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NSF/ITR: LARGE-SCALE QUANTUM-MECHANICAL MOLECULAR
DYNAMICS SIMULATIONS
C. S. Jayanthi and S.Y. Wu (Principal Investigators)
Lei Liu (Post-doc)Ming Yu (Post-doc)
Chris Leahy (Graduate Student)Alex Tchernatinsky (Graduate Student)Kevin Driver (Undergraduate Student)
University of Louisville
Work supported by:NSF (DMR-0112824)
DoE/EPSCoR (DE-FG02-00ER45832)
Motivation and Objective� The objective of our research is to develop transferable and reliable
semi-empirical LCAO Hamiltonians and the O(N) molecular dynamics corresponding to this Hamiltonian so that properties of complex systems with reduced symmetry may be studied.
� Why develop another LCAO Hamiltonian ?
� Will it have the predictive power of a first-principles calculation?
OBJECTIVESA GENERAL FRAMEWORK FOR
SEMI-EMPIRICAL HAMILTONIAN
Multi-Center Interactions Charge Redistributions
SCED-LCAO
LARGE-SCALE SIMULATIONSO(N)/SCED-LCAO
APPLICATIONS TO CARBON-BASED NANOSTRUCTURES
Self-consistencyEnvironment-Dependent Effects
CURRENT STATUS OF LCAO HAMILTONIANS
Two-center + Henv**
2-center terms explicitly calculated using �pseudo-atomic� orbitals
YesYes**Frauenheim
NOTB**NoNoKaxiras
NOTB**NoNoMenon
NOTB **NoYesNRL
OTB **NoYesAmes
Other FeaturesSelf-consistencyEnvironment Effects
**Environment-dependent effects disappear for systems
with no charge redistributions => Poor bulk phase
diagram for high coordinated bulk phases (FCC, etc)
!
Hiα,jβ = H0iα,jβ +
12· [(Ni − Zi) + (Nj − Zj)] · U
+12·∑
k �=i
Nk · VN (Rik) − Zk · VZ(Rik)
· Siα,jβ
+12·∑
k �=j
Nk · VN (Rjk) − Zk · VZ(Rjk)
· Siα,jβ
SCED-LCAO HAMILTONIAN
! Multi-Center Interactions and Environment-Dependence included
! On-Site Electron-Electron Correlations modeled via Hubbard-like Term
! Inter-site Electron-Electron Correlations modeled via a parameterized function VN
! Electron-Ion interactions modeled via a parameterized function VZ
! Charge distribution Nk at a given site (k) depends on its environment and is
determined Self-Consistently
TOTAL ENERGY WITHIN SCED-LCAO
Etot = Eband +12·∑
i
(Z2i − N2
i ) · U − 12·
∑i,k : k �=i
NiNk · VN (Rik)
+12·
∑i,k : k �=i
ZiZk · VC(Rik)
VC(R) =e2
4πε0· 1R
=E0
R
I: Band Structure Energy (Sum over eigenenergies of occupied states)
II and III: Double-counting corrections
IV: Repulsive ion-ion interaction energy
Coulomb Term
BULK PHASE DIAGRAMS FOR SILICON
0.4 0.6 0.8 1 1.20
0.2
0.4
0.6
0.8
10.4 0.6 0.8 1 1.2
0
0.2
0.4
0.6
0.8
1
LCAODFT
0.4 0.6 0.8 1 1.2
0.4 0.6 0.8 1 1.2
Phase diagrams of bulk Si
0.4 0.6 0.8 1 1.2
0.4 0.6 0.8 1 1.2
Wu
Menon
Kaxiras
Frauenheim
Wang and Ho
NRL
relative atomic volume
bindin
g ene
rgy pe
r atom
cdia
sc
bccfcc
cdia
sc
fccbcc
cdia
sc
bccfcc
cdia
sc
fccbcc
cdiasc
bcc
fcc
BULK PHASE DIAGRAMS FOR CARBON
0.5 1 1.5 2−0.02
0.03
0.08
0.13
0.18
0.23
0.28
0.33
0.38
Ene
rgy p
er A
tom
(Ry)
LCAODFT
0.5 1 1.5 2Relative Atomic Volume
−0.02
0.08
0.18
0.28
0.38
0.5 1 1.5 2−0.02
0.08
0.18
0.28
0.38
sc
graphite
cdia
fcc
bcc
sc
fccbcc
graphite
cdia cdia
graphite
sc
fcc
bcc
SCED−LCAO Frauenheim Menon
graphite
BULK PHASE DIAGRAM OF GERMANIUM
0.6 0.7 0.8 0.9 1 1.1relative atomic volume
−4.3
−4.1
−3.9
−3.7
−3.5
−3.3bi
ndin
g en
ergy
per
ato
m (
eV)
LCAOLDA
cdia
sc
bccfcc
TEST OF SCED-LCAO-MD
A MOLECULAR DYNAMICS STUDY OF THE LOCAL BENDING OF A SWCNT BY AN AFM TIP
The buckle region behaves as a nanoscale potential barrier
sp2
sp3
Buckle
Magnetic Moments for Carbon Structures
Magnetic Moment (emu/g) B=0.1 Tesla
Benzene 0.0017
C60 -0.00036
Graphite -0.03 ( T < 100 K)
Carbon Nanotube -0.025
Carbon Nanotori ~ 27
V.Elser and R.C. Haddon, Nature 325, 792 (1987). R.C. Haddon et al., Nature 350, 46 (1991). J. Heremans, C.H. Olk, and D.T. Morelli, Phys. Rev. B49, 15122 (1994) R.S. Ruoff et al, J. Phys. Chem. 95, 3457 (1991) A.P. Ramirez et al, Science 265, 84 (1994)
Magnetic Responses of Carbon Tori
Ring Current - Metal
(5,5)/1200
A Simple Picture for Colossal Paramgnetism
mB
-mBB
E
0 100 200 300 400 500Temperature (K)
−0.2
−0.1
0.0
Mag
netic
Mom
ent (
µ B)
(5,5)/1480 L=74T(7,4)/1364 L=11T(7,3)/1580;(10,0)/1600
10−1
100
101
102
(5,5)/1500 L=75T(5,5)/1200 L=60T(7,4)/1860 L=15T(9,0)/1332 L=37T(9,0)/1296 L=36T
FqλpTL ==
Metal Tori
qp =q3p =
Semiconducting q3p ≠
}}
}Formed fromSemiconducting NT
Magnetic Responses of all types of Carbon Nanotori
� Nanotori formed from Metal-I Carbon Nanotubes exhibit Giant Paramagnetic moments at any Radius
� Nanotori formed from Metal-II Carbon Nanotubes exhibit Giant Paramagnetic moments at Selected Radii or "Magic Radii", as dictated by the relation
� The enhanced magnetic moment has been explained in terms of the interplay between the geometric structure and the ballistic motion of de-localized π-electrons in the metallic nanotube.
q)T3(L =
Vdc
Bperpendicular Bparallel
Multi-walled nanotube differential resistance measuredin either parallel or perpendicular magnetic field
30x106
25
20
15
10
5
0
dV
/ d
I (o
hm
s)
840-4
Bias ( mV )
B = 3.375 T
30x106
25
20
15
10
5
0
dV
/ d
I (o
hm
s)
840-4
Bias ( mV )
B = 6.75 T
2.5
2.0
1.5
1.0
0.5
V m
ax (
mV
)
86420
B ( T )
B parallel B perpendicular
Splitting reflects Fermi energy shift between two field orientations
Bias for maximum resistance (Vmax) shifts with increasing magnetic field.
S. Chakraborty, B.W. Alphenaar, and K. Tsukagoshi
Magnetic Field Orientation Dependence in MWNT Resistance
EXPERIMENTAL MOTIVATION FOR STUDYING THE ELECTRONC STRUCTURE OF A MWCNT
Questions
� How does the band structure evolve as additional shells are added to the MWNT?
� How does the Fermi Energy Change as a function of the applied magnetic field?
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV) (12,12)
0.6 0.7 k (π/a)
−0.6
−0.3
0
0.3
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
Single Wall: (7,7) and (12,12)
(7,7)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Double Walls: (7,7)@(12,12)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Three Walls: (7,7)@.@(17,17)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Four Walls: (7,7)@..@(22,22)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Five Walls: (7,7)@...@(27,27)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Six Walls: (7,7)@...@(32,32)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Seven Walls: (7,7)@...@(37,37)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
0 0.2 0.4 0.6 0.8 1 k (π/a)
−5
−4
−3
−2
−1
0
1
2
3
4
5
ε (eV)
Eight Walls: (7,7)@...@(42,42)
0.6 0.7 k (π/a)
−0.6
−0.4
−0.2
0.0
0.2
0.4
0.6
ε (eV)
ELECTRONIC STRUCTUREOF MULTI-WALL CARBON NANOTUBES
(7,7)@(12,12)@(17,17)@(22,22)@(27,27)@(32,32)@(37,37)@(42,42)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
0 50 100 150 200H (T)
40
41
42
(EHO
MO+E
LUM
O)/2
23
24
25
26
E F (meV
) Double Walls: (7,7)@(12,12)
ParallelVertical
0 50 100 150 200H (T)
76
77
78
E LUM
O (m
eV)
2.0
4.0
6.0
8.0
E HOM
O (m
eV)
0 20 40 60 80H (T)
3436384042
(EHO
MO+E
LUM
O)/2
34
35
36
E F (meV
)
Three Walls: (7,7)@.@(17,17)
0 20 40 60 80H (T)
55.6
55.8
56.0
E LUM
O (m
eV)
10
15
20
25
30
E HOM
O (m
eV)
0 20 40 60 80H (T)
54.8
54.9
55.0
55.1
(EHO
MO+E
LUM
O)/2
34
35
36
37
38
E F (meV
)
Four Walls: (7,7)@..@(22,22)
0 20 40 60 80H (T)
57
58
E LUM
O (m
eV)
52
53
54
E HOM
O (m
eV)
0 20 40 60 80H (T)
52
53
54
55
(EHO
MO+E
LUM
O)/2
39
40
41
42
E F (meV
)
Five Walls: (7,7)@...@(27,27)
0 20 40 60 80H (T)
55
56
57
58
E LUM
O (m
eV)
49
50
51
52
E HOM
O (m
eV)
0 20 40 60 80H (T)
54
55
56
(EHO
MO+E
LUM
O)/2
404142434445
E F (meV
)
Six Walls: (7,7)@...@(32,32)
0 20 40 60 80H (T)
55
56
57
58
59
E LUM
O (m
eV)
53
54
E HOM
O (m
eV)
0 10 20 30 40H (T)
52
53
54
(EHO
MO+E
LUM
O)/2
41
42
43
E F (meV
) Seven Walls: (7,7)@...@(37,37)
0 10 20 30 40H (T)
53
54
55
56
E LUM
O (m
eV)
50
51
52
E HOM
O (m
eV)
Magnetic Field-Dependence of Fermi Energy
PROJECTS COMPLETED
◆ The framework of our SCED-LCAO Hamiltonian is complete and the parameterized semi-empirical Hamiltonian for Si, Ge, and C are available for applications.
◆ Codes for total energy calculations and molecular dynamics, including the O(N)scheme for large-scale simulations are complete.
◆ Bulk phases of Silicon, Carbon, and Germanium have been tested against first-principles calculations and compared with other LCAO Hamiltonians
◆ SCED-LCAO-MD has been applied to study the surface reconstruction of Si(100) and the stable configurations of ad-dimers of silicon on Si(100).
◆ In tandem with the methodology development of SCED-LCAO, studies on the electronic, magnetic, and the mechanical properties of carbon nanostructures have been initiated. Specifically, the projects studied include:
* The electronic structure of multi-wall carbon nanotubes* Colossal paramagnetism in metallic carbon nanotori* A molecular dynamics study of the various stages of bending including the
cutting of a nanotube by an AFM tip
Significance of our Findings and their Scientific Impact
� The framework of our SCED-LCAO Hamiltonian has a transparent physicalfoundation. Our case studies have demonstrated that the inclusion of environment-dependent and charge redistribution effects in a flexible manner allows the Hamiltonian to predict the properties of complex systems with low-symmetries.
� Our finding on the �giant paramagnetic moment of metallic carbon nanotori� may lead to the development of nano-scale ultra-sensitive magnetic sensors.
� Our simulation study on the deformation of SWCNTs has clarified the nature of nanoscale potential barriers created by the buckle.
� Our study on the electronic structure of MWCNTs is expected to provide an understanding of the quantum transport in these systems.
OUTREACH EFFORTS
◆ Collaborations with the Experimental Group of Dr. J. Liu (Duke University) on the � magnetic properties of carbon nanotori”
◆ Collaborations with Dr. Alphenaar (EE Department , University of Louisville) on the �Electronic and Transport properties of Multi-wall carbon nanotubes”
◆ Collaborations with Dr. Dai at Stanford University on the �Manipulation of SWCNTs by an AFM tip”
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