We revisit the molecular line growth mechanism of styrene on the hydrogenated Si(001) 2x1 surface. In particular, we investigate the energetics of the radical chain reaction mechanism by means of diffusion quantum Monte Carlo (QMC) and density functional theory (DFT) calculations. For the exchange correlation (XC) functional we use the non-empirical generalized-gradient approximation (GGA) and meta-GGA. We find that the QMC result also predicts the intra dimer-row growth of the molecular line over the inter dimer-row growth, supporting the conclusion based on DFT results. However, the absolute magnitudes of the adsorption and reaction energies, and the heights of the energy barriers differ considerably between the QMC and DFT with the GGA/meta-GGA XC functionals.