Which Byzantine emperor was betrothed to Charlemagne's daughter Rotrude?

The Byzantine emperor betrothed to Charlemagne’s daughter Rotrude was Constantine VI.

The arrangement was made in 781, when Rotrude was still a child and Constantine VI was the young Byzantine emperor under the regency of his mother, Empress Irene. The proposed marriage was a diplomatic effort to improve relations between the Frankish kingdom and the Byzantine Empire, whose rulers both claimed a central place in the Christian Roman world.

Rotrude was reportedly taught Greek by a Byzantine scholar named Elisaeus, and Greek sources referred to her as Erythro. The engagement was never completed. Political circumstances changed, and Irene eventually broke off the arrangement, usually dated to 787 or 788. Rotrude remained in the Frankish world and later became a nun.

This betrothal is easy to mix up with other Byzantine-Frankish marriage negotiations. Nicephorus I, Michael I, and Leo III were not the emperor named in this particular agreement. Constantine VI ruled from 780 to 797, with Irene exercising decisive power during much of his early reign.