UC Berkeley

This dissertation is concerned with the development and applications of approaches to the electron correlation problem. We start with an introduction that summarizes modern approaches to the electron correlation problem. In our view, there are two remaining challenges that modern density functional theory cannot satisfactorily solve. The first challenge is due to self-interaction error and the second is due to strong correlation. We discuss two methods developed by the author that attempt to make progress to address the second challenge.

The first approach is useful in distinguishing strong and weak correlation in a computationally economical way. It is based on orbital optimization in the presence of regularized second-order Moller-Plesset perturbation theory (k-OOMP2), which is an approximate method to obtain Brueckner orbitals. k-OOMP2 includes weak correlation while attenuating strong correlation. As such, it distinguishes artificial and essential symmetry breaking which occur at the Hartree-Fock (HF) level. Artificial symmetry breaking appears due to the lack of weak correlation, not due to the lack of strong correlation. Therefore, the common wisdom in quantum chemistry, which equates symmetry breaking at the HF level and strong correlation, can result in a wrong understanding of the system. Essential symmetry breaking, on the other hand, signals strong correlation that is beyond the scope of simple perturbation theory. k-OOMP2 has been shown to reliably distinguish these two: symmetry breaking in the k-OOMP2 orbitals is essential. This has been applied to a recent controversy about whether C60 is strongly correlated. Starting from a broken-symmetry HF solution, k-OOMP2 restores every symmetry. As such, C60 is not strongly correlated. Moreover, k-OOMP2 successfully predicts strong correlation for a known biradicaloid, C36, by showing essential symmetry breaking in its orbitals. We also exploited essential symmetry breaking in singlet biradicaloids using k-OOMP2 and showed quantitative accuracy in obtaining singlet-triplet gaps of various molecules. This new approach should be helpful for redefining the common wisdom in quantum chemistry.

The second method is an exact, spin-pure, polynomial-scaling way to describe strong spin-correlation (SSC). SSC is present when there are many spatially separate open-shell electrons with small spin-flip energy cost. Describing SSC exactly requires the inclusion of all essential spin-couplings. The number of such spin-couplings scales exponentially with the number of electrons. Because of this, SSC was thought to require an exponential number of wavefunction parameters in general. However, new development suggests that there is an efficient way to obtain all these spin-couplings with only a quadratic number of wavefunction parameters, which is called the coupled-cluster valence-bond (CCVB) method. We discuss different challenges in CCVB: (1) its non-black-box nature and (2) its inability to describe SSC in spin-frustrated systems. We present two improved CCVB approaches that address these two challenges. These approaches were applied to describe emergent strong correlation in oligoacenes and SSC in spin-frustrated systems such as single molecular magnets and metalloenzymes. The remaining challenges in CCVB are the inclusion of ionic excitations which are not relevant for SSC, but crucial for obtaining quantitative accuracy.