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The first and second homogeneous strain derivatives of the Lorentz-factor dipole-tensor lattice sum are expressed in terms of wave-vector derivatives of modulated higher multipole-tensor sums. Such derivatives can be calculated rapidly by the Ewald method, for which computationally convenient expressions are given. The first strain derivatives are highly symmetrical, but the symmetry of the second derivatives is lower and more complicated. The method is illustrated by calculations for anthracene and tetragonal hydrogen cyanide; it appears to be superior to more direct methods of calculation.