I have already argued that God is materially simple and efficiently free.
Thus, for example, God is not composed of several material parts distinct from God. God’s material cause is God Himself. Note that an electron, as far as it’s an elementary particle, too, is simple; but God is like an electron only in regard to what it is not (i.e., in this particular case, not composite); not in regard to what it is.
Again, there are no “laws” of God’s operation that God obeys; rather, God’s operation (of self-contemplation) is God’s essence itself.
Further, it’s not the case that God’s “pursuit” of happiness causes God to be, as man’s pursuit is the cause of man; God is perfectly happy, and His enjoyment is His very essence and self.
God’s formal cause is goodness on the 3rd level. But God is formally uncaused on the 2nd level, as well. He is not a thing, such that the thing’s specificity and particularity causes it to be what it is. “God is not in a genus as if He were a species. From this it is also plain that He has no genus nor difference, nor can there be any definition of Him; nor, save through His effects, a demonstration of Him: for a definition is from genus and difference; and the mean of a demonstration is a definition.” (ST, I, 3, 5) God is the principle of all possible things and all being, but “what God is” cannot be known by any finite creature. God is on the one hand is something perfectly definite, but on the other hand we can only understand God as such a principle, containing all things’ actualities and perfections yet infinitely transcending any actual creature.
God’s nature does not, by specifying what God is, determine God’s existence as a concrete being or suppositum, but is identical with it. Also, God’s nature does not cause God to exist, nor is joined with His existence by some force, but is existence itself.
The idea of divine simplicity takes note of all these, including the concrete and abstract simplicity.