Since the discovery of single-walled carbon nanotubes (SWNTs) in the early 1990s, the most commonly accepted model of SWNT growth on traditional catalysts (i.e., transition metals including Fe, Co, Ni, etc.) is the vapor-liquid-solid (VLS) mechanism. In more recent years, the synthesis of SWNTs on nontraditional catalysts, such as SiO2, has also been reported. The precise atomistic mechanism explaining SWNT growth on nontraditional catalysts, however, remains unknown. In this work, CH4 chemical vapor deposition (CVD) and single-walled carbon nanotube (SWNT) nucleation on SiO2 nanoparticles have been investigated using quantum-chemical molecular dynamics (QM/MD) methods. Upon supply of CHx species to the surface of a model SiO2 nanoparticle, CO was produced as the main chemical product of the CH4 CVD process, in agreement with a recent experimental investigation [Bachmatiuk et al., ACS Nano 2009, 3, 4098]. The production of CO occurred simultaneously with the carbothermal reduction of the SiO2 nanoparticle. However, this reduction, and the formation of amorphous SiC, was restricted to the nanoparticle surface, with the core of the SiO2 nanoparticle remaining oxygen-rich. In cases of high carbon concentration, SWNT nucleation then followed, and was driven by the formation of isolated sp(2)-carbon networks via the gradual coalescence of adjacent polyyne chains. These simulations indicate that the carbon saturation of the SiO2 surface was a necessary prerequisite for SWNT nucleation. These simulations also indicate that a vapor-solid-solid mechanism, rather than a VLS mechanism, is responsible for SWNT nucleation on SiO2. Fundamental differences between SWNT nucleation on nontraditional and traditional catalysts are therefore observed.