In this thesis, we search for ways to make density functional theory (DFT) more accurate. Inspired by the w(r12) methods developed for coupled cluster theory, we present UnsöldW12 (UW12): an approximation to the correlation energy of molecules that is an explicit functional of the single-particle reduced density matrix. The approximation resembles one part of modern explicitly-correlated second-order Møller-Plesset (MP2) theory, and is intended as an alternative to MP2 in double-hybrid (rung-5) exchange-correlation functionals. Orbital optimization with UW12 is straightforward, and the UW12 energy is evaluated without a double summation over unoccupied orbitals, leading to a faster basis-set convergence than is seen in double-hybrid functionals. We show that the formal scaling for evaluating the UW12 energy is N^4 (where N represents the size of the system), and describe how UW12 may be implemented in electronic structure codes. Having deﬁned the UW12 correlation model, we suggest three new hybrid (rung-4) exchange correlation functionals: XCH-BLYP-UW12, rBLYP-osUW12, and BLYP-osUW12. All three of these new functionals reduce(to varying degrees)the delocalization error present in DFT. We conclude by suggesting ways in which UW12 functionals could be improved in the future in terms of both accuracy and computational cost. They may soon outperform double-hybrid (rung-5) functionals in both these areas.
|Date of Award||28 Nov 2019|
- The University of Bristol
|Supervisor||Frederick R Manby (Supervisor)|