Objection 1. It would seem that the power of begetting, or of spirating, signifies the relation and not the essence. For power signifies a principle, as appears from its definition: for active power is the principle of action, as we find in Metaph. v, text 17. But in God principle in regard to Person is said notionally. Therefore, in God, power does not signify essence but relation.
Objection 2. Further, in God, the power to act [posse] and 'to act' are not distinct. But in God, begetting signifies relation. Therefore, the same applies to the power of begetting.
Objection 3. Further, terms signifying the essence in God, are common to the three persons. But the power of begetting is not common to the three persons, but proper to the Father. Therefore it does not signify the essence.
On the contrary, As God has the power to beget the Son, so also He wills to beget Him. But the will to beget signifies the essence. Therefore, also, the power to beget.
I answer that, Some have said that the power to beget signifies relation in God. But this is not possible. For in every agent, that is properly called power, by which the agent acts. Now, everything that produces something by its action, produces something like itself, as to the form by which it acts; just as man begotten is like his begetter in his human nature, in virtue of which the father has the power to beget a man. In every begetter, therefore, that is the power of begetting in which the begotten is like the begetter.
Now the Son of God is like the Father, who begets Him, in the divine nature. Wherefore the divine nature in the Father is in Him the power of begetting. And so Hilary says (De Trin. v): "The birth of God cannot but contain that nature from which it proceeded; for He cannot subsist other than God, Who subsists from no other source than God."
We must therefore conclude that the power of begetting signifies principally the divine essence as the Master says (Sent. i, D, vii), and not the relation only. Nor does it signify the essence as identified with the relation, so as to signify both equally. For although paternity is signified as the form of the Father, nevertheless it is a personal property, being in respect to the person of the Father, what the individual form is to the individual creature. Now the individual form in things created constitutes the person begetting, but is not that by which the begetter begets, otherwise Socrates would beget Socrates. So neither can paternity be understood as that by which the Father begets, but as constituting the person of the Father, otherwise the Father would beget the Father. But that by which the Father begets is the divine nature, in which the Son is like to Him. And in this sense Damascene says (De Fide Orth. i, 18) that generation is the "work of nature," not of nature generating, but of nature, as being that by which the generator generates. And therefore the power of begetting signifies the divine nature directly, but the relation indirectly.
Reply to Objection 1. Power does not signify the relation itself of a principle, for thus it would be in the genus of relation; but it signifies that which is a principle; not, indeed, in the sense in which we call the agent a principle, but in the sense of being that by which the agent acts. Now the agent is distinct from that which it makes, and the generator from that which it generates: but that by which the generator generates is common to generated and generator, and so much more perfectly, as the generation is more perfect. Since, therefore, the divine generation is most perfect, that by which the Begetter begets, is common to Begotten and Begetter by a community of identity, and not only of species, as in things created. Therefore, from the fact that we say that the divine essence "is the principle by which the Begetter begets," it does not follow that the divine essence is distinct (from the Begotten): which would follow if we were to say that the divine essence begets.
Reply to Objection 2. As in God, the power of begetting is the same as the act of begetting, so the divine essence is the same in reality as the act of begetting or paternity; although there is a distinction of reason.
Reply to Objection 3. When I speak of the "power of begetting," power is signified directly, generation indirectly: just as if I were to say, the "essence of the Father." Wherefore in respect of the essence, which is signified, the power of begetting is common to the three persons: but in respect of the notion that is connoted, it is proper to the person of the Father.
Source: Summa Theologica (New Advent)