Atomic MP2 correlation energies fast and accurately calculated by FEM extrapolations

A p-version FEM-MP2 (finite element Moller-Plesset second order perturbation) program for accurate MP2 correlation energies of closed shell atoms has been further improved: by radial transformations r = a sinh(bx), inclusion of global radial factors of the form exp(-alpha(r)r) with a sloping function alpha(r) and discretization in x rather than r. Adding logarithmic extrapolations to a sequence E-n, of MP2 energies obtained from low order (linear) finite-element calculations resulted in a very fast high precision approach to MP2 correlation energies. The accuracy gain over the directry calculated values is around five orders for He bare nucleus, He-HF and Be-HF, four orders for Ne-HF almost tripling the number of significant digits. Maximal effective numbers n(eff) of 16 to 18 radial points were sufficient. A coupling between the maximal l-value(here l(max) = 12) and a suitable maximal number of radial points is observed amounting to about n(eff) = 3/2 l(max).