What is the relationship between Ha and Hb in the given compound, trans-1,3 dichlorocyclobutane. Are they enantiotopic or homotopic?

The question is to find the TOPICITY relationship between Ha and Hb in the given compound, (trans 1,3 dichlorocyclobutane)
[![enter image description here](https://i.stack.imgur.com/3jUTs.jpg)](https://i.stack.imgur.com/3jUTs.jpg)


They seem to be in the same chemical environment, so I tried the substitution method, and replaced Ha and Hb with an X\* atom in-turn (for convenience, I have used Br as the X\* atom ). Then, I used CIP rules to assign priority, and got RR and SS configuration respectively. (See img below) I concluded them to be enantiotopic.


However, I am still confused because I cannot imagine any plane which would be used to show the mirror image relationship between the two.


[![enter image description here](https://i.stack.imgur.com/YQntB.jpg)](https://i.stack.imgur.com/YQntB.jpg)
[![enter image description here](https://i.stack.imgur.com/B02K1.png)](https://i.stack.imgur.com/B02K1.png)


Is my answer and reasoning correct?


If so, kindly demonstrate the mirror plane which makes the two compounds enantiomers.


If not, please explain.


Nb: I couldn't find an axis of symmetry that makes Ha and Hb equivalent. That led me to the conclusion that thay are not Homotopic.




The correct answer is, they are HOMOTOPIC.


Let us use the substitution method to see.
First, I am substituting Ha with Br. Now, using the CIP rules, first priority goes to Br, and the last priority goes to H. Now the problem arises. How to assign second and third priorities.


This problem is solved using the Zeroth Rule. "If two groups are completely equal except for their spatial arrangement, assign priority to the group that is pointing towards you".


Thus, I have numbered the groups, and found out that the configuration is 'S' (anticlockwise).
[![enter image description here](https://i.stack.imgur.com/J7phM.png)](https://i.stack.imgur.com/J7phM.png)


Remember to view the molecule in such a way that the least priority group is pointing away from you.
(I have included the fiscer projection too, for ease of understanding)


Now, let's replace Hb with Br, and assign the configuration as earlier. Note that the Zeroth rule is used here also. Again, the configuration is 'S'.
Thus, they are in the same chemical environment, and are HOMOTOPIC.


In an *ALTERNATE METHOD*, there are two Chlorine atoms adjacent to Ha, one cis to Ha, and the other trans.
Likewise, Hb also has two adjacent Cl atoms, one cis and another trans. Also, there is no other element of chirality on the molecule.
ie, it doesn't have a point, axis or plane of chirality. Therefore they are chemically similar, and are HOMOTOPIC.


However, it's better to use the first method, since it is the best one.


NOTE: I would be happy if anyone can suggest a more verbally accurate statement of the 'Zeroth law'. ( If mine seems flawed)
I have confirmed the answer from my professor, but I have written the law in my own words.


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