Density Functional Theory Transformed into a One-Electron Reduced Density Matrix Functional Theory for the Description of Static Correlation

Kohn-Sham Density Functional Theory (KS-DFT or just DFT) as become a go-to method for electronic structure calculations due to its low computational scaling, allowing it to treat large systems, while still being relatively accurate. However, DFT still struggles in strongly correlated systems due to its inability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. This error is primarily driven by the single Slater determinant representation of the Kohn-Sham non-interacting auxiliary wave function, which leads to integer occupations of the electronic orbitals. In this thesis, we address this shortcoming by combining DFT with Semi-Definite Programming (SDP) and a 1-Electron Reduced Density Matrix Functional (RDMF) to capture static electron correlation through fractional orbital occupations. We derive our method termed Reduced Density Matrix Functional Theory (RDMFT) from a unitary decomposition of the 2-electron reduced density matrix's cumulant to obtain a system-specific dependence on the electron repulsion integrals. This methodology retains DFT's O(N 3) computational scaling while describing static correlation through fractional occupation. We apply this approach to a series of small molecules such as the benzynes and find noticeable improvements over DFT in each system tested. We've also modified the dependence of our method on the 2-electron integrals using the Cauchy-Schwarz inequalities to prevent the RDMF term from decaying to zero with growing system sizes, leading to size extensivity issues. We apply this modification to a series of linear hydrogen chains and find it remedies the size extensive issues of the original derivation. We further apply the modification to the singlet-triplet gaps of the acenes from pentacene to dodecacene and find excellent agreement with variational 2-RDM calculations.