For Bulk we start with a small number of K-points and then increase it step by step until we get convergence with respect to the target property. This is generally done with respect to the SCF energy that is obtained at the end. The procedure to be used here is quite similar to convergence of cutoff energy as has been shown here.
The key difference between nano structures and Bulk systems is that in nano structures electrons are confined in a few directions(for Quantum Dots electrons are confined in all 3 directions), whereas in bulk they are allowed to move in all directions. This leads to flat bands in the case of a nano structure, due to which a single k-point should be enough.
Another way to look at this is when performing calculations on such systems with plane wave codes we need to introduce vacuum around our system, such that one particular quantum dot does not interact with itself image. In order to know the amount of vacuum to be inserted we need to again perform convergence testing. The addition of vacuum generally leads to big cells. As you must know bigger the real cell smaller the k space. So in order to traverse this small k-space a single k point is enough.
Now only one question stands if taking more k points leads to some problems for optical properties and DOS. I am not sure about this but I think that the answers obtained should be correct, it would just be much more inefficient.
Key takeaway is that if you are performing calculations with Bulk run convergence tests with K point and if calculations are being run with Quantum Dots choose a single k point.
1 1 1for ground state minimization but I am still a little unsure about using
1 1 1for different properties. Mainly for DOS and Linear optical properties. I have also read that increasing the number of KPoints actually gives me wrong results. Is that true ?? $\endgroup$