Ab initio molecular dynamics: Theory and Implementation

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John von Neumann Institute for Comp
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2500Number200015001000CP PRL 1985AI
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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
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Figure 4. (a) Comparison of the x-c
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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
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f(G) are related by three-dimension
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where j l are spherical Bessel func
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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
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¢¢¢¢¢i = 1 . . .N b¢c i (G)¢
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¢¢¢¢¢c i (G)123g, E self∆V I
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where G c is a free parameter that
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and a matrix form of the Gram-Schmi
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The two sets of equations are coupl
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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
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of the G vectors, and only real ope
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CALL SGEMM(’T’,’N’,M,N b ,2
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ing standard communication librarie
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over processors. All processors sho
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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 138 and 139: 313. T. Ikeda, M. Sprik, K. Terakur
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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