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 N2 × O(L3) for both the energy and its derivatives.

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