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The effects of volatile species on vitreous SiO<sub>2</sub> (<i>v</i>-SiO<sub>2</sub>) influence transport and physical properties that have important implications for telecommunications and geological applications. While the effects of monovalent anions such as fluorine, chlorine, and hydroxyl on the transport and optical properties of <i>v</i>-SiO<sub>2</sub> are highly studied, their effects on elastic properties are less well-known. We measured density and performed resonance ultrasound spectroscopy, gigahertz ultrasonic interferometry, Raman spectroscopy, Fourier transform infrared spectroscopy, and molecular dynamics simulations to obtain the elastic moduli, elastic wave speeds, structural properties, and fictive temperatures of F-, Cl-, and OH-doped <i>v</i>-SiO<sub>2</sub>. We find that while density reductions as a function of mol % dopant are the same for both F and Cl, the elasticity and structural data show that the addition of Cl to <i>v</i>-SiO<sub>2</sub> has a buttressing effect on the network, leading to a stiffer material relative to the F-doped <i>v</i>-SiO<sub>2</sub> with the formation of percolation channels. Although all three monovalent anions are incorporated into <i>v</i>-SiO<sub>2</sub> by replacing an oxygen atom in SiO<sub>4</sub><sup>4-</sup> tetrahedra, the halogens and OH have markedly different effects on the medium-range order of <i>v</i>-SiO<sub>2</sub>. Poisson's ratio and structural data show that the incorporation of halogen anions leads to closer packing of tetrahedra and an increase in the populations of smaller tetrahedral rings (3- and 4-membered) at the expense of larger tetrahedral rings (≥5-membered). In contrast, there is little distinguishable change in larger ring size in hydroxyl-doped <i>v</i>-SiO<sub>2</sub> as the populations of smaller tetrahedral rings decrease, and Poisson's ratio indicates a more open, less densely packed structure. These results imply that OH-doped <i>v</i>-SiO<sub>2</sub> will be able to accommodate more stress before the onset of permanent densification than halogen-doped <i>v</i>-SiO<sub>2</sub>. The results of this study offer new insights into the relationship between the structure and properties of F-, Cl-, and OH-doped fused silica glasses, which are particularly applicable to the understanding of Rayleigh scattering.