Locally-projected SCF cannot quantitatively reproduce the full SCF
intermolecular interaction energies for systems with significant
charge-transfer between the fragments (*e.g.*, hydrogen bonding energies in
water clusters). Good accuracy in the intermolecular binding energies can be
achieved if the locally-projected SCF MI iteration scheme is combined with a
charge-transfer perturbative correction.^{Khaliullin:2006} To account for
charge-transfer, one diagonalization of the full Fock matrix is performed after
the locally-projected SCF equations are converged and the final energy is
calculated as infinite-order perturbative correction to the locally-projected
SCF energy. This procedure is known as single Roothaan-step (RS)
correction.^{Khaliullin:2006, Liang:2004a, Liang:2004b} It is performed if
FRGM_LPCORR is set to RS. To speed up evaluation of the
charge-transfer correction, second-order perturbative correction to the energy
can be evaluated by solving the linearized single-excitation amplitude
equations. This algorithm is called the approximate Roothaan-step correction
and can be requested by setting FRGM_LPCORR to ARS.

Both ARS and RS corrected energies are very close to the full SCF energy for systems of weakly interacting fragments but are less computationally expensive than the full SCF calculations. To test the accuracy of the ARS and RS methods, the full SCF calculation can be done in the same job with the perturbative correction by setting FRGM_LPCORR to RS_EXACT_SCF or to ARS_EXACT_SCF. It is also possible to evaluate only the full SCF correction by setting FRGM_LPCORR to EXACT_SCF.

The iterative solution of the linear single-excitation amplitude equations in the ARS method is controlled by a set of NVO keywords described below.

*Restrictions.* Only single point HF and DFT energies can be evaluated
with the locally-projected methods. Geometry optimization can be performed
using numerical gradients. Wave function correlation methods (MP2, CC, *etc.*.)
are not implemented for the absolutely-localized molecular orbitals.
SCF_ALGORITHM cannot be set to anything but DIIS, however,
all SCF convergence algorithms can be used on isolated fragments (set
SCF_ALGORITHM in the *$rem_frgm* section).

$molecule 0 1 -- 0 1 O -1.56875 0.11876 0.00000 H -1.90909 -0.78106 0.00000 H -0.60363 0.02937 0.00000 -- 0 1 O 1.33393 -0.05433 0.00000 H 1.77383 0.32710 -0.76814 H 1.77383 0.32710 0.76814 $end $rem METHOD HF BASIS AUG-CC-PVTZ FRGM_METHOD GIA FRGM_LPCORR RS_EXACT_SCF $end $rem_frgm SCF_CONVERGENCE 2 THRESH 5 $end