@article{THESIS,
      recid = {12962},
      author = {Gibney, Daniel},
      title = {Density Functional Theory Transformed into a One-Electron  Reduced Density Matrix Functional Theory for the  Description of Static Correlation},
      publisher = {University of Chicago},
      school = {Ph.D.},
      address = {2024-08},
      number = {THESIS},
      abstract = {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.},
      url = {http://knowledge.uchicago.edu/record/12962},
      doi = {https://doi.org/10.6082/uchicago.12962},
}