  The rapidly growing interest in simulating condensed-phase materials using
quantum chemistry methods calls for a library of high-quality Gaussian basis
sets suitable for periodic calculations. Unfortunately, most standard Gaussian
basis sets commonly used in molecular simulation show significant linear
dependencies when used in close-packed solids, leading to severe numerical
issues that hamper the convergence to the complete basis set (CBS) limit,
especially in correlated calculations. In this work, we revisit Dunning's
strategy for construction of correlation-consistent basis sets and examine the
relationship between accuracy and numerical stability in periodic settings.
Specifically, we find that limiting the number of primitive functions avoids
the appearance of problematic small exponents while still providing smooth
convergence to the CBS limit. As an example, we generate double-, triple-, and
quadruple-zeta correlation-consistent Gaussian basis sets for periodic
calculations with Goedecker-Teter-Hutter (GTH) pseudopotentials. Our basis sets
cover the main-group elements from the first three rows of the periodic table.
Especially for atoms on the left side of the periodic table, our basis sets are
less diffuse than those used in molecular calculations. We verify the fast and
reliable convergence to the CBS limit in both Hartree-Fock and
post-Hartree-Fock (MP2) calculations, using a diverse test set of $19$
semiconductors and insulators.
