Fireball Fireball http://www.fireball-dft.org/web/ SIESTA SIESTA - - PowerPoint PPT Presentation

Fireball Fireball

http://www.fireball-dft.org/web/

• atomic-like Numerical basis set
• Density and Potential on grid
• Fast Fourier Transform

to solve Poisson's equation ρ → Vh

a r t r e e

• atomic-like Numerical basis set
• Density and Potential on grid
• Fast Fourier Transform

to solve Poisson's equation ρ → Vh

a r t r e e

SIESTA SIESTA

• atomic-like Numerical basis set
• Precomputed 2 and 3 center integrals

... saved to disk before computation

• Kohn-Sham or McWEDA SCF-loop
• Kohn-Sham is like SIESTA (on grid)

... more precise calculations

• McWEDA use atomic charges

... faster, approximative

• atomic-like Numerical basis set
• Precomputed 2 and 3 center integrals

... saved to disk before computation

• Kohn-Sham or McWEDA SCF-loop
• Kohn-Sham is like SIESTA (on grid)

... more precise calculations

• McWEDA use atomic charges

... faster, approximative

Fireball Fireball

Pseudopotentials Basis Fuctions pseudo-atomic orbitals solutions with pseudopotential in finite box Interaction integrals Vμνij (r) = < μ (R) | V[ ρi j ] | ν(R+r) > "fireball-prog" "create" "begin" System of interest System of interest

McWEDA McWEDA Multi-center Weighted Exchange- correlation Density Approximation

Vμνij ij (r,r',r'' r',r'') = < μ (0) | V [ ρi j

i j ( r', r'')

( r', r'') ] | ν(r) > Vμνs s (r,r' r') = < μ (0) | V'[ Charge s

s (r')

(r') ] | ν(r) > 4-centre integrals 4-centre integrals 3-centre integrals 3-centre integrals i,j ....... index of atomic orbitals |i> ≡ | iatom, n, L, m > effective charge r' r'' r'' r r s ....... index of atomic shell Charge(s) ≡ Charge( iatom, n, L) ... Lowdin, Mulliken ...

Fireball2Smeagol Fireball2Smeagol

Eigenstates (k) Eigenstates (k) Kohn-Sham Grid density Grid potantial Kohn-Sham Grid density Grid potantial McWEDA CHARGES McWEDA CHARGES Real space Hamiltonian Real space Hamiltonian k-space Hamiltonian(k) k-space Hamiltonian(k)

Fireball SCF Fireball SCF

Density Matrix (k) Density Matrix (k) Diagonalization Diagonalization Real space Density Matrix Real space Density Matrix Real space Hamiltonian Real space Hamiltonian k-space Hamiltonian(k) k-space Hamiltonian(k) Density Matrix (k) Density Matrix (k) Smeagol contour integration Smeagol contour integration Real space Density Matrix Real space Density Matrix

Fireball2Smeagol SCF Fireball2Smeagol SCF

Kohn-Sham Grid density Grid potantial Kohn-Sham Grid density Grid potantial McWEDA CHARGES McWEDA CHARGES

• r
• r
• r
• r

SCF SCF export leads export leads SCF SCF Smeagol run Smeagol run

CHARGES CHARGES H.scf H.scf ELECTRODE.left ELECTRODE.right CHARGES.left CHARGES.right

Basic scheme of Fireball2Smeagol Run Basic scheme of Fireball2Smeagol Run

PRINCIPAL LAYER directory PRINCIPAL LAYER directory EXTENDED MOLECULE directory EXTENDED MOLECULE directory

BULK calculation BULK calculation

Projection H, S, ρ k-points in x,y (exported leads) k-points in x,y,z (for bulk) SCF export leads

x y z element

ansewer.bas cel.lvs input.kpts fireball.in fireball.in MOLECULE.kpts geometry lattice Output ELECTRODE H_k (μ,ν) S_k (μ,ν) rho_k (μ,ν)

μ ν Re H0 Im H0 Re H1 Im H1 Re S0 Im S0 Re S1 Im S1 Re ρ0 Im ρ0 Re ρ1 Im ρ1 H1 H0

Principal layer

ELECTRODE.left or .right

Extended molecule calculation Extended molecule calculation

ansewer.bas LEADS must be in the same

• rder as in BULK calculation

cel.lvs input.kpts smeagol.optional Output smeagol.CUR ... current .... I(V) curve smeagol.TRC ... Transmission ... T(E)

HL

M

HM

R

HM → GM HR → ΣR HL → ΣL

decimation → ΣR decimation → ΣL Effective hamiltonian: Effective hamiltonian: Green's function: Green's function: Spectral function: Spectral function: Conductance: Conductance:

Example 1 H2

quantum dot

in non-selfconsistent potential Example 1 H2

quantum dot

in non-selfconsistent potential

12.0 Å 0.7 Å

HOMO LUMO

15.0 Å 5.0 eV

smeagol.optional

12.0 Å 0.7 Å

HOMO LUMO

15.0 Å 5.0 eV

Why you don't see this state? V bias

1.0 Å 11.0 Å 16.0 Å 13.5 Å 0.7 Å 12.0 Å 12.5 Å

HOMO LUMO G/G0 V bias

HOMO bonding LUMO antibonding ... ... t1

2 ~

<s3|H|s1

+ s2>

≠ 0 t1

2 ~

<s3|H|s1

• s2>

= 0 V = 0 eV V = +5 eV V = -5 eV T(E)

• +

+ +

H2 quantum dot (exlanation) H2 quantum dot (exlanation)

t u n n e l l i n g b a l l i s t i c forbidden by symmetry

1.0 Å 11.0 Å 16.0 Å 13.5 Å 12.0 Å 0.7 Å 0.7 Å 15.0 Å

antibonding bonding G/G0 V bias

1.0 Å 11.0 Å 16.0 Å 13.5 Å 12.0 Å 0.7 Å 12.5 Å

antibonding bonding G/G0 V bias

Example 2 Breaking Gold Chain with extended hopping Example 2 Breaking Gold Chain with extended hopping

no overlap This is replaced to H and S matrix in apex region before before construction of Green's function

extended hopping extended hopping

interaction.optional Original basis function Extended basis function 7 Å

d d s p

3.0 Å 3.0 Å

T(E) for 1D Gold chain by breaking G/G0

function used for smearing f(r) = 1/ (1+ exp (r - r_start / r_scale ))

r_start = 4.0 r_scale = 0.25

t t1

2 1 2 = f . H

H1

2 1 2 + (1-f) . H'

H'1

2 1 2

• riginal

extended S-matrix as well

Example 3 Conductance of molecules

AuB1 AuB3 AuBSH AuBNH2 AuT1 AuT3 AuSH AuNH2 S: Au :S: H Au :N H Au H

covalent bonds weaker bonds Total energy by pulling of molecules

eV

I-z curve I-z curve

Suplementary Suplementary

Directories of smeagol solve H for new density new SCF loop for non-equlibirum calculation module_smeagol.f90 ... global variables We will provide makefile to incorporate Smeagol to Fireball

Instalation of Smeagol into Fireball Instalation of Smeagol into Fireball