The geminal basis in explicitly correlated wave functions

In 1985 Kutzelnigg showed that a large percentage of the electron correlation energy for helium can be recovered using a single explicitly correlated basis function, chosen to fit the cusp at the correlation hole. In particular the simple wave function Ψ=(1+12r12)Φ returned more than 80% of the correlation energy. In this paper we return to Kutzelnigg's simple ansatz and remove the conventional double excitations in explicitly correlated CC2 theory (denoted as CCS(F12)), applying all established developments in modern F12 theory, such as replacing linear r12 with f(r12) = exp(−γr12) and the use of auxiliary basis sets for the standard RI approximation in R12 theory. Analysing different approximations we show that in general the CCS(F12) approach yields 80-95% of the CC2 correlation energy, which is astonishingly large considering the small number and restricted form of the geminal basis functions.