Are the given compounds enantiomers or diastereomers? Or are they identical? The compound is trans-1,2-dimethylcyclobutane:
My reasoning is that they are identical. They are not mirror images, and on rotating 180° give the other compound.
Is my answer and reasoning correct?
Note: Ignore the confirmations of cyclobutane.
The given compound, 1,2-dimethylcyclobutane has two chiral centers, and hence, has maximum of $2^2 = 4$ stereoisomers. However, as shown in the scheme below, the cis-isomer has a plane of symmetry, and as a consequence, it is a meso-isomer:
However, trans-isomer can exists in two forms: (1R,2R)-1,2-dimethylcyclobutane and (1S,2S)-1,2-dimethylcyclobutane (see Scheme $\bf{A}$).
The two isomers given in the question are both trans-isomers. Thus, they woul be either identical or enanthiomers as shown in the Scheme $\bf{A}$ (cannot be diastereomers). Although, the OP's visualization is correct and can use to identify simple molecule like this, it is hard to visualize if presented complex molecule. The best way to identify stereoisomers are assign their appropriate (R/S)-configurations as I have done for OP's structures (see Scheme $\bf{B}$).
Accordingly, both structures are (1R,2R)-1,2-dimethylcyclobutane. Thus, the compounds are identical.
