To further illustrate the capabilities of the present VFCI, we investigate in this section the dependence on the magnetic eld, B, of the spectra of a Si 2e-DQD in the (1,1) charge conguration. For the example case here, we use an individual-dot connement hω 0 = 0.40 meV, an interdot separation d = 150 nm, and a valley splitting E V = 0.06 meV = 14.508h GHz, as was the case in Sec. II A. For the detuning, a small value of ε = 0.05 meV was used to guarantee that the DQD remains in the (1,1) charge conguration. The Landé factor was taken as g * = 2, appropriate for silicon. We note that consideration of the full spin-isospin coupling requires the enlargement of the Hilbert space dened by the basis Slater determinants (see Sec. III), i.e., Slater determinants preserving individually all three values (0, ±1) of the total spin projection, S z , and isospin projection, V z , must be included in the basis, and this was done for the calculations in both Figs. 4(a) and 4(b).