  In this correspondence, we introduced the concept of minimum roman dominating
distance energy $E_{RDd}(G)$ of a graph $G$ and computed minimum roman
dominating distance energy of some standard graphs. Also, we discussed the
properties of eigenvalues of a minimum roman dominating distance matrix
$A_{RDd}(G).$ Finally, we derived the Upper and lower bounds for $E_{RDd}(G).$
