# Quantum Chemistry: from Theory to Application

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2019

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## Abstract

Hartree-Fock (HF) theory is one of the fundamental theories in electronic structure calculations. It can provide the basic description of the system, however, as the zeroth order approximation, it cannot describe the electronic structure accurately. Nevertheless, it is the starting reference for many beyond-HF wavefunction methods. Another fundamental theory in electronic structure is the density functional theory (DFT). It is usually ignored that DFT has an important connection with the HF theory. This connection is the single excitation (SE) contribution. In HF, SE does not contribute because of the Brillouin's theorem. On the other hand, SE contributes to DFT and plays a significant role in beyond-DFT many-body methods. One example is the correlation energy calculated by random phase approximation (RPA). Here we would like to discuss SE in different scenarios and extend the topic. First, the optimized effective potential (OEP) does not perform accurately in minimizing the RPA total energy functional. To overcome this problem, we developed a generalized optimized effective potential (GOEP) method. This method can describe the dissociation of weakly interacting diatomic systems accurately. From the analysis of the energy structure, the GOEP absorbs the SE contribution in contrast with the OEP method. We also notice that by performing GOEP for RPA, the physical density of the system is no longer the reference density, which is not traditionally recognized in DFT. This conclusion can be generally applied to any exchange-correlation functional that depends explicitly on the external potential. And we have shown that this physical density performs better than both the reference density and the original density of the starting reference calculated from HF or DFT. Second, the $GW$ approximation is widely used in different research areas. Especially, the $G_0W_0$ method can improve the ionization potential for both molecule and solids calculated from the ground state DFT calculation. However, the $G_0W_0$ method has a strong starting-point dependence. We have recognized that this starting-point dependence largely originates from the lack of SE contribution to the single-particle Green's function. We developed an effective and simple solution by using a subspace diagonalization of the HF Hamiltonian with the DFT density matrix to construct the renormalized singles Green's function and replace the reference Green's function $G_0$. Our method works extremely well for molecules and we are still testing it for solid states. Besides, we have developed a new method to extract excitation energies directly from the quasi-particle energies based on the $GW$ approximation. Starting from the $(N-1)$-electron system, we are able to calculate molecular excitation energies with orbital energies at the $GW$ level. We have demonstrated that this method can accurately capture low-lying local excitations as well as charge transfer excitations in many molecular systems. This provides a new perspective in applying the single-particle Green's function.

Electron transfer (ET) and excitation energy transfer (EET) are widely observed in various research areas, for example, electronic devices, biomolecular systems, light harvesting systems, etc. Here we discuss two topics. First, we study circularly polarized light (CPL) induced ET process. CPL induced coherent electron transfer (ET) process can be affected by the direction of the CPL. In particular, the yield on the acceptor through the CPL-induced ET can be asymmetrical. Previous study suggests that this yield asymmetry on the acceptor is related with the initial angular momentum polarization on the donor, which can be created by different directions of the CPL. Here we further investigate how the CPL affects the yield asymmetry by studying the yield asymmetry dependence on the molecular energetics, CPL field, and the environment perturbation. We have built a simple 4-state Hamiltonian with one ground state, two degenerate excited donor states and one acceptor and provided the optimal choice of parameters to maximize the yield asymmetry. Both analytical and numerical results suggest that the yield asymmetry is mainly created by the phase and population difference between two excited states under L- and R-CPL. Among different parameters, a slow dephasing rate is most important for observing a large yield asymmetry. With a 200 fs dephasing rate, the yield asymmetry can be as large as 5\%. One should perform the experiment in low temperature to slow the dephasing rate. Second, we study the hole length along the DNA base pairs. Knowing the length of the hole is important to understand the mechanism of the ET process through DNA. The length of the hole is determined by the competition between the delocalization (ionization) and localization (solvation) effect of the DNA. We have revisited the previous work in our group (10.1021/jp0132329) with more advanced quantum chemistry methods to calculate the hole length in AT and GC pairs. Localized scaling orbital correction (LOSC) is used to calculate the ionization potential (IP), which is usually underestimated by traditional DFT calculations because of the size-consistent problem. And we will use the Poisson-Boltzmann equation to calculate the solvation energy contribution. From the LOSC calculation, the IP is in agreement with the high-level ab-initio calculations. This result shows that the LOSC calculation overcomes the problem in traditional DFT. And we have also shown that the IP decreases faster for the increasing length of the GC pair as compared to the AT pair.

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## Citation

Jin, Ye (2019). *Quantum Chemistry: from Theory to Application*. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/19801.

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Dukes student scholarship is made available to the public using a Creative Commons Attribution / Non-commercial / No derivative (CC-BY-NC-ND) license.