# 12.4.1 Locally-Projected SCF Methods with Single Roothaan-Step Correction

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.473 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.473, 581, 582 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). Example 12.6 Comparison between the RS corrected energies and the conventional SCF energies can be made by calculating both energies in a single run. $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