1. DFT Density Functional theory and the description of Nature
Edison Z. da Silva
Instituto de Física "Gleb Wataghin",
UNICAMP, Campinas - SP, Brazil

2. Outline DFT, What it is, how it came about, what it is used for.....
Solids and DFT
Probing the Earth´s Inner Core
Gold Nanowires

3. We have a well defined system
Nuclei +
Electrons
Molecules
Atoms
Solids
Liquids

4. DFT, theoretical framework
Electrons are the “glue” which holds matter together
DFT, theoretical framework
Description of known materials, prediction of new
materials, explanation of many questions

5. Electromagnetic Forces
Fundamental laws of electronic and nuclear motions well known
Electromagnetic Forces +
Quantum Mechanics
H ( {ri , r} ) = ETOT ( {ri , r} ) ^
H =  ( -½2i ) +  ( -½ 2 ) +  ( - ) +   Z
ri
___
i<j Ne
i=1 ^ 1
rij
=1 Nn
<
ZZ
_____
r M Te ^ Tn ^
Ve-n ^
Ve-e ^
Vn-n ^

6. “There is an oral tradition that, shortly after Schrödinger’s equation for the electronic wavefunction  had been put forward and spectacularly validated for small systems like He and H2, P. A. M. Dirac declared that chemistry had come to an end - its content was entirely contained in that powerful equation. Too bad, he is said to have added, that in almost all cases, this equation was far too complex to allow solution.”
W. Kohn, Reviews of Modern Physics 71, 1253 (1999).

7. Therefore, we have a well posed problem, but too complex and difficult to solve
Impossible to have exact solution except in very few cases
Need of approximations

8. Born-Oppenheimer (1927) Approximation (Qualitatively)
Based on the fact that nuclear masses are much larger than the electronic ones
Therefore, electrons move on a different time-scale than the nuclei (nuclei move much more slowly)
Thus, electrons follow the nuclei “instantaneously”
This allows us to consider the nuclei fixed when solving for the electronic motion

9. Helecaelec({ri};{r}) = Eaelec({r}) aelec({ri};{r})
Born-Oppenheimer Approximation
Helec =  ( -½2i ) +  ( - ) +   Z
ri
___
i<j Ne
i=1 ^ 1
rij
=1 Nn
ZZ
_____
r
< Te ^
Ve-n ^
Ve-e ^
Vn-n ^
Helecaelec({ri};{r}) = Eaelec({r}) aelec({ri};{r}) ^
aelec({ri};{r}) depends explicitly on the electronic coordinates {ri} but only parametrically on the nuclear coordinates {r}, as does Eaelec({r})

10. (r , Q) =  a(Q) aelec(r;Q)
Born-Oppenheimer Approximation
As the {aelec(r;Q)}, for a fixed Q, form a complete orthonormalized set, one can write:
(r , Q) =  a(Q) aelec(r;Q) a
[Tn + Ebelec(Q)] b(Q) +  ba(Q) a(Q) = Etot b(Q) ^ a
Roughly speaking, if the kinetic energy of the nuclei is small when compared to |Ebelec(Q) - Eaelec(Q)|, the non-diagonal terms ba can be neglected

11. (r , Q) = b(Q) belec(r;Q)
Born-Oppenheimer Approximation
[Tn + Ebelec(Q)] b(Q) = Etot b(Q) ^
(r , Q) = b(Q) belec(r;Q)
The total electronic energy Ebelec(Q) acts as a potential energy for the nuclear motion, which occurs in a single electronic state belec .
The nuclear motion simply deforms the electronic distribution, and does not cause transitions between different electronic states.

12. Born-Oppenheimer Approximation
Important concepts:
Molecular geometry

13. Born-Oppenheimer Approximation
Crystal structure
Important concepts:
Molecular geometry

14. Born-Oppenheimer Approximation
Important concepts:
Molecular geometry
Crystal structure
Potential Energy Surface (PES)
Geometrical
coordinate
PES
Ex: Carbon
Amorphous
Graphite
Diamond

15. Two issues How to calculate (as accurately as possible) the PES
electronic degrees of freedom
How to sample the PES (or how to move the atoms)
nuclear degrees of freedom

16. How to solve Helecelec = Eelecelec
Traditional way of thinking would be to describe the wavefunction as well as possible However, WF for a many electron system is a very complicated object!

17. YES Is there another way to solve the problem (ab initio)?
Electronic density e(r) as the fundamental object
(and not wavefunction elec)

18. Density Functional Theory (DFT)
Proc. Cambridge Philos. Soc. 26, 376 (1930)
Roots in the works of Thomas (1926), Fermi (1928), Dirac (1930), Slater, etc.
Chemistry Nobel prize
Formally well founded in the works of W. Kohn
P. Hohenberg and W. Kohn, Phys. Rev 136, 864B (1964)
W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)

19. DFT - Two basic theorems P. Hohenberg and W. Kohn, Phys
DFT - Two basic theorems P. Hohenberg and W. Kohn, Phys. Rev 136, 864B (1964)
Let’s consider a system of N interacting electrons in the ground-state associated with an external potential v(r)
1) The ground state density 0e(r) uniquely determines the potential v(r)
Since with v(r) the full electronic Hamiltonian is known, 0e(r) completely determines all properties of the system
2) There exists a functional E[e(r)] which has its minimum for the ground-state density 0e(r)
Can use this variational principle to calculate 0e(r)

20. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
E[e] =  v(r) e(r) d3r + T[e] + U[e]
I don’t know how to solve this problem, but I know how to solve the following problem:
If I had a system of non-interacting electrons, in an external potential veff(r), then:
Es[e] =  veff(r) e(r) d3r + Ts[e]
Ts[e] = kinetic energy of a non-interacting system with density e

21. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
The ground-state wavefunction in this case is a Slater determinant of N orbitals i (i=1,N), which satisfy the equations:
[-½ 2 + veff(r)] i(r) = i i(r)
And the ground-state density can be written as:
0e(r) =  |i(r)|2
lowest N i

22. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
However, from the Hohenberg-Kohn theorem, a completely equivalent way of calculating 0e(r) would be through the minimization of E[e(r)]: 
 e(r)
Es[e] -   e(r’) d3r’
= 0
+ veff(r) -  = 0
Ts[e]
 e(r)
0e(r) =  |i(r)|2 i
Gives same density as

23. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
Application of the Hohenberg-Kohn theorem to E[e] gives 
 e(r)
E[e] -   e(r’) d3r’
= 0
Ts[e] +  v(r’) e(r’) d3r’ + UH[e] + EXC[e] -   e(r’) d3r’ 
 e(r)
= 0
+ v(r) +  d3r’e(r’)/|r-r’| +
Ts[e]
 e(r)
EXC[e]
-  = 0

24. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
Comparison with similar equation for non-interacting electrons gives:
+ v(r) +  d3r’e(r’)/|r-r’| +
Ts[e]
 e(r)
EXC[e]
-  = 0
Interacting electrons
+ veff(r) -  = 0
Ts[e]
 e(r)
Non-interacting electrons
v(r) +  d3r’e(r’)/|r-r’| +
EXC[e]
 e(r)
veff(r) =

25. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
We can, therefore, calculate exactly (in principle) the problem of the interacting electrons through the solution of the following equations:
[-½ 2 + veff(r)] i(r) = i i(r)
0e(r) =  |i(r)|2
lowest N i
v(r) +  d3r’e(r’)/|r-r’| +
EXC[e]
 e(r)
veff(r) =

26. DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev
DFT - How to calculate 0e W. Kohn and L. J. Sham, Phys. Rev. 140, 1133A (1965)
Problem of many-electrons mapped exactly (in principle) into the problem of non-interacting electrons subjected to an effective potential!
v(r) +  d3r’e(r’)/|r-r’| +
EXC[e]
 e(r)
veff(r) =
However, we don’t know how to calculate this effective potential:
We need approximations for EXC[e] and vXC[e] =
EXC[e]
 e(r)

27. DFT - Local Density Approximation (LDA)
Let’s consider the exchange-correlation energy, per particle, for a homogeneous electron gas, ehXC
This quantity can be calculated very accurately (Quantum Monte Carlo)
Let’s imagine the real system divided in small cells:
Ni Vi  i = Ni / Vi i

28. DFT - Local Density Approximation (LDA)
If we consider that the density is approximately homogeneous inside cell i, then we can write for the XC energy in cell i
EiXC ehXC (i) Ni
= ehXC (i) Ni (Vi / Vi) =
= ehXC (i) (Ni / Vi) Vi
= ehXC (i) i Vi i
Ni Vi  i = Ni / Vi

29. DFT - Local Density Approximation (LDA)
Summing over all the cells i will give for the total XC energy
EXC   ehXC(i) i Vi i
EXC   ehXC((r)) (r) d3r = ELDAXC i
Ni Vi  i = Ni / Vi

30. DFT - Local Density Approximation (LDA)
And from this we can get the XC potential vLDAXC
ELDAXC
 e
vLDAXC =
=  ehXC((r)) (r) d3r 
 e
= ehXC()  d
d e i
Ni Vi  i = Ni / Vi

31. DFT - Self-consistency cycle
Still a problem: veff depends one ande depends on veff
Solution: self-consistency cycle
1. Choose an initial density 0e and determine the effective potential veff (0e)
2. Solve the Kohn-Sham equations
[-½ 2 + veff(r)] i(r) = i i(r)
3. Calculate the density
1e(r) =  |i(r)|2
lowest N i
4. Check if 1e = 0e. If yes, end of cycle. If not, go back to 2. (with 0e = 1e)

32. Crystal - Bloch functions
veff has the periodicity of the crystal
According to Bloch’s theorem, the i will have the following form:
(n,k)(r) = exp(i k•r) u(n,k)(r)
The function u(n,k) also has the periodicity of the crystal
Therefore, it can be expanded in a discrete set of plane waves whose wave vectors are reciprocal lattice vectors of the crystal
u(r) =  cGexp(i G•r) G

33. Crystal - Bloch functions
Therefore
(n,k)(r) =  cnk+G exp[i (k+G)•r] G
For a crystal, the density will be given by
e(r) =  |i(r)|2 = 2   |(n,k)(r)|2
lowest N i
occ.
bands n k BZ

34. Crystal - Bloch functions
Two approximations:
1) Maximum value of G=GC  number of basis function (plane wave)
(n,k)(r) =  cnk+G exp[i (k+G)•r] G Gc
To determine GC one gives the kinetic energy associated with the GC
Cutoff energy  EC = GC2/2m
2) Number of Brillouin-zone points - set of “special points”
e(r) = 2   |(n,k)(r)|2
occ.
bands n k SP

35. Strong oscillations in the core region
Crystal - Bloch functions
Strong oscillations in the core region
All electron
valence WF

36. These strong oscillations are bad for plane-wave expansion (large value of GC to describe small features in real space)
Either use a different basis function in the core region, or change the function in the core region

37. Pseudopotentials Valence electrons are the chemically relevant ones
Removes the core electrons and replaces them and the strong potential by an effective, weaker potential that acts on the valence electrons rc r
V, 

38. All electron
Pseudo

39. Si, The credibility of DFT

40. How to solve the KS equations
After all these approximations, I have to find the cnk+G through the self-consistent solution of the KS equations
HKS i(r) = i i(r)
(n,k)(r) =  cnk+G exp[i (k+G)•r] G Gc

41. =  c HKS Traditional method - diagonalization
Write the matrix for the KS Hamiltonian in the plane wave basis set and diagonalize it
 HKSk+G,k+G’ cnk+G’ = nk+G cnk+G G’
HKS c
= 

42. Perfect crystal
             

43. Crystal with a defect
             

44.  Crystal with a defect              
             
             

45.    Crystal with a defect              
             
             

46. Surfaces
 
             

47. Surfaces
 
             

48. Surfaces
 
 
 
             

49. Applications Understanding the Earth´s inner core
Breaking of Gold nanowires

50. Elasticity of Iron at the temperature of the Earth´s inner core
G. Stainle-Neumann, L. Stixrude, R. Cohen & O. Gulseren
Nature, 413, 57 (2001)

51. General picture

52. Seismological Studies:
Compressional waves travel faster along polar paths
than in equatorial plane.
Earth´s center, 2,440 km across is nearly pure Iron
At high temperatures and pressures iron goes to an
hcp phase called e-phase

53. Iron at Temperatures and pressures of the Earth´s core.
Crystal structure distorts unexpectedly
Inner core believed to be made up of Iron crystals in hcp
structure
Observed seismic anisotropy must arise from differences
in elastic response of hcp Iron
Densities for iron
7.87 Mg m atmospheric pressure
13.04 Mg m-3 at Earth´s core pressures

54. Iron at Temperatures and pressures of the Earth´s core.
DFT calculations of elastic constants
Thermodynamics given by the Helmholtz free energy
F(V,T) = E0(V) + Eel(V,T) -T Sel(V,T) + Fvib(V,T)
E0(V) static total energy
Eel(V,T) due to thermal excitations
Sel(V,T) electronic entropy
Fvib(V,T) phonon contribution (particle in a cell )

55. r(Mg m-3)
12.52
13.04
13.62
Equilibrium structure of hcp iron over a range
of densities and temperatures of the Earth´s core.
Computing F for different c/a and finding the minima

56. Elastic constants
Elasticity of hcp iron for a
density Mgm-3

57. Velocity Acoustic properties of iron for the Earth´s core.
Adiabatic bulk modulus (KS)
and shear modulus (m)
as function of temperature
compared with inner core at
the same density Mgm-3
Travel time anomaly
Solid line , model with 1/3
of crystals with basal planes
aligned with rotation axis

58. Conclusions Seismological Studies:
Compressional waves travel faster along polar paths
than in equatorial plane.
At high temperatures and pressures iron goes to an
hcp phase called e -phase.
With c/a = 1.7 seismic waves travel 12 % faster in
the ab plane.
This anisotropy is too strong, if crystals are
aligned it accounts for the experimental findings.

59. Breaking of Gold Nanowires: A Computer Simulation study
E. Z. da Silva
Instituto de Física "Gleb Wataghin", UNICAMP, Campinas - SP, Brazil

60. Participants, motivation...
Theory
Antonio José R. da Silva(IF-USP)
Adalberto Fazzio (IF-USP)
Frederico D. Novaes (PhD-IF-USP)
Experimental motivation
Daniel Ugarte (LNLS)
Varlei Rodrigues

61. When we get to the very, very small
world - say circuits of seven atoms -
we have a lot of new things that would
happen that represent completelly new
opportunities for design. Atoms on a
small scale behave like nothing on the
large scale, for they satisfy the laws of
quantum mechanics.
Richard Feynman
Plenty of Room at the Bottom(1959)

62. Program Why study Au nanowires? Experiments Theory TBMD simulations
Impurities
Conclusions

63. Why study Au nanowires? Gold nanowires are produced in the lab!
Understanding of its properties is fundamental.
Gold is the electrical contact in nanotechnology.
When Gold nanowires become very thin,
interesting surprises are found:
Conductivity is quantized.
Possibility of helical structures.
One-atom thick wires are produced.

64. Gold in devices
J Reichert, et al., Phys. Rev. Lett., 88, (2002)

65. Experiments, How it all started!
Pin-plate experiment:
nanowire formed
conductance during elongation and contraction
U.Landman, W.D.Luedtke, B.E.Salisbury, and R.L.Whetten, Phys. Rev. Lett. 77, 1362, (1996)

66. Theoretical Predictions
Computer simulations with a “glue” type empirical
many-body potential (for Al and Pb) predicted:
As the diameter decrease, thin metal wires develop
exotic stable noncrystalline structures:
Existence of critical diameter
Formation of helical, spiral-structured wires
O. Gulseren, F Ercolessi, and E. Tosatti, Phys. Rev. Lett. 80, 3775, (1998)

67. Theory Weird Nanowires
O. Gulseren, F Ercolessi, and E. Tosatti, Phys. Rev. Lett. 80, 3775, (1998)

68. How to make a wire

69. Theorist´s view: production and imaging process!

70. Y. Kondo and K. Takayanagi, Phys. Rev. Lett. 79, 3455, (1997)
Stable Au Nanowires from surface structures
Production
Au thin films (3nm) in UHVTEM
electron beam irradiation (100 A/cm2)
produced many holes  nanowires
Imaging
Straight nanowires
images produced with electron
beam irradiation (5 A/cm2)
Y. Kondo and K. Takayanagi, Phys. Rev. Lett. 79, 3455, (1997)

71. Interpretation of the Experiments
1-7
4-11
6-13
1-7-14
1-8-15

72. Folding of a (111) plane Cylindrical folding of a
triangular lattice for
an (m, n) tube, with
views of several coaxial
tube nanowires. Each atom
is pictured as a sphere of
atomic radius. The (7, 3) gold
nanowire (note its chirality)
was reported to be magic in (3).

73. V. Rodrigues and D. Ugarte, Phys. Rev. B 63, 073405-1, (2001)
Real time imaging of one-atom-thick Au nanowires
The film irradiation technique
from Kondo and Takayanagi
produced stable one-atom-thick
Au- nanowires.
Time sequence of formation,
elongation and fracture of a
chain of gold atoms.
V. Rodrigues and D. Ugarte, Phys. Rev. B 63, , (2001)

74. Dynamical Simulations of Gold nanowires
Is it possible to simulate the evolution of a
gold nanowire under stress with a reliable
electronic structure method?
Wire under tension.
It forms, starts to thin ( atoms going to the wire edges)
neck is produced (one atom constriction).
Atoms from the wire,( near the tips) are draw back and
are incorporated into the one -atom thick neck.
This thin neck grows to 4-5 atoms
The wire finally breaks

75. (three orders of magnitude faster)
Ab Initio DFT Methods
(costly in terms of computer time!)
NRL-TBMD
keeps the electrons
(three orders of magnitude faster)
Number of atoms
ACCURACY
MD with Classical Potentials
Embedded-atom, Effective medium,
Finnis-Sinclair, Second Moment(TB)
(No electrons!)

76. The Tight -Binding Method
Slater and Koster proposed in 1954 a modified
combination of atomic orbitals (LCAO) as a
interpolation scheme to determine energy bands.
In 1986 Papaconstantopoulos published a handbook
of SK parameters for most elements in the periodic table.
As DFT ab initio methods improve, so does the
Papaconstantopoulos TB fits with updates the
of SK parameters for most elements in the periodic table.

77. The NRL tight-binding method
Procedure,
The method fits TB parameters to reproduce ab initio total energies (DFT) calculated with full-potential linear aumented plane wave method.
Slater-Koster parameters are fitted to LAPW bands and
total energies as function of volume for 10 fcc structures,
6 bcc structures and 5 sc structures.
Perdue-Wang parametrization to LDA
M.J.Mehl and D. A.Papacontantopoulos, Phys. Rev. B 54, 4519 (1996)

78. Tight-binding and Molecular Dynamics
TB basis set
The Slater-Koster (SK) parameters
Tight-binding Fit of the ab initio Potential energy surface
Ab initio molecular dynamics

79. TB basis set Minimum basis set of atomic like orbitals,
for transition metals;
Number of basis functions per atom N0. Number of atoms Na,
dimension space spanned by this basis set Nb = N0 Na.
States are expressed as linear combinations of these orbitals:

80. The Slater-Koster parameters
Matrix elements of the Hamiltonian and overlap gives:
Hopping terms
Overlap terms
SK-parameters

81. Tight-Binding Fit of the ab initio Potential energy surface
Formalism
Parametrization

82. Complicated Transition Metal-Mn
Manganese crystallizes
in the -Mn structure
with 29 atoms 
Above 710 0C, Mn
transforms to the -Mn
with 20 atoms 
Calculated TB total energy

83. Fitting Procedure for Au, using the static TB code
Equation of state
How good is the TB
parametrization for
fcc bulk Au?
Data basis:
10 fcc structures,
6 bcc structures,
5 sc structures.
Phonon dispersion, T = 0
Fcc structure,
lowest energy
F.Kirchhhoff et al. Phys. Rev. B, (2001)

84. Ab initio molecular dynamics steps of the simulation
Input, Ri, positions of the atoms  H the Hamiltonian
The electronic ground state of the system is calculated.
Eigenvectors 
Forces on the atoms.
Forces  (EOM) integrated
and new positions found.
Where states are expanded using the TB orbitals

85. Electronic DOS for Au, using TBMD code
Solid, T dependence
MD simulations:
Microcanonical ensemble,
EM with Verlet algo,
t = 2 fs,  point sampling.
Liquid Au, T = 1773 K
F.Kirchhhoff et al. Phys. Rev. B, (2001)

86. Au-nanowires, simulations E. Z. da Silva. A J. R. da Silva and A
Au-nanowires, simulations E. Z. da Silva. A J. R.da Silva and A. Fazzio, Phys. Rev. Lett., 87 , (2001)
Front view 
Starting structures:
nanowire along the
along the(111) direction
- 10 atom planes
- 7atoms in each plane.
Top
view 

87. Simulation Protocol EM integrated using Verlet algo, t =1 fs
The system is heated to T = 600 K, MD steps, 7ps
Elongation of the wire by L = 0.5 Å
The system is heated to T = 400 K, 4000 MD steps, 4ps
Previous two steps are repeated
Procedure done for Å < LW < 44.0 Å

88. Au nanowire, 6 (111) planes of 7 Au atoms,
unrelaxed structure
relaxed structure

89. Similarities for the breaking the one-atom necklace
Experiment
2.99 
 2.98
2.89 
 2.74
2.63 
 2.91
2.61 
 2.89
Simulation

90. Evolution and breaking
Atomic configurations
(in Å)
(a) 25.5, (b) 33.0, (c) 37.0
(a) 38.0, (b) 40.5, (d) 41.0

91. Defect structure, one atom neck
(i) Defect structure
(iii) 4-5 atoms planes
(iv) atoms planes
(v) one atom neck

92. Forces
Saw-tooth
behavior

93. Before breaking the one-atom necklace
The nanowire develops a
one-atom thick necklace
with five atoms in its final
structure.
Just before breaking, the
apex-apex distance gets to
da-a ~ Å.

94. Animation of the simulation
See this animation at

95. Pending problems Are TBMD results reproducible using ab initio DFT.
Large Au-Au distances seen in the experiments

96. Real time imaging of one-atom-thick Au nanowires
HRTEM image of atom chain
with three gold atoms. Atomic
positions are the dark spots
Large Au-Au distances!!!!
Schematic representation
V. Rodrigues and D. Ugarte, Phys. Rev. B 63, , (2001)

97. Simulations give shorter Au-Au distances
Before breaking: one-atom necklace
Simulations give shorter Au-Au distances

98. Ab initio DFT (Siesta) Fully self-consistent DFT LCAO
Extremely fast simulation using minimal basis set
Kohn-Sham equations
Exchange-correlation (GGA)
Norm conserving pseudopotentials (Troullier-Martins)
Total energy
Forces

99. Ab initio evolution Starting structure Before breaking
Au-Au distance  3.0 Å
After breaking

100. Large distances, Impurities?
The statistics
The Images
Au-Au distances 3.6±0.2
(Au-Au)Max  3.1 Å
(Au-X-Au)Max 3.6 Å
X = ?
Legoas,Galvão, Rodrigues ,
Ugarte , PRL, 88, , (2002)

101. Reasoning for impurities
Structure
simulation
TEM simulation
2.9
2.8
3.6
3.1

102. Carbon, structure right before breaking
Carbon in Au nanowire
Carbon, initial structure
Au-nanowire
Carbon intermediate
structure,
3.73
Carbon, structure right before breaking
Quebra

103. Considered the effect of the impurities, H, B, C, N, O and S
Impurities and the Au-Au Bond Length Frederico D. Novaes, A.J.R. da Silva, E.Z. da Silva and A.Fazzio, Phys. Rev. Lett. 90, (2003)22 january
Use ab initio DFT to study contamination of the pure Au nanowire by impurities.
Considered the effect of the impurities, H, B, C, N, O and S
Experiment gives Au-?-Au = 3.6 Å
Au-??-Au = 4.8 Å

104. Contamination by H and S

105. H Impurities? 3.5 3.5 4.9 Our simulation Experiments:
Legoas,Galvão, Rodrigues ,
Ugarte , PRL, 88, , (2002)
4.9
3.5

106. General Conclusions Future: Importance of Gold nanowires.
Simulations can help understand the dynamical evolution
and finally the breaking of metal nanowires.
TBMD is reliable and fast.
Can be used to study dynamical evolution of metal nanowires.
Future:
Study of other directions for wire formation.
Investigation of nanowires of other metals (Ag, Pt etc..)
Use nanowires and their tips to design devices.

107. Conclusions
DFT, A effective way of studying and projecting interesting materials.
Solids and DFT
Probing the Earth´s Inner Core
Gold Nanowires