Lewis & Short

1. ai, in old Lat., corresponding to ae: AIDILIS, CAISAR, AITERNOS, for Aedilis, Caesar, aeternus; also, still later, sometimes in the poets in the termination of the genitive of the first decl.; but, as in Enn. and Lucr., per diaeresin always dissyl. with long penult: furit intus aquāï, Verg. A. 7, 464: aurāï simplicis ignem, id. ib. 6, 747: terrāï frugiferāï, Mart. 11, 91, 5; cf. Quint. 1, 7, 18; Spauld. Prisc. 728; Prob. 1438; Vel. Long. 2222; Mart. Vict. 2460 P.
In prim. syllables, as in voc. Gaĭ, ăi could not be changed to ae if i was an ending; but i was changed to i cons., when the word received accession, e. g. Gaius.
When a conson. followed ai, as in CNAIVOS for ΓΝΑΙϝΟΣ (v. the Epitaphs of the Scipios, in the Append.), ae was written at a later per., as Gnaeus; hence from Γράϊος both Graecus and Graius; from Αἴακος, Aeacus, and Aiax, for Αἴας, were formed; just as Achaeus or Achivus with Achaĭus or Achaĭcus was used.

    1. 2. * ai = αἴ, interj., denoting grief, ah! alas! Ov. M. 10, 215.