One can also pose the opposite question, which may be more interesting: what significant matter modelling methods are implemented in open source software, for which there is no commercial alternative? Anna's answer above had a lot of important considerations, but also this reverse question is important to keep in mind; commercial software is not always free of shortcomings, either!
The thing about modern open source development is that new features may spread very easily from one code to another. The KISS (keep it simple, stupid!) principle familiar for a long time in computer science and UNIX systems is gaining traction in science, too: code development is moving to small, modular projects focused on solving a defined problem as well as possible. When the implementation is separated from the interface, the pieces are easy to interface to various codes, and the improvements made within the module spread quickly to all the programs interfaced with the module.
But, many of these open source projects have also been interfaced by big commercial programs; this is only possible if the license is permissive enough. Some examples of are libxc (Mozilla Public License) and libecpint (MIT license), which despite being open source are bundled with major commercial programs to offer core functionalities.