========================================================= DFT+U(MO) - Applying potentials to arbitrary orbitals ========================================================= ------- Basics ------- We can employ the molecular orbital projections we have introduced in the le :math:`\Delta`\SCF formalism 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 J. Chem. Phys. 144, 024701 (2016). In order to use this functionality we need to put following sequence into the .param :: %BLOCK DEVEL_CODE DeltaSCF %ENDBLOCK DEVEL_CODE and add following keyword to .deltascf :: deltascf_mode : 2 In this mode we add a potential to the Hamiltonian for each defined constraint, which has the following form: .. math:: V_c = \frac{U}{2} \cdot|\phi_c\rangle\langle\phi_c| If we specify :: %BLOCK DEVEL_CODE DeltaSCF norealCDFT %ENDBLOCK DEVEL_CODE following potential is applied .. math:: V_c = \frac{U}{2} \cdot(1-2n_c)|\phi_c\rangle\langle\phi_c| Here :math:`n_c` is the occupation of the projected state :math:`\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", `Doctoral Thesis`_, Technische Universität München, 2014 .. _Doctoral Thesis: http://mediatum.ub.tum.de/?id=1190934 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Keywords allowed in .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 | arguments and FORTRAN format | | | appearance | | +=====================+============+=====================================================+ | deltascf_iprint | No | | +---------------------+------------+-----------------------------------------------------+ | deltascf_file | No | | +---------------------+------------+-----------------------------------------------------+ | deltascf_ldau_file | No | | +---------------------+------------+-----------------------------------------------------+ | deltascf_constraint | Yes | <#state I5>1X1X1X| +---------------------+------------+-----------------------------------------------------+ | overlap_cutoff | No | , default: 0.01 | +---------------------+------------+-----------------------------------------------------+ | deltascf_mixing | No | , default: mix_charge_amp | +---------------------+------------+-----------------------------------------------------+ Example .deltascf file:: deltascf_mode : 2 deltascf_file : bla.check deltascf_ldau_file : bla2.check deltascf_iprint : 1 #mode 2 constraints add. deltascf_excite commands## # band occ spin +U in eV deltascf_constraint : 34 0.0000 1 -1.40 deltascf_constraint : 35 1.0000 2 0.70 deltascf_excite overlap_cutoff : 0.01 deltascf_mixing : 0.05 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 channeltaken from the deltascf_ldau_file bla2.check. In addition, the occupation of orbital no. 35 taken from file deltascf_file bla.check is constrained to the occupation 1.000. Excitation constraints are activated by following a deltascf_constraint with the deltascf_excite command. ------------------------------------------------------- Example 3: Controlling the HOMO-LUMO gap of Azobenzene ------------------------------------------------------- For this example we need the following files azo.param azo.cell azo.deltascf *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.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.deltascf* :: deltascf_mode : 2 deltascf_iprint : 1 deltascf_file : bla.check deltascf_ldau_file : bla.check # band occ spin +U in eV deltascf_constraint : 34 0.5000 1 -1.00 #deltascf_excite deltascf_constraint : 35 0.5000 1 1.00 #deltascf_excite We first calculate the ground state of azobenzene and copy the corresponding wavefunction file azo.check to the file bla.check. We use this file for reference orbitals for +U(MO), but also for :math:`\Delta`\SCF excitation constraints. We find a HOMO-LUMO gap with PBE of 1.51 eV, which is significantly lower than the HOMO-LUMO gap estimated with a hybrid functional. After running the DFT+U(MO) calculation with a -1.00 eV constraint on MO 34 and a +1.00 constraint on MO 35, we find a HOMO-LUMO gap of 2.46 eV. If we now uncomment the deltascf_excite commands, we can apply the MO constraints and enforce excited state occupations that model the S1 excitation of azobenzene. The corresponding excitation energy is 2.90 eV (compared to 1.96 eV in Example 1). --------------------- **WARNING** This module gives a lot of freedom in combining methods and parameters. However, only few combinations are physically sensible. ---------------------