Quantum Simulations on Nano-Structured Materials Takahisa Ohno - - PowerPoint PPT Presentation

Quantum Simulations on Nano-Structured Materials

Takahisa Ohno Takahisa Ohno Computational Materials Science Center (CMSC) Computational Materials Science Center (CMSC) National Institute for Materials Science (NIMS) National Institute for Materials Science (NIMS)

Acknowledgement Acknowledgement

• Dr. J. Nara, Dr. T. Miyazaki, Dr. H. Kino, Dr. H. Kondo,
• Dr. J. Nara, Dr. T. Miyazaki, Dr. H. Kino, Dr. H. Kondo,
• Dr. Y. Tateyama, Dr. H. Oyama (NIMS)
• Dr. Y. Tateyama, Dr. H. Oyama (NIMS)
• Prof. T. Ozaki (JAIST) , Prof. G.T. Wang
• Prof. T. Ozaki (JAIST) , Prof. G.T. Wang
• Prof. M Gillan, Dr. D, Bowler (UCL)
• Prof. M Gillan, Dr. D, Bowler (UCL)

Japan-Germany Joint Workshop 2009 “Nanoelectonics”

• Jan. 21-23, 2009, Kyoto

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2

Surface dynamics (DFT/ Hybrid) Surface dynamics (DFT/ Hybrid)

(i) Diffusion of (i) Diffusion of F on Si(111) F on Si(111) : Si Si-

• F complex diffusion

F complex diffusion (ii) Adsorption of (ii) Adsorption of O2 on Si(001) O2 on Si(001) : : Energy dissipation Energy dissipation (iii) Atomic structure of AFM tip apex (iii) Atomic structure of AFM tip apex

Nano-structured materials

To understand their formation processes & properties/functions at the atomistic level, FP simulation methods based on DFT are an ideal tool.

Transport through molecular junctions (NEGF) Transport through molecular junctions (NEGF)

(i) p (i) p-

• stacked systems: styrene wires on H/Si(001)

stacked systems: styrene wires on H/Si(001) (ii) Molecular sensors: (ii) Molecular sensors: iron iron-

• porphyrin

porphyrin (iii) Molecular switch: biphenyl dithiol

Photochemical reaction (RTP Photochemical reaction (RTP-

• TDDFT)

TDDFT)

(i) Photoisomerization: azobenzene (i) Photoisomerization: azobenzene

Redox reaction Redox reaction

(i) RuO4: (i) RuO4:

RuO RuO4-

• (aq) + H

(aq) + H2O(l) + e O(l) + e- --

• -> [RuO

> [RuO3(OH) (OH)2]2-

• (aq)

(aq)

Large nano Large nano-

• structured systems

structured systems

(i) PW electronic structure codes (i) PW electronic structure codes : : shallow impurity in Si shallow impurity in Si (ii) Linear scaling algorithms: (ii) Linear scaling algorithms: (a) Surface nano (a) Surface nano-

• structures;

structures; Ge cluster on Si(001) Ge cluster on Si(001) (b) Bio (b) Bio-

• molecules:

molecules: DNA DNA

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Diffusion of F on Si(111) Diffusion of F on Si(111)

After 90 sec. After 90 sec.

adsorbed F adsorbed F Si adatom Si adatom @300 @300℃

The F diffusion is assisted by excess Si atoms. The F diffusion is assisted by excess Si atoms. Surface diffusion which depends on diffusing Si density has not been observed so far. Surface diffusion which depends on diffusing Si density has not been observed so far. The diffusion mechanism in atomic scale is not clarified. The diffusion mechanism in atomic scale is not clarified.

• 10
• 9
• 8
• 7
• 6
• 5
• 4

18 19 20 21 22 23 24

1/kT

F蒸着表面 F+Si 蒸着表面

lnκ

• 10
• 9
• 8
• 7
• 6
• 5
• 4

18 19 20 21 22 23 24

1/kT

F F+Si

lnκ

F： ΘF= 0.012ML, T = 235～350℃ F+Si：ΘF= 0.013ML, ΘSi=0.005ML, T = 258～325℃

Ea=1.3 eV Ea=1.3 eV The deposition of excess Si adsatoms The deposition of excess Si adsatoms

• n Si(111) enhances the diffusion !
• n Si(111) enhances the diffusion !

F diffusion on Si(111) F diffusion on Si(111)-

• (7x7)

(7x7)

Si(001) Si(001) Si(111) Si(111) n.n. Si n.n. Si-

• Si

Si Ediff Ediff 3.8 A 3.8 A 4.5 A 4.5 A 1.8 eV 1.8 eV 1.3 eV 1.3 eV done by Prof. Sakurai’s group done by Prof. Sakurai’s group

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Diffusion of F on Si(111) Diffusion of F on Si(111)

F Si F Si Si

Ea=2.32 eV Ea=2.32 eV (1) Single F atom hopping (1) Single F atom hopping

Si Si F Si F

Ea=1.34 eV Ea=1.34 eV (3) Si (3) Si-

• F complex diffusion

F complex diffusion

Si F F Si

Ea > 2eV Ea > 2eV (2) Si assisted F diffusion (2) Si assisted F diffusion

F Si

Top view Top view Side view Side view

Si Si

Top view Top view Side view Side view

Adsorbed F Adsorbed F Adsorbed Si Adsorbed Si SiF complex diffusion model can explain experiments. SiF complex diffusion model can explain experiments.

Si(111) Si(111)-

• (5x5)

(5x5)

• Y. Fujikawa, et. al. : J. Chem. Phys. 129, 234710 (2008)

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5 +0.03 +0.41 +0.52 +1.18 +0.32 +0.27 +0.36 +0.49 +0.41 SiF (単位: eV)

• ：F ●：excessSi ●: adatom (complex) ●: adatom ●：restatom

c a b d e f g h i

+1.34 +0.56 +1.10 +0.82 +0.43 +1.04 +0.70 +0.87 Energy (eV)

0.0 0.5 1.0 1.5

c a b d e f g h i

Diffusion of Si Diffusion of Si-

• F complex

F complex

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O2 Si Si Si Si [001] [001]

Back Back-

• bond oxidation

bond oxidation

FP/TB/MM hybrid calculations FP/TB/MM hybrid calculations

FP FP TB TB MM MM 65 atomic layers atomic layers

ソース ソース ドレイン ドレイン ゲート ゲート Si Si基板 基板

Si/SiO Si/SiO2

Adsorption of O2 on Si(111): hybrid method Adsorption of O2 on Si(111): hybrid method

How the adsorption/reaction energy is used for the formation of the final adsorption geometry. How the adsorption/reaction energy is used for the formation of the final adsorption geometry. It is important to deal with the dissipation It is important to deal with the dissipation

• f the released energy properly.
• f the released energy properly.
• N. Takahashi, T. Ohno: Surf. Sci. 602, 768 (2008)

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7 ■AFM

AFM

SEM SEM image image (〜μm)

Hybrid calculations Hybrid calculations

FP FP TB TB MM MM

(〜10nm)

~5000 ~5000 Si Si atoms atoms

A B

Atomic protrusion Atomic protrusion

AFM tip apex: hybrid method AFM tip apex: hybrid method

Nakamura, Takahashi, Uda, and Ohno: PRL 97, 086103 (2006) Nakamura, Takahashi, Uda, and Ohno: PRL 97, 086103 (2006)

@300K @300K How does the atomic protrusion exists at the AFT tip apex? How does the atomic protrusion exists at the AFT tip apex? AFM performance depends on the atomic structure of the tip. AFM performance depends on the atomic structure of the tip. By the present techniques, the atomic geometry of the very end By the present techniques, the atomic geometry of the very end

• f the tip is practically impossible to control.
• f the tip is practically impossible to control.

But, we can obtain AFM images with atomic resolution. But, we can obtain AFM images with atomic resolution.

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2 nm

Concentration Concentration～10 1020

20/cm

/cm3 ■ As shallow impurity in Si

As shallow impurity in Si

As As atom atom Si10647As

16.2 Tflop/s (50%)

Theoretical peak performance

Wavefunction Wavefunction PHASE performance on ES PHASE performance on ES

*SC07: Gordon Bell prize finalist *SC07: Gordon Bell prize finalist (2007/11/14) (2007/11/14)

Source Drai n Gate e-e-e- Donor levels e-

Shallow Impurity in Si Shallow Impurity in Si

Conventional PW electronic structure code parallelized for Earth Simulator

Impurity level

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Linear Linear-

• Scaling DFT Calculations

Scaling DFT Calculations Order Order-

• N code: CONQUEST

N code: CONQUEST

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10 Bulk Si (4096 Bulk Si (4096-

• 12288 atoms)

12288 atoms)

Numer of atoms Numer of atoms 14000 14000 CPU time CPU time (sec) (sec) 300.0 300.0

First First-

• Principles Order

Principles Order-

• N methods

N methods

First First-

• Principles Order

Principles Order-

• N methods

N methods

Ge clusters on Si(001) Ge clusters on Si(001) Bio Bio-

• materials

materials Scaling linearly with N Scaling linearly with N CONQUEST CONQUEST： density matrix density matrix

In collaboration with Prof. Gillan (UCL) In collaboration with Prof. Gillan (UCL) limited limited β-version released on version released on May 16th, 2007 May 16th, 2007

DNA DNA

Application to nano Application to nano-

• materials

materials Quantum Quantum-

• dots

dots Bio Bio-materials materials

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Density matrix minimization method Density matrix minimization method

Kohn Kohn-

• sham density matrix:

sham density matrix: ρ(r,r’) = (r,r’) = Σν fν ψν*(r) (r) ψν(r’) (r’) (ψν(r) : Kohn (r) : Kohn-

• Sham eigen

Sham eigen-

• function,

function, fν : occupation number) : occupation number) Locality of density matrix: Locality of density matrix: ρ(r,r’)→0 for |r (r,r’)→0 for |r-

• r’|→∞

r’|→∞ Optimisation of Optimisation of ρ, ρ, using McWeeny purification using McWeeny purification + LNV (Lee, Nunes, Vanderbilt) method + LNV (Lee, Nunes, Vanderbilt) method

• Idempotency

Idempotency ρ2= ρ ρ

• ρ = 3σ

= 3σ2−2σ −2σ3 (σ: σ: auxiliary density matrix) auxiliary density matrix)

We express the density matrix using local orbitals We express the density matrix using local orbitals φiα(r) (r)

ρ(r,r’) = (r,r’) = Σiα, j

, jβ φiα*(r)

(r) Kiα, j

, jβ φjβ (r’)

(r’) support functions support functions φiα(r) : centered on atom j with the orbital (r) : centered on atom j with the orbital α

Two types of basis sets are provided for Two types of basis sets are provided for φi

iα(r) .

(r) .

Blip functions: Blip functions: accurate accurate

B-

• splines on 3D regular grids around each atom

splines on 3D regular grids around each atom

PAOs (pseudo atomic orbital) : PAOs (pseudo atomic orbital) : efficient efficient

Common with Siesta or Plato Common with Siesta or Plato

O(N) DFT code CONQUEST (I) ) DFT code CONQUEST (I)

Blip functions Blip functions

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O(N) DFT code CONQUEST (II) ) DFT code CONQUEST (II)

Efficient on parallel machines Efficient on parallel machines

Vector parallel, RISC

Vector parallel, RISC-

• based, PC clusters

based, PC clusters

Diagonalisation with ScaLapack (not O(N))

Diagonalisation with ScaLapack (not O(N))

CONQUEST can employ various methods having different accuracies. CONQUEST can employ various methods having different accuracies. Full DFT:

Full DFT:

• ptimization of support functions is performed.
• ptimization of support functions is performed.

SCF and density matrix minimization are also performed.

SCF and density matrix minimization are also performed.

SC

SC-

• AITB (self

AITB (self-

• consistent ab initio TB):

consistent ab initio TB):

Fixed support functions (ex. single

Fixed support functions (ex. single-

• ζ)

)

NSC

NSC-

• AITB (non

AITB (non-

• self

self-

• consistent ab

consistent ab-

• initio TB):

initio TB):

Harris

Harris-

• Foulkes energy functional + superposition of atomic charge

Foulkes energy functional + superposition of atomic charge

(Semi

(Semi-

• empirical TB) by DensEl

empirical TB) by DensEl

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The Energetics of Hut The Energetics of Hut-

• Cluster Self

Cluster Self-

• Assembly

Assembly in Ge/Si(001) using CONQUEST in Ge/Si(001) using CONQUEST

• T. Miyazaki, D. R. Bowler, M. J. Gillan, and T. Ohno
• T. Miyazaki, D. R. Bowler, M. J. Gillan, and T. Ohno
• J. Phys. Soc. Jpn, 77, 123706 (2008)
• J. Phys. Soc. Jpn, 77, 123706 (2008)

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2 x N 2 x N M x N M x N “hut “hut” cluster cluster

Ge/Si(001) Ge/Si(001)

Lattice mismatch Lattice mismatch （4% 4%）

Relaxation of strain

Relaxation of strain

SK

SK-

• growth (Stranski

growth (Stranski-

• Krastanov growth)

Krastanov growth) 2D => 3D at ~3 ML coverage 2D => 3D at ~3 ML coverage

No dislocations

No dislocations

Nano Nano-

• strucure

strucure

~10nm x ~10nm ~10nm x ~10nm

• I. Goldfarb et al., PRL 78, 3959 (1997))
• I. Goldfarb et al., PRL 78, 3959 (1997))

“dome”

• G. Medeiros
• G. Medeiros-
• Ribeiro et al.,

Ribeiro et al., Science 279, 353 (1998) Science 279, 353 (1998)

2D 2D 2D 2D 3D 3D Hetero Hetero-

• epatixy system

epatixy system

Ge 3D hut cluster on Si(001) Ge 3D hut cluster on Si(001)

Self Self-

• assembled quantum dots

assembled quantum dots

Pyramid Pyramid-

• like

like shape

shape Four (105) Four (105) facets facets

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Eform

form= E

= Erelax

relax+ E

+ Esurf

surf+ E

+ Eedge

edge

• Erelax

relax : relaxation by the 3D structure

: relaxation by the 3D structure (calculated by Finite Element method.) (calculated by Finite Element method.)

• Esurf

surf: surface energy, usually unfavorable for

: surface energy, usually unfavorable for 3D structure (calculated by DFT) 3D structure (calculated by DFT)

• Eedge

edge: energy of the edges (difficult to calculate.

: energy of the edges (difficult to calculate. A parameter in this work.) A parameter in this work.)

• O. E. Shklaev et al., PRL 94, 176102 (2005)
• O. E. Shklaev et al., PRL 94, 176102 (2005)

Ge 3D hut cluster on Si(001) Ge 3D hut cluster on Si(001)

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Ge/Si (001) Ge/Si (001) Ge hut cluster Ge hut cluster ~ 200 Å ~ 200 Å ~ 20 Å ~ 20 Å To determine the stability and size of the To determine the stability and size of the hut cluster, hut cluster,

• effects of boundary, ridge, top

effects of boundary, ridge, top

• effect of distortion from {105} planes

effect of distortion from {105} planes

• effect of the finite surface area

effect of the finite surface area may be also important. may be also important.

“DFT DFT calculations

calculations on the entire hut

• n the entire hut

cluster systems are desirable. “ cluster systems are desirable. “

• rder
• rder-
• N method

N method

Si(001) Si(001)表面上 表面上Ge Geクラスター： クラスター： 構造安定性 構造安定性

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Etot Etot-a curve by a curve by NSC NSC-

• AITB or SC

AITB or SC-AITB AITB (minimal basis set calculations ) (minimal basis set calculations )

Full DFT using Full DFT using blip functions blip functions 1) 1) Etot Etot-

• Rreg

Rreg 2) 2) Etot Etot-

• Ecutoff

Ecutoff (blip (blip-

• grid spacing)

grid spacing)

Results: bulk Ge Results: bulk Ge -

• calculation condition

calculation condition -

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Strained Ge(105) Strained Ge(105)

Bulk Ge

Bulk Ge

Strained bulk Ge

Strained bulk Ge

Strained Ge(105)

Strained Ge(105) Ge hut cluster on Si(001) Ge hut cluster on Si(001) Ge(2xN) < Ge(2xN) <-

• > Ge hut cluster

> Ge hut cluster

semiempirical TB (DensEl) semiempirical TB (DensEl) NSC NSC-

• AITB

AITB SC SC-

• AITB (CONQUEST)

AITB (CONQUEST) Full DFT Full DFT planewave (STATE or V ASP) planewave (STATE or V ASP) semiempirical TB semiempirical TB NSC NSC-

• AITB

AITB (SC (SC-AITB) AITB)

“Accuracy and calculation conditions of various localized orbital methods” “Initial atomic positions are made by semiempirical TB calculations.” “modelling of Ge(105) surfaces”

Method: strategy for Ge/Si(001) Method: strategy for Ge/Si(001)

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strained Ge(105): accuracy of various methods strained Ge(105): accuracy of various methods

DensEl DensEl CONQUEST CONQUEST STATE STATE

Method Method Surface energy Surface energy (meV/Å (meV/Å2) semi semi-

• empirical

empirical NSC NSC-

• AITB

AITB SC SC-

• AITB

AITB full DFT( blip, full DFT( blip, Rreg

reg=3.85 Å)

=3.85 Å) full DFT( blip, full DFT( blip, Rreg

reg=4.23 Å)

=4.23 Å) planewave planewave 74.3 74.3 76.5 76.5 81.5 81.5 83.5 83.5 74.8 74.8 70.0 70.0

Surface energy of type Surface energy of type-

• I strained Ge(105) surface

I strained Ge(105) surface

NSC NSC-

• AITB is reasonably accurate.

AITB is reasonably accurate. Reliable calculation conditions have been determined. Reliable calculation conditions have been determined. (for surface energy, we need large (for surface energy, we need large Rreg

reg)

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22746 atoms 22746 atoms 174 x 174 x 47.5 Å 174 x 174 x 47.5 Å3 Earth Simulator 512 proc. (64 nodes) Earth Simulator 512 proc. (64 nodes)

Ge ‘hut’ cluster on Si(001) Ge ‘hut’ cluster on Si(001) -

• system size

system size -

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28x28on32x32: 28x28on32x32: 22747 atoms 22747 atoms Total Energy Total Energy Force

Ge ‘hut’ cluster on Si(001) Ge ‘hut’ cluster on Si(001)： NSC NSC-

• AITB

AITB

Structure optimization

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Stability: Ge/Si(001) Stability: Ge/Si(001)-

• 2xN vs 3D hut cluster

2xN vs 3D hut cluster 2D: 2xN 3D: hut cluster εGe

Ge= (E

= (Etot

tot-E

Esub

sub)/(# of Ge hut atoms)

)/(# of Ge hut atoms)

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• Accuracy and calculation condition for order

Accuracy and calculation condition for order-

• N calculations on

N calculations on Ge/Si(001) have been investigated by the study on the strained Ge/Si(001) have been investigated by the study on the strained Ge(105) surfaces. Ge(105) surfaces.

• Order

Order-

• N DFT calculations with structure optimization are now

N DFT calculations with structure optimization are now possible for Ge/Si(001) 23,000 possible for Ge/Si(001) 23,000-

• atom systems. (within NSC

atom systems. (within NSC-

• AITB

AITB level) level)

• Ge hut 3D islands are more stable than Ge 2xN structure when the

Ge hut 3D islands are more stable than Ge 2xN structure when the coverage of Ge is more than 3. coverage of Ge is more than 3.

• Our results suggest that the initial emergence of 3D Ge hut clusters

Our results suggest that the initial emergence of 3D Ge hut clusters is determinde mainly by energetics, and that kinetic effects do not is determinde mainly by energetics, and that kinetic effects do not need to be considered. need to be considered.

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O(N) DFT calculations on DNA systems O(N) DFT calculations on DNA systems using CONQUEST using CONQUEST

1. 1. Pseudo Atomic Orbitals Pseudo Atomic Orbitals 2. 2. Exchange Exchange-correlation functional correlation functional 3. 3. O(N) method by Density matrix minimisation O(N) method by Density matrix minimisation

• single DNA base

single DNA base

• DNA base pairs

DNA base pairs

• DNA + water molecules

DNA + water molecules

• T. Otsuka, T. Miyazaki, T. Ohno, D. R. Bowler and M. J. Gillan,
• T. Otsuka, T. Miyazaki, T. Ohno, D. R. Bowler and M. J. Gillan,
• J. Phys.: Cond. Matter, 20, 294201 (2008)
• J. Phys.: Cond. Matter, 20, 294201 (2008)

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Bio Bio-

• materials: DNA

materials: DNA

DNA DNA

adenine adenine thymine thymine cytosine cytosine guanine guanine

Base pairs Base pairs A-

• T pair

T pair G-

• C pair

C pair Bio Bio-

• materials: Proteins, DNA, et. al.

materials: Proteins, DNA, et. al. One of the important targets One of the important targets

• f O(N) calculations
• f O(N) calculations

Can describe base pairs properly? Can describe base pairs properly? Parameterized interaction model Parameterized interaction model

Transferability for different environments ? Transferability for different environments ?

Interaction between bio Interaction between bio-

• and inorganic materials

and inorganic materials

Quantum mechanical modeling is required Quantum mechanical modeling is required

Pseudo Atomic Orbitals Pseudo Atomic Orbitals SZ: single SZ: single-

• ζ

DZP DZP: double : double-

• ζ with polarization function

with polarization function Exchange Exchange-

• correlation functional

correlation functional LDA, LDA, GGA GGA-

• PBE

PBE O(N) method by Density matrix minimization O(N) method by Density matrix minimization single DNA base single DNA base DNA base pairs DNA base pairs DNA + water molecules DNA + water molecules

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• 0.030
• 0.020
• 0.010

0.000 0.010 0.020 0.030 0.040 0.050 N 1 C 2 C 2 N 3 N 3 C 4 C 4 N 1 C 4 C 5 C 5 C 6 C 6 N 1 C 5 N 7 N 7 C 8 C 8 N 9 N 9 C 6 CQ LDA (300meV) CQ PBE (100meV) VASP G03 SVWN5 G03 PBE G03 B3LYP G03 HF-MP2

0.00 0.50 1.00 1.50 2.00 2.50 CQ LDA (300meV) CQ PBE (100meV) VASP G03 SVWN5 G03 PBE G03 B3LYP G03 HF- MP2 A C G T total 0.000 0.005 0.010 0.015 0.020 0.025 CQ LDA (300meV) CQ PBE (100meV) VASP G03 SVWN5 G03 PBE G03 B3LYP G03 HF- MP2 A C G T total

Difference Difference of structure

• f structure between theor

between theory y and experiment and experiment. .

Difference ( Difference (Å) Å) Difference (degree Difference (degree) )

Bond distance Bond angle

Difference Difference of

• f structure

structure for Adenine for Adenine molecule molecule between theor between theory y and experiment. and experiment.

Bond distance Bond angle

• 4.0
• 3.0
• 2.0
• 1.0

0.0 1.0 2.0 3.0 C 2 N 3 C 4 N 3 C 2 N 1 C 2 N 1 C 6 N 1 C 6 C 5 N 1 C 6 N 9 C 5 C 6 N 9 C 6 C 5 C 4 C 6 C 5 N 7 C 4 C 5 N 7 N 3 C 4 C 5 N 3 C 4 N 1 C 5 C 4 N 1 C 6 N 9 C 8 N 9 C 8 N 7 C 5 N 7 C 8 CQ LDA (300meV) CQ PBE (100meV) VASP G03 SVWN5 G03 PBE G03 B3LYP G03 HF-MP2

Difference (Å) Difference (degree)

Structure optimization: single DNA bases (A, C, G, T) Structure optimization: single DNA bases (A, C, G, T)

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A B

Hydrogen bond distances of A-T pair by various methods 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

300 meV 100 meV 50 meV 300 meV 100 meV 50 meV DZP DZP PW Hamann PP 6-31G(d,p) 6-31++G(d,p) cc-pVDZ cc-pVDZ cc-pVDZ cc-pVDZ LDA PBE BLYP BLYP SVWN5 PBE B3LYP HF-MP2 CONQUEST Jeep G98 G03

methods distance (angstroms)

A: H(A)-O(T) B: N(A)-H(T) C: H(A)-O(T)

Adenine Thymine

Siesta PAOs : DZP Siesta PAOs : DZP diagonalisation diagonalisation

C

A-

• T pair

T pair

accurate efficient

CQ on DNA systems: base pairs CQ on DNA systems: base pairs

• PBE results → close to MP2 results

PBE results → close to MP2 results

Hydrogen bond distances of A Hydrogen bond distances of A-

• T pair

T pair

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CQ on DNA systems: base pairs CQ on DNA systems: base pairs

Hydrogen bond distances of G-C pair by various methods 0.0 0.5 1.0 1.5 2.0 2.5

300 meV 100 meV 50 meV 300 meV 100 meV 50 meV DZP DZP PW Hamann PP 6-31G(d,p) 6-31++G(d,p) cc-pVDZ cc-pVDZ cc-pVDZ cc-pVDZ LDA PBE BLYP BLYP SVWN5 PBE B3LYP HF-MP2 CONQUEST Jeep G98 G03

methods distance (angstroms)

A: O(G)-H(C) B: H(G)-N(C) C: H(G)-O(C)

A B C

Guanine Cytosine

Siesta PAOs : DZP Siesta PAOs : DZP diagonalisation diagonalisation

G-

• C pair

C pair

• PBE results → close to MP2 results

PBE results → close to MP2 results

Hydrogen bond distances of G Hydrogen bond distances of G-

• C pair

C pair

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Binding energy (eV) Binding energy (eV)

A B A B C

Structure optimization: DNA base pairs (A Structure optimization: DNA base pairs (A-

• T, G

T, G-

• C)

C)

• PBE results are very close to RI

PBE results are very close to RI-

• MP2 results

MP2 results

• PBE looks good for hydrogen bonds!

PBE looks good for hydrogen bonds! With Counterpoise correction for basis set superposition error (BSSE) With Counterpoise correction for basis set superposition error (BSSE)

Extrapolated value of MP2 results with respect to the increase of basis sets

CONQUEST

Gaussian03

• Ref. (a)

LDA PBE SVWN5 PBE B3LYP MP2 RI-MP2 CCSD(T) corrected basis DZP cc-pVDZ CBS A-T

• 1.11
• 0.64
• 1.05
• 0.60
• 0.50
• 0.48
• 0.67
• 0.67

G-C

• 1.84
• 1.20
• 1.77
• 1.15
• 1.05
• 0.94
• 1.22
• 1.25

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DNA (1WQZ) : DNA (1WQZ) : by Neutron Diffraction Measurements by Neutron Diffraction Measurements

• DNA:

DNA:

• Mg

Mg2+

2+:

• Total H

Total H2O: O:

• Total # of atoms:

Total # of atoms: 634 atoms 634 atoms 9 atoms 9 atoms 932 molecules 932 molecules = 2796 atoms = 2796 atoms 3439 atoms 3439 atoms

• Hydrating water molecules were

Hydrating water molecules were generated by AMBER. generated by AMBER.

• Snapshot of MD after the equilibrium

Snapshot of MD after the equilibrium by AMBER. by AMBER.

Application to DNA systems Application to DNA systems

A MD snapshot from equilibrium A MD snapshot from equilibrium

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SZ (single zeta) calculations on SZ (single zeta) calculations on

• DNA (+Mg) without water molecules : 643 atoms

DNA (+Mg) without water molecules : 643 atoms

• DNA (+Mg) with hydrating water molecules: 3439 atoms

DNA (+Mg) with hydrating water molecules: 3439 atoms

CQ on DNA systems CQ on DNA systems

Hydrogen bond distances of G Hydrogen bond distances of G-

• C pair

C pair

L matrix c matrix cutoff dependenc utoff dependence e of total energy

• f total energy
• without H

without H2O: diag. vs order O: diag. vs order-

• N

N → convergence from → convergence from RL

L = 16.0

= 16.0 the error is 1.7 mHartree/(643 atoms) the error is 1.7 mHartree/(643 atoms)

• with H

with H2O → convergence is same behavior O → convergence is same behavior at RL=16.0 bohr at RL=16.0 bohr the error is 3.5 mHartree/ (3439 atoms) the error is 3.5 mHartree/ (3439 atoms) at RL=18.0 borh at RL=18.0 borh the error is 0.64 mHartree/ (3439 atoms) the error is 0.64 mHartree/ (3439 atoms)

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CQ on DNA systems: Summary CQ on DNA systems: Summary

CONQUEST calculations on single DNA bases agree with those by other CONQUEST calculations on single DNA bases agree with those by other codes (Gaussian, V ASP). codes (Gaussian, V ASP). PBE is accurate to represent hydrogen bonds in A PBE is accurate to represent hydrogen bonds in A-

• T and G

T and G-

• C pairs.

C pairs. O(N) calculations using DMM technique is extremely accurate on DNA O(N) calculations using DMM technique is extremely accurate on DNA systems. systems. Error = 0.64 mHartree/3439 atoms at Error = 0.64 mHartree/3439 atoms at RL = 18.0 bohr = 18.0 bohr

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Novel Nano Devices Novel Nano Devices

■ Molecular electronics

Molecular electronics

Elements of nano Elements of nano-

• structures

structures : CNT : CNT、atomic wires, molecular wires, atomic wires, molecular wires,

Structure change & conductance Structure change & conductance

0.15 0.10 0.05 0.00 T(εF) 180 150 120 90 angle [degree]

0.128 0.092 0.001

Angle dependence of T Angle dependence of T

On/off On/off ratio=128 ratio=128

Control of molecular structures (angles) Control of molecular structures (angles)

Electric field Electric field STM STM-

• manufacturing

manufacturing Photo Photo-

• isomerization

isomerization Gas adsorption Gas adsorption NH NH2+ NO NO2− polarization polarization

E=0 E=0

θ=89 =89o （stable stable） θ=180 =180o

■ Design of molecular devices

Design of molecular devices

Molecular Electronics Molecular Electronics

Bottom Bottom-

• up device

up device （ Top Top-

• down

down）

Molecular switch, sensor, organic EL, , Molecular switch, sensor, organic EL, , HP HP Electric field Electric field

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Non Non-

• Equilibrium Green’s Function method (NEGF)

Equilibrium Green’s Function method (NEGF)

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I-

• V curve

V curve

Transport: benzene dithiol molecule (BDT) Transport: benzene dithiol molecule (BDT)

Contact geometries Contact geometries

Hollow Hollow Bridge Bridge Ontop Ontop Hollow Hollow Bridge Bridge Ontop Ontop

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Dependence of the conduction of a BPD molecule Dependence of the conduction of a BPD molecule

• n the dihedral angle between the phenyl rings
• n the dihedral angle between the phenyl rings

and its application to a nano and its application to a nano-

• rectifier

rectifier

• H. Kondo, J. Nara, H. Kino, and T. Ohno,
• H. Kondo, J. Nara, H. Kino, and T. Ohno,
• J. Chem. Phys. 128, 064701 (2008)
• J. Chem. Phys. 128, 064701 (2008)

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Dihedral-angle dependence

Transport: biphenyl dithiol molecule (BPD) Transport: biphenyl dithiol molecule (BPD)

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Molecular Rectifier Molecular Rectifier

By y applying applying an an electric field, electric field, the dihedral angle is controllable the dihedral angle is controllable. . → works as a nano works as a nano-

• rectifier.

rectifier. Total energy Total energy For E For Ez

z<0

<0 ϕ ~ 150 ~ 150o Off On D： dipole moment E： electric field Current Current I I: large : large Current Current I: small : small For E For Ez>0 >0 ϕ ~ 90 ~ 90o

Bi-stability

BPD Functionalized with NH2, NO2 groups

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O ϕ = = ϕ0 ϕ = 90 = 90o S Se Se Te Te

Molecular Rectifier: End Molecular Rectifier: End-

• group dependence

group dependence

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Transmission Transmission The O end The O end-

• atom gives the largest ON/OFF ratio

atom gives the largest ON/OFF ratio

Molecular Rectifier: End Molecular Rectifier: End-

• group dependence

group dependence

I-

• V curve

V curve

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O2 sensitivity of SWNT O2 sensitivity of SWNT

Science 207, 1801 (2000) Science 207, 1801 (2000)

Enzyme Enzyme-

• coated CNT as single molecule biosensors

coated CNT as single molecule biosensors

Nano Letters 3, 727 (2003) Nano Letters 3, 727 (2003)

Molecular Sensor Molecular Sensor

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Investigate whether the adsorption of molecules can be detected by the electronic transport? Investigate whether the adsorption of molecules can be detected by the electronic transport?

Iron Iron-

• porphyrin

porphyrin (FeP) (FeP)

• Ion porphyrin (FeP) is an important molecule in biological systems.

Ion porphyrin (FeP) is an important molecule in biological systems.

• the basic unit of many proteins and enzymes

the basic unit of many proteins and enzymes

• a planar molecule with one Fe atom chelated at the center of a porphyrin cycle.

a planar molecule with one Fe atom chelated at the center of a porphyrin cycle.

• its derivatives display a surprising variety of

its derivatives display a surprising variety of biological functions biological functions, acting as carriers , acting as carriers

• f metabolic species (O2) and signal transmitters (NO), as well as redox centers.
• f metabolic species (O2) and signal transmitters (NO), as well as redox centers.
• Fe plays a central role in

Fe plays a central role in molecular recognition molecular recognition and chemical selectivity of FeP. and chemical selectivity of FeP.

• FeP will be used in the design of chemical sensors such as an electronic nose/tongue.

FeP will be used in the design of chemical sensors such as an electronic nose/tongue.

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Molecular sensor: iron Molecular sensor: iron-

• porphyrin

porphyrin (FeP) (FeP)

Junction geometry Junction geometry

Adsorption of molecules Adsorption of molecules

Geometry of molecular sensor Geometry of molecular sensor

O2, CO, NO O2, CO, NO

Au electrode Au electrode Au electrode Au electrode

S S

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Dependence on junction geometry Dependence on junction geometry

1.0 0.5 0.0 T(ε)

• 4
• 2

2 4 ε [eV]

FeP: minority spin

1.0 0.5 0.0 T(ε)

FeP: majority spin

1.0 0.5 0.0 T(ε)

• 4
• 2

2 4 ε [eV]

FeP: minority spin

1.0 0.5 0.0 T(ε)

FeP: majority spin

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H-

• S

S-

• FeP

FeP-

• S

S-

• H

H

HOMO HOMO HOMO HOMO-

• 1

1 HOMO HOMO-

• 2

2 HOMO HOMO-

• 3

3 HOMO HOMO HOMO HOMO-

• 1

1 HOMO HOMO-

• 2

2 HOMO HOMO-

• 3

3

π σ π π π π π σ

d(3z d(3z2-r r2) d(yz) d(yz) d(x d(x2-y y2) d(3z d(3z2-r r2) d(x d(x2-y y2) d(yz) d(yz)

Molecular orbitals: FeP Molecular orbitals: FeP

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Transport property: Transport property: iron iron-

• porphyrin

porphyrin (FeP) (FeP)

1.0 0.5 0.0 T(ε)

FeP: majority spin FeP: minority spin

12.0 9.0 6.0 3.0 0.0 pDOS

• 4
• 2

2 4 ε [eV]

FeP: majority spin

• 4
• 2

2 4 ε [eV]

FeP: minority spin

• 2
• 1

1 2 ε [eV]

HOMO HOMO LUMO LUMO HOMO HOMO LUMO LUMO

• S

S-

• FeP

FeP-

• S

S-

• LUMO

LUMO HOMO HOMO

d(3z d(3z2-r r2) d(3z d(3z2-r r2) d(3z d(3z2-r r2) )

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Adsorption geometries of XO on FeP Adsorption geometries of XO on FeP

H-

• FeP

FeP-

• H

H-

• S-
• FeP

FeP-

• S-
• H

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• 4.0
• 3.5
• 3.0
• 2.5

ε [eV] FeP CO-FeP NO-FeP O2-FeP

H-

• S

S-

• FeP

FeP-

• S

S-

• H

H

d(3z d(3z2-r r2) d(yz) d(yz) d(x d(x2-y y2) d(xz) d(xz) d(x d(x2-y y2) d(yz) d(yz) d(xz) d(xz) w/o 3d w/o 3d

Molecular orbitals: XO adsorbed FeP Molecular orbitals: XO adsorbed FeP

The influence of axial ligands on the MOs of FeP The influence of axial ligands on the MOs of FeP

The energy level of the Fe The energy level of the Fe-

• dz

dz2 MO in FeP is sensitive to the presence of the ligands. MO in FeP is sensitive to the presence of the ligands. d(3z d(3z2-r r2) ) d(3z d(3z2-r r2) d(3z d(3z2-r r2)

HOMO HOMO HOMO HOMO HOMO HOMO HOMO HOMO

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Transport: XO adsorbed FeP Transport: XO adsorbed FeP

1.0 0.5 0.0 T(ε)

FeP

majority spin

FeP

minority spin

1.0 0.5 0.0 T(ε)

CO-FeP CO-FeP

1.0 0.5 0.0 T(ε)

• 4
• 2

2 4 ε [eV]

O2-FeP

• 4
• 2

2 4 ε [eV]

O2-FeP

1.0 0.5 0.0 T(ε)

NO-FeP NO-FeP

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Transport: XO adsorbed FeP Transport: XO adsorbed FeP

• 1.6
• 0.8

0.0 0.8 1.6 ε [eV] FeP CO-FeP NO-FeP O2-FeP

minority spin

LUMO

3 majority spin

LUMO (a) FeP

3 pDOS

(b) CO-FeP

• 2

2 ε [eV] 3

• 2

2

(d) O2-FeP

3

(c) NO-FeP

• S

S-

• FeP

FeP-

• S

S-

• d(3z

d(3z2-r r2)

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Possibility of Molecular Sensing Possibility of Molecular Sensing

40 30 20 10 I [µA] 2.0 1.6 1.2 0.8 0.4 0.0 V [V]

total FeP CO-FeP NO-FeP O2-FeP

FeP FeP O2 O2 CO CO NO NO The adsorption of molecules (CO, NO, O2) can be detected by the electronic transport. The adsorption of molecules (CO, NO, O2) can be detected by the electronic transport. The molecular species can be also distinguished from each other. The molecular species can be also distinguished from each other.

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Surface dynamics (DFT/ Hybrid) Surface dynamics (DFT/ Hybrid)

(i) Diffusion of (i) Diffusion of F on Si(111) F on Si(111) : Si Si-

• F complex diffusion

F complex diffusion (ii) Adsorption of (ii) Adsorption of O2 on Si(001) O2 on Si(001) : : Energy dissipation Energy dissipation (iii) Atomic structure of AFM tip apex (iii) Atomic structure of AFM tip apex

Nano-structured materials

To understand their formation processes & properties/functions at the atomistic level, FP simulation methods based on DFT are an ideal tool.

Transport through molecular junctions (NEGF) Transport through molecular junctions (NEGF)

(i) p (i) p-

• stacked systems: styrene wires on H/Si(001)

stacked systems: styrene wires on H/Si(001) (ii) Molecular sensors: (ii) Molecular sensors: iron iron-

• porphyrin

porphyrin (iii) Molecular switch: biphenyl dithiol

Photochemical reaction (RTP Photochemical reaction (RTP-

• TDDFT)

TDDFT)

(i) Photoisomerization: azobenzene (i) Photoisomerization: azobenzene

Redox reaction Redox reaction

(i) RuO4: (i) RuO4:

RuO RuO4-

• (aq) + H

(aq) + H2O(l) + e O(l) + e- --

• -> [RuO

> [RuO3(OH) (OH)2]2-

• (aq)

(aq)

Large nano Large nano-

• structured systems

structured systems

(i) PW electronic structure codes (i) PW electronic structure codes : : shallow impurity in Si shallow impurity in Si (ii) Linear scaling algorithms: (ii) Linear scaling algorithms: (a) Surface nano (a) Surface nano-

• structures;

structures; Ge cluster on Si(001) Ge cluster on Si(001) (b) Bio (b) Bio-

• molecules:

molecules: DNA DNA

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design of properties & functions design of properties & functions

nano nano-

• devices, nano

devices, nano-

• complex, bio

complex, bio-

• systems

systems

complex/ hierarchical structures complex/ hierarchical structures mono mono-

• structures

structures

crystal, nano crystal, nano-

• structure, bio

structure, bio-

• polymers

polymers

analysis of structures & properties analysis of structures & properties

Large Large-

• scale, multi

scale, multi-

• scale, multi

scale, multi-

• physics,

physics, high high-

• accuracy

accuracy

Simulations for nano Simulations for nano-

• structured materials

structured materials Nano Nano-

• technology / Nano

technology / Nano-

• science

science

Advanced Simulation Technology Advanced Simulation Technology for Innovation of Nano for Innovation of Nano-

• Scale Materials

Scale Materials

Bio systems Bio systems Nano Nano-

• electronics

electronics