Periodic Green function for calculation of coloumbic lattice potentials

Journal of Physics Condensed Matter

Volumn 12, Issue 21, 2000, Pages 4575-4601

  Marshall, Simon L ^a  

^a OAK RIDGE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; GREEN'S FUNCTION; POTENTIAL ENERGY;

COLOUMBIC LATTICE POTENTIALS; EWALD SUM; LAPLACE EQUATION; POISSON-JACOBI FORMULA;

CRYSTAL LATTICES;

EID: 0033746854     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/12/21/304     Document Type: Article

References (57)

1. Abramowitz M and Stegun I A (eds) 1964 Handbook of Mathematical Functions (Washington, DC: National Bureau of Standards)
2. Barton G 1989 Elements of Green's Functions and Propagation (Oxford: Oxford University Press)
3. Bellman R 1961 A Brief Introduction to Theta Functions (New York: Holt, Rinehart and Winston)
4. Berendsen H J C, Grigera J R and Straatsma T P 1987 The missing term in effective pair potentials J. Phys. Chem. 91 6269-71
5. Chaba A N and Pathria R K 1975 Evaluation of a class of lattice sums in arbitrary dimensions J. Math. Phys. 16 1457-60
6. _ 1976a Evaluation of lattice sums using Poisson's summation formula II J. Phys. A: Math. Gen. 9 1411-23
7. _ 1976b Evaluation of lattice sums using Poisson's summation formula III J. Phys. A: Math. Gen. 9 1801-10
8. Chialvo A A and Cummings P T 1999 Molecular-based modeling of water and aqueous solutions at supercritical conditions Adv. Chem. Phys. 109 115-205
9. De Leeuw, S W, Perram J W and Smith E R 1980 Simulation of electrostatic systems in periodic boundary conditions. I, Lattice sums and dielectric constants Proc. R. Soc. A 373 27-56
10. Erdélyi A, Magnus W, Oberhettinger F and Tricomi F G 1954 Tables of Integral Transforms vol 1 (New York: McGraw-Hill)
11. Euwema R N and Surratt G T 1975 The absolute positions of calculated energy bands J. Phys. Chem. Solids 326 67-71
12. Ewald P P 1921 Die Berechnung optischer und elektrostatischer Gitterpotentiale Ann. Phys., Lpz. 64 253-87
13. Glasser M L 1973a The evaluation of lattice sums. I. Analytic procedures J. Math. Phys. 14 409-13
14. _ 1973b The evaluation of lattice sums. II. Number-theoretic approach J. Math. Phys. 14 701-3
15. Gradshteyn I S and Ryzhik I M 1994 Table of Series, Products and Integrals 4th edn (Boston: Academic)
16. Gray A, Mathews G B and Macrobert T M 1931 A Treatise on Bessel Functions and their Applications to Physics (London: Macmillan)
17. Grønbech-Jensen N, Hummer G and Beardmore K M 1997 Lekner summation of Coolumb interactions in partially-periodic systems Mol. Phys. 92 941-5
18. Haq B U 1998 Gas hydrates: Greenhouse nightmare, energy panacea or pipe dream? GSA Today 8 2-6
19. Hautot A 1974 New method for evaluation of slowly-convergent series J. Math. Phys. 15 1722-7
20. Herzig P 1985 Electrostatic potentials, fields and field gradients from a general crystalline charge density Theo. Chim. Acta 67 323-33
21. Jones W and March N H 1973 Theoretical Solid State Physics vol 1 (London: Wiley-Interscience)
22. Krasovskii E E, Starrost F and Schattke W 1999 Augmented Fourier components method for constructing the crystal potential in self-consistent band-structure calculations Phys. Rev. B 59 10504-11
23. Kvamme B and Florrisdahl O K 1996 Methane clathrate hydrates: melting, supercooling and phase separation from molecular dynamics computer simulations Mol. Phys. 89 819-34
24. Kvenvolden K A 1988 Methane hydrate. A major reservoir of carbon in the shallow geosphere Chem. Geol. 71 41-51
25. Leibfried G 1955 Mechanische und thermische Eigenschaften der Kristalle Handbuch der Physik vol 7, ed S Flügge (Berlin: Springer) part 1, pp 132-8
26. Lekner J 1991 Summation of Coulomb fields in computer-simulated disordered systems Physica A 176 485-98
27. _ 1998 Coulomb forces and potentials in systems with an orthorhombic unit cell Mol. Simul. 20 357-68
28. Lennard-Jones J E and Ingham A E 1925 On the calculation of certain crystal potential constants, and on the cubic crystal of least potential energy Proc. R. Soc. A 107 636-53
29. Linton C M 1999 Rapidly convergent representations for Green's functions for Laplace's equation Proc. R. Soc. A 455 1767-97
30. Macdonald J R and Barlow C A Jr 1966 Discreteness-of-charge adsorption micropotentials. III. Dielectric-conductive imaging J. Electrochem. Soc. 113 978-92
31. Marshall S L 1986 Theoretical analysis of molecular polarization and adsorption at interfaces PhD Thesis University of Ottawa
32. _ 1998a Convergence acceleration of Fourier series by analytical and numerical application of Poisson's formula J. Phys. A: Math. Gen. 31 2691-704
33. _ 1998b On the analytical summation of Fourier series and its relation to the asymptotic properties of Fourier transforms J. Phys. A: Math. Gen. 31 9957-73
34. _ 1999 A rapidly-converging modified Green's function for Laplace's equation in a rectangle Proc. R. Soc. A 455 1739-66
35. Marshall S L and Conway B E 1992a Analysis of molecular polarization and interaction in adsorbed monolayers at interfaces Part 3: ionic adsorption isotherm with mean-field treatment of interactions involving ions and dipoles J. Electroanal. Chem. 337 45-66
36. _ 1992b Analysis of molecular polarization and interaction in adsorbed monolayers at interfaces Part 4: Madelung constants for hexagonal lattices of adsorbed ions and dipoles J. Electroanal. Chem. 337 67-89
37. Miller A R 1995 On certain two-dimensional Schlömilch series J. Phys. A: Math. Gen. 28 735-45
38. Morse P M and Feshbach H 1953 Methods of Theoretical Physics (New York: McGraw-Hill)
39. Oh Y, Badralexe E, Marksteiner P and Freeman A 1992 Poisson equation with periodic boundary conditions: multipole-expansion solution Phys. Rev. B 46 4495-501
40. Redlack A and Grindlay J 1975 Coulombic potential lattice sums J. Phys. Chem. Solids 36 73-82
41. Rodger P M 1990 Stability of gas hydrates J. Phys. Chem. 94 6080-9
42. _ 1991 Lattice relaxation in type I gas hydrates AIChE J. 37 1511-16
43. Schadler G H 1992 Solution of Poisson's equation for arbitrarily shaped overlapping or nonoverlapping charge densities in terms of multipole moments Phys. Rev. B 45 11 314-17
44. Sloan E D 1998 Clathrate Hydrates of Natural Gases (New York: Dekker)
45. Stakgold I 1967 Boundary Value Problems of Mathematical Physics 2 vols (New York: Macmillan)
46. Stuart S N 1978 Depolarization corrections for Coulomb lattice sums J. Comput. Phys. 29 127-32
47. Terras A A 1985 Harmonic Analysis on Symmetric Spaces and Applications I (New York: Springer)
48. Topping J 1927 On the mutual potential energy of a plane network of doublets Proc. R. Soc. A 114 67-72
49. Tse J S, Klein M L and McDonald I R 1984 Computer simulation studies of the structure I clathrate hydrates of methane, tetrafluoromethane, cyclopropane and ethylene oxide J. Chem. Phys. 81 6146-53
50. van der Hoff B M E and Benson G C 1953 A method for the evaluation of some lattice sums occurring in calculations of physical properties of crystals Can. J. Phys. 31 1087-94
51. Watson G N 1944 A Treatise on the Theory of Bessel Functions 2nd edn (London: Cambridge University Press)
52. Weinert M 1981 Solution of Poisson's equation: beyond Ewald-type methods J. Math. Phys. 22 2433-9
53. Whittaker E T and Watson G N 1944 Modern Analysis (London: Cambridge University Press)
54. Zhang X-G, Butler W H, McLaren J M and van Ek J 1994 Cellular solutions for the Poisson equation in extended systems Phys. Rev. B 49 13 383-93
55. Zucker I J 1974 Exact results for some lattice sums in 2, 4, 6, and 8 dimensions J. Phys. A: Math. Gen. 7 1568-75
56. _ 1975 Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structures J. Phys. A: Math. Gen. 8 1734-45
57. _ 1976 Functional equations for poly-dimensional zeta functions and the evaluation of Madelung constants J. Phys. A: Math. Gen. 9 499-505