According to [1] the Troullier-Martins pseudopotential for quantum number $l$ is computed by $$ V^{\textrm{KB}}_{\textrm{nonlocal},l}(r) = \frac{\vert{}V_{\textrm{nonlocal},l}(r)\Phi^{\textrm{PP},0}_l(r)\rangle \langle\Phi^{\textrm{PP},0}_l(r)V_{\textrm{nonlocal},l}(r)\vert} {\langle\Phi^{\textrm{PP},0}_l(r)\vert{}V_{\textrm{nonlocal},l}(r) \vert\Phi^{\textrm{PP},0}_l(r)\rangle} $$ where $$ \Phi^{\textrm{PP},0}_l(r) = R^{\textrm{PP}}_l(r)A(r) $$ and $A(r)$ is the angular part for which the pseudopotential was calculated.

Suppose that $l \neq 0$. Should we include all the pseudowavefunctions with angular parts $Y_{lm}$, $m = -l,\ldots,l$ in the computation of the total pseudopotential?

[1] Troullier and Martins. Efficient pseudopotentials for plane-wave calculations. Phys. Rev. B vol. 43, no. 3, pp. 1993-2006 (1991).

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