# 4.5.11 Maximum Overlap Method (MOM)

(June 30, 2021)

In general, the DIIS procedure (Section 4.5.3) is remarkably successful. One difficulty that is occasionally encountered is the problem of an SCF that occupies two different sets of orbitals on alternating iterations, and therefore oscillates and fails to converge. This can be overcome by choosing orbital occupancies that maximize the overlap of the new occupied orbitals with the set previously occupied. Q-Chem contains the maximum overlap method (MOM), developed by Andrew Gilbert and Peter Gill. With GEN_SCFMAN, the MOM algorithm can be applied to R, U, and RO SCF calculations when paired with the DIIS algorithm.

MOM is therefore is a useful adjunct to DIIS in convergence problems involving flipping of orbital occupancies. It is controlled by the $rem variable MOM_START, which specifies the SCF iteration on which the MOM procedure is first enabled. There are two strategies that are useful in setting a value for MOM_START. To help maintain an initial configuration it should be set to start on the first cycle. On the other hand, to assist convergence it should come on later to avoid holding on to an initial configuration that may be far from the converged one. The MOM-related$rem variables in full are the following:

MOM_PRINT
Switches printing on within the MOM procedure.
TYPE:
LOGICAL
DEFAULT:
FALSE
OPTIONS:
FALSE Printing is turned off TRUE Printing is turned on.
RECOMMENDATION:
None

MOM_START
Determines when MOM is switched on to stabilize DIIS iterations.
TYPE:
INTEGER
DEFAULT:
0 (FALSE)
OPTIONS:
0 (FALSE) MOM is not used $n$ MOM begins on cycle $n$.
RECOMMENDATION:
Set to 1 if preservation of initial orbitals is desired. If MOM is to be used to aid convergence, an SCF without MOM should be run to determine when the SCF starts oscillating. MOM should be set to start just before the oscillations.

MOM_METHOD
Determines the target orbitals with which to maximize the overlap on each SCF cycle.
TYPE:
INTEGER
DEFAULT:
MOM
OPTIONS:
MOM Maximize overlap with the orbitals from the previous SCF cycle. IMOM Maximize overlap with the initial guess orbitals.
RECOMMENDATION:
If appropriate guess orbitals can be obtained, then IMOM can provide more reliable convergence to the desired solution.

Example 4.15  An example showing how to converge a ROHF calculation on the ${}^{3}\!A_{2}$ state of DMX. Note the use of reading in orbitals from a previous closed-shell calculation and the use of MOM to maintain the orbital occupancies. The ${}^{3}B_{1}$ is obtained if MOM is not used.

$molecule +1 1 C 0.000000 0.000000 0.990770 H 0.000000 0.000000 2.081970 C -1.233954 0.000000 0.290926 C -2.444677 0.000000 1.001437 H -2.464545 0.000000 2.089088 H -3.400657 0.000000 0.486785 C -1.175344 0.000000 -1.151599 H -2.151707 0.000000 -1.649364 C 0.000000 0.000000 -1.928130 C 1.175344 0.000000 -1.151599 H 2.151707 0.000000 -1.649364 C 1.233954 0.000000 0.290926 C 2.444677 0.000000 1.001437 H 2.464545 0.000000 2.089088 H 3.400657 0.000000 0.486785$end

$rem UNRESTRICTED false METHOD hf BASIS 6-31+G* SCF_GUESS core THRESH 12$end

@@@

$molecule read$end

$rem UNRESTRICTED false METHOD hf BASIS 6-31+G* SCF_GUESS read MOM_START 1 THRESH 12$end

$occupied 1:26 28 1:26 28$end

@@@

$molecule -1 3 read$end

$rem UNRESTRICTED false METHOD hf BASIS 6-31+G* SCF_GUESS read THRESH 12$end


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