Richard A. Creel (Divine Impassibility. Cambridge: Cambridge University Press, 1986) rigorously outlines and discusses eight possible senses of the term "impassibility," and it appears from his study that the ancients and a number of modern theologians thought/think divine APAQEIA rules out God having any emotions (i.e., passions) or at least emotions as we know of them. To be fair, Joseph M. Hallman (The Descent of God: Divine Suffering in History and Theology) shows that the ANF and PNF treatment of God's supposed impassiblity is by no means neat or tidy. For instance, some of the ancient Fathers seem to affirm God's impassibility on one hand while qualifying it on the other. As with any theological subject, there are opposing viewpoints.
Jaroslav Pelikan (The Christian Tradition, 1:53)
"Some [ancient] Christian theologians went so far as
simply to identify the Christian doctrine of God with
the philosophical rejection of anthropomorphism;
Arnobius [of Sicca] argued that God (the gods) had to
be 'immune to every disturbance and every
perturbation,' with no 'agitation of spirit' or wrath.
Others did not go to this extreme, but maintained that
the philosophical doctrine of impassiblity was not
incompatible with the biblical language about the
wrath of God; Justin referred to God as impassible,
but also spoke 'again and again of God in the most
However, it seems that Justin's thought was inchoate and less than complete.
The Fathers admittedly spoke of God being impassible and simultaneously attributed emotions (in a way) to Him. But as the writings of Tertullian suggests, they tended to think that God certainly does not experience emotions in a human
manner and possibly He does not have emotions (on the "meta" level) at all.
John Thompson (Modern Trinitarian Perspectives. Oxford and New York: Oxford University Press, 1994. Page 55) writes:
"In line, therefore, with most modern theologians [Karl] Barth rejects the idea of APAQEIA, of God as an unmoved, unfeeling being beyond the reach of suffering."
"In most places in his work, Gregory [of Nyssa] tends
to use APAQEIA in reference to all feelings and to
exalt the Christian attempt to attain it. APAQEIA in
its usual meaning is the absence of all the passions
[i.e. emotions], and Gregory inherits this usage. At
times, however, he does give a positive valuation of
some human emotions" (Hallman, op. cit. 89).
And while he is not an "ancient," I believe that Anselm of Canterbury sums up the thought of the ANF and PNF well:
"How, then, art though compassionate and not
compassionate, O Lord, unless because thou art
compassionate in terms of our experience, and not
compassionate in terms of thy being" (Proslogium 8).