Inoue Nobuki, Watanabe Yoshihiro, Nakano Haruyuki
Department of Chemistry, Graduate School of Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan.
J Chem Phys. 2023 Aug 7;159(5). doi: 10.1063/5.0145577.
Theoretical discussions are given on issues in relativistic molecular orbital theory to which the quantum electrodynamics (QED) Hamiltonian is applied. First, several QED Hamiltonians previously proposed are sifted by the orbital rotation invariance, the charge conjugation and time reversal invariance, and the nonrelativistic limit. The discussion on orbital rotation invariance shows that orbitals giving a stationary point of total energy should be adopted for QED Hamiltonians that are not orbital rotation invariant. A new total energy expression is then proposed, in which a counter term corresponding to the energy of the polarized vacuum is subtracted from the total energy. This expression prevents the possibility of total energy divergence due to electron correlations, stemming from the fact that the QED Hamiltonian does not conserve the number of particles. Finally, based on the Hamiltonian and energy expression, the Dirac-Hartree-Fock (DHF) and electron correlation methods are reintroduced. The QED-based DHF equation is shown to give information on positrons from negative-energy orbitals while having the same form as the conventional DHF equation. Three electron correlation methods are derived: the QED-based configuration interactions and single- and multireference perturbation methods. Numerical calculations show that the total energy of the QED Hamiltonian indeed diverged and that the counter term is effective in avoiding the divergence. The relativistic molecular orbital theory presented in this article also provides a methodology for dealing with systems containing positrons based on the QED Hamiltonian.
本文针对应用量子电动力学（QED）哈密顿量的相对论分子轨道理论中的问题进行了理论探讨。首先，通过轨道旋转不变性、电荷共轭和时间反演不变性以及非相对论极限，对先前提出的几种QED哈密顿量进行了筛选。关于轨道旋转不变性的讨论表明，对于非轨道旋转不变的QED哈密顿量，应采用给出总能量驻点的轨道。然后提出了一种新的总能量表达式，其中从总能量中减去了与极化真空能量相对应的抵消项。由于QED哈密顿量不守恒粒子数，该表达式避免了因电子关联导致总能量发散的可能性。最后，基于哈密顿量和能量表达式，重新引入了狄拉克 - 哈特里 - 福克（DHF）方法和电子关联方法。基于QED的DHF方程与传统DHF方程形式相同，但能给出来自负能轨道的正电子信息。推导了三种电子关联方法：基于QED的组态相互作用方法以及单参考和多参考微扰方法。数值计算表明，QED哈密顿量的总能量确实发散，且抵消项能有效避免发散。本文提出的相对论分子轨道理论还基于QED哈密顿量提供了一种处理含正电子体系的方法。
