International Tables for Crystallography (2010). Vol. B, ch. 3.5, pp. 458-481
doi: 10.1107/97809553602060000772

Chapter 3.5. Extensions of the Ewald method for Coulomb interactions in crystals

Contents

  • 3.5. Extensions of the Ewald method for Coulomb interactions in crystals  (pp. 458-481) | html | pdf | chapter contents |
    • 3.5.1. Introduction  (pp. 458-460) | html | pdf |
    • 3.5.2. Lattice sums of point charges  (pp. 460-471) | html | pdf |
      • 3.5.2.1. Basic quantities  (pp. 460-461) | html | pdf |
      • 3.5.2.2. Ewald sum: first derivation  (pp. 461-463) | html | pdf |
      • 3.5.2.3. Ewald sum: more complete derivation  (pp. 463-467) | html | pdf |
        • 3.5.2.3.1. The case of p > 3  (pp. 464-465) | html | pdf |
        • 3.5.2.3.2. The case p = 1  (pp. 465-467) | html | pdf |
      • 3.5.2.4. The surface term  (p. 467) | html | pdf |
      • 3.5.2.5. The polarization response  (pp. 467-470) | html | pdf |
      • 3.5.2.6. Calculating the pressure  (pp. 470-471) | html | pdf |
    • 3.5.3. Generalization to Gaussian- and Hermite-based continuous charge distributions  (pp. 471-474) | html | pdf |
      • 3.5.3.1. Lattice sums of interacting spherical Gaussians  (pp. 471-473) | html | pdf |
      • 3.5.3.2. Higher angular momentum: Hermite Gaussians  (pp. 473-474) | html | pdf |
    • 3.5.4. Computational efficiency  (pp. 474-480) | html | pdf |
      • 3.5.4.1. The direct sum  (pp. 474-475) | html | pdf |
      • 3.5.4.2. Reciprocal-sum speed-ups: the smooth particle mesh Ewald and fast Fourier Poisson methods  (pp. 475-480) | html | pdf |
        • 3.5.4.2.1. The smooth PME approach  (pp. 475-478) | html | pdf |
          • 3.5.4.2.1.1. Properties of B-splines  (pp. 476-477) | html | pdf |
          • 3.5.4.2.1.2. B-spline approximation to trigonometric functions  (pp. 477-478) | html | pdf |
        • 3.5.4.2.2. The fast Fourier Poisson approach  (pp. 478-480) | html | pdf |
    • References | html | pdf |
    • Tables
      • Table 3.5.4.1. Timing versus accuracy for smooth PME, FFP and regular Ewald sum reciprocal-space approaches  (p. 479) | html | pdf |