Fireball.
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1 Fireball
2 SIESTA Fireball atomic-like atomic-like Numerical Numerical basis basis set set Precomputed 2 and 3 center integrals Precomputed 2 and 3 center integrals atomic-like atomic-like Numerical Numerical basis basis set set Density and Potential on grid Density and Potential on grid Fast Fast Fourier Fourier Transform Transform to to solve solve Poisson's Poisson's equation equation saved saved to to disk disk before before computation computation Kohn-Sham or McWEDA SCF-loop Kohn-Sham or McWEDA SCF-loop ρρ VVhhaarrttrreeee Kohn-Sham Kohn-Sham is is like like SIESTA SIESTA (on (on grid) grid) more more precise precise calculations calculations McWEDA McWEDA use use atomic atomic charges charges faster, faster, approximative approximative
3 Pseudopotentials "begin" Basis Fuctions pseudo-atomic orbitals solutions with pseudopotential in finite box "create" Interaction integrals Vμνij (r) = < μ (R) V[ ρij ] ν(r+r) > "fireball-prog" System of interest
4 McWEDA Multi-center Weighted Exchangecorrelation Density Approximation 4-centre integrals Vμνij (r,r',r'') r',r'' = < μ (0) V [ ρij ( r', r'') ] ν(r) > r' 0 3-centre integrals Vμνs (r,r') r' = < μ (0) V'[ Charge s (r') ] ν(r) > r'' r'' r i,j... index of atomic orbitals i> iatom, n, L, m > 0 effective charge r s... index of atomic shell Charge(s) Charge( iatom, n, L)... Lowdin, Mulliken...
5 Fireball2Smeagol
6 Fireball SCF Fireball2Smeagol SCF Real Real space space Hamiltonian Hamiltonian Real Real space space Hamiltonian Hamiltonian k-space k-space Hamiltonian(k) Hamiltonian(k) k-space k-space Hamiltonian(k) Hamiltonian(k) Diagonalization Diagonalization Eigenstates Eigenstates (k) (k) Smeagol Smeagol contour contour integration integration Density Density Matrix Matrix (k) (k) Real Real space space Density Density Matrix Matrix Kohn-Sham Kohn-Sham Grid Grid density density Grid Grid potantial potantial Density Density Matrix Matrix (k) (k) Real Real space space Density Density Matrix Matrix McWEDA McWEDA or or CHARGES CHARGES Kohn-Sham Kohn-Sham Grid Grid density density Grid Grid potantial potantial or or McWEDA McWEDA CHARGES CHARGES
7 Basic scheme of Fireball2Smeagol Run PRINCIPAL LAYER directory SCF SCF CHARGES export export leads leads ELECTRODE.left ELECTRODE.right CHARGES.left CHARGES.right EXTENDED MOLECULE directory SCF SCF H.scf Smeagol Smeagol run run
8 BULK calculation fireball.in geometry ansewer.bas element fireball.in x y z cel.lvs lattice input.kpts k-points in x,y,z (for bulk) SCF export leads Output MOLECULE.kpts k-points in x,y (exported leads) Projection H, S, ρ ELECTRODE H_k (μ,ν) S_k (μ,ν) rho_k (μ,ν)
9 ELECTRODE.left μ ν Re H0 or.right Im H0 Re H1 Im H1 Re S0 Im S0 Re S1 Im S1 Re ρ0 Im ρ0 H0 H1 Principal layer Re ρ1 Im ρ1
10 ansewer.bas Extended molecule calculation smeagol.optional LEADS must be in the same order as in BULK calculation cel.lvs input.kpts Output smeagol.cur... current... I(V) curve smeagol.trc... Transmission... T(E)
11 HL ΣL decimation ΣL HL M decimation HM GM Effective hamiltonian: Green's function: Spectral function: HMR HR ΣR Conductance: ΣR
12 Example 1 H22 quantum dot in non-selfconsistent potential
13 smeagol.optional LUMO 12.0 Å 0.7 Å 15.0 Å 5.0 ev HOMO
14 LUMO 12.0 Å 0.7 Å 15.0 Å 5.0 ev HOMO Why you don't see this state? V bias
15 HOMO LUMO 1.0 Å 11.0 Å 12.0 Å 12.5 Å 13.5 Å 0.7 Å G/G Å V bias
16 H2 quantum dot (exlanation)... HOMO bonding... LUMO antibonding T(E) V = 0 ev V = +5 ev tu nn el lin g forbidden by symmetry V = -5 ev tic t12 ~ <s3 H s1 - s2> =0 ba llis t12 ~ <s3 H s1 + s2> 0
17 antibonding 1.0 Å bonding 11.0 Å 12.0 Å 13.5 Å 15.0 Å 0.7 Å G/G Å V bias
18 antibonding 1.0 Å bonding 11.0 Å 12.0 Å 12.5 Å 13.5 Å 0.7 Å G/G Å V bias
19 Example 2 Breaking Gold Chain with extended hopping
20 extended hopping Original basis function Extended basis function 7Å no overlap interaction.optional This is replaced to H and S matrix in apex region before before construction of Green's function
21 T(E) for 1D Gold chain by breaking 3.0 Å G/G0 d d s p
22 function used for smearing f(r) = 1/ (1+ exp (r - r_start / r_scale r_start = 4.0 r_scale = 0.25 t12 = f. H12 + (1-f). H'12 original extended S-matrix as well ))
23 Example 3 Conductance of molecules
24 Au AuT1 AuT3 AuSH S: AuNH2 H Au :S: H AuB1 AuB3 AuBSH AuBNH2 Au :N H
25 Total energy by pulling of molecules weaker bonds covalent bonds
26
27 I-z curve ev
28 Suplementary
29 Instalation of Smeagol into Fireball We will provide makefile to incorporate Smeagol to Fireball new SCF loop for non-equlibirum calculation module_smeagol.f90... global variables Directories of smeagol solve H for new density
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