"on this account" is correct and usable in written English
You can use it when you want to refer to the reason for something. For example, "She was late for the meeting on this account."
On this account, both nature and capacity are determined by one's qi endowment.
On this account, young Aelita faces a sterner test.
On this account, acting with free will requires alternative possibilities.
On this account, causation is not constituted by causal dependence.
On this account, experimental systems are construed as very inclusive entities.
On this account, computations are technical artifacts whose function is fixed by an abstract specification.
On this account, the work process itself can have aesthetic value.
On this account, the practice of public reason is a constitutive part of a valuable relationship.
On this account, the model itself is the explanation we seek.
On this account of the doctrine of acquisition, it holds that God alone has causal power.
On this account law claims the right to obedience wherever it sets out obligations.
