# Troullier-Martins pseudopotential with nonzero angular momentum quantum number

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).

• You might consider committing to the Materials Modeling SE proposal. Questions like these are bound to receive more activity in that site after it is launched as many experts from the field of computational physics, chemistry and materials science will be more concentrated and engaged there. – rashid Jan 5 at 5:10