Assessment of the Second-Order Statically Screened Exchange Correction to the Random Phase Approximation for Correlation Energies

With increasing interelectronic distance, the screening
of the
electron–electron interaction by the presence of other electrons
becomes the dominant source of electron correlation. This effect is
described by the random phase approximation (RPA) which is therefore
a promising method for the calculation of weak interactions. The success
of the RPA relies on the cancellation of errors, which can be traced
back to the violation of the crossing symmetry of the 4-point vertex,
leading to strongly overestimated total correlation energies. By the
addition of second-order screened exchange (SOSEX) to the correlation
energy, this issue is substantially reduced. In the adiabatic connection
(AC) SOSEX formalism, one of the two electron–electron interaction
lines in the second-order exchange term is dynamically screened (SOSEX­(W, vc)). A
related SOSEX expression in which both electron–electron interaction
lines are statically screened (SOSEX­(W(0), W(0))) is obtained from the G3W2 contribution to the electronic self-energy. In contrast to SOSEX­(W, vc), the
evaluation of this correlation energy expression does not require
an expensive numerical frequency integration and is therefore advantageous
from a computational perspective. We compare the accuracy of the statically
screened variant to RPA and RPA+SOSEX­(W, vc) for a wide range of chemical
reactions. While both methods fail for barrier heights, SOSEX­(W(0), W(0)) agrees very well with SOSEX­(W, vc) for
charged excitations and noncovalent interactions where they lead to
major improvements over RPA.