  We make use of the action of $H_1(Y)$ in Heegaard Floer homology to
generalize the Ozsv\'ath-Szab\'o correction terms for $3$-manifolds with
standard $\operatorname{HF}^\infty$. We establish the basic properties of these
invariants: conjugation invariance, behavior under orientation reversal,
additivity, and spin$^c$ rational homology cobordism invariance.
