  The classical frame potential in a finite dimensional Hilbert space has been
introduced by Benedetto and Fickus, who showed that all finite unit-norm tight
frames can be characterized as the minimizers of this energy functional. This
was the start point of a series of new results in frame theory, related to
finding tight frames with determined length. The frame potential has been
studied in the traditional setting as well as in the finite-dimensional fusion
frame context. In this work we introduce the concept of {\sl mixed frame
potential}, which generalizes the notion of the Benedetto-Fickus frame
potential. We study properties of this new potential, and give the structure of
its critical pairs of sequences on a suitable restricted domain. For a given
sequence ${\alpha_m}_{m=1,...,N}$ in $K,$ where $K$ is $\mathbb{R}$ or
$\mathbb{C},$ we obtain necessary and sufficient conditions in order to have a
dual pair of frames ${f_m}_{m=1,...,N}$, ${g_m}_{m=1,...,N}$ such that $<f_m,
g_m>=\alpha_m$ for all $m=1,..., N.$
