Adiabatic Connection without Coupling Constant Integration

Using a second-order approximation
to Random Phase Approximation
renormalized (RPAr) many-body perturbation theory for the interacting
density–density response function, we have developed a so-called
higher-order terms (HOT) approximation for the correlation energy.
In combination with the first-order RPAr correction, our new method
faithfully captures the infinite-order correlation for a given exchange-correlation
kernel, yielding errors of the total correlation energy on the order
of 1% or less for most systems. For exchange-like kernels, our new
method has the further benefit that the coupling-strength integration
can be completely eliminated resulting in a modest reduction in computational
cost compared to the traditional approach. When the correlation energy
is accurately reproduced by the HOT approximation, structural properties
and energy differences are also accurately reproduced, as we demonstrate
for several periodic solids and some molecular systems. Energy differences
involving fragmentation are challenging for the HOT method, however,
due to errors that may not cancel between a composite system and its
constituent pieces.