Исследование молекулярной подвижности в микро-и мезопористых материалах методами 2Н ЯМР спектроскопии и нейтронного рассеяния
Диссертация
Н ЯМР эксперименты позволили показать, что С6Н4 фрагменты в MIL-47(V) и MIL-53(Сг) вовлечены в сравнительно медленное вращательное движение: 180°-е прыжки относительно С2 оси симметрии бензольного кольца. Движение бензольных колец в гибком MIL-53(Cr) заметно быстрее, чем в жестком MIL-47(V) и характеризуются меньшим ак-тивациопным барьером. Это указывает на то, что органические фрагменты… Читать ещё >
Список литературы
- Kirk-Othmer Encyclopedia of Chemical Technology, 5th Edition. New York: wiley, 2007.
- Aristov Yu. I. Novel materials for adsorptive heat pumping and storage: screening and nanotailoring of sorption properties //J. Chem. Engn. Japan. 2007. Vol. 40, no. 13. Pp. 1241−1251.
- Aristov Yu. I., Glaznev I. S., Freni A., Restuccia G. Kinetics of water sorption on SWS-1L (calcium chloride confined to mesoporous silica gel): Influence of grain size and temperature // Chem. Engn. Sci. 2005. Vol. 125. P. 367.
- Aristov Yu. I., Tokarev M.M., Cacciola G., Restuccia G. Selective water sorbents for multiple applications: 1. СаСЬ confined in mesopores of the silica gel: sorption properties // React. Kinet. Catal. Lett. 1996. Vol. 59, no. 2. Pp. 325−334.
- Simonova I. A., Aristov Yu. I. Sorption properties of calcium nitrate dispersed in silica gel: the effect of pore size // Rus. J. Phys. Chem. 2005. Vol. 79, no. 8. Pp. 1307−1311. '
- Токарев M.M., Козлова С. Г., Габуда С. П., Аристов Ю. И. ЯМР *Н в наиокристаллах СаС12хН20 и изобары сорбции воды в системе СаС^-силикагель // Журнал Структурной Химии. 1998. Т. 39, № 2. С. 261−266.
- Leclaire A., Borel М. Le dichlorure de calcium dihydrate // Acta Cryst. 1977. Vol. B33. Pp. 1608−1610.
- Thewalt U., Bugg C.E. Crystal structure of calcium cloride tetrahydrate // Acta Cryst. 1973. Vol. B29. P. 615.
- Leclaire Andre, Borel Marie-Madeleine. Le dichlorure el le dibromure de Calcium hexahydrates // Acta Cryst. 1977. Vol. B33. Pp. 2938−2940.
- Agron P.A., Busing W.R. Calcium and strontium dichloride hexahydrates by neutron diffraction // Acta Cryst. 1986. Vol. C42. Pp. 141−143.
- Emons Hans Heinz. Structure and properties of molten salt hydrates // Electrochimica Acta. 1988. Vol. 33. P. 1243.
- Brovchenko I., Oleinikova A. Interfacial and Confined Water. New York and Londona: ELSEVIER, 1971.
- Dash J.G., Rempel A.W., Wettlaufer J.S. The physics of premelted ice and its geophysical consequences // Rev. Mod. Phys. 2006. Vol. 78, no. 3. P. 695.
- Li J. Hydrocarbons from Methanol // J. Chem. Phys. 1996. Vol. 16. P. 6733.
- Tayal V.P., Srivastava B.K., Khndelwal D.P. Librational modes of water in nickel formate dihydrate // Appl. Spectrosc. Rev. 1980. Vol. 16, no. 1. P. 43.
- Parker S.F., Shankland K., Sprunt J.C., Jayasooriya U.A. The nine modes of complexed water // Spect. Acta A. 1997. Vol. 53. P. 2333.
- Plazanet M., Glaznev I. S., Stepanov A. G., Aristov Yu. I., Jobic H. Dynamics of hydrated water in CaCl2 complexes // Chem. Phys. Lett. 2006. Vol. 419, no. 1. Pp. 111−114.
- Chiba T. Deuteron Magnetic Resonance Study of Barium Chlorate Monohydrate //J. Chem. Phys. 1963. Vol. 39, no. 4. Pp. 947−953.
- Chiba T. Deuteron Magnetic Resonance Study of Some Crystals Containing an О—D---0 Bond // J.Chem. Phys. 1964. Vol. 41, no. 5. Pp. 1352−1358.
- Long J. R., Ebelhaeuser R., Griffin R. G. 2H NMR Line Shapes and Spin-Lattice Relaxation in Ba(C103)2Px2H20. // J. Phys. Chem. A. 1997. Vol. 101, no. 6. Pp. 988−994.
- Wittebort R. J., Olejniczak E. T, Griffin R. G. Analysis of deuterium nuclear magnetic resonance line shapes in anisotropic media //J. Chem. Phys. 1987. Vol. 86. Pp. 5411−5420.
- Stepanov A. G., Shegai Т. O., Luzgin M. V., Essayem N., Jobic H. Deuterium Solid-State NMR Study of the Dynamic Behavior of Deuterons and Water Molecules in Solid D3PW1204o. // J- Phys. Chem. B. 2003. Vol. 107, no. 45. Pp. 12 438−12 443.
- Габуда С.П., Лундин А. Г. Диффузия молекул воды в гидратах и спектры ЯМР // ЖЭТФ. 1968. Т. 55. С. 1066−1071.
- Karger J., Ruthven D. M. Diffusion in Zeolites and Other Microporous Solids. New York: Wiley-Interscience, 1992.
- Chen N. Y., Degnan T. F., Jr., Smith С. M. Molecular Transport and Reactions in Zeolites. Design and Application of Shape Selective Catalysts. Weinheim: VCH Publishers, Inc., 1994.
- Yang R. T. Gas Separation in Adsorption Processes. Stoneham, MA: Butterworth Publishers, 1987.
- Bee M. Quasielastic neutron scattering. Adam Hilger, Bristol, 1988.
- Mezei F. (Editor). Neutron Spin Echo. Berlin: Springer-Verlag, 1979. Vol. 128 of Lect. Notes Phys.
- Theodorou D. N., Snurr R. Q., Bell A. T. Comprehensive Supramolecular Chemistry. 1996. Vol. 7.
- Auerbach S. M. Theory and Simulation of Jump Dynamics, Diffusion and Phase Equilibrium in Nanopores // Int. Rev. Phys. Chem. 2000. Vol. 19. P. 155.
- Dubbeldam D., Calero S., Maesen T. L. M., Smit B. Incommensurate Diffusion in Confined Systems // Phys. Rev. Lett. 2003. Vol. 90, no. 24. P. 245 901.
- Zorine Vadim E., Magusin Pieter С. M. M., Santen Rutger A. van. Rotational Motion of, Alkanes on Zeolite ZK-5 Studied from 1H-13C NMR Cross-Relaxation // J. Phys. Chem.
- B. 2004. Vol. 108. Pp. 5600−5608.
- Stepanov A. G., Alkaev M. M., Shubin A. A. Molecular Dynamics of Isobutyl Alcohol Inside Zeolite H-ZSM-5 as Studied by Deuterium Solid-State NMR Spectroscopy. // J. Phys. Chem. B. 2000. Vol. 104, no. 32. Pp. 7677−7685.
- Stepanov A. G., Alkaev M. M., Shubin A. A., Luzgin M. V., Shegai Т. O., Jobic H. Dynamics of Isobutane inside Zeolite ZSM-5. A Study with Deuterium Solid-State NMR // J. Phys. Chem. B. 2002. Vol. 106, no. 39. Pp. 10 114−10 120.
- Stepanov A. G., Shegai Т. O., Luzgin M. V., Jobic H. Comparison of the Dynamics of n-Hexane in ZSM-5 and 5A Zeolite Structures // Eur. Phys. J. E. 2003. Vol. 12, no. 1. Pp. 57−61.
- Stepanov A. G., Shubin A. A., Luzgin M. V., Shegai Т. O., Jobic H. Dynamics of n-Hexane Inside Silicalite, as Studied by 2H NMR // J. Phys. Chem. B. 2003. Vol. 107, no. 29. Pp. 7095−7101.
- Stepanov A. G., Shubin A. A., Luzgin M. V., Jobic H., Tuel A. Molecular dynamics of n-octane inside zeolite ZSM-5 as studied by deuterium solid-state NMR and quasi-elastic neutron scattering // J. Phys. Chem. B. 1998. Vol. 102, no. 52. Pp. 10 860−10 870.
- Gorring R. L. Diffusion of Normal Paraffins in Zeolite T. Occurence of Window Effect // J.Catal. 1973. Vol. 31. Pp. 13−26.
- Chen N. Y., Lucki S. J., Mower E. B. Cage effect on product distribution from cracking over crystalline aluminosilicate zeolites //J. Catal. 1969. Vol. 13. Pp. 329−332.
- Baerlocher C., Meier W. M., Olson D. H. Atlas of Zeolite Framework Types. Fifth revised edition edition. Amsterdam: Elsevier, 2001.
- Dubbeldam D., Smit B. Computer Simutation of Incommensurate Diffusion in Zeolites: Understanding Window Effects // J. Phys. Chem. B. 2003. Vol. 107, no. 44. Pp. 1 213 812 152.
- Jobic H., Methivier A., Ehlers G., Farago В., Haeussler W. Accelerated Diffusion of Long-Chain Alkanes between Nanosized Cavities // Angew. Chem. Int. Ed. 2004. Vol. 43. Pp. 364−366.
- Jobic H., Theodorou D. N. Diffusion of Long n-Alkanes in Silicalite. A Comparison between Neutron Scattering Experiments and Hierarchical Simulation Results // J. Phys. Chem. B. 2006. Vol. 110. Pp. 1964−1967.
- Millot В., Methivier A., Jobic H., Moueddeb H., Dalmon J. A. Permeation of linear and branched alkanes in ZSM-5 supported membranes. // Microporous Mesoporous Materials. 2000. Vol. 38, no. 1. Pp. 85−95.
- Jobic H. Diffusion of linear and branched alkanes in ZSM-5. A quasi-elastic neutron scattering study // J. Mol. Catal. A. 2000. Vol. 158. P. 135.
- Leroy F., Rousseau В., Fuchs A.H. Self-diffusion of n-alkanes in silicalite using molecular dynamics simulation: A comparison between rigid and flexible frameworks // Phys. Chem. Chem. Phys. 2004. Vol. 6. P. 775.
- Leroy F., Jobic H. Influence of extra-framework cations on the diffusion of alkanes in silicalite: Comparison between quasi-elastic neutron scattering and molecular simulations // Chem. Phys. Lett. 2005. Vol. 406. P. 375.
- Maginn Edward J., Bell Alexis Т., Theodorou Doros N. Sorption Thermodynamics, Siting, and Conformation of Long n-Alkanes in Silicalite As Predicted by Configurational-Bias Monte Carlo Integration // J. Phys. Chem. 1995. Vol. 99. Pp. 2057 2079.
- Maginn Edward J., Bell Alexis Т., Theodorou Doros N. Dynamics of Long n-Alkanes in Silicalite: A Hierarchical Simulation Approach. // J. Phys. Chem. 1996. Vol. 100, no. 17. Pp. 7155−73.
- Vasenkov S., Bohlmann W., Galvosas P., Geier O., Liu H., Karger J. PFG NMR Study of Diffusion in MFI-Type Zeolites: Evidence of the Existence of Intracrystalline Transport Barriers // J. Phys. Chem. B. 2001. Vol. 105. Pp. 5922−5927.
- June R. L., Bell А. Т., Theodorou D. N. Prediction of low occupancy Sorption of Alkanes in Silicalite // J. Phys. Chem. 1990. Vol. 94, no. 4. Pp. 1508−1516.
- June R. L., Bell А. Т., Theodorou D. N. Molecular Dynamics Studies of Butane and hexane in Silicalite // J. Phys. Chem. 1992. Vol. 96. Pp. 1051−1060.
- Li H., Eddaoudi M., O’Keeffe M., Yaghi O.M. Design and Synthesis of an Exceptionally Stable and Highly Porous Metal-Organic Framework // Nature. 1999. Vol. 402. P. 276.
- Ferey G. Hybrid porous solids: past, present, future // Chem. Soc. Rev. 2008. Vol. 37. P. 191.
- Farrusseng D., Aguado S., Pinel C. Metal-Organic Frameworks: Opportunities for Catalysis // Angew. Chem. Int. Ed. 2009. Vol. 48. P. 7502.
- Ferey G., Serre C. Large breathing effects in three-dimensional porous hybrid matter: facts, analyses, rules and consequences // Chem. Soc. Rev. 2009. Vol. 38. P. 1380.
- Boutin A., Springuel-Huet M. A., Nossov A., Gedeon A., Loiseau Т., Volkringer C., Ferey G., Coudert F. X., Fuchs A. Breathing Transitions in MIL-53(A1) Metal-Organic Framework Upon Xenon Adsorption, // Angew. Chem. Int. Ed. 2009. Vol. 48. P. 8314.
- Liu Y., Her J. H., Dailly A., Ramirez-Cuesta A. J., Neumann D. A., Brown С. M. Reversible structural transition in MIL-53 with large temperature hysteresis // J. Am. Chem. Soc. 2008. Vol. 130. P. 11 813.
- Greathouse J. A., Allendorf M. D. Force field validation for molecular dynamics simulations of IRMOF-1 and other isoreticular zinc carboxylate coordination polymers // J. Phys. Chem. C. 2008. Vol. 112. P. 5795.
- Tafipolsky M., Amirjalaycr S., Schmid R. Ab initio parametrized MM3 force field for the metal-organic framework MOF-5 // J. Comput. Chem. 2007. Vol. 28. P. 1169.
- Zhou W., Yildirim T. Lattice Dynamics of Metal-Organic Frameworks: Neutron Inelastic Scattering and First-Principles Calculations // Phys. Rev. B. 2006. Vol. 74. P. 180 301.
- Jobic H., Theodorou D. N. Quasi-elastic neutron scattering and molecular dynamics simulation as complementary techniques for studying diffusion in zeolites // Micropor. Mesopor. Mater. 2007. Vol. 102. P. 21.
- Gonzalez J., Devi R. N., Tunstall D. P., Cox P. O., Wright P. A. Deuterium NMR studies of framework and guest mobility in the metal-organic framework compound MOF-5,
- Zn40(02C-C6H4-C02)3. // Micropor. Mesopor. Mater. 2005. Vol. 84. P. 97.
- Gould S. L., Tranchemontagne D., Yaghi О. M., Garcia-Garibay M. A. The Amphidynamic Character of Crystalline MOF-5: Rotational Dynamics in a Free-Volume Environment // J. Am. Chem. Soc. 2008. Vol. 130. P. 3246.
- Salles F., Jobic H., Maurin G., Koza M. M., Llewellyn P. L., Devic Т., Serre C., Ferey G. Experimental evidence supported by simulations of a very high H-2 diffusion in metal organic framework materials // Phys. Rev. Lett. 2008. Vol. 100, no. 24.
- Salles F., Jobic H., Ghoufi A., Llewellyn P. L., Serre C., Bourrelly S., Ferey G., Maurin G. Transport Diffusivit. y of C02 in the Highly Flexible Metal-Organic Framework MIL-53(Cr) // Angew. Chem. Int. Ed. 2009. Vol. 48. P. 8335.
- Barthelet K., Marrot J., Riou D., Ferey G. A Breathing Hybrid Organic-Inorganic Solid with Very Large Pores and High Magnetic Characteristics // Angew. Chem. Int. Ed. 2002. Vol. 41, no. 2. Pp. 281−284.
- Romannikov V. N., Mastikhin V. M., Hocevar S., Drzaj B. Laws observed in the synthesis of zeolites having the structure of H-ZSM-5 and varying chemical composition // Zeolites. 1983. Vol. 3. Pp. 311−320.
- Baerloche Ch., McCusker L.B. // Database of Zeolite Structures: http://www.iza-structure. org/databases /.
- Ferey G., Mellot-Draznieks C., Serre C., Millange F., Dutour J., Surble S., Margiolaki I. A chromium terephthalate-based solid with unusually large pore volumes and surface area // Science. 2005. Vol. 309, no. 5743. Pp. 2040−2042.
- Powles J. G., Strange J. H. Zero Time Resolution Nuclear Magnetic Resonance Transients in Solids // Proc. Phys. Soc. Vol. 82. P. 6.
- Davis J. H., Jeffery K. R., Bloom M., Valic M. I., Higgs T. P. Quadrupolar ceho deuteron magnetic resonance spectroscopy in ordered hydrocarbon chains. // Chem. Phys. Lett. 1976. Vol. 42. P. 390.
- Farrar Т. C., Becker E.D. Pulse and Fourier Transform NMR. Introduction to Theory and Methods. New York and Londona: Academic Press, 1971.
- Abragam A. The Principles of Nuclear Magnetism. Oxford: Oxford University Press, 1961.
- Spiess H. W. // Dynamic NMR Spectroscopy. Berlin: Springer-Verlag, 1978. Vol. 15. Pp. 55−214.
- Ландау JT.Д., Лифшиц Е. М. Квантовая Механика, перялетивисткая теория. Москва: ФИЗМАТЛИТ, 2001.
- Ernst R. R., Bodenhausen G., Wokaun A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Oxford: Oxford University, 1987.
- Macho V., Brombacher L., Spiess H.W. The NMR-WEBLAB: an internet approach to NMR lincshapc analysis // Appl. Magn. Reson. 2001. Vol. 20, no. 3. Pp. 405−432.
- Mizuno Motohiro, Itakura Naohisa, Endo Kazunaka. Effects of strong paramagnetic interactions on solid-state deuterium NMR spectra // Chem. Phys. Lett. 2005. Vol. 416. Pp. 358−363.
- Torchia D. A., Szabo A. Spin-Lattice Relaxation in Solids // J. Magn. Reson. 1982. Vol. 49. Pp. 107−121.
- Wittebort R. J., Szabo A. Theory of NMR relaxation in macromolecules: Restricted diffusion and jump models for multiple internal rotations in amino acid side chains // J. Chem. Phys. 1978. Vol. 69. P. 1722.
- Schmidt-Rohr K., Spiess H. W. Multidimensional Solid-State NMR and Polymers. London: Academic Press, 1994.
- Kolokolov D. I., Glaznev I. S., Aristov Y. I., Stepanov A. G., Jobic H. Water dynamics in bulk and dispersed in silica CaCl2 hydrates studied by 2H NMR // J. Phys. Chem. C. 2008. Vol. 112, no. 33. Pp. 12 853−12 860.
- Kolokolov D. I., Stepanov A. G., Glaznev I. S., Aristov Y. I., Plazanet M., Jobic H. Water dynamics in bulk and dispersed in silica CaCl2 hydrates studied by neutron scattering methods // Microporous and Mesoporous Materials. 2009. Vol. 125. P. 46−50.
- Soda Gen, Chiba Takehiko. Deuteron Magnetic Resonance Study of Cupric Formate Tetrahydrate Cu (DC00)2−4D20 // J. Phys. Chem. 1968. Vol. 50, no. 1.
- Wittebort R. J., Usha M.G., Ruben D.J., Wemmer D.E., Pines A. Observation of molecular reorientation in ice by proton and deuterium magnetic resonance // J. Am. Chem. Soc. 1988. Vol. 110, no. 17. Pp. 5668−5671.
- Лебедев В.В. Флуктуациоииые эффекты в макрофизике. Москва: МЦНМО, 2004.
- Kats E.I., Lebedev V.V., Muratov A.R. Weak crystallization theory // Physics Report. 1993. Vol. 228. Pp. 1−91.
- Beck В., Villanueva-Garibay J.A., Muller K., Roduner E. 2II NMR study of dynamics, ordering, and phase transition in ferroelectric pyridinium tetrafluoroborate // Chem. Mater. 2003. Vol. 15. Pp. 1739−1748.
- Hindman J. C., Svirmick.A. Relaxation Processes in Water Spin-Lattice Relaxation of D20 in Supercooled Water // Journal of Physical Chemistry. 1973. Vol. 77, no. 20. Pp. 2487−2489.
- Teixeira M., Bellissent-Funel M.-C., Chen S.H., Dianoux A.J. Experimental Determination of the nature of diffusive motions of water molecules at low temperatures // Phys. Rev. A. 1985. Vol. 31, no. 3. Pp. 1913−1917.
- Pimentel G.C., McClellan A.L. The Hydrogen Bond. New York: Freeman, 1960.
- Schmider J., Muller K. 2H NMR investigations of the hexadecane/urea inclusion compound // J. Phys. Chem. A. 1998. Vol. 102. Pp. 1181−1193.
- Lim Ae Ran, Jeong S. Y. and 2H NMR relaxation study on the phase transition of (NH4)3H (S04)2 and (NH4)3D (S04)2 single crystals // J. Phys. Condens. Mat. 2006. Vol. 18. Pp. 6759−6768.
- Tang X. P., Wang J.C., Cary L.W., Kleinhammes A., Wu Y. A 13C NMR study of the molecular Dynamics and Phase transition of confined Benzene inside Titanate Nanotubes // J. Am. Chem. Soc. 2005. Vol. 127. Pp. 9255−9259.
- Singwi K.S., Sjolander A. Diffusive Motions in Water and Cold Neutron Scattering // Phys. Rev. Vol. 119. P. 863.
- Aristov Y.I., Glaznev I.S., Gordeeva L.G., Koptyug I.V., Ilyina L.Y., Karger J., Krause C., Dawoud B. NATO-ASI Series, Series II. Springer, 2006.
- Kolokolov D. I., Arzumanov S. S., Stepanov A. G., Jobic H. Dynamics of linear п-Сб-п-С22 alkanes inside 5A zeolite studied by 2H NMR // J. Phys. Chem. C. 2007. Vol. Ill, no. 11. Pp. 4393−4403.
- Boddenberg В., Beerwerth B. Proton and Deuteron Magnetic Resonance Relaxation of Benzene Adsorbed on Alumina and on a Platinum/Alumina Catalyst //J. Phys. Chem. 1989. Vol. 93, no. 4. Pp. 1440−1447.
- Meirovitch E., Rananavare S.B., Freed J. H. Comments of the Interpretation of Dynamics Deuterium NMR Spectra from, Solid Inclusion Compounds //J. Phys. Chem. 1987. Vol. 91. Pp. 5014−5020.
- Schwartz L. J., Meirovitch E., Ripmeester J. A., Freed J. H. Quadrupole Echo Study of Internal Motions in Polycrystalline Media // J. Phys. Chem. 1983. Vol. 87. Pp. 4453−4467.
- Morrison R. Т., Boyd R. N. Organic Chemistry. Boston: Allyn & Bacon, Inc., 1970.
- Kolokolov D. I., Jobic H., Stepanov A. G. Mobility of n-Butane in ZSM-5 Zeolite Studied by 2II NMR //J. Phys. Chem. C. 2009. Vol. 114. P. 2958−2966.
- Jelinski L.W. // Annual Review of Materials Science. 1985. Vol. 15. Pp. 359−377.
- Jelinski L. W. Deuterium NMR of Solid Polymers // High Resolution NMR Spectroscopy of Synthetic Polymers in Bulk (Methods and Stereochemical Analysis) / Ed. by R. A. Komoroski. New York: VCH Publishers, 1986. Vol. 7. P. 335.
- Meirovitch E., Samulski E. Т., Leed A., Scheraga H. A., Rananavare S., Nemethy G., Freed J. H. Deuterium NMR study of the structure and dynamic of the side chains of several solid polyglutamates // J. Phys. Chem. 1987. Vol. 91, no. 18. Pp. 4840−4851.
- Feldhoff A., Caro J., Jobic H., Ollivier J., Krause С. В., Galvosas P., Karger J. Intracrystalline Transport Resistance in Nanoporous Zeolite X // ChemPhysChem. 2009. Vol. 10. P. 2429.
- Millot В., Methivier A., Jobic H. Adsorption of n-Alkanes on Silicalite Crystals. A Temperature-Programmed Desorption Study //J. Phys. Chem. B. 1998. Vol. 102. Pp. 3210−3215.
- Kolokolov D. I., Jobic H., Stepanov A. G., Guillerm V., Devic Т., Serre C., Ferey G. Dynamics of benzene rings in MIL-53(Cr) and MIL-47(V) frameworks studied by 2H NMR // Angew. Chem. Int. Ed. 2010. Vol. in press.
- Rinne M., Depireux J. Nuclear quadrupole coupling constant of deuterium bound to carbon in organic molecules // Adv. Nucl. Quadrupole Reson. 1974. Vol. 1. Pp. 357−374.
- Kresse G., Hafner J. Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germanium // Phys. Rev. B, http://cms.mpi.univie.ac.at/vasp/. Vol. 49. P. 14 251.
- Kresse G., Hafner J. Ab initio molecular dynamics for liquid metals // Phys. Rev. B. Vol. 47. P. 558.
- Kresse G., Furthmuller J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set // Comput. Mater. Sci. Vol. 6. P. 15.
- Kresse G., Furthmuller J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set // Phys. Rev. B. Vol. 54. P. 11 169.