The adverb can usually easily follow the first element of a verb phrase (among other places)-- I have never seen; we have eagerly been awaiting . There is obviously no rule against it, though certain kinds of adverbs rest more comfortably elsewhere. The 'rule' against splitting infinitives is long defunct; it need be observed only if your teacher insists on it in his/her assignments or tests.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.