Which conformations of 2,3-dimethylbutane are more stable?
The correct arrangement (from least stable to most stable) is probably: $4 &gt; 2 &gt; 3 \gtrapprox 1$ based on my calculations for the four gas phase rotamers you can see in the figure below.



Your reasoning for 4 over 2 sounds good, that would also be my point. For the two minima 1 and 3 (with Boltzmann weights of 46%:54% at the highest calc. niveau (red), 33%:66% at the lowest (blue)) you might also be right. But from the really small energy difference I don’t want to argue too much about it.



My calculation methods seem a bit random, but at first I only wanted to make that fast wB97X-D3/def2-TZVP//HF-3c scan and then decided to calculate the bigger one.