With all of the recent modalizations of St. Anselm's ontological argument, I was surprised to see how few attempts have been made to do the same with Descartes' arguments from First Meditations.
In short, Descartes reasons that he has the concept of God in his mind. He then asks, what is the cause of this conception? For example, we have the concept of an apple because we know such things exist. We have the concept of a unicorn, not because they exist, but because we composite different parts (a horse's body, the horn of any number of animals, and the wings of a majestic bird). For Descartes, then, the ability to have a clear and distinct conceptualization of a thing points to that thing's having existence in reality.
Here's how a modal version of the argument might look:
1. If a concept of C is held by person S, then C possibly corresponds to an objective reality. (Premise)
2. The concept of a maximally great being is a concept of S. (Premise)
3. Hence, the concept of a maximally great being possibly corresponds to an objective reality. (From 1 and 2)
4. A maximally great being possibly exists. (3, simplification)
5. A being is maximally great if and only if it is maximally excellent in every possible world. (Premise)
6. A being is maximally excellent if and only if it is omnipotent, omniscient, and morally perfect. (Premise)
7. Hence, an omnipotent, omniscient, and morally perfect being exists in all possible worlds. (From 5, 6, and S5)
8. Therefore, an omnipotent, omniscient, and morally perfect being exists. (From 7)
9. Therefore, God exists. (From 8)