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 open-KIM 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.