The spin-singlet ground states of a D − ion both in uniaxially stressed Si and in Si/ SiO 2 quantum wells have been investigated for two types of donors, substitutional P and interstitial Li atoms, using a diffusion quantum Monte Carlo method. The valley-orbit interaction due to the singular donor ion potential is taken into account by diagonalizing the multiplet Hamiltonian matrix in the basis set of the ground-state wave functions assigned by the valley indexes. In the uniaxial compressive stress along the ͓100͔ direction, the binding energy of a negative P donor with A 1 symmetry decreases at first and then increases gradually with the stress-induced splitting in the valley energy. This nonmonotonic dependence is attributed to the disparity between the population probability in the stress-deepened valleys for the neutral donor and that for the negative donor. As for Li donors with E symmetry, the binding energy of a negative donor decreases linearly with the stress-induced splitting and then takes a constant value, caused by the transition of the ground state of the negative donor from the intervalley configuration to the intravalley configuration. These calculated behaviors agree with the experiment. In the quantum well in the ͓100͔ direction, the quantum confinement effect deepens the binding energy of a negative donor without the valley-orbit interaction. The same confinement effect is predicted for a Li negative donor ground state with E symmetry, and the binding energy increases monotonically with decrease in the well width. As for a P negative donor with A 1 symmetry, the enhanced binding energy is recovered at the well width of 5 nm although the valley-orbit interaction suppresses the enhancement of the binding energy in wider wells.