  In this communication we present a method of complete basis set (CBS)
extrapolation of correlation energies obtained with a systematic sequence of
one-electron basis sets. Instead of fitting the finite-basis results with a
certain functional form, we perform analytic re-summation of the missing
contributions coming from higher angular momenta, $l$. The assumption that they
vanish asymptotically as an inverse power of $l$ leads to an expression for the
CBS limit given in terms of the Riemann zeta function. This result is turned
into an extrapolation method that is very easy to use and requires no
"empirical" parameters to be optimized. The performance of the proposed method
is assessed by comparing the results with accurate reference data obtained with
explicitly correlated theories and with results obtained with standard
extrapolation schemes. On average, the errors of the zeta-function
extrapolation are several times smaller compared with the conventional schemes
employing the same number of points. A recipe for estimation of the residual
extrapolation error is also proposed.
