When solving for the equilibrium using some large mechanisms, especially involving alkanes, it has been noticed that the convergence using the VCS method is nonrobust, bordering on nonconvergent. The total Gibbs free energy decreases at each iteration, for sure. However, the convergence rate can be terrible. The solution is pretty obvious: for those cases where there is trouble do a full invert of the hessian matrix, instead of just "inverting" the diagonal of the hessian. This only need be done on a subset of the species in a large equilibrium problem, the "major species" , a category which has already been identified and used within vcs.
Note, the choice of component species has a large effect on the convergence rate. I have twiddled with the algorithm for choosing which species are selected as the component species. However, I feel that a more robust approach is needed to ensure that the solver works well for all possible cases.