ab = 2 * sdot(2 * N p D ,A(1),1,B(1),1)END IFCALL GlobalSum[ab]MODULE OverlapCALL SGEMM(’T’,’N’,N b ,N b ,2*N p PW ,2,&& ca(1,1),2*N p PW ,cb(1,1),2*N p PW ,0,smat,N b)IF (p == P0) CALL SDER(N b ,N b ,-1,ca(1,1),2*N p PW ,&& cb(1,1),2*N p PW ,smat,N b)CALL GlobalSum[smat]Similarly, the overlap part of the FNL routine has to be changed <strong>and</strong> the loopsrestricted to the local number of plane waves.MODULE FNLFOR i=1:N p ,MIF (MOD(lp(i),2) == 0) THENFOR j=0:M-1pf = -1**(lp(i+j)/2)FOR k=1:N p PWt = pro(k) * pfer = REAL[eigr(k,iat(i+j))]ei = IMAG[eigr(k,iat(i+j))]scr(k,j) = CMPLX[t * er,t * ei]ENDENDELSEFOR j=0:M-1pf = -1**(lp(i+j)/2+1)FOR k=1:N p PWt = pro(k) * pfer = REAL[eigr(k,iat(i+j))]ei = IMAG[eigr(k,iat(i+j))]scr(k,j) = CMPLX[-t * ei,t * er]ENDENDEND IFIF (p == P0) scr(1,0:M-1) = scr(1,0:M-1)/2CALL SGEMM(’T’,’N’,M,N b ,2*N p PW ,2,&& scr(1,0),2*N p PW ,cr(1,1),2*N p PW ,0,fnl(i,1),N p)ENDCALL GlobalSum[fnl]The routines that need the most changes are the once that include Fourier transforms.Due to the complicated break up of the plane waves a new mapping has tobe introduced. The map mapxy ensures that all pencils occupy contiguous memory87
locations on each processor.MODULE INVFFTscr1(1:N x ,1:N D pencil ) = 0FOR i=1:N p Dscr1(ipg(1,i),mapxy(ipg(2,i),ipg(3,i))) = rhog(i)scr1(img(1,i),mapxy(img(2,i),img(3,i))) = CONJG[rhog(i)]ENDCALL ParallelFFT3D("INV",scr1,scr2)n(1:N p x,1:N y ,1:N z ) = REAL[scr2(1:N p x,1:N y ,1:N z )]MODULE FWFFTscr2(1:N p x,1:N y ,1:N z ) = n(1:N p x,1:N y ,1:N z )CALL ParallelFFT3D("FW",scr1,scr2)FOR i=1:N p Drhog(i) = scr1(ipg(1,i),mapxy(ipg(2,i),ipg(3,i)))ENDDue to the mapping of the y <strong>and</strong> z direction in Fourier space onto a single dimension,input <strong>and</strong> output array of the parallel Fourier transform do have different shapes.MODULE Densityrho(1:Nx,1:N p y ,1:N z ) = 0FOR i=1:N b ,2scr1(1:N x ,1:Npencil PW ) = 0FOR j=1:N p PWscr1(ipg(1,i),mapxy(ipg(2,i),ipg(3,i))) = && c(j,i) + I * c(j,i+1)scr1(img(1,i),mapxy(img(2,i),img(3,i))) = && CONJG[c(j,i) + I * c(j,i+1)]ENDCALL ParallelFFT3D("INV",scr1,scr2)rho(1:Nx,1:N p y ,1:N z ) = rho(1:Nx,1:N p y ,1:N z ) + && REAL[scr2(1:Nx,1:N p y ,1:N z )]**2 + && IMAG[scr2(1:Nx,1:N p y ,1:N z )]**2ENDMODULE VPSIFOR i=1:N b ,2scr1(1:N x ,1:Npencil PW ) = 0FOR j=1:N p PWscr1(ipg(1,i),mapxy(ipg(2,i),ipg(3,i))) = && c(j,i) + I * c(j,i+1)scr1(img(1,i),mapxy(img(2,i),img(3,i))) = && CONJG[c(j,i) + I * c(j,i+1)]88
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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
- Page 38 and 39: from a set of one-particle spin orb
- Page 40 and 41: is used, which represents exactly a
- Page 42 and 43: 2.8.3 Generalized Plane WavesAn ext
- Page 44 and 45: disposable parameters that can be o
- Page 46 and 47: 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.
- Page 54 and 55: ¢££¤¤¢¢¢n tot (G)inv FTn to
- Page 56 and 57: correlation energyΩ ∑E xc = ε x
- Page 58 and 59: 3.4 Total Energy, Gradients, and St
- Page 60 and 61: 3.4.3 Gradient for Nuclear Position
- Page 62 and 63: The local part of the pseudopotenti
- Page 64 and 65: ¢¢¢¢¢i = 1 . . .N b¢c i (G)¢
- Page 66 and 67: ¢¢¢¢¢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
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- Page 78 and 79: Table 3. Relative size of character
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- Page 82 and 83: CALL SGEMM(’T’,’N’,M,N b ,2
- Page 84 and 85: ing standard communication librarie
- Page 86 and 87: over processors. All processors sho
- 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
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- Page 108 and 109: Figure 16. Four patterns of spin de
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- Page 114 and 115: up e.g. in Refs. 132,37,596,597,428
- Page 116 and 117: The eigenvalues of A when multiplie
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- 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
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313. T. Ikeda, M. Sprik, K. Terakur
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384. N. A. Marks, D. R. McKenzie, B
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442. S. Nosé and M. L. Klein, Mol.
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502. L. M. Ramaniah, M. Bernasconi,
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562. F. Shimojo, K. Hoshino, and Y.
- Page 148 and 149:
620. A. Tongraar, K. R. Liedl, and
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682. R. M. Wentzcovitch, Phys. Rev.
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