The construction of realistic atomistic models for amorphous solids is complicated by the fact that they do not have a unique structure. Among the different computational procedures available for this purpose, the melting and rapid quenching process using molecular dynamics simulations is commonly employed as it is simple and physically based. Nevertheless, the cooling rate used during quenching strongly affects the reliability of generated samples, as fast cooling rates result in unrealistic atomistic models. In this study, we have determined the conditions to be fulfilled when simulating the quenching process with molecular dynamics for obtaining amorphous Si (a-Si) atomistic models structurally compatible with experimental samples. We have analyzed the structure of samples generated with cooling rates ranging from 3.3 10 10 to 8.5 10 14 K/s. The obtained results were compared with experimental data available in the literature, and with samples generated by other state-of-the-art and more sophisticated computational procedures. For cooling rates below 10 11 K/s, a-Si samples generated had structural parameters within the range of experimental samples, and comparable to those obtained from other refined modeling procedures. These computationally slow cooling rates are of the same order of magnitude than those experimentally achieved with pulsed energy melting techniques. Samples obtained with faster cooling rates can be further relaxed with annealing simulations, resulting in structural parameters within the range of experimental samples. Nevertheless, the required annealing times are on the order of microseconds, which makes this annealing step non practical from a computational point of view.