# DFT energy matrices

Hi,

I’m decomposing the matrices of HF and DFT results but have some problems about the DFT Fock and DFT exchange-correlation energy matrices, with numpy library.

I could gain HF Fock matrix with

np.asarray(hf_wfn.Fa()) (np is numpy)

option and I guess this Fock matrix is constructed as

F=H+2J-K

However, when I do the same thing with the DFTs wfn, (e.g. np.asarray(dft_wfn.Fa())), I guess the output Fock matrix is not the desired one like

F=H+2J+Vxc, (I’m using GGA like pbe and, so, there is no K)

So, my question is

1. Is it right to get DFT’s Fock matrix with np.asarray(dft_wfn.Fa()) option?
2. How can I get Vxc matrix from SCF converged calculation?

1. Yes, `dft_wfn.Fa()` will return the full Fock matrix. You should probably verify this for your own edification.
2. The Vxc matrix can be obtained by `dft_wfn.Va()`.

Please note that a freshly constructed `F` will differ slightly from `hf_wfn.Fa()` as the orbitals are one “step” past the current Fock matrix. The size of the difference will depend on how converged your Wavefunction is. See here for further information.

PS: I forget when I added the `Va` constructor, you may need a fresh version from `GitHub.com/psi4/psi4`.

Dear dgasmith,
Thank you for the kind reply.
I could gain Va matrix successfully via upgrading the psi4 version as you told.
Actually, I’m trying to reproduce the DFT energies with matrices.
For the RHF, I could gain HF energy as

Etot=(H+F)*D+E_nuc (where Etot = total energy, H is core-Hamiltonian, T+Vne and E_nuc is nuclear-nuclear repulsion one.)

But in the case of DFT, I couldn’t get the same value with that.
I saw the tutorial you’ve mentioned but it is kind of hard to me since I’m lack of information to know what the psi4 module is doing such as Vpot.properties()[0], Vpot.functional(), superfunctional, etc.

My goal is calculating DFT like the psi4numpy tutorial 3a.(https://github.com/psi4/psi4numpy/blob/master/Tutorials/03_Hartree-Fock/3a_restricted-hartree-fock.ipynb)
And, therefore, I’m trying to modify that tutorial 3a to do the DFT.
I’ve found ks_helper.py in the Tutorial 04 but couldn’t use it for the same reason above…

So, my main question is if it is possible to create Exc directly with DFT Fock matrix (=H+2J+Vxc).

Thank you very much.

@nesquik91 Exc is not computed by a contraction of Vxc with the density, it is computed as a direct summation of the xc energy at every grid point. I don’t think its possible to do what you ask.