International Tables for Crystallography (2006). Vol. B, ch. 3.4, pp. 385-397   | 1 | 2 |
doi: 10.1107/97809553602060000562

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

Contents

  • 3.4. Accelerated convergence treatment of R n lattice sums  (pp. 385-397) | html | pdf | chapter contents |
    • 3.4.1. Introduction  (p. 385) | html | pdf |
    • 3.4.2. Definition and behaviour of the direct-space sum  (p. 385) | html | pdf |
    • 3.4.3. Preliminary description of the method  (pp. 385-386) | html | pdf |
    • 3.4.4. Preliminary derivation to obtain a formula which accelerates the convergence of an [{\bi R}^{\bf -{\bi n}}] sum over lattice points X ( d )  (pp. 386-388) | html | pdf |
    • 3.4.5. Extension of the method to a composite lattice  (pp. 388-389) | html | pdf |
    • 3.4.6. The case of [{\bf{\bi n} = 1}] (Coulombic lattice energy)  (p. 389) | html | pdf |
    • 3.4.7. The cases of [{\bf{\bi n} = 2}] and [{\bf{\bi n} = 3}]  (p. 389) | html | pdf |
    • 3.4.8. Derivation of the accelerated convergence formula via the Patterson function  (pp. 389-390) | html | pdf |
    • 3.4.9. Evaluation of the incomplete gamma function  (p. 390) | html | pdf |
    • 3.4.10. Summation over the asymmetric unit and elimination of intramolecular energy terms  (p. 390) | html | pdf |
    • 3.4.11. Reference formulae for particular values of n   (pp. 390-391) | html | pdf |
    • 3.4.12. Numerical illustrations  (pp. 391-392) | 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. 385) | 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. 386) | 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. 391) | 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. 392) | 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. 392) | 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. 392) | 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. 392) | html | pdf |