Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

Visualizing Rare Watson-Crick-Like Tautomeric and Anionic Mismatches in DNA and RNA

The central dogma of molecular biology relies on the correct Watson-Crick (WC) geometry of canonical deoxyribonucleic acid (DNA) dG•dC and dA•dT base pairs to replicate and transcribe genetic information with speed and an astonishing level of fidelity. In addition, the Watson-Crick geometry of canonical ribonucleic acid (RNA) rG•rC and rA•rU base pairs is highly conserved to ensure that proteins are translated with high fidelity. However, numerous other potential nucleobase tautomeric and ionic configurations are possible that can give rise to entirely new pairing modes between the nucleotide bases. Very early on, James Watson and Francis Crick recognized their importance and in 1953 postulated that if bases adopted one of their less energetically disfavored tautomeric forms (and later ionic forms) during replication it could lead to the formation of a mismatch with a Watson-Crick-like geometry and could give rise to “natural mutations.”

Since this time numerous studies have provided evidence in support of this hypothesis and have expanded upon it; computational studies have addressed the energetic feasibilities of different nucleobases’ tautomeric and ionic forms in siico; crystallographic studies have trapped different mismatches with WC-like geometries in polymerase or ribosome active sites. However, no direct evidence has been given for (i) the direct existence of these WC-like mismatches in canonical DNA duplex, RNA duplexes, or non-coding RNAs; (ii) which, if any, tautomeric or ionic form stabilizes the WC-like geometry. This thesis utilizes nuclear magnetic resonance (NMR) spectroscopy and rotating frame relaxation dispersion (R1ρ RD) in combination with density functional theory (DFT), biochemical assays, and targeted chemical perturbations to show that (i) dG•dT mismatches in DNA duplexes, as well as rG•rU mismatches RNA duplexes and non-coding RNAs, transiently adopt a WC-like geometry that is stabilized by (ii) an interconnected network of rapidly interconverting rare tautomers and anionic bases. These results support Watson and Crick’s tautomer hypothesis, but additionally support subsequent hypotheses invoking anionic mismatches and ultimately tie them together. This dissertation shows that a common mismatch can adopt a Watson-Crick-like geometry globally, in both DNA and RNA, and whose geometry is stabilized by a kinetically linked network of rare tautomeric and anionic bases. The studies herein also provide compelling evidence for their involvement in spontaneous replication and translation errors.