Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations

Longitudinal wavevector- and frequency-dependent dielectric constant of the TIP4P water model

“…Above some ω=1-10 THz, where THz=ps −1 , the relaxation process gradually changes into a resonance process characterized by an frequency of 60-200 THz (which depends on wavevector) and reflecting the rapid librational motion of the molecules. The main differences at zero wavevector between the frequencydependent dielectric constant for the TIP4P water, Debye and Stockmayer models as well as real water have been done already [6,26]. Now we consider differences in the behaviour on frequency between the longitudinal dielectric constant of the TIP4P water and the Stockmayer model [1] at nonzero wavevector values.…”

Dielectric properties of liquid ethanol. A computer simulation study

“…Another approach for the determination of ⑀͑ ͒ is based on the calculation of the total dipole moment of the primitive cube of the simulation M ជ (t)ϭ ͚ jϭ1 N ជ j (t). If the Ewald summation technique is used to handle with the longrange interactions and conducting walls boundary conditions are assumed, the relation between ⑀͑ ͒ and the total dipole moment correlation is given by 17,18 …”

Communication: On the origin of the surface term in the Ewald formula

“…(23)]. By expanding the parenthesis in (17) at small k and by using i q i = 0, it is easy to verify that the k = 0 term vanishes thanks to the regularization. 21 One finds therefore…”

“…The integral over V cell in (17) vanishes for all wave vectors except for k = 0 where it gives V cell . The regularization introduced in (14) to make the sum absolutely convergent affects therefore only the zero Fourier mode.…”

“…It should also be helpful for deriving generalizations of the Ewald formula to other long-range interactions. The surface term in the Ewald formula takes a special importance when computing absolute positions of crystalline energy bands, 16 when simulating dielectric fluids [17][18][19] and when using the Ewald method to simulate interfacial properties of three-dimensional systems. 20 The main trick in the present proof of the Ewald formula is to isolate the conditionally convergent contributions in the lattice sum (1) by merely adding and subtracting a well chosen conditionally convergent series according to…”