy which is often, but not always, similar to high-quality wave-function calculations. Part of this thesis concerns overcoming difficulties involving the approximate functionals used in present-day TD-DFT. In particular, we have examined the quality of conical intersections when the Ziegler-Wang noncollinear spin-flip approach is used and have shown that the spin-flip approach has merit as a particular solution in particular cases but is not a general solution to improving the description of conical intersections in photochemical simulations based upon TD-DFT. Most of this thesis concerns algorithmic improvements aimed at either improving the analysis of TD-DFT results or extending practical TD-DFT calculations to larger molecules. The implementation of automatic molecular orbital symmetry analysis in deMon2k is one contribution to improving the analysis of TD-DFT results. It also served as an introduction to a major programming project. The major methodological contribution in this thesis is the implementation of Casida’s equations in the wavelet-based code BigDFT and the subsequent analysis of the pros and cons of wavelet-based TD-DFT where it is shown that accurate molecular orbitals are more easily obtained in BigDFT than with deMon2k but that handling the contribution of unoccupied orbitals in wavelet-based TD-DFT is potentially more problematic than it is in a Gaussian-based TD-DFT code such as de- Mon2k. Finally the basic equations for TD-DFT excited state gradients are derived. The thesis concludes with some perspectives about future work.