Reducing the Many-Electron Self-Interaction Error in the Second-Order Screened Exchange Method

Preserving the beneficial properties of the second-order screened exchange (SOSEX) method, such as its freedom from one-body self-correlation error, and its seamless treatment of long-range dispersion interaction, we construct new nonlocal functionals by down-scaling the higher-order terms in the SOSEX series to reduce the many-body self-correlation error in molecular systems. Our down-scaled SOSEX (dsSOSEX) and scaled equation SOSEX (seSOSEX) approaches deliver considerably more accurate noncovalent interaction energies, reaction energies, and barrier heights than the original SOSEX method. The dsSOSEX approach improves on the description of medium- and long-range correlation, for example, in isogyric processes, while the seSOSEX approach improves on the description of processes with short- and medium-range rearrangement in the electronic structure, such as atomization. The He₂⁺ potential energy curve shows that the many-body self-correlation error is slightly smaller in the dsSOSEX method than in the seSOSEX approach. Furthermore, the H₂ potential energy curve reveals that the static correlation error can also be reduced at medium range by the dsSOSEX and seSOSEX schemes. As our dsSOSEX method provides a better description of medium- and long-range correlation, it generally leads to more accurate energetics than the seSOSEX method; hence it should be preferred over the latter. We compare our results to other empirical and nonempirical direct random phase approximation (dRPA) and beyond-dRPA methods and also discuss the possibilities for further development.