Objection 1. It would seem that to create is proper to some Person. For what comes first is the cause of what is after; and what is perfect is the cause of what is imperfect. But the procession of the divine Person is prior to the procession of the creature: and is more perfect, because the divine Person proceeds in perfect similitude of its principle; whereas the creature proceeds in imperfect similitude. Therefore the processions of the divine Persons are the cause of the processions of things, and so to create belongs to a Person.
Objection 2. Further, the divine Persons are distinguished from each other only by their processions and relations. Therefore whatever difference is attributed to the divine Persons belongs to them according to the processions and relations of the Persons. But the causation of creatures is diversely attributed to the divine Persons; for in the Creed, to the Father is attributed that "He is the Creator of all things visible and invisible"; to the Son is attributed that by Him "all things were made"; and to the Holy Ghost is attributed that He is "Lord and Life-giver." Therefore the causation of creatures belongs to the Persons according to processions and relations.
Objection 3. Further, if it be said that the causation of the creature flows from some essential attribute appropriated to some one Person, this does not appear to be sufficient; because every divine effect is caused by every essential attribute--viz. by power, goodness and wisdom--and thus does not belong to one more than to another. Therefore any determinate mode of causation ought not to be attributed to one Person more than to another, unless they are distinguished in creating according to relations and processions.
On the contrary, Dionysius says (Div. Nom. ii) that all things caused are the common work of the whole Godhead.
I answer that, To create is, properly speaking, to cause or produce the being of things. And as every agent produces its like, the principle of action can be considered from the effect of the action; for it must be fire that generates fire. And therefore to create belongs to God according to His being, that is, His essence, which is common to the three Persons. Hence to create is not proper to any one Person, but is common to the whole Trinity.
Nevertheless the divine Persons, according to the nature of their procession, have a causality respecting the creation of things. For as was said above (14, 8; 19, 4), when treating of the knowledge and will of God, God is the cause of things by His intellect and will, just as the craftsman is cause of the things made by his craft. Now the craftsman works through the word conceived in his mind, and through the love of his will regarding some object. Hence also God the Father made the creature through His Word, which is His Son; and through His Love, which is the Holy Ghost. And so the processions of the Persons are the type of the productions of creatures inasmuch as they include the essential attributes, knowledge and will.
Reply to Objection 1. The processions of the divine Persons are the cause of creation, as above explained.
Reply to Objection 2. As the divine nature, although common to the three Persons, still belongs to them in a kind of order, inasmuch as the Son receives the divine nature from the Father, and the Holy Ghost from both: so also likewise the power of creation, whilst common to the three Persons, belongs to them in a kind of order. For the Son receives it from the Father, and the Holy Ghost from both. Hence to be the Creator is attributed to the Father as to Him Who does not receive the power of creation from another. And of the Son it is said (John 1:3), "Through Him all things were made," inasmuch as He has the same power, but from another; for this preposition "through" usually denotes a mediate cause, or "a principle from a principle." But to the Holy Ghost, Who has the same power from both, is attributed that by His sway He governs, and quickens what is created by the Father through the Son. Again, the reason for this particular appropriation may be taken from the common notion of the appropriation of the essential attributes. For, as above stated (39, 8, ad 3), to the Father is appropriated power which is chiefly shown in creation, and therefore it is attributed to Him to be the Creator. To the Son is appropriated wisdom, through which the intellectual agent acts; and therefore it is said: "Through Whom all things were made." And to the Holy Ghost is appropriated goodness, to which belong both government, which brings things to their proper end, and the giving of life--for life consists in a certain interior movement; and the first mover is the end, and goodness.
Reply to Objection 3. Although every effect of God proceeds from each attribute, each effect is reduced to that attribute with which it is naturally connected; thus the order of things is reduced to "wisdom," and the justification of the sinner to "mercy" and "goodness" poured out super-abundantly. But creation, which is the production of the very substance of a thing, is reduced to "power."
Source: Summa Theologica (New Advent)