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Mathematical aspects and chemical applications of density functional theory Zhang, Yu

Abstract

My Ph. D. work is about theoretical basis and applications of density functional theory (DFT). DFT has demonstrated a good balance between computing costand accuracy, so it has become one of the most popular daily-used quantum chemistry methods. The first part of my work is about the asymptotic behavior of finite-system wave-functions. The exponential decaying asymptotic behavior is confirmed andthe structure of the prefactors is further explored. By comparing the asymptotic behavior of the Dyson orbitals and the Kohn-Sham orbitals, we have also provided a physical interpretation of the Kohn-Sham orbital energies. Then we want to rebut the theory of "unconventional density variation" proposed more than 20 years ago. Supported by theoretical analysis and numericalevidence, we proved that all density variations are the same in nature. We have also extended two total energy functionals suggested before to the Hartree-Fock method. Numerical tests on different molecules show these functionals are very promising in accelerating the SCF convergence of quantum chemistry calculations. Finally, we completed a comprehensive theoretical study on the tautomers of pyridinethiones. Many molecular properties predicted from theory are comparedwith those got from experiments. The dominant forms of the tautomers are confirmed to be the thione forms. This demonstrates the power of DFT methods, and this work can serve as a reference for studying similar molecules.

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