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The infrared absorption spectrum of atom- and molecule-doped solid parahydrogen $(p-H2)$ exhibits features near $4160cm-1$ which are absent from the spectrum of pure solid $p-H2$. These absorption features are associated with the $Q1(0)$ pure vibrational transitions of $H2$ molecules located near impurities; the transition moment responsible for this infrared activity arises from weak overlap-induced dopant-$H2$ and $H2-H2$ dipoles, and from dopant-induced symmetry breaking of the p-$H2$ crystal lattice. Because the transition dipole moment for these infrared features depends sensitively on the structure of the p-$H2$ matrix surrounding the dopant, studies of the $Q1(0)$ absorption feature could provide detailed information about the physics of solvation in highly quantum systems. We present the results of diffusion quantum Monte Carlo (DQMC) simulations of the $Q1(0)$ absorption lineshape for isolated dopants in solid p-$H2$, and briefly discuss the structural and dynamical information provided by our DQMC simulations.