In standard ab initio molecular quantum-mechanical calculations it is difficult, if at all possible, to calculate fundamental chemical properties like atomisation energies and reaction enthalpies to the chemical accuracy of 1 kcal/mol approximate to 4 M/mol. The principal obstacle is the presence of the Coulomb hole in the electronic wave function, whose description converges slowly with the size of the basis set. From a systematic sequence of basis-set calculations, we demonstrate that physically motivated extrapolations can be used to accelerate the basis-set convergence significantly and that, for highly correlated wave functions, chemical accuracy is obtained even with medium-sized basis sets when the extrapolation is used. (C) 2001 Elsevier Science B.V. All rights reserved.