Here, we ll this gap by introducing a valleytronic FCI (VFCI) approach that employs single-particle (onebody) bases associated with the continuum-model (effective mass approximation of the two-band structure in Si QDs ). Our VFCI enables the acquisition of numerical results complete with full spin-isospin assignments that reveal an underlying SU(4) ⊃ SU(2) × SU [4547] group-chain organization of the spectra of Si double-quantum-dot (DQD) qubits. Specically, the valley isospin assignments in our VFCI consist of a pair of indices (V, V z ) in analogy with the two indices (S, S z ) of the regular spin. (This is in contrast with earlier CI implementations in single QDs constructed from other materials exhibiting a VDOF, which have been restricted to characterizing the CI states using one valley index only, namely the valley projection V z .)