A robustnumericalmethod forgeneralizedcoulomb and self-polarization potentials ofdielectric spheroids

Communications in Computational Physics

Volumn 8, Issue 2, 2010, Pages 374-402

  Xue, Changfeng ^a   Deng, Shaozhong ^b  

^a YANCHENG INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Generalized Coulomb potential; Hybrid solvation model; Poisson equation; Quantum dot; Self polarization potential

Indexed keywords

EID: 77951165912     PISSN: 18152406     EISSN: 19917120     Source Type: Journal    
DOI: 10.4208/cicp.041009.301109a     Document Type: Article

References (45)

1. L. E. Brus Electron-electron and electron-hole interactions in small semiconductor crystallites: The size dependence of the lowest excited electronic state J. Chem. Phys 80;1984:4403.
2. M. Lannoo, C. Delerue, G. Allan, Screening in semiconductor nanocrystallites and its consequences for porous silicon, Phys. Rev. Lett. 74 (1995) 3415-3418.
3. P. G. Bolcatto, C. R. Proetto, Partially confined excitons in semiconductor nanocrystals with a finite size dielectric interface, J. Phys. Condens. Matter 13 (2001) 319-334.
4. A. Okur, C. Simmerling, Hybrid explicit/implicit solvation methods, in: D. C. Spellmeyer (Ed.), Annu. Rep. Comput. Chem., Vol.2, Chemistry of the American Chemical Society, 2006, Ch. 6, pp. 97-109.
5. D. B. Tran Thoai, R. Zimmermann, M. Grundmann, D. Bimberg, Image charges in semiconductor quantum wells: Effect on exciton binding energy, Phys. Rev. B 42 (1990) 5906-5909.
6. L. Bányai, P. Gilliot, Y. Z. Hu, S. W. Koch, Surface-polarization instabilities of electron-hole pairs in semiconductor quantum dots, Phys. Rev. B 45 (1992) 14136-14142.
7. P. G. Bolcatto, C. R. Proetto, Self-polarization energies of semiconductor quantum dots with finite confinement barriers, Phys. Stat. Sol. 220 (2000) 191-194.
8. J. L. Movilla, J. Planelles, Image charges in spherical quantum dots with an off-centered impurity: algorithm and numerical results, Comput. Phys. Commun. 170 (2005) 144-152.
9. P. Qin, Z. Xu, W. Cai, D. Jacobs, Image charge methods for a three-dielectric-layer hybrid solvation model of biomolecules, Commun. Comput. Phys. 6 (2009) 955-977.
10. S. Deng, A robust numerical method for self-polarization energy of spherical quantum dots with finite confinement barriers, Comput. Phys. Commun. 181 (2010) 787-799.
11. M. Feig, C. L. Brooks III, Recent advances in the development and application of implicit solvent models in biomolecule simulations, Curr. Opin. Struct. Biol. 14 (2004) 217-224.
12. N. A. Baker, Improving implicit solvent simulations: a Poisson-centric view, Curr. Opin. Struct. Biol. 15 (2005) 137-143.
13. T. Lazaridis, M. Karplus, Effective energy function for proteins in solution, Proteins: Struct., Funct., Genet. 35 (1999) 133-152.
14. A. Warshel, M. Levitt, Theoretical studies of enzymic reactions: Dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme, J. Mol. Biol. 103 (1976) 227-249.
15. A. Warshel, Conversion of light energy to electrostatic energy in the proton pump of Halobacterium halobium, Photochem. Photobiol. 30 (1979) 285-290.
16. B. E. Hingerty, R. H. Ritchie, T. L. Ferrell, J. E. Turner, Dielectric effects in biopolymers: The theory of ionic saturation revisited, Biopolymers 24 (1985) 427-439.
17. J. Ramstein, R. Lavery, Energetic coupling between DNA bending and base pair opening, Proc. Natl. Acad. Sci. USA. 85 (1988) 7231-7235.
18. M. Shen, K. F. Freed, All-atom fast protein folding simulations: The villin headpiece, Proteins: Struct. Funct. Genet. 49 (2002) 439-445.
19. A. K. Jha, K. F. Freed, Solvation effect on conformations of 1,2:Dimethoxyethane: Charge dependent nonlinear response in implicit solvent models, J. Chem. Phys. 128 (2008) 034501.
20. B. Mallik, A. Masunov, T. Lazaridis, Distance and exposure dependent effective dielectric function, J. Comput. Chem. 23 (2002) 1090-1099.
21. Y. Okamoto, Dependence on the dielectric model and pH in a synthetic helical peptide studied by Monte Carlo simulated annealing, Biopolymers 34 (1994) 529-539.
22. V. Daggett, P. A. Kollman, I. D. Kuntz, Molecular dynamics simulations of small peptides: dependence on dielectric model and pH, Biopolymers 31 (1991) 285-304.
23. R. Constanciel, R. Contreras, Self consistent field theory of solvent effects representation by continuum models: Introduction of desolvation contribution, Theoret. Chim. Acta. (Berl) 65 (1984) 1-11.
24. W. C. Still, A. Tempczyk, R. C. Hawley, T. Hendrickson, Semianalytical treatment of solva-tion for molecular mechanics and dynamics, J. Am. Chem. Soc. 112 (1990) 61276129.
25. M. Califano, P. Harrison, Approximate methods for the solution of quantum wires and dots: Connection rules between pyramidal, cuboidal, and cubic dots, J. Appl. Phys. 86 (1999) 5054.
26. L. Serra, A. Puente, E. Lipparini, Orbital current mode in elliptical quantum dots, Phys. Rev. B 60 (1999) R13966-R13969.
27. K. Hirose, N. S. Wingreen, Spin-density-functional theory of circular and elliptical quantum dots, Phys. Rev. B 59 (1999) 4604.
28. G. Cantele, D. Ninno, G. Iadonisi, Confined states in ellipsoidal quantum dots, J. Phys. Con-dens. Matter 12 (2000) 9019-9036.
29. K. G. Dvoyana, E. M. Kazaryana, L. S. Petrosyan, Electronic states in quantum dots with ellipsoidal symmetry, Physica E: Low-dimensional Systems and Nanostructures 28 (2005) 333-338.
30. P. M. Morse, H. Feshbach, Methods of Theoretical Physcs, McGraw-Hill, New York, 1953.
31. T. Miloh, Forces and moments on a tri-axial ellipsoid in potential flow, Israel J. Tech. 11 (1973) 63-74.
32. J. W. Perram, P. J. Stiles, On the application of ellipsoidal harmonics to potential problems in molecular electrostatics and magnetostatics, Proc. R. Soc. Lond. A 349 (1976) 125-139.
33. T. Miloh, Maneuvering hydrodynamicsof ellipsoidal forms, J. Ship Research23 (1979) 66-75.
34. J. C. E. Sten, Ellipsoidal harmonics and their application in electrostatics, J. Electrostatics 64 (2006) 647-654.
35. L. C. Lew Yan Voon, M. Willatzen, On triaxial ellipsoidal quantum dots, J. Phys. Condens. Matter 16 (2004) 1087-1093
36. D. V. Redz?ić, An electrostatic problem: A point charge outside a prolate dielectric spheroid, Am. J. Phys. 62 (1994) 1118-1121.
37. S. Deng, Electrostatic potential of point charges inside dielectric prolate spheroids, J. Electrostatics 66 (2008) 549-560.
38. A. H. Sihvola, I. V. Lindell, Polarizability and effective permittivity of layered and continuously inhomogeneous dielectric spheres, J. Electro. Waves Appl. 3 (1989) 37-60.
39. A. H. Sihvola, I. V. Lindell, Polarizability and effective permittivity of layered and continuously inhomogeneous dielectric ellipsoids, J. Electro. Waves Appl. 4 (1990) 1-26.
40. I. V. Lindell, M. E. Ermutlu, A. H. Sihvola, Electrostatic image theory for layered dielectric sphere, IEE Proc.-H 139 (1992) 186-192.
41. A. H. Sihvola, I. V. Lindell, Transmission line analogy for calculating the effective permittivity of mixtures with spherical multilayer scatterers, J. Electro. Waves Appl. 2 (1988) 741-756.
42. J. C. de Munck, The potential distribution in a layered anisotropic spheroidal volume conductor, J. Appl. Phys. 64 (1988) 464-470.
43. C. Xue, S. Deng, Three-dielectric-layer hybrid solvation model with spheroidal cavities in biomolecular simulations, Phys. Rev. E 81 (2010) 016701.
44. E. W. Hobson, The Theory of Spherical And Ellipsoidal Harmonics, Cambridge University Press, Cambridge, England, 1931.
45. W. R. Smythe, Static and Dynamic Electricity, 3rd Edition, Hemisphere, New York, 1989.