[DFTB-Plus-User] The derivation for SCC analytic force

[이인성 (화학과)]

Hello, DFTB+ developers.


I want to know about the derivation of analytic force.

The analytic force is comprised of three terms, which are (1) hamiltonian derivative, (2) double counting SCC force, (3) repulsive terms.

And, the hamiltonian derivative terms are consisted of three terms, which are (4) non-scc ham, (5) scc term, (6) epsilon*S term.


Here, the analytic force is derived by using Hellman-Feymann theorem.

In this process, upper (2) double counting SCC force term is derived from H^(1) by differentiating gamma variables.

( The differentiation of overlap is included in hamiltonian derivative, which means (5) scc term. )


I want to know the exact derivation process about this (2) term.

How do I derive (2) term?

( This question is consistent with the question "What is the analytic form of Hamiltonian derivative with respect to the coordinate?" )

I failed to derive this term due to the gamma derivative terms.


Thanks.


In Seong Lee.
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