Conventional Delta-Self-Consistent-Field-DFT Calculations

Basics

In \DeltaSCF-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 \DeltaSCF-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 J. Chem. Phys. 135, 224303 (2011)

For the \DeltaSCF calculation, we have to add following keyword to <seed>.param

%BLOCK DEVEL_CODE
  DeltaSCF
%ENDBLOCK DEVEL_CODE

and add following keyword in <seed>.deltascf

deltascf_mode        :  1

Keywords allowed in <seed>.deltascf

In the .deltascf file, the keyword title plus colon takes exactly 23 columns (A20,3X). The keyword content starts after that. Lines with ‘#’ are ignored.


WARNING
The number of blanks between the keywords does count!! The best thing is to copy and modify the example from the manual.

keyword multiple appearance arguments and FORTRAN format
deltascf_iprint No <integer I>
deltascf_mode No <integer I>, 1, 2, 3, or 4
deltascf_constraint Yes <#state I5>1X<occ. F8.4>1X<spin I4><from I4><to I4>
overlap_cutoff No <float F8.4>, default: 0.01
deltascf_smearing No <float F8.4>, default: 0.01 eV
deltascf_mixing No <float F8.4>, default: mix_charge_amp

Example .deltascf file:

deltascf_mode        :  1
deltascf_iprint      :  1
# mode 1 constraints ##
#                       band  occ  spin from_band to_band
deltascf_constraint  :  34    0.0000  1   34   34
deltascf_constraint  :  35    1.0000  1   35   35
overlap_cutoff       :  0.01
deltascf_smearing    :  0.01

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.

Example 1: Electronic excitations of the Azobenzene molecule

In this example we calculate the first two electronic excited states of E-Azobenzene in a supercell.

The required files are azo.cell, azo.param, azo.deltascf

azo.param

task: SinglePoint

%BLOCK DEVEL_CODE
  DeltaSCF
%ENDBLOCK DEVEL_CODE

reuse: default

spin_polarized : False
cut_off_energy : 350.0
elec_energy_tol : 1e-07
fix_occupancy : False
iprint : 1
max_scf_cycles : 200
metals_method : dm
mixing_scheme : Pulay
nextra_bands : 10
num_dump_cycles : 0
opt_strategy_bias : 3
smearing_scheme : Gaussian
smearing_width : 0.1
xc_functional : PBE

azo.cell

%BLOCK LATTICE_CART
    10.0000000 0.0000000000 0.0000000000
    0.0000000000 20.0000000 0.0000000000
    0.0000000000 0.0000000000 10.0000000000
%ENDBLOCK LATTICE_CART

%BLOCK POSITIONS_ABS
C         -6.72081       -1.66625        0.00000
C         -6.64967       -0.26964        0.00000
C         -5.40647        0.36858       -0.00000
C         -4.23175       -0.38857       -0.00000
C         -4.29745       -1.78579       -0.00000
C         -5.54882       -2.43430       -0.00000
H         -7.68820       -2.15296        0.00000
H         -7.55879        0.31772        0.00000
H         -5.35348        1.44963       -0.00000
H         -3.26966        0.10734       -0.00000
H         -3.37789       -2.35693       -0.00000
N         -5.65342       -3.85046       -0.00000
N         -4.64259       -4.58194       -0.00000
C         -4.75058       -5.99808       -0.00000
C         -6.00434       -6.64214       -0.00000
C         -6.07567       -8.03881       -0.00000
C         -4.90409       -8.80053       -0.00000
C         -3.65828       -8.16721       -0.00000
C         -3.58139       -6.77065       -0.00000
H         -2.61200       -6.28795       -0.00000
H         -6.92178       -6.06761       -0.00000
H         -7.03986       -8.53061       -0.00000
H         -4.96168       -9.88134       -0.00000
H         -2.75170       -8.75849       -0.00000
%ENDBLOCK POSITIONS_ABS

FIX_ALL_CELL : True
KPOINTS_MP_GRID : 1 1 1

azo.deltascf

deltascf_mode        :  1
deltascf_iprint      :  1
# mode 1 constraints ##
#                       band  occ spin from_band to_band
deltascf_constraint  :  34    0.5000  1   34   34
deltascf_constraint  :  35    0.5000  1   35   35

We start by calculating the total DFT ground state energy as

Final energy, E             =  -2597.665647686     eV

Now we reuse the calculated wavefunctions and switch to the DeltaSCF calculation

%BLOCK DEVEL_CODE
  DeltaSCF
%ENDBLOCK DEVEL_CODE

There are 68 valence electrons. Therefore, for this non-spin-polarized system the HOMO orbital is orbital no. 34. The LUMO is orbital no. 35.

The first two excited states of azobenzene are known to be S1(n->pi*) and S2(pi->pi*) transitions between the HOMO and LUMO and the HOMO-1 and the LUMO.

The corresponding constraint sequence in azo.deltascf for the S1 excitation is

deltascf_constraint  :  34    0.5000  1   34   34
deltascf_constraint  :  35    0.5000  1   35   35

WARNING
When running non-spin-polarized calculations, orbital occupations range from 0 to 1. !!When running a spin-polarized calculation, they also range from 0 to 1, although they contain 0 to 2 electrons. In this (non-spin-polarized) case, if we want to transfer an electron from the HOMO(34) to LUMO(35) we need to enforce the occupation of both to be 0.50.

Feel free to increase the print level with deltascf_iprint to study the output in more detail.

The corresponding total energy is

Final energy, E             =  -2595.702720896     eV

This corresponds to an S1 excitation energy of 1.96 eV.

The constraint sequence for an S2 excitation is

deltascf_constraint  :  33    0.5000  1   33   33
deltascf_constraint  :  35    0.5000  1   35   35

The resulting final energy is

Final energy, E             =  -2594.762182241     eV

The corresponding S2 excitation energy is 2.90 eV.