  We apply the recently introduced Hubbard model approach to quantitatively
describe the experimental charge stability diagram and tunnel coupling of
silicon double quantum dot systems. The results calculated from both the
generalized Hubbard model and the microscopic theory are compared with existing
experimental data, and excellent agreement between theory and experiment is
found. The central approximation of our theory is a reduction of the full
multi-electron multi-band system to an effective two-electron model, which is
numerically tractable. In the microscopic theory we utilize the Hund-Mulliken
approximation to the electron wave functions and compare the results calculated
with two different forms of confinement potentials (biquadratic and Gaussian).
We discuss the implications of our work for future studies.
