International Tables for Crystallography (2010). Vol. B. ch. 3.4, pp. 449-457   | 1 | 2 |
https://doi.org/10.1107/97809553602060000771

Chapter 3.4. Accelerated convergence treatment of R−n lattice sums

Contents

  • 3.4. Accelerated convergence treatment of R−n lattice sums  (pp. 449-457) | html | pdf | chapter contents |
    D. E. Williams
    • 3.4.1. Introduction  (p. 449) | html | pdf |
    • 3.4.2. Definition and behaviour of the direct-space sum  (p. 449) | html | pdf |
    • 3.4.3. Preliminary description of the method  (pp. 449-450) | html | pdf |
    • 3.4.4. Preliminary derivation to obtain a formula which accelerates the convergence of an R−n sum over lattice points X(d)  (pp. 450-452) | html | pdf |
    • 3.4.5. Extension of the method to a composite lattice  (pp. 452-453) | html | pdf |
    • 3.4.6. The case of n = 1 (Coulombic lattice energy)  (pp. 453-454) | html | pdf |
    • 3.4.7. The cases of n = 2 and n = 3  (p. 454) | html | pdf |
    • 3.4.8. Derivation of the accelerated convergence formula via the Patterson function  (p. 454) | html | pdf |
    • 3.4.9. Evaluation of the incomplete gamma function  (pp. 454-455) | html | pdf |
    • 3.4.10. Summation over the asymmetric unit and elimination of intramolecular energy terms  (p. 455) | html | pdf |
    • 3.4.11. Reference formulae for particular values of n  (pp. 455-456) | html | pdf |
    • 3.4.12. Numerical illustrations  (pp. 456-457) | html | pdf |
    • References | html | pdf |
    • Tables
      • Table 3.4.2.1. Untreated lattice-sum results for the Coulombic energy (n = 1) of sodium chloride (kJ mol−1, Å); the lattice constant is taken as 5.628 Å  (p. 449) | html | pdf |
      • Table 3.4.2.2. Untreated lattice-sum results for the dispersion energy (n = 6) of crystalline benzene (kJ mol−1, Å)  (p. 450) | html | pdf |
      • Table 3.4.12.1. Accelerated-convergence results for the Coulombic sum (n = 1) of sodium chloride (kJ mol−1, Å): the direct sum plus the constant term  (p. 456) | html | pdf |
      • Table 3.4.12.2. The reciprocal-lattice results (kJ mol−1, Å) for the Coulombic sum (n = 1) of sodium chloride  (p. 456) | html | pdf |
      • Table 3.4.12.3. Accelerated-convergence results for the dispersion sum (n = 6) of crystalline benzene (kJ mol−1, Å); the figures shown are the direct-lattice sum plus the two constant terms  (p. 456) | html | pdf |
      • Table 3.4.12.4. The reciprocal-lattice results (kJ mol−1, Å) for the dispersion sum (n = 6) of crystalline benzene  (p. 456) | html | pdf |
      • Table 3.4.12.5. Approximate time (s) required to evaluate the dispersion sum (n = 6) for crystalline benzene within 0.001 kJ mol−1 truncation error  (p. 457) | html | pdf |