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Finite-range numerical atomic orbitals are the basis functions of choice forseveral first principles methods, due to their flexibility and scalability.Generating and testing such basis sets, however, remains a significantchallenge for the end user. We discuss these issues and present a new schemefor generating improved polarization orbitals of finite range. We then developa series of high-accuracy basis sets for the water molecule, and report ontheir performance in describing the monomer and dimer, two phases of ice, andliquid water at ambient and high density. The tests are performed by comparisonwith plane-wave calculations, and show the atomic orbital basis sets to exhibitan excellent level of transferability and consistency. The highest-order bases(quadruple-zeta) are shown to give accuracies comparable to a plane-wavekinetic energy cutoff of at least ~1000 eV for quantities such as energydifferences and ionic forces, as well as achieving significantly greateraccuracies for total energies and absolute pressures.

Optimal finite-range atomic basis sets for liquid water and ice