DFT+U(MO) - Applying potentials to arbitrary orbitals

Basics

We can employ the molecular orbital projections we have introduced in the le $\Delta$ SCF section to also introduce penalty potentials that shift specific orbitals up or down. This can be used to specify the HOMO-LUMO of an adsorbed molecule or to modify the level alignment with the metal substrate. This constraint potential can be combined with population constraints.

For more details and an example application on Porphine molecules adsorbed at coinage metal surfaces, see Müller et al. (2016)¹.

For a le $\Delta$ SCF calculation, we have to set deltascf_method = linear expansion in the <seed>.param file. The constraint must also be specifed, as discussed in the overview section.

The only additional relevant $\Delta$ SCF keywords is deltascf_dftu_checkpoint

Example .param file:

reuse               : <base>.check
calculate_deltascf  : true
deltascf_checkpoint : <base>.check
deltascf_dftu_checkpoint : <base2>.check
deltascf_method     : DFT+U(MO)

#band  occ spin    +U in eV  excite?
%block deltascf_constraints
34    0.0000  1   -1.40         Y
35    1.0000  2    0.70         Y
%endblock deltascf_constraints

In this mode we add a potential to the Hamiltonian for each defined constraint, which has the following form:

$V_c = \frac{U}{2} \cdot|\phi_c\rangle\langle\phi_c|$

You can find a detailed description of these potentials in Appendix D of First-Principles Description of the Isomerization Dynamics of Surface-Adsorbed Molecular Switches ²

In this example, two +U constraint potentials act on orbital no. 34 of the majority spin channel and orbital no. 35 of the minority spin channel, taken from the deltascf_dftu_checkpoint=<base2>.check file. In addition, the occupation of orbital no. 35 taken from file deltascf_checkpoint=<base>.check file is constrained to the occupation 1.000. Excitation constraints on each state can be activated (or not) by adding the final 'Y' or 'N' to the relevant line.

Moritz Müller, Katharina Diller, Reinhard J. Maurer, and Karsten Reuter. Interfacial charge rearrangement and intermolecular interactions: Density-functional theory study of free-base porphine adsorbed on Ag(111) and Cu(111). The Journal of Chemical Physics, 144(2):024701, 01 2016. doi:10.1063/1.4938259. ↩
Reinhard Johann Maurer. First-Principles Description of the Isomerization Dynamics of Surface-Adsorbed Molecular Switches. PhD thesis, Technische Universität München, 2014. URL: https://mediatum.ub.tum.de/1190934. ↩