Quantum Simulations of Nano- Materials for Renewable Energy Zhigang Wu zhiwu@mines.edu Department of Physics Colorado School of Mines, Golden, CO 80401 Extra Lecture in Modern Physics Class, CSM, 05/04/2010
Outline � � Introduction � � Renewable energy � � Nanomaterials and nanotechnology � � Quantum Simulation Methods � � Density functional theory, Quantum Monte Carlo � � Challenges for simulating nanomaterials for energy � � My Research Work � � Complex-structured silicon nanowires � � Energy-level alignment at hybrid nano-interfaces � � MgH 2 nano-clusters for hydrogen storage 1
Why Do We Care About Renewable Energy? “The possibilities of renewable energy are limitless …We’ve heard promises about it in every State of the Union for the last three decades. But each and every year, we become more, not less, addicted to oil — a 19th-century fossil fuel.” —— Barack Obama 2
What is Renewable Energy? Renewable energy comes from natural resources such as sunlight, wind, tides, biological materials, geothermal heat, etc. 3
What is Non-Renewable Energy? Fossil fuels : petroleum, coal, natural gas, formed by buried organism through anaerobic decomposition with millions of years. 4
The Greenhouse effect The greenhouse effect occurs because windows are transparent in the visible but absorbing in the mid-IR, where most materials re-emit. The same is true of the atmosphere. Greenhouse gases: Sun carbon dioxide water vapor methane nitrous oxide Methane, emitted by microbes called methanogens, kept the early earth warm. 5
Why Do We Care About Renewable Energy? 6
USA Energy Consumption in 2008 7
Is Renewable Energy Enough? There is more energy in sunlight striking on the surface of earth for 1 hour than total global energy consumption per year . 8
U.S. Renewable Resources (100 miles) 2 solar panels ( 10% ef fi ciency ) in Nevada would power the U.S. Turner, Science 285 , 687 (1999). $ 20 Trillion using Si solar panels. 9
A Challenge with Solar Energy For comparison: the cost of coal/oil/gas is 1-4¢ /kWh 3-4¢ 20¢ 3¢ 6-7¢ 5¢ Need major improvement in efficiency and cost to take advantage of solar energy: Nanotechnology 10
There is Plenty Room at the Bottom Why cannot we write the entire 24 volumes of the Encyclopedia Brittanica on the head of a pin? Now, the name of this talk is “There is Plenty of Room at the Bottom”---not just “There is Room at the Bottom.” What I have demonstrated is that there is room--- that you can decrease the size of things in a practical way . I now want to show that there is plenty of room. I will not now discuss how we are going to do it, but only what is possible in principle---in other words, what is possible according to the laws of physics. We are not doing it now simply because we haven't yet gotten around to it. Dec. 29, 1959, Annual APS Meeting Richard Feynman (1918 � 1988) 11
Nanoscience and Nanotechnology 1 nm = 10 -9 m = 10 Å Nanoscale : ~ 1 � 100 nm Nanomaterials : at least one Nanoparticle Ant Motor Speedway dimension in the nanoscale. 4 nm diameter 4 mm long 4km per lap Nanoscience is the study of phenomena and manipulation of nanomaterials. Nanotechnology is the design, characterization, production and application of structures, devices and systems by controlling size and shape at nanoscales. http://www.nano.gov 12
Applications of Nanotechnology . . . nanoscience and nanotechnology will change the nature of almost every human-made object in the next century. —The Interagency Working Group on Nanotechnology, 1999 $1 trillion market by 2011-2015 (NSF 2004) Anti-cancer drug Cheap and clean Next-generation delivery system energy computer Michigan Center for Biological Nanotechnology UCSB Bazan Group 13
Quantum Effects at the Nanoscale � = 729 nm UV UV light light CdSe A bulk material’s properties are fixed. Properties of nanomaterials can be tuned by varying the size. http://nanocluster.mit.edu/ 14
Complex Structures of Nanomaterials Nature Nanotech. 1 , 186 (2006) CdSe Tapered Si Nanowires Properties of nano- materials are affected by their shapes significantly. Exp. characterization of nanomaterials is Thermoelectricity: Good Poor extremely challenging. Theory and simulations are in critical need for advancing nanotech. 4nm 3nm Smooth Si Nanowire Rough Si Nanowire Hochbaum et al ., Nature 451 , 163 (2008) 15
Quantum Mechanical Simulations � � First-principles (or ab initio): no experimental input and start from beginning – solving the many-electron Schrödinger Equation: ˆ � = E � H � � Explain key processes and mechanisms from fundamental theory . � � Empirical models need experimental data. � � Materials properties depend strongly on atomistic details. � � Predict new materials with better properties. 16
Solving Many-Electron Schrödinger Equation � � 2 2 m � 2 � ( � 1 , � 2 ,..., � r N ) + V ( � 1 , � 2 ,..., � r N ) � ( � 1 , � 2 ,..., � r N ) = E � ( � 1 , � 2 ,..., � r N ) r r r r r r r r 3 N - dimensional problem Interacting Interacting N - Exponential wall : the time t needed Electron System to solve this equation is prop. to e N . N = 1, t = 1 s - - N = 2, t = 7 s - N = 10, t = 2.2 � 10 4 s = 6.1 h - - N = 20, t = 4.9 � 10 8 s = 15 years - - - N = 100, t = 2.7 � 10 43 s = 8.5 � 10 35 years! 17
Density Functional Theory 18
Density Functional Theory Many-body Schrödinger equation: � � � = E � , where � = � ( � 1 , � 2 ,..., � ˆ H r r r N ) Intractable 3 N -dimentional equation t � e N Hohenberg-Kohn (HK) theorem 1 : ground-state total energy can be � � expressed in terms of electron density n ( r ), instead of wave functions. E 0 = E [ n ( � r )] Kohn-Sham (KS) theory 2 : mapping an interacting many-body system � � to a non-interacting single-particle system in a mean field. ˆ H � � = � � � � Interacting Non-interacting where � � = � � ( � r ) - - - - Solvable 3-dimentional equation! - - t � N 3 - - - [1] Phys. Rev. 136, B864 (1964) [2] Phys. Rev. 140, A1133 (1965) 19
KS Single-Particle Equation � � � � 2 � 2 2 m + v KS ( � � � i ( � r ) = � i � i ( � r ) r ) � � � where v KS ( � r ) = v ext ( � r ) + v H ( � r ) + v xc ( � r ) n ( � r ') with v H ( � d � � r ) = r ' | � r � � r ' | r )= � E xc [ n ( � r )] v xc ( � Need approximation, � n ( � but simple form r ) works pretty well. OCC and n ( � | � i ( � � r ) = r ) | 2 i 20
The Triumph of DFT Methanol inside a cage of the zeolite Clathrate Sr 8 Ga 16 Ge 30 sodalite (Blue: Si; Yellow: Al; Red: O) (Red: Sr; Blue: Ga; white: Ge) N = O (1000) 21
Challenges Nanomaterials are complicated. CdSe Nano- particle with d = 4 nm ~ 2,000 atoms ~ 20,000 electrons t � N Solution : better scaling scheme: . 22
Challenges Accuracy is limited by the approximation for the exchange- r )= � E xc [ n ( � correlation energy: r )] v xc ( � � n ( � r ) Solution : better E xc guided by results obtained from more accurate methods. 23
Challenges Excitations : DFT is NOT a theory for excited properties. Band gap problem DFT = 0.6 eV Si: E g EXP = 1.2 eV E g Solution : go beyond the single-particle method to include the many-body interactions due to excitation. 24
Quasiparticle Bare particle Quasiparticle Excitations of many-electron system can often be described in terms of weakly interacting - - “quasiparticles”. Quasiparticle (QP) = bare particle + polarization clouds . E QP = E 0 + � � : response of system to the excitation(self-energy) 25
Beyond DFT � � Quantum chemistry post-HF methods: CI, CC, MCSCF, MP2, etc. � � Very accurate for small systems � � But very bad scaling of N 5-7 � � Many-body perturbation methods: GW/BSE � � Accurate for excitations, scaling as N 4-7 � � Quantum Monte Carlo ( QMC ) methods � � Fully-correlated many-body calculation Stochastic solution to Schrödinger equation � � Scaling as N 3 : most accurate benchmarks for medium-size systems 26
Monte Carlo Technique Random numbers can be used to help solve complicated problems in physics. 27
Diffusion Monte Carlo (DMC) Ref: Foulkes et al ., RMP 73 , 33 (2001) 28
How to Perform the Projection? 29
G( R ’, R , � ) as a Transition Probability H=T+V V=0 V � 0 30
Diffusion and Branching 31
A Toy Model: 1D Harmonic Oscillator t DMC ~ O (100 � 1000) t DFT DMC is Intrinsic parallel. 32
An Analogy of QM Methods DFT Post-HF, GW/BSE QMC 33
Complex-Structured Si Nanowires Wu , Neaton & Grossman, PRL 100 , 246804 (2008) Wu , Neaton & Grossman, Nano Lett. 9 , 2418 (2009) 34
Tapering in Nanowires Chan et al ., Nature Nanotech. 1 , 186 (2006) � � Nanowires (NWs) are often tapered rather than straight. � � The tapering can be as large as 2 nm reduction in d for 10 nm in L . 35
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