Conventional Delta-Self-Consistent-Field-DFT Calculations

Basics

In $\Delta$ SCF-DFT we calculate electronic excited states by assuming a certain non-equilibrium orbital occupation and by self-consistently solving the Kohn-Sham equations with this excited state population.

The excitation energy is then simply the energy difference between the ground state KS-DFT calculation and the $\Delta$ SCF-DFT calculation:

$\Delta E = E(\Delta SCF)-E(DFT)$

We therefore need to perform two calculations, the ground state DFT calculation and the DeltaSCF calculation. For a more detailed explanation, see Maurer and Reuter (2011)¹.

For this simple $\Delta$ SCF calculation, we have to set deltascf_method = simple 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_smearing

Example .param file:

reuse               : <base>.check
calculate_deltascf  : true
deltascf_checkpoint : <base>.check
deltascf_method     : simple
deltascf_smearing   : 0.01

#band  occ spin from_band to_band
%block deltascf_constraints
34    0.0000  1   34   34
35    1.0000  1   35   35
%endblock deltascf_constraints

In this example, we enforce an occupation of 0.00 electrons in the electronic state 34, spin channel 1 and an occupation of 1.00 electrons in the electronic state 35, spin channel 1. The last two numbers in each line specify a window of states in which the corresponding state is searched if it changes its position between SCF cycles. In that way we can ensure that we constrain the correct state.

deltascf_smearing is a mechanism which relaxes the constraints minimally to facilitate convergence. Sometimes, especially in the case of degenerate states, deltascf_smearing is necessary.

Reinhard J. Maurer and Karsten Reuter. Assessing computationally efficient isomerization dynamics: ΔSCF density-functional theory study of azobenzene molecular switching. The Journal of Chemical Physics, 135(22):224303, 12 2011. doi:10.1063/1.3664305. ↩