Fireball Fireball http://www.fireball-dft.org/web/
SIESTA SIESTA Fireball Fireball ● atomic-like Numerical basis set ● atomic-like Numerical basis set ● atomic-like Numerical basis set ● atomic-like Numerical basis set ● Precomputed 2 and 3 center integrals ● Precomputed 2 and 3 center integrals ● Density and Potential on grid ● Density and Potential on grid ... saved to disk before computation ... saved to disk before computation ● Fast Fourier Transform ● Fast Fourier Transform ● Kohn-Sham or McWEDA SCF-loop ● Kohn-Sham or McWEDA SCF-loop to solve Poisson's equation to solve Poisson's equation ● Kohn-Sham is like SIESTA (on grid) ● Kohn-Sham is like SIESTA (on grid) ρ → V h ρ → V h ... more precise calculations ... more precise calculations a r t r e e a r t r e e ● McWEDA use atomic charges ● McWEDA use atomic charges ... faster, approximative ... faster, approximative
Pseudopotentials "begin" Basis Fuctions pseudo- atomic orbitals solutions with pseudopotential in finite box "create" Interaction integrals Vμνij (r) = < μ (R) | V[ ρ i j ] | ν(R+r) > "fireball-prog" System of interest System of interest
McWEDA McWEDA M ulti-center W eighted E xchange- correlation D ensity A pproximation 4-centre integrals 4-centre integrals 3-centre integrals 3-centre integrals Vμν ij ij (r, r',r'' r',r'' ) Vμν s s (r, r' r' ) = = < μ (0) | V [ ρ i j ( r', r'') ] | ν(r) > i j ( r', r'') < μ (0) | V' [ Charge s (r') ] | ν(r) > s (r') r'' r' effective r'' charge r 0 0 r i,j ....... index of atomic orbitals s ....... index of atomic shell |i> ≡ | iatom, n, L, m > Charge(s) ≡ Charge( iatom, n, L) ... Lowdin, Mulliken ...
Fireball2Smeagol Fireball2Smeagol
Fireball2Smeagol SCF Fireball2Smeagol SCF Fireball SCF Fireball SCF Real space Real space Hamiltonian Hamiltonian Real space Real space k-space Hamiltonian k-space Hamiltonian Hamiltonian(k) Hamiltonian(k) k-space k-space Hamiltonian(k) Hamiltonian(k) Diagonalization Smeagol Diagonalization Smeagol contour contour integration integration Eigenstates (k) Eigenstates (k) Density Matrix (k) Density Matrix (k) Density Matrix (k) Density Matrix (k) Real space Real space Density Matrix Density Matrix Real space Real space Density Matrix Density Matrix McWEDA Kohn-Sham McWEDA Kohn-Sham or or CHARGES Grid density CHARGES Grid density Grid potantial Grid potantial McWEDA McWEDA Kohn-Sham Kohn-Sham or or CHARGES CHARGES Grid density Grid density Grid potantial Grid potantial
Basic scheme of Fireball2Smeagol Run Basic scheme of Fireball2Smeagol Run PRINCIPAL LAYER EXTENDED MOLECULE PRINCIPAL LAYER EXTENDED MOLECULE directory directory directory directory SCF SCF SCF SCF H.scf H.scf CHARGES CHARGES Smeagol run export leads export leads Smeagol run ELECTRODE.left ELECTRODE.right CHARGES.left CHARGES.right
BULK calculation BULK calculation fireball.in fireball.in geometry ansewer.bas x y z element lattice cel.lvs export SCF k-points in x,y,z (for bulk) input.kpts leads Output Projection ELECTRODE k-points in x,y (exported leads) H, S, ρ MOLECULE.kpts H_k (μ,ν) S_k (μ,ν) rho_k (μ,ν)
ELECTRODE.left or .right μ ν Re H 0 Im H 0 Re H 1 Im H 1 Re S 0 Im S 0 Re S 1 Im S 1 Re ρ 0 Im ρ 0 Re ρ 1 Im ρ 1 H 0 H 1 Principal layer
Extended molecule smeagol.optional Extended molecule calculation calculation ansewer.bas LEADS must be in the same order as in BULK calculation cel.lvs Output smeagol.CUR ... current .... I(V) curve input.kpts smeagol.TRC ... Transmission ... T(E)
decimation → Σ L H L → Σ L H L M decimation → Σ R H M → G M Effective Effective hamiltonian: hamiltonian: Green's Green's function: function: Spectral Spectral function : function : H R → Σ R H M R Conductance: Conductance:
Example 1 Example 1 H 2 quantum dot H 2 quantum dot in non-selfconsistent in non-selfconsistent potential potential
smeagol.optional LUMO HOMO 12.0 Å 0.7 Å 15.0 Å 5.0 eV
LUMO HOMO 12.0 Å 0.7 Å 15.0 Å 5.0 eV Why you don't see this state? V bias
LUMO HOMO 1.0 Å 11.0 Å 12.0 Å 12.5 Å 13.5 Å 0.7 Å 16.0 Å G/G 0 V bias
H2 quantum dot (exlanation) H2 quantum dot (exlanation) ... ... T(E) HOMO LUMO bonding antibonding V = 0 eV + + - + V = +5 eV t 1 2 ~ t 1 2 ~ <s 3 |H|s 1 + s 2 > <s 3 |H|s 1 - s 2 > ≠ 0 = 0 V = -5 eV forbidden g c n by symmetry i i t l l s e i l n l a n b u t
antibonding 1.0 Å bonding 11.0 Å 12.0 Å 13.5 Å 0.7 Å 0.7 Å 15.0 Å 16.0 Å G/G 0 V bias
antibonding 1.0 Å bonding 11.0 Å 12.0 Å 12.5 Å 13.5 Å 0.7 Å 16.0 Å G/G 0 V bias
Example 2 Example 2 Breaking Gold Chain Breaking Gold Chain with extended with extended hopping hopping
extended hopping extended hopping Extended basis function Original basis function 7 Å This is replaced to H and S matrix no overlap in apex region before before construction of Green's function interaction.optional
T(E) for 1D Gold chain by breaking 3.0 Å 3.0 Å d G/G 0 d p s
function used for smearing f(r) = 1/ (1+ exp (r - r_start / r_scale )) r_start = 4.0 r_scale = 0.25 t t 1 2 = f . H H 1 2 + (1-f) . H' H' 1 2 1 1 1 2 2 2 original extended S-matrix as well
Example 3 Conductance of molecules
Au S: AuT1 AuT3 AuSH AuNH2 H Au :S: H H Au :N AuB1 AuB3 AuBSH AuBNH2
Total energy by pulling of molecules weaker bonds covalent bonds
I-z curve I-z curve eV
Suplementary Suplementary
Instalation of Smeagol into Fireball 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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