The Maximum Overlap Method (MOM) is a useful alternative to CIS and TDDFT for
obtaining low-cost excited states.
J. Phys. Chem. A
(2008), 112, pp. 13164. It works by modifying the orbital selection step in the SCF procedure. By choosing orbitals that most resemble those from the previous cycle, rather than those with the lowest eigenvalues, non-aufbau, excited-state SCF determinants can be determined, in what has sometimes been called excited-state Kohn-Sham theory. 459 J. Chem. Phys.
(2013), 138, pp. 064101. This represents a form of “SCF” approach to computing excitation energies, which has advantages over TDDFT is certain cases. For example, TDDFT exhibits systemic problems with the description of charge-transfer and Rydberg excitations, both of which can be modeled using the SCF approach. The use of MOM also allows the user to easily target very high energy states, such as those involving excitation of core electrons, 104 J. Chem. Phys.
(2009), 130, pp. 124308. which can be difficult to capture using other excited state methods. Other SCF approaches are described in Section 7.9.
In order to calculate an excited state using MOM, the user must correctly identify the orbitals involved in the transition. For example, in a transition, the and orbitals must be identified and this usually requires a preliminary calculation. The user then manipulates the orbital occupancies using the $occupied section, removing an electron from the and placing it in the . The MOM is then invoked to preserve this orbital occupancy. The success of the MOM relies on the quality of the initial guess for the calculation. If the virtual orbitals are of poor quality then the calculation may ‘fall down’ to a lower energy state of the same symmetry. Often the virtual orbitals of the corresponding cation are more appropriate for using as initial guess orbitals for the excited state.
Because the MOM states are single determinants, all of Q-Chem’s existing single determinant properties and derivatives are available. This allows, for example, analytic harmonic frequencies to be computed on excited states. The orbitals from a Hartree-Fock MOM calculation can also be used in an MP2 calculation. For all excited state calculations, it is important to add diffuse functions to the basis set. This is particularly true if Rydberg transitions are being sought. For DFT based methods, it is also advisable to increase the size of the quadrature grid so that the more diffuse densities are accurately integrated.
The MOM-based SCF method can be combined with a PCM based solvation description for both equilibrium and non-equilibrium effects (for more details see Section 7.9.6).
The following $rem is used to invoke the MOM:
$comment CO spin-purified calculation Step 1: prepare MOs $end $molecule 0 1 C O C 1.05 $end $rem METHOD B3LYP BASIS 6-31G* $end @@@ $comment Step 2: spin purification (OPSING=TRUE) $end $molecule read $end $rem METHOD B3LYP BASIS 6-31G* SCF_GUESS read MOM_START 1 UNRESTRICTED true OPSING true $end $occupied 1 2 3 4 5 6 7 1 2 3 4 5 6 8 $end
$molecule 1 2 C H 1 1.091480 O 1 1.214713 2 123.10 N 1 1.359042 2 111.98 3 -180.00 H 4 0.996369 1 121.06 2 -0.00 H 4 0.998965 1 119.25 2 -180.00 $end $rem METHOD B3LYP BASIS 6-311(2+,2+)G(d,p) XC_GRID 000100000194 $end @@@ $molecule 0 1 C H 1 1.091480 O 1 1.214713 2 123.10 N 1 1.359042 2 111.98 3 -180.00 H 4 0.996369 1 121.06 2 -0.00 H 4 0.998965 1 119.25 2 -180.00 $end $rem METHOD B3LYP BASIS 6-311(2+,2+)G(d,p) XC_GRID 000100000194 MOM_START 1 SCF_GUESS read UNRESTRICTED true $end $occupied 1:12 1:11 13 $end
Additionally, it is possible to perform a CIS/TDDFT calculation on top of the MOM excitation. This capability can be useful when modeling pump-probe spectra. In order to run MOM followed by CIS/TDDFT, the $rem variable CIS_N_ROOTS must be specified. Truncated subspaces may also be used, see Section 7.3.2.
$molecule 0 1 O 0.0000 0.0000 0.1168 H 0.0000 0.7629 -0.4672 H 0.0000 -0.7629 -0.4672 $end $rem METHOD B3LYP BASIS aug-cc-pvdz integral_symmetry false point_group_symmetry False $end @@@ $molecule read $end $rem METHOD B3LYP BASIS aug-cc-pvdz SCF_GUESS read MOM_START 1 UNRESTRICTED true integral_symmetry false point_group_symmetry False CIS_N_ROOTS 5 TRNSS true ! use truncated subspace for TDDFT TRTYPE 3 ! specify occupied orbitals CUTVIR 15 ! truncate high energy virtual orbitals N_SOL 1 ! number core orbitals, specified in $solute section $end $solute 1 $end $occupied 1 2 3 4 5 1 2 3 4 6 $end
If the MOM excitation corresponds to a core hole, a reduced subspace must be used to avoid de-excitations to the core hole. The $rem variable CORE_IONIZE allows only the hole to be specified so that not all occupied orbitals need to be entered in the $solute section.
$molecule 0 1 O 0.0000 0.0000 0.1168 H 0.0000 0.7629 -0.4672 H 0.0000 -0.7629 -0.4672 $end $rem METHOD B3LYP BASIS aug-cc-pvdz integral_symmetry false point_group_symmetry False $end @@@ $molecule read $end $rem METHOD B3LYP BASIS aug-cc-pvdz SCF_GUESS read MOM_START 1 UNRESTRICTED true integral_symmetry false integral_symmetry true CIS_N_ROOTS 5 TRNSS true ! use truncated subspace for TDDFT TRTYPE 3 ! specify occupied orbitals N_SOL 1 ! number core holes, specified in $solute section CORE_IONIZE 2 ! hole orbital specified $end $solute 6 $end $occupied 1 2 3 4 5 2 3 4 5 6 $end