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 between the HF. 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 method. 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 interacted 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 by 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 by HF or DFT. Second, GW approximation is widely used in different research areas. Especially, the G0W0 method can improve the ionization potential for both molecule and solid state calculated by the ground state DFT calculation. However, G0W0 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. The procedure is simple: use a subspace diagonalization of the HF Hamiltonian with the DFT density matrix to construct the renormalized Green's function and replace the reference Green's function G0. Our method works extremely well for molecules and we are still testing it for solid states.
Electron transfer (ET) is widely observed in various research areas, for example, electronic devices, biomolecular systems, light harvesting systems, etc. Here we discuss the circularly polarized light (CPL) induced ET process. CPL induced coherent 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.