Ab initio molecular dynamics: Theory and Implementation

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313. T. Ikeda, M. Sprik, K. Terakura, and M. Parrinello, Phys. Rev. Lett. 81,4416 (1998).314. Y. Imamura, N. Matsui, Y. Morikawa, M. Hada, T. Kubo, M. Nishijima, andH. Nakatsuji, Chem. Phys. Lett. 287 131 (1998).315. Y. Jeanvoine, J. G. Ángyán, G. Kresse, and J. Hafner, J. Phys. Chem. B 102,7307 (1998).316. J. Jellinek, V. Bona˘cić–Koutecký, P. Fantucci, and M. Wiechert, J. Chem.Phys. 101, 10 092 (1994).317. J. Jellinek, S. Srinivas, and P. Fantucci, Chem. Phys. Lett. 288, 705 (1998).318. B. G. Johnson, P. M. W. Gill, and J. A. Pople, J. Chem. Phys. 98, 5612(1993).319. D. D. Johnson, Phys. Rev. B 38, 12087 (1988).320. R. O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).321. R. O. Jones, Angew. Chem. Int. Ed. Engl. 30, 630 (1991).322. Y.–M. Juan and E. Kaxiras, Phys. Rev. B 48, 14 944 (1993).323. R. Kaschner and D. Hohl, J. Phys. Chem. A 102, 5111 (1998).324. C. Katan, J. Phys. Chem. A 103, 1407 (1999).325. M. I. Katsnelson, M. van Schilfgaarde, V. P. Antropov, and B. N. Harmon,Phys. Rev. A 54, 4802 (1996).326. G. P. Kerker, J. Phys. C 13, L189 (1980).327. G. Kern and J. Hafner, Phys. Rev. B 58, 13 167 (1998).328. V. Keshari and Y. Ishikawa, Chem. Phys. Lett. 218, 406 (1994).329. E. Kim, Y. H. Lee, J. J. Lee, and Y. G. Hwang, Europhys. Lett. 40, 147(1997).330. E. Kim, C. W. Oh, Y. H. Lee, Phys. Rev. Lett. 79, 4621 (1997).331. F. Kirchhoff, G. Kresse, and M. J. Gillan, Phys. Rev. B 57, 10 482 (1998).332. S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220, 671 (1983).333. H. Kitamura, S. Tsuneyuki, T. Ogitsu, and T. Miyake, Quantum distributionof protons in solid molecular hydrogen under megabar pressure, preprint.334. H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and PolymerPhysics (World Scientific, Singapore, 1990).335. L. Kleinman and D. M. Bylander, Phys. Rev. Lett. 48, 1425 (1982).336. A. Klesing, D. Labrenz, R. A. van Santen, J. Chem. Soc., Faraday Trans. 94,3229 (1998).337. J. Kohanoff, S. Scandolo, G. L. Chiarotti, and E. Tosatti, Phys. Rev. Lett.78, 2783 (1997).338. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).339. W. Kohn, Chem. Phys. Lett. 208, 167 (1993).340. W. Ko̷los, Adv. Quant. Chem. 5, 99 (1970).341. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).342. R. Kosloff, Annu. Rev. Phys. Chem. 45, 145 (1994).343. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).344. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11 169 (1996).345. G. Kresse and J. Furthmüller, Comput. Mat. Sci 6, 15 (1996).346. G. Kresse and J. Hafner, Phys. Rev. B 55, 7539 (1997).347. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).137
348. V. Kumar and V. Sundararajan, Phys. Rev. B 57, 4939 (1998).349. V. Kumar, Phys. Rev.B 60, 2916 (1999).350. W. Kutzelnigg, Mol. Phys. 90, 909 (1997).351. K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt, Phys. Rev.B 47, 10 142 (1993).352. K. Laasonen, M. Sprik, M. Parrinello, and R. Car, J. Chem. Phys. 99, 9080(1993).353. K. Laasonen and M. L. Klein, J. Amer. Chem. Soc. 116, 11 620 (1994).354. K. Laasonen and M. L. Klein, J. Phys. Chem. 98, 10 079 (1994).355. D. Lamoen, P. Ballone, and M. Parrinello, Phys. Rev. B 54, 5097 (1996).356. D. Lamoen and M. Parrinello, Chem. Phys. Lett. 248, 309 (1996).357. C. Lanczos, J. Res. Nat. Bur. Stand. 45, 255 (1950).358. W. Langel and M. Parrinello, Phys. Rev. Lett. 73, 504 (1994).359. W. Langel and M. Parrinello, J. Chem. Phys. 103, 3240 (1995).360. W. Langel, Chem. Phys. Lett. 259, 7 (1996).361. G. Lauritsch and P.–G. Reinhard, Int. J. Mod. Phys. C 5, 65 (1994).362. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988).363. C. Lee, D. Vanderbilt, K. Laasonen, R. Car, and M. Parrinello, Phys. Rev.Lett. 69, 462 (1992).364. C. Lee, D. Vanderbilt, K. Laasonen, R. Car, and M. Parrinello, Phys. Rev. B47, 4863 (1993).365. C. Leforestier, J. Chem. Phys. 68, 4406 (1978).366. C. Leforestier, R. H. Bisseling, C. Cerjan, M. D. Feit, R. Friesner, A. Guldberg,A. Hammerich, G. Jolicard, W. Karrlein, H.–D. Meyer, N. Lipkin, O. Roncero,and R. Kosloff, J. Comp. Phys. 94, 59 (1991).367. J. G. LePage, M. Alouani, D. L. Dorsey, J. W. Wilkins, and P. E. Blöchl, Phys.Rev. B 58, 1499 (1998).368. I. N. Levine, Quantum Chemistry (Allyn and Bacon, Boston, 1983).369. J.S. Lin, A. Qteish, M.C. Payne, and V. Heine, Phys. Rev. B 47, 4174 (1993).370. G. Lippert, J. Hutter, and M. Parrinello, Molec. Phys. 92, 477 (1997).371. G. Lippert, J. Hutter, and M. Parrinello, Theor. Chem. Acc. 103, 124 (1999).372. Z. Liu, L. E. Carter, and E. A. Carter, J. Phys. Chem. 99, 4355 (1995).373. Z. F. Liu, C. K. Siu, and J. S. Tse, Chem. Phys. Lett. 309, 335 (1999).374. S. G. Louie, S. Froyen, and M. L. Cohen, Phys. Rev. B 26, 1738 (1982).375. H. Löwen, P. A. Madden, and J.–P. Hansen, Phys. Rev. Lett. 68, 1081 (1992);see also Ref. 376 .376. H. Löwen and I. D’amico, J. Phys.: Condens. Matter 9, 8879 (1997).377. M. Lubin and J. H. Weare, Mineral. Mag. 62A, 915 (1998).378. G. Makov and M. C. Payne, Phys. Rev. B 51, 4014 (1995).379. S. A. Maluendes and M. Dupuis, Int. J. Quantum Chem. 42, 1327 (1992).380. A. Marcellini, C. A. Pignedoli, M. Ferrario, and C. M. Bertoni, Surf. Sci.402–404, 47 (1998).381. M. Marchi, J. Hutter, and M. Parrinello, J. Am. Chem. Soc. 118, 7847 (1996).382. P. Margl, T. Ziegler, and P. E. Blöchl, J. Am. Chem. Soc. 117, 12 625 (1995).383. P. M. Margl, T. K. Woo, P. E. Blöchl, and T. Ziegler, J. Am. Chem. Soc.120, 2174 (1998).138
Page 1 and 2:
John von Neumann Institute for Comp
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2500Number200015001000CP PRL 1985AI
Page 7 and 8:
The goal of this section is to deri
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¡the Newtonian equation of motion
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Ehrenfest molecular dynamics is cer
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the Car-Parrinello approach 108 , s
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According to the Car-Parrinello equ
Page 20 and 21:
Figure 4. (a) Comparison of the x-c
Page 22 and 23:
Up to this point the entire discuss
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parameters are those used to repres
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in terms of a linear combination of
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structure calculations, see e.g. Re
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“unbound electrons” dissolved i
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Table 1. Timings in cpu seconds and
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stressed that the energy conservati
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see e.g. the discussion following E
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from a set of one-particle spin orb
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is used, which represents exactly a
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2.8.3 Generalized Plane WavesAn ext
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disposable parameters that can be o
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The index i runs over all states an
Page 48 and 49:
f(G) are related by three-dimension
Page 50 and 51:
where j l are spherical Bessel func
Page 52 and 53:
andE self = ∑ I1√2πZ 2 IR c I.
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¢££¤¤¢¢¢n tot (G)inv FTn to
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correlation energyΩ ∑E xc = ε x
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3.4 Total Energy, Gradients, and St
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3.4.3 Gradient for Nuclear Position
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The local part of the pseudopotenti
Page 64 and 65:
¢¢¢¢¢i = 1 . . .N b¢c i (G)¢
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¢¢¢¢¢c i (G)123g, E self∆V I
Page 68 and 69:
where G c is a free parameter that
Page 70 and 71:
and a matrix form of the Gram-Schmi
Page 72 and 73:
The two sets of equations are coupl
Page 74 and 75:
introducing different masses for di
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The Lagrange multiplier have to be
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Table 3. Relative size of character
Page 80 and 81:
of the G vectors, and only real ope
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CALL SGEMM(’T’,’N’,M,N b ,2
Page 84 and 85:
ing standard communication librarie
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over processors. All processors sho
Page 88 and 89: ab = 2 * sdot(2 * N p D ,A(1),1,B(1
Page 90 and 91: ENDCALL ParallelFFT3D("INV",scr1,sc
Page 92 and 93: are the improved load-balancing for
Page 94 and 95: situations where• it is necessary
Page 96 and 97: espectively), but completely analog
Page 98 and 99: 4.2.3 Imposing Pressure: BarostatsK
Page 100 and 101: in the previous section. The isobar
Page 102 and 103: 4.3.2 Many Excited States: Free Ene
Page 104 and 105: down the generalization of the Helm
Page 106 and 107: free energy functional discussed in
Page 108 and 109: Figure 16. Four patterns of spin de
Page 110 and 111: and electrons r = {r i } can be wri
Page 112 and 113: The effective classical partition f
Page 114 and 115: up e.g. in Refs. 132,37,596,597,428
Page 116 and 117: The eigenvalues of A when multiplie
Page 118 and 119: frequency of the electronic degrees
Page 120 and 121: 5.2 Solids, Polymers, and Materials
Page 122 and 123: the penetration of the oxidation la
Page 124 and 125: in terms of their electronic struct
Page 126 and 127: culations on very accurate global p
Page 128 and 129: AcknowledgmentsOur knowledge on ab
Page 130 and 131: 57. M. Bernasconi, G. L. Chiarotti,
Page 132 and 133: Superiore di Studi Avanzati (SISSA)
Page 134 and 135: 175. E. Ermakova, J. Solca, H. Hube
Page 136 and 137: 244. H. Goldstein, Klassische Mecha
Page 140 and 141: 384. N. A. Marks, D. R. McKenzie, B
Page 142 and 143: 442. S. Nosé and M. L. Klein, Mol.
Page 144 and 145: 502. L. M. Ramaniah, M. Bernasconi,
Page 146 and 147: 562. F. Shimojo, K. Hoshino, and Y.
Page 148 and 149: 620. A. Tongraar, K. R. Liedl, and
Page 150: 682. R. M. Wentzcovitch, Phys. Rev.
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