The ANO‑R Basis Set

In this work, the new ANO-R basis set for all elements
of the first
six periods is introduced. The ANO-R basis set is an all-electron
basis set that was constructed including scalar-relativistic effects
of the exact-two component (X2C) Hamiltonian and modeling the atomic
nucleus by a Gaussian charge distribution, which makes the basis set
suitable for calculations of both light and heavy elements. For high
accuracy, it takes advantage of the general contraction scheme and
was developed at the CASSCF/CASPT2 level of theory. The distinguishing
feature of the ANO-R basis set is its compactness in terms of both
primitive and contracted basis functions, thus containing no superfluous
functions for a given quality. An optimum number of primitive basis
functions was selected based on studying the convergence toward the
complete basis set limit for each element individually. The primitive
basis sets were then contracted using the density-averaged atomic-natural-orbital
(ANO) scheme, and suitable contraction levels were determined solely
based on the natural orbital occupation numbers that describe the
contribution of each natural orbital to the one-particle density matrix.
Rather than following the common “split-valence n-tuple zeta plus polarization functions” structure, the resulting
basis sets ANO-R0 to ANO-R3 possess a unique composition for each
element, ensuring that no unnecessary functions are included while
the basis sets are still balanced across the first six periods (H–Rn).