29.9.3 Localization

By default, Pipek-Mezey localization is used and performed automatically in the beginning of a local correlation calculation. Thus

df-hf        !Hartree-Fock with density fitting
df-lmp2      !LMP2 using the Pipek-Mezey LMOs

is equivalent to

df-hf        !Hartree-Fock with density fitting
locali,pipek !Orbital localization using the Pipek-Mezey criterion
df-lmp2      !LMP2 using the Pipek-Mezey LMOs

Boys localization can be used as well, but in this case the localization must be done beforehand, e.g.

df-hf        !Hartree-Fock with density fitting
locali,boys  !Orbital localization using the Boys criterion
df-lmp2      !LMP2 using the Boys LMOs

Poor localization is sometimes an intrinsic problem, in particular for strongly conjugated systems or when diffuse basis sets are used. This is caused by localization tails due to the overlapping diffuse functions. The problem is particularly frequent in calculations of systems with short bonds, e.g., aromatic molecules. It can be avoided using directive

PIPEK,DELETE=$n$

with $n=1$ or $2$. This means that the contributions of the $n$ most diffuse basis functions of each angular momentum type are ignored in the localization. This often yields much better localized orbitals when diffuse basis sets are used. For aug-cc-pVTZ, $n=2$ has been found to work very well, while for aug-cc-pVDZ $n$=1

In rare cases it might also happen that the localization procedure does not converge. It is them possible to choose a second-order Newton-Raphson localization scheme, using the directive

PIPEK,METHOD=2,[DELETE=$n$]

Alternatively (recommended) one can use

PIPEK,METHOD=3,[DELETE=$n$]

which first performs a few standard Pipek-Mezey iterations and the invokes the second-order localization scheme. This then usually converges very quickly.