For type F4, O_q(G) is generated by generalized quantum minors and therefore admits a quantized cluster algebra structure over Q(q^{1/2}).
Kashiwara, On crystal bases of the q -analogue of universal enveloping algebras, Duke Math.\ J.\ 63 (1991), 465--516
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Generalized Quantum Minors Generate Quantized Coordinate Rings
For type F4, O_q(G) is generated by generalized quantum minors and therefore admits a quantized cluster algebra structure over Q(q^{1/2}).