Force, torque, and stress in systems with slab geometry

2 Force, torque, and stress in systems with slab geometry 

For ionic systems, the total Coulomb force acting on particle i within the slab-adapted three-dimensional Ewald sum [see Eq. (6.40)] can be cast as 

Regarding the stress tensor of the system, the (Coulomb) components corresponding to the two orthogonal directions parallel to the walls (i.e., 7 = x,y) can be calculated exactly as in the three-dimensional case (see Appendix F.1.2.2). On the other hand, the normal component (7 = z) is given by 

To evaluate the Fourier-spac e contribution, wc note that, because 

Filially, as the energy correction tcnn given in Eq. (6.39) depends on. s only through the -components of the position vectors Tj, the expression for the corresponding stress in the direction normal to the confining substrates follows as 

To evaluate the Fourier-spaicHJ contribution, Tct z that, because of the artificial elongation of the basis cell in z-direction, neither the wavevec-tors involved in the Fourier contribution to the Ewald energy [see Eq. (6.18) with the wavevectors given in Eq. (6.41)] nor the volume V depend on s -The vectors r, = xi yi, s Zi), on the other hand, depend on if we employ scaled z-coordinates as indicated. Differentiation thus yields 

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