NSF/ITR: LARGE-SCALE QUANTUM- MECHANICAL MOLECULAR DYNAMICS - PowerPoint PPT Presentation

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?

OBJECTIVES A GENERAL FRAMEWORK FOR SEMI-EMPIRICAL HAMILTONIAN Multi-Center Interactions Charge Redistributions Environment- Dependent Effects Self-consistency SCED-LCAO LARGE-SCALE SIMULATIONS O(N)/SCED-LCAO APPLICATIONS TO CARBON-BASED NANOSTRUCTURES

CURRENT STATUS OF LCAO HAMILTONIANS Environment Self-consistency Other Features Effects Ames Yes No OTB ** NRL Yes No NOTB ** Menon No No NOTB** Kaxiras No No NOTB** Frauenheim Yes** Yes Two-center + H env ** 2-center terms explicitly calculated using “pseudo-atomic” orbitals **Environment-dependent effects disappear for systems ! with no charge redistributions => Poor bulk phase diagram for high coordinated bulk phases (FCC, etc)

SCED-LCAO HAMILTONIAN iα,jβ + 1 H 0 = 2 · [( N i − Z i ) + ( N j − Z j )] · U H iα,jβ   +1 � N k · V N ( R ik ) − Z k · V Z ( R ik )  · S iα,jβ 2 · k � = i   +1 � N k · V N ( R jk ) − Z k · V Z ( R jk )  · S iα,jβ 2 · k � = j ! 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 V N ! Electron-Ion interactions modeled via a parameterized function V Z ! Charge distribution N k at a given site ( k) depends on its environment and is determined Self-Consistently

TOTAL ENERGY WITHIN SCED- LCAO E band + 1 i ) · U − 1 � � ( Z 2 i − N 2 = N i N k · V N ( R ik ) E tot 2 · 2 · i i,k : k � = i +1 � Z i Z k · V C ( R ik ) 2 · i,k : k � = i e 2 · 1 R = E 0 V C ( R ) = Coulomb Term 4 πε 0 R I: Band Structure Energy (Sum over eigenenergies of occupied states) II and III: Double-counting corrections IV: Repulsive ion-ion interaction energy

BULK PHASE DIAGRAMS FOR SILICON Phase diagrams of bulk Si 1 fcc Menon Wu Kaxiras 0.8 bcc fcc 0.6 bcc m 0.4 sc o LCAO sc t a r 0.2 DFT e p cdia cdia y g 0 r e 10.4 0.6 0.8 1 1.2 0.4 0.6 0.8 1 1.2 0.4 0.6 0.8 1 1.2 n e g fcc n Wang and Ho NRL i Frauenheim fcc d 0.8 bcc n i b bcc fcc 0.6 bcc sc 0.4 sc sc 0.2 cdia cdia cdia 0 0.4 0.6 0.8 1 1.2 0.4 0.6 0.8 1 1.2 0.4 0.6 0.8 1 1.2 relative atomic volume

BULK PHASE DIAGRAMS FOR CARBON Menon Frauenheim SCED−LCAO 0.38 0.38 0.38 LCAO 0.33 DFT fcc 0.28 0.28 0.28 Energy per Atom (Ry) 0.23 bcc 0.18 0.18 0.18 fcc fcc bcc bcc 0.13 graphite sc sc sc 0.08 0.08 0.08 0.03 graphite graphite graphite cdia cdia cdia −0.02 −0.02 −0.02 0.5 1 1.5 2 0.5 1 1.5 2 0.5 1 1.5 2 Relative Atomic Volume

BULK PHASE DIAGRAM OF GERMANIUM −3.3 LCAO −3.5 LDA binding energy per atom (eV) −3.7 fcc bcc sc −3.9 −4.1 cdia −4.3 0.6 0.7 0.8 0.9 1 1.1 relative atomic volume

TEST OF SCED-LCAO-MD

A MOLECULAR DYNAMICS STUDY OF THE LOCAL BENDING OF A SWCNT BY AN AFM TIP sp 2 The buckle region behaves as a sp 3 nanoscale potential barrier Buckle

Magnetic Moments for Carbon Structures Magnetic Moment (emu/g) B=0.1 Tesla Benzene 0.0017 C 60 -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 E mB B -mB

Magnetic Responses of all types of Carbon Nanotori 2 10 } (5,5)/1500 L=75T p = 3 q Metal Tori 1 (5,5)/1200 L=60T 10 Magnetic Moment ( µ B ) (7,4)/1860 L=15T p = } q 0 (9,0)/1332 L=37T 10 (9,0)/1296 L=36T = = −1 L pT q λ 10 F Formed from Semiconducting NT 0.0 } p ≠ Semiconducting 3 q −0.1 (5,5)/1480 L=74T (7,4)/1364 L=11T −0.2 (7,3)/1580;(10,0)/1600 0 100 200 300 400 500 Temperature (K)

• 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 L = ( 3 q)T 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.

EXPERIMENTAL MOTIVATION FOR STUDYING THE ELECTRONC STRUCTURE OF A MWCNT Magnetic Field Orientation Dependence in MWNT Resistance S. Chakraborty, B.W. Alphenaar, and K. Tsukagoshi B perpendicular B parallel Bias for maximum resistance (Vmax) shifts with increasing magnetic field. 6 30x10 B = 3.375 T 25 V dc dV / dI (ohms) 20 Multi-walled nanotube differential resistance measured 15 in either parallel or perpendicular magnetic field 10 5 0 -4 0 4 8 2.5 Bias ( mV ) B parallel B perpendicular 6 2.0 30x10 V max ( mV ) B = 6.75 T 25 dV / dI (ohms) 20 1.5 15 10 1.0 5 0 0.5 -4 0 4 8 0 2 4 6 8 Bias ( mV ) B ( T ) Splitting reflects Fermi energy shift between two field orientations

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?

ELECTRONIC STRUCTURE OF MULTI-WALL CARBON NANOTUBES (7,7)@( 1 2, 1 2)@( 1 7, 1 7)@(22,22) @(27,27)@(32,32)@(37,37)@(42, 42) Single Wall: (7,7) and (12,12) Five Walls: (7,7)@...@(27,27) 5 0.6 5 0.6 ( 1 ) 4 4 0.4 3 3 0.3 2 (5) 2 0.2 1 1 ε (eV) (7,7) ε (eV) ε (eV) ε (eV) 0 0 0 0.0 (12,12) −1 −1 −0.2 −2 −2 −0.3 −3 −3 −0.4 −4 −4 −5 −0.6 −5 −0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.7 0 0.2 0.4 0.6 0.8 1 0.6 0.7 k ( π / a ) k ( π / a ) k ( π / a ) k ( π / a ) Double Walls: (7,7)@(12,12) Six Walls: (7,7)@...@(32,32) 5 0.6 5 0.6 4 4 0.4 3 (2) 0.4 3 2 0.2 1 2 (6) ε (eV) ε (eV) 0.2 0 0.0 1 ε (eV) ε (eV) −1 0 0.0 −0.2 −2 −1 −3 −0.4 −0.2 −4 −2 −5 −0.6 −3 0 0.2 0.4 0.6 0.8 1 0.6 0.7 −0.4 k ( π / a ) k ( π / a ) −4 −5 −0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.7 k ( π / a ) k ( π / a ) Seven Walls: (7,7)@...@(37,37) Three Walls: (7,7)@.@(17,17) 5 0.6 5 0.6 4 0.4 4 3 0.4 3 2 0.2 (3) 2 1 0.2 ε (eV) ε (eV) 1 (7) 0 0.0 ε (eV) ε (eV) 0 0.0 −1 −0.2 −1 −2 −0.2 −2 −3 −0.4 −3 −0.4 −4 −4 −5 −0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.7 −5 −0.6 k ( π / a ) k ( π / a ) 0 0.2 0.4 0.6 0.8 1 0.6 0.7 k ( π / a ) k ( π / a ) Four Walls: (7,7)@..@(22,22) Eight Walls: (7,7)@...@(42,42) 5 0.6 5 0.6 4 4 0.4 3 0.4 3 2 0.2 (8) 2 (4) 1 0.2 ε (eV) ε (eV) 0 0.0 1 ε (eV) ε (eV) −1 0 0.0 −0.2 −2 −1 −3 −0.4 −0.2 −2 −4 −3 −5 −0.6 −0.4 0 0.2 0.4 0.6 0.8 1 0.6 0.7 k ( π / a ) k ( π / a ) −4 −5 −0.6 0 0.2 0.4 0.6 0.8 1 0.6 0.7 k ( π / a ) k ( π / a )

Magnetic Field-Dependence of Fermi Energy Double Walls: (7,7)@(12,12) Four Walls: (7,7)@..@(22,22) 8.0 26 E HOMO (meV) 6.0 38 54 E F (meV) 25 37 Parallel 4.0 E HOMO (meV) E F (meV) 24 36 53 Vertical 2.0 23 35 34 52 78 (E HOMO +E LUMO )/2 42 E LUMO (meV) 55.1 41 77 (E HOMO +E LUMO )/2 58 E LUMO (meV) 55.0 40 76 54.9 57 0 50 100 150 200 0 50 100 150 200 54.8 H (T) H (T) 0 20 40 60 80 0 20 40 60 80 Three Walls: (7,7)@.@(17,17) H (T) H (T) Five Walls: (7,7)@...@(27,27) 30 42 36 52 E HOMO (meV) E F (meV) 25 E HOMO (meV) 41 E F (meV) 51 35 20 50 40 15 34 49 10 39 42 55 (E HOMO +E LUMO )/2 E LUMO (meV) 58 40 56.0 (E HOMO +E LUMO )/2 E LUMO (meV) 54 57 38 55.8 53 56 36 34 55 52 55.6 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 H (T) H (T) H (T) H (T) Six Walls: (7,7)@...@(32,32) Seven Walls: (7,7)@...@(37,37) 45 43 44 52 54 E HOMO (meV) E HOMO (meV) E F (meV) E F (meV) 43 42 42 51 41 53 40 41 50 59 56 54 (E HOMO +E LUMO )/2 (E HOMO +E LUMO )/2 56 E LUMO (meV) E LUMO (meV) 58 55 57 55 53 54 56 54 55 52 53 0 20 40 60 80 0 20 40 60 80 0 10 20 30 40 0 10 20 30 40 H (T) H (T) H (T) H (T)