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Derivatives of the local energy

It is very simple to evaluate the terms appearing in B.5 and B.6 in fact using B.29 and B.28 and considering only the $ m$ orbital dependent by the parameter $ a$ we obtain:
$\displaystyle \partial_a \vec{\nabla}_k \ln U$ $\displaystyle =$ $\displaystyle \sum_{j}\sum_{n} \lambda_{mn} \partial_a \vec{\nabla}_k \phi_m(r_...
...\sum_{j}\sum_{n} \lambda_{nm} \vec{\nabla}_k \phi_n(r_k) \partial_a \phi_m(r_j)$  
$\displaystyle \partial_a \nabla^2_k \ln U$ $\displaystyle =$ $\displaystyle \sum_{j}\sum_{n} \lambda_{mn} \partial_a \nabla^2_k \phi_m(r_k) \...
... + \sum_{j }\sum_{n} \lambda_{nm} \nabla^2_k \phi_n(r_k) \partial_a \phi_m(r_j)$  

Claudio Attaccalite 2005-11-07