We demonstrate the applicability of correlated Gaussian functions with terms linear in the interparticle distance using the helium atom as an example. Hamiltonian matrix elements can be integrated analytically for atoms with an arbitrary number of electrons in terms of inverse trigonometric and dilogarithmic functions. This allows a full optimization of exponents through minimization of the nonrelativistic binding energy. In the new basis energy convergence is faster compared to that observed for regular correlated Gaussian functions. In addition, the cusp condition can be fulfilled to a high degree of precision. (C) 2004 Published by Elsevier B.V.