# PhotonXCEnergyMethod

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#### PhotonXCEnergyMethod

Section Hamiltonian::XC
Type integer
Default 1

There are different ways to calculate the energy,

Options:

• virial:
(modified) virial approach
$(E_{\rm{px}}^{\rm{virial}} = \frac{1}{2}\int d\mathbf{r}\ \mathbf{r}\cdot[ -\rho(\mathbf{r})\nabla v_{\rm{px}}(\mathbf{r})])$

• expectation_value:
expectation value w.tr.t. the wave functions (valid only for 1 electron)
$E_{\rm{px}}[\rho] = -\sum_{\alpha=1}^{M_{p}}\frac{\tilde{\lambda}_{\alpha}^{2}}{2\tilde{\omega}_{\alpha}^{2}} \langle (\tilde{\mathbf{{\varepsilon}}}_{\alpha}\cdot\hat{\mathbf{J}}_{\rm{p}})\Phi[\rho] | (\tilde{\mathbf{{\varepsilon}}}_{\alpha}\cdot\hat{\mathbf{J}}_{\rm{p}})\Phi[\rho] \rangle$
This option only works for the wave function based electron-photon functionals
• LDA:
energy from electron density
$E_{\rm pxLDA}[\rho] = \frac{-2\pi^{2}}{(d+2)({2V_{d}})^{\frac{2}{d}}} \sum_{\alpha=1}^{M_{p}}\frac{\tilde{\lambda}_{\alpha}^{2}}{\tilde{\omega}_{\alpha}^{2}} \int d\mathbf{r}\ \rho^{\frac{2+d}{d}}(\mathbf{r})$
This option only works with LDA electron-photon functionals.

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