Developping new functionals for KS or RS-DFT

The very basics

To develop new functionals for DFT (or RSDFT) to be used in the SCF programs (ks_scf or rs_ks_scf ) or in multi-configurational RSDFT (see, you need to specify, at the end of the day, two things:

  • exchange/correlation energy functionals used to compute the energy

  • exchange/correlation potentials for (alpha/beta electrons) used to optimize the wave function

The providers to define such quantities, and then used by all the all the DFT programs, are (see dft_one_e):

  • energy_x and energy_c : the exchange and correlation energy functionals (see e_xc_genera l.irp.f)

  • potential_x_alpha_ao and potential_x_beta_ao : the exchange potential for alpha/beta electrons on the AO basis (se e pot_general.irp.f)

  • potential_c_alpha_ao and potential_c_beta_ao : the correlation potential for alpha/beta electrons on the AO basis ( see pot_general.irp.f)

From the AO basis, the providers for the exchange/correlation potentials of alpha/beta electrons on the MO basis are automatically obtained by a AO –> MO transformation.

So, at the end of the day, adding a new functional consists only in setting a new value to these providers.

The general philosphy

The directory functionals contains only files ending with .irp.f whose name being the name of a specific functional. All files in a_functional.irp.f must contain at least the following providers

  • energy_x_a_functional and energy_c_a_functional which are of course the exchange and correlation energies

  • potential_x_alpha_ao_a_functional and potential_x_beta_ao_a_functional which are the exchange alpha/beta potentials

  • potential_c_alpha_ao_a_functional and potential_c_beta_ao_a_functional which are the correlation alpha/beta potentials

For instance, the file sr_lda.irp.f contains the following providers

  • energy_x_sr_lda and energy_c_sr_lda which are of course the exchange and correlation energies

  • potential_x_alpha_ao_sr_lda and potential_x_beta_ao_sr_lda which are the exchange alpha/beta potentials

  • potential_c_alpha_ao_sr_lda and potential_c_beta_ao_sr_lda which are the correlation alpha/beta potentials

Therefore, if you want to develop a new functional, just design a provider

To use a functional

Using the density for DFT calculations in the Quantum Package

Different ways of defining the density for the DFT

There are many ways of defining a density, and the keyword to define it is density_for_dft density_for_dft. Here are the following options for that keyword:

  • “KS” : density is obtained from a single Slater determinant

  • “WFT” : density is obtained from the wave function which is stored in the EZFIO data base

  • “input_density” : a one-body density matrix on the MO basis is read from the EZFIO data base, and the density is built from there (see data_one_e_dm_alpha_mo)

  • “damping_rs_dft” : damped density between “WFT” and “input_density” with the damping factor density_for_dft damping_for_rs_dft.


If an MO basis is already defined in the  EZFIO data base, the one-body density matrices will be defined according to this MO basis. For instance, if “KS”, the density constructed will be density of a single Slater determinant built with the current MO basis stored in the EZFIO data base.

Once that you have defined how to define the density, you can easily access to the providers associated to it.

Value of the density and its gradients in real space

The density and its gradients evaluated on all grid points are (see dft_utils_in_r):

  • one_e_dm_alpha_at_r and one_e_dm_beta_at_r : alpha/beta density at grid points

  • one_e_dm_and_grad_alpha_in_r, one_e_dm_and_grad_beta_in_r: alpha/beta gradients (and densities)

If you want to evaluate the density and its gradients at a given point in space, please refer to:

  • density_and_grad_alpha_beta_and_all_aos_and_grad_aos_at_r()

If you use these providers and subroutines, the density computed will be coherent with the choice of density that you specified with density_for_dft density_for_dft, and it will impact automatically the general providers of dft_one_e.