This paper addresses the question for which varieties of boolean algebras with operators membership of an atomic algebra Θ is determined by its atom structure Θt Θ. We prove a positive answer for conjugated Sahlqvist varieties; we also show that the conjugation condition is necessary. As a corollary to the positive result and a recent result by I. Hodkinson, we prove that the variety RRA of representable relation algebras, although canonical, cannot be axiomatized by Sahlqvist equations.