Basis-set extrapolation of the correlation energy

A simple theoretically motivated model to extrapolate the correlation energy based on correlation-consistent polarized X-tuple basis sets is suggested. It has the form EXcor=E∞cor[1+A3 X−3(1+A4 X−1)], where EXcor is the energy for the X-tuple basis set, E∞cor and A3 are parameters to be determined from a set (Xmin−Xmax) of correlation consistent basis sets at a given level of theory, and A4 is a function of A3. Even for the simple (2,3) extrapolation scheme, the method is shown to yield energies for 33 test data sets that are more accurate than those obtained from pure correlation consistent sextuple-zeta basis sets at a much lower computational cost. Other extrapolation schemes have also been investigated, including a simple one-parameter rule EXcor=E∞cor(1–2.4X−3).