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Localized atomic orbitals are the preferred basis-set choice for large-scaleexplicit correlated calculations, and high-quality hierarchicalcorrelation-consistent basis sets are a prerequisite for correlated methods todeliver numerically reliable results. At present, Numeric Atom-centered Orbital(NAO) basis sets with valence correlation consistency (VCC), designated asNAO-VCC-$n$Z, are only available for light elements from hydrogen (H) to argon(Ar) (\textit{New J. Phys.} \textbf{15}, 123033, (2013) ). In this work, weextend this series by developing NAO-VCC-$n$Z basis sets for krypton (Kr), aprototypical element in the fourth row of periodic table. We demonstrate thatNAO-VCC-$n$Z basis sets facilitate the convergence of electronic total-energycalculations using the Random Phase Approximation (RPA), which can be usedtogether with a two-point extrapolation scheme to approach thecomplete-basis-set (CBS) limit. Notably, the Basis Set Superposition Error(BSSE) associated with the newly generated NAO basis sets is minimal, makingthem suitable for applications where BSSE correction is either cumbersome orimpractical to do. After confirming the reliability of NAO basis sets for Kr,we proceed to calculate the Helmholtz free energy for Kr crystal at thetheoretical level of RPA plus renormalized single excitation (rSE) correction.From this, we derive the pressure-volume ($P$-$V$) diagram, which showsexcellent agreement with the latest experimental data. Our work demonstratesthe capability of correlation-consistent NAO basis sets for heavy elements,paving the way toward numerically reliable correlated calculations for bulkmaterials.

Developing correlation-consistent numeric atom-centered orbital basis sets for Krypton: Applications in RPA-based correlated calculations