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On the calculation of derivatives for Coulomb-type interaction
energies and general anisotropic pair potentials

Christof Hättig

*Department of Chemistry, Århus University,
DK-8000 Århus C, Denmark
*

*Chem. Phys. Lett. ***268**, 521-530 (1997)

(Received 13 January 1997; in final form 18 February 1997)

We derive efficient algorithms for the derivatives, in particular
the forces, torques and the hessian, for coulomb-type interactions
and for general anisotropic pair potentials.
We use spherical tensor techniques and an intermediate transformation
to a quasi-internal coordinate system, proposed recently
to obtain a factorization of the multipole interaction tensors.
By these means we obtain a unified approach to the derivatives
at small extra computational cost to the energy calculation.
For the special case of an electrostatic interaction
the computational cost scales for a system of *N* molecules
through rank $L$ in the multipole expansion as
*N*^{2} × O(L^{3})
for both the energy and its derivatives.

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