Accelerated convergence treatment of R−n lattice sums

Williams, D. E.

doi:10.1107/97809553602060000562

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

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

3.4. Accelerated convergence treatment of R⁻ⁿ lattice sums (pp. 385-397) | html | pdf | chapter contents |
D. E. Williams
- 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 () 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 () of crystalline benzene (kJ mol⁻¹, Å) (p. 386) | html | pdf |
  - Table 3.4.12.1. Accelerated-convergence results for the Coulombic sum () 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 () of sodium chloride (p. 392) | html | pdf |
  - Table 3.4.12.3. Accelerated-convergence results for the dispersion sum () 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 () of crystalline benzene (p. 392) | html | pdf |
  - Table 3.4.12.5. Approximate time (s) required to evaluate the dispersion sum () for crystalline benzene within 0.001 kJ mol⁻¹ truncation error (p. 392) | html | pdf |

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

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