TOMBO Ver.2 Manual

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1.3 All-electron charge density and potential 9 +d sinGr c /G 3 + cosGr c /G 2 }. (1.29) This analytic Fourier coefficients are added to the rest part of the Fourier coefficients of both the Hartree potential ¯ρ rest (G) and the exchange-correlation potential ¯µ xcrest (G) to give an additional contribution to the spherical potential in the jth atomic sphere. That is, this additional contribution to the spherical potential from the three kinds of Fourier coefficients are expressed as: Vj rest (r j ) = ∑ G sinGr j e iG·R j Gr j [ ∑ k ¯V interpo k (G) + 4π Ω ¯ρ rest (G) G 2 + ¯µ xcrest (G) ] . (1.30) Here we note that v interpo j (r j ) defined by Eq.(1.25) is different from the first term in the l.h.d. of Eq.(1.30). The latter includes all the tails of the interpolated Coulomb potential centered at all k ≠ j atoms. This is obvious from the nature of the Fourier transformation. Thus the total effective potential used in the AO-related matrix elements is given by V j (r j ) = Vj trunc (r j ) +Vj rest (r j ). (1.31) All the AO-related matrix elements are calculated by using this spherical potential. If iCheb = 1 is set in INPUT.inp, a Chebyshev polynomial fitting to this spherical potential inside atomic sphere is used to accelerate the computational speed. The contribution from the asymmetric part of the potential is treated separately in a large Fourier space when iAsym = 1 is set in INPUT.inp. Fig. 1.4 How to calculate periodic Hartree potential V H (r) inside non-overlapping atomic spheres?
1.4 Calculation flow 10 1.4 Calculation flow Flowchart of the first-principles molecular dynamics (MD) is shown in Fig. 1.5. Set initial atomic positions ❄ Assume initial charge density ❄ Initialize coefficients C λ i ✲ ❄ Calculate charge density ❄ Mix the charge density with that of the previous step Calculate the KS potential ❄ Calculate matrix ❄ elements ❄ Update Ci λ according to matrix diagonalization or steepest-descent method ❄ NO ✘✘✘✘✘✘✘ ✛ ✘❳❳❳❳❳❳❳❳❳❳❳❳❳❳❳❳❳❳ ✘ If |E new − E old | < precLDA ✘✘✘✘✘✘✘✘✘ YES ❄ Calculate forces on atoms ❄ Update atomic positions Check self-consistency Fig. 1.5 Flowchart of the first-principles MD. The convergence of the electronic states is checked by the difference between the total energies at the present and previous steps. If convergence is achieved, the atomic positions are updated by using the calculated force.
Page 1 and 2: TOMBO Ver.2 Manual for LDA and GW C
Page 3 and 4: Table of contents 1 Introduction 1
Page 5 and 6: Table of contents v 3.2.42 Mcheb .
Page 7 and 8: 1.2 Mixed basis formulation 2 to th
Page 9 and 10: 1.2 Mixed basis formulation 4 Many-
Page 11 and 12: 1.3 All-electron charge density and
Page 13: 1.3 All-electron charge density and
Page 17 and 18: 1.5 TDDFT dynamics simulation 12 of
Page 19 and 20: 2.2 The Green function 14 2.2 The G
Page 21 and 22: 2.4 Hedin’s equations (GWΓ metho
Page 23 and 24: 2.5 The GW approximation 18 The GW
Page 25 and 26: 2.6 One-shot GW approximation 20 or
Page 27 and 28: 3.1 COORDINATES.inp 22 3.1 COORDINA
Page 29 and 30: 3.1 COORDINATES.inp 24 10. The Atom
Page 31 and 32: 3.2 INPUT.inp 26 3.1.1 rct "XX_rct"
Page 33 and 34: 3.2 INPUT.inp 28 An example of INPU
Page 35 and 36: 3.2 INPUT.inp 30 3.2.5 Ulevel, Llev
Page 37 and 38: 3.2 INPUT.inp 32 calculation of the
Page 39 and 40: 3.2 INPUT.inp 34 Whether the subtra
Page 41 and 42: 3.2 INPUT.inp 36 3.2.30 smixSCF Cha
Page 43 and 44: 3.3 KPOINT.inp 38 3.2.42 Mcheb Numb
Page 45 and 46: 3.4 QPOINT.inp 40 10, line 15, and
Page 47 and 48: 3.5 SPOINT.inp 42 Table 3.9 QPOINT.
Page 49 and 50: Chapter 4 Output Files Note: 1. In
Page 51 and 52: 4.8 WaveF_HOMO-1.cube, WaveF_HOMO-1
Page 53 and 54: 4.9 GWA.out 48 Table 4.2 GWA.out of
Page 55 and 56: Chapter 5 Examples 5.1 LDA calculat
Page 57 and 58: 5.1 LDA calculation of isolated dim
Page 59 and 60: 5.2 Molecular Dynamics 54 Fig. 5.4
Page 61 and 62: 5.4 LDA calculation of rutile TiO 2
Page 63 and 64: 5.4 LDA calculation of rutile TiO 2
Page 65 and 66:
5.5 Wave function calculation of ru
Page 67 and 68:
References 62 [12] M. S. Bahrany, M
Page 69 and 70:
A.1 Build crystal model 64 A.1 Buil
Page 71 and 72:
A.3 *.cell file 66 Fig. A.4 1 st Br
Page 73 and 74:
A.3 *.cell file 68 Step 4 In "CASTE
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