I have questions about dEdr and d2Edr2.

According to my understanding about dEdr, each call to dEdr returns only a fragmented contribution to the partial derivative so that, for example, the completed value for d E / d r_12 can be obtained by adding the contributions from all the dEdr process calls with (1,2) or (2,1). I’m wondering if it is right.

For the second derivative I think there’s some ambiguity regarding whether we consider, e.g., d^2 E / d r_12 d_34 and d^2 E / d r_34 d_12 as the same thing or two things with the same value. So, for example, when we compute d^2 E / d r_12 d r_34, the two following interpretations are possible:
(1) Add all contributions from (1,2)/(3,4), (2,1)/(3,4), (1,2)/(4,3), (2,1)/(4,3) or
(2) Add all contributions from (1,2)/(3,4), (2,1)/(3,4), (1,2)/(4,3), (2,1)/(4,3) + (3,4)/(1,2), (4,3)/(1,2), (3,4)/(2,1), (4,3)/(2,1).
I did some tests with an openKIM EAM potential and found that (1) is the way to obtain the right result, but the standard doesn’t seem to state this point clearly. So, I just want to check if my understanding is correct.