LSCRPA

LSCRPA = [logical]
Default: LSCRPA = .FALSE. 

Description: LSCRPA selects the spectral cRPA method.

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Mind: Recommended cRPA method as of version 6.6.0.

When selected the spectral method in constrained RPA (cRPA) calculations is selected. The screening effects in the target space are calculated as follows

${\tilde{\chi }}_{{\mathbf{𝐆},\mathbf{𝐆}}^{\prime }}^{\sigma }(\mathbf{𝐪},i\omega )\approx \frac{1}{N_k}\sum _{n{n}^{\prime }\mathbf{𝐤}}\frac{f_{n\mathbf{𝐤}}-f_{n^{\prime }\mathbf{𝐤}\mathbf{-}\mathbf{𝐪}}}{{ϵ}_{n\mathbf{𝐤}}-{ϵ}_{n^{\prime }\mathbf{𝐤}\mathbf{-}\mathbf{𝐪}}-i\omega }{\theta }_{n\mathbf{𝐤}}^{\sigma }{\theta }_{n^{\prime }\mathbf{𝐤}\mathbf{-}\mathbf{𝐩}}^{{\sigma }^{\prime }}⟨u_{n\mathbf{𝐤}}^{\sigma }|e^{-i\mathbf{(}\mathbf{𝐆}\mathbf{+}\mathbf{𝐪}\mathbf{)}\mathbf{𝐫}}|u_{n^{\prime }\mathbf{𝐤}\mathbf{-}\mathbf{𝐪}}^{{\sigma }^{\prime }}⟩⟨u_{n^{\prime }\mathbf{𝐤}\mathbf{-}\mathbf{𝐪}}^{{\sigma }^{\prime }}|e^{-i\mathbf{(}{\mathbf{𝐆}}^{\prime }\mathbf{-}\mathbf{𝐪}\mathbf{)}{\mathbf{𝐫}}^{\prime }}|u_{n^{\prime }\mathbf{𝐤}}^{\sigma }⟩$

Here ${\theta }_{n\mathbf{𝐤}}^{\sigma }$ are the eigenvalues of the correlated projectors

$P_{mn}^{\sigma (\mathbf{𝐤})}=\sum _{i\in {𝒯}}{T}_{im}^{*\sigma (\mathbf{𝐤})}{T}_{in}^{\sigma (\mathbf{𝐤})}$

ordered according to their leverage scores. The s-cRPA method results in larger effective interactions compared to w-cRPA or the projector method and conserves the number of electrons.

Related tags and articles

LDISENTANGLED, LWEIGHTED, ALGO

Examples that use this tag

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