Notes about Sarc basis sets
-------------------------------
SARC  (segmented all-electron relativistically contracted)
SARC2 (second-generation segmented all-electron relativistically contracted)
ZORA  (zeroth-order regular approximation)
DKH2  (second-order Douglar-Kroll-Hess)

A family of segmented all-electron relativistically contracted (SARC) basis sets for
the elements Hf-Hg is constructed for use in conjunction with the Douglas-Kroll-Hess (DKH)
and zeroth-order regular approximation (ZORA) scalar relativistic Hamiltonians. The SARC basis
sets are loosely contracted and thus offer computational advantages compared to generally
contracted relativistic basis sets, while their sufficiently small size allows them to be used in
place of effective core potentials (ECPs) for routine studies of molecules.

Scalar relativistic basis sets for the ZORA approximation have been developed by the Amsterdam group
for Slater functions and are available in the Amsterdam Density Functional code. Recent reports on
basis sets for transition metal atoms that are contracted to be consistent with the
second- or third-order DKH (DKH2, DKH3) procedures.


Pantazis2008a found that the ZORA and DKH results are essentially of the same quality. Most importantly,
the transition from the uncontracted WTBS to the much more compact SARC has minimal impact on the
accuracy of the computed values, the rms error increasing by a mere 0.01 eV.

              Ionization Energies (eV) computed with the B3LYP
              Functional and the SARC Basis Sets, Compared to
              Experimental Values
              -------------------------------------------------
                               DKH2            ZORA          -
                    exp      IE      ∆E      IE      ∆E       -
              Hf    6.825    6.711   -0.115  6.716   -0.109   -
              Ta    7.550    7.466   -0.084  7.481   -0.069   -
              W     7.864    7.791   -0.073  7.807   -0.057   -
              Re    7.834    7.915    0.081  7.933    0.099   -
              Os    8.438    8.483    0.045  8.503    0.065   -
              Ir    8.967    8.896   -0.071  8.904   -0.063   -
              Pt    8.959    9.197    0.238  9.223    0.264   -
              Au    9.226    9.382    0.157  9.412    0.186   -
              Hg    10.438   10.342  -0.096  10.373  -0.065   -
              -------------------------------------------------

The behavior of the DKH2 and ZORA orbitals is understood from the well-known fact that the deep core
orbital energies are much too low in the ZORA method.


The SARC2 basis sets extend the applicability of the first-generation DFT-oriented basis sets to routine
all-electron wave function-based treatments of lanthanide complexes. The new basis sets are benchmarked
with respect to excitation energies, radial distribution functions, optimized geometries, orbital
eigenvalues, ionization potentials, and spin–orbit coupling parameters of lanthanide systems and are shown
to be suitable for the description of magnetic and spectroscopic properties using both DFT and
multireference wave function-based methods.
