On Improving Density Functional Approximations: When Optimization Matters

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The Kohn-Sham density functional theory has been the most popular method in electronic structure calculations. Although the theory is in principle exact, approximations are needed for the exchange-correlation energy to make practical calculations possible. This dissertation focuses on one aspect to seek for better approximations: optimization. Optimization has many different meanings in quantum chemistry. Specifically, we carry out energy optimization for a few known energy forms to get insight about what self-consistency can achieve. One kind of them is designed from linear response theories (two-electron addition energies from the particle-particle random phase approximation and spin-flip excitation energies from the spin-flip linear-response time-dependent density functional theory). The post-self-consistency versions are already known to produce excellent results for states that involve static correlations, while the energy optimization further improves the accuracy, especially when the total energy is a quantity of interest. The optimization technique used is the generalized optimized effective potential method, which is a non-local counterpart to the well-established optimized effective potential method. The other part is related to the local orbital scaling correction method, which mostly deals with delocalization errors. We designed a robust self-consistent workflow to avoid the difficult exact-Hamiltonian derivation, and observed reliable prediction on electron densities, total energies, and energy-level alignments. Machine-learning can also be considered as an optimization technique, which is used to minimize the errors of a density functional approximation in the provided database. Special treatment was carried out to transfer electron densities in 3D to neural network compatible input variables (translational and rotational invariant; discrete numbers). The outcome is a finite-range non-local density functional correction to low cost functionals, which is able to achieve similar level of accuracy as compared to accurate and expensive functionals, while keeping the computational cost low. In summary, "optimization" over existing functional approximations is a reliable way to get an improvement, and sometimes new physics can be discovered. On the other hand, "optimization" can also be done by "machines", which may become more and more popular in the future.






Chen, Zehua (2021). On Improving Density Functional Approximations: When Optimization Matters. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/23043.


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