Ion and Electron Interaction Terms

For any practical OFDFT calculation of a real system, all three of the

• ion-ion interaction term,

• ion-electron interaction term, and

• electron-electron interaction term (Hartree term)

must be included in the calculation. Some of these terms can be omitted depending on the use case or for testing purposes.

Ion-Ion Interaction

functionals.IonIon()

Ion-ion interaction energy

This is a dummy function used purely for consistency in how the energy terms are used as input during initialization of a system object. Inclusion of this term causes the system object to include an ion-ion interaction energy term during the system object’s energy computations.

Ion-Electron Interaction

functionals.IonElectron(box_vecs, den, v_ext)

Ion-electron energy functional

The ion-electron energy functional is given by

\[U_\text{ion-electron}[n] = \int d^3\mathbf{r}~ n(\mathbf{r}) v_\text{ext}(\mathbf{r}).\]

Parameters:

• box_vecs (torch.Tensor) – Lattice vectors

• den (torch.Tensor) – Electron density

• v_ext (torch.Tensor) – Ionic/external potential

Returns:

Ion-electron interaction energy

Return type:

torch.Tensor

Hartree Energy

functionals.Hartree(box_vecs, den)

Hartree energy functional

The Hartree energy functional is the classical mean-field electron-electron interaction energy. It is given by

\[U_\text{Hartree}[n] = \frac{1}{2} \int d^3\mathbf{r} d^3\mathbf{r}'~ \frac{n(\mathbf{r})n(\mathbf{r}')}{|\mathbf{r}-\mathbf{r}'|} .\]

Parameters:

• box_vecs (torch.Tensor) – Lattice vectors

• den (torch.Tensor) – Electron density

Returns:

Hartree energy

Return type:

torch.Tensor