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## Scholarly Works (24 results)

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.

*c*

_{ISDF}controls the trade-off between accuracy and cost. In particular,

*c*

_{ISDF}sets the number of interpolation points used in THC,

*N*

_{IP}=

*c*

_{ISDF}×

*N*

_{X}with

*N*

_{X}being the number of auxiliary basis functions. In conjunction with the resolution-of-the-identity (RI) technique, we develop and investigate the THC-RI algorithms for cubic-scaling exact exchange for Hartree-Fock and range-separated hybrids (e.g., ωB97X-V) and quartic-scaling second- and third-order Møller-Plesset theory (MP2 and MP3). These algorithms were evaluated over the W4-11 thermochemistry (atomization energy) set and A24 noncovalent interaction benchmark set with standard Dunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ, and aug-cc-pVTZ). We demonstrate the convergence of THC-RI algorithms to numerically exact RI results using ISDF points. Based on these, we make recommendations on

*c*

_{ISDF}for each basis set and method. We also demonstrate the utility of THC-RI exact exchange and MP2 for larger systems such as water clusters and C

_{20}. We stress that more challenges await in obtaining accurate and numerically stable THC factorization for wave function amplitudes as well as for the space spanned by virtual orbitals in large basis sets and implementing sparsity-aware THC-RI algorithms.

_{2}, water, and hydrated ion clusters, with a variety of interaction mechanisms, from weak dispersion to strong electrostatics considered in this work. We further demonstrate that the PolBE interaction energy is predominantly pairwise unlike the usual vacuum MBE that requires higher-order terms to achieve similar accuracy. We numerically show that PolBE often performs better than other widely used embedded MBE methods such as the electrostatically embedded MBE. Owing to the lack of expensive diagonalization of Fock matrices and its embarrassingly parallel nature, PolBE is a promising way to access condensed phase systems with hybrid density functionals that are difficult to treat with currently available methods.

### Polishing the Gold Standard: The Role of Orbital Choice in CCSD(T) Vibrational Frequency Prediction.

^{-1}, and 8.50 cm

^{-1}, and 8.75 cm

^{-1}respectively, outperforming CCSD(T):UHF by nearly a factor of 5. Moreover, the performance on the closed- and open-shell subsets shows these methods are able to treat open-shell and closed-shell systems with comparable accuracy and robustness. CCSD(T) with RHF orbitals is seen to improve upon UHF for the closed-shell species, while spatial symmetry breaking in a number of restricted open-shell HF (ROHF) references leads CCSD(T) with ROHF reference orbitals to exhibit the poorest statistical performance of all methods surveyed for open-shell species. The use of κ-OOMP2 orbitals has also proven useful in diagnosing multireference character that can hinder the reliability of CCSD(T).

- 1 supplemental PDF

*N*

^{6}) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.