This paper introduces two developments for the application of plane wave basis sets for accurate molecular calculations. (1) An analytical formula is introduced for the momentum space representation of a Coulomb operator truncated to a finite range. Using this operator, interactions between the molecule and its periodic replicas can be exactly eliminated. Examples demonstrating the accuracy of our scheme are given. Calculations using a good-quality plane wave basis yield variational total SCF energies which are lower than those obtained with the cc-pvQZ basis for simple two-electron systems. (2) A new mixed-basis augmented plane wave all-electron method, the plane wave core Gaussian method has been developed which expands the valence part of the molecular orbitals in plane waves, and the corelike part in nonoverlapping compact Gaussians. Analytic equations have been derived for the necessary mixed Gaussian/plane wave electron repulsion integrals. Using such augmented basis set, we were able to reproduce the Gaussian-basis Hartree energies of small molecules to within a few muE(h).