TOMBO Ver.2 Manual

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Chapter 1 Introduction TOMBO[1, 2], all-electron mixed-basis code, is short for "TOhoku Mixed Basis Orbitals ab initio program". In this thesis, electronic structures of transition metal oxides are calculated by our original all-electron mixed basis code TOMBO developed by Prof. Kaoru Ohno, et al.. 1.1 Short introduction of TOMBO Density funcitonal theroy (DFT) [3] and local density approximation (LDA) [4] have been used in numerous electronic structure calculations and firt-principles molecular dynamics (MD) simulations. To perform those calculations, Kohn–Sham (KS) equation needs to be solved self-consistently such that the input potential is identical to the output potential [4]. The electronic wave function has to be described by appropriate functions to solve the KS equation. Among the plane wave (PW) expansion approach has been applied to the ab-initio molecular dynamics (MD) simulations with reasonably high accuracy [5]. However, it is difficult to treat phenomena (hyperfine interaction, XPS, XANES, etc.) related to core electrons by this method. One problem in generating good pseudo potentials is related to the fact that the core contribution to the exchangecorrelation potential is not simply an additive quantity. Moreover, it is not easy to create efficient pseudopotentials, which require only small number of plane waves. On the other hand, linear combination of atomic orbitals (LCAO) approaches can treat all electrons. However, these methods have an intrinsic problem of incomplete basis set, and therefore there is a problem in applying them in perturbation theory or spectral expansion, which requires a description in the complete Hilbert space. It is also difficult to consider a negative affinity problem by these methods. Related but slightly different problem inherent
1.2 Mixed basis formulation 2 to these methods is a basis set superposition error (BSSE) [6, 7]. There is also some trouble in the Gaussian basis method [8] to describe cusp in the wave-funcion at the nuclear position. In these respects, it is highly desirable to develop new method, which combines the PW expansion technique with the LCAO technique to remove pseudopotentials in the PW expansion methods and to make the basis set complete in the LCAO methods. This is the main idea to introduce the all-electron mixed basis approach. TOMBO [1, 2] is the program package using this approach. TOMBO is the all-electron first-principles method, which can be applicable to both isolated and periodic systems with complete basis set. It is not the overcomplete basis set because only limited number of PWs is used in the computation. The powerfulness of TOMBO is not only based on these features but also based on the fact that it enables us to perform the state-of-the-art calculations such as GW approximation and Bether–Salpeter equation (BSE). Using these methods, TOMBO can treat the problems related to electron correlations, electronic structure around the band gap, excitation spectra, and so forth. This TOMBO Ver.2 is a new version made by unifying preexiting several versions: Molecular dynamics code [9], crystal code [10], T -matrix and GW + BSE code [11], and TOMBO Ver.1 [12]. 1.2 Mixed basis formulation The “mixed-basis” indicates the method using both plane waves and Bloch sums made of atomic orbitals as the basis set. For an isolated atom, it is possible to solves the Kohn–Sham equation very rigorously, because of the system has a spherical symmetry. In this case, the Kohn-Sham wave function is expressed as a product of radial function R jnl (r) and spherical harmonics Y lm (r) as ϕ AO jnlm (r) = R jnl(r)Y lm (ˆr) (1.1) Here, j, n, l, and m are atomic species, principal quantum number, angular momentum quantum number, and magnetic quantum number. In the mixed basis code, the KS wave function is expressed as a linear combination of PWs and AOs (Fig. 1.1), ψ v (r) = √ 1 Ω ∑ c PW G v (G)e i(k+G)·r +∑ j ∑ nlm c AO v ( jnlm)ϕ Bloch (k,r) (1.2) jnlm with ϕ Bloch jnlm (k,r) = eik·R j ∑ R e ik·R ϕ AO jnlm (r − R j − R). (1.3)
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: Table of contents v 3.2.42 Mcheb .
Page 9 and 10: 1.2 Mixed basis formulation 4 Many-
Page 11 and 12: 1.3 All-electron charge density and
Page 13 and 14: 1.3 All-electron charge density and
Page 15 and 16: 1.4 Calculation flow 10 1.4 Calcula
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
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A.1 Build crystal model 64 A.1 Buil
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A.3 *.cell file 66 Fig. A.4 1 st Br
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A.3 *.cell file 68 Step 4 In "CASTE
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