What is Nanoscience and what can nanoscience be used for

theory meets experiment molecular nanoscience and applications and what is nanoscience and nanotechnology and write their importance
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Theory and Modeling in Nanoscience Report of the May 10–11, 2002, Workshop Conducted by the Basic Energy Sciences and Advanced Scientific Computing Advisory Committees to the Office of Science, Department of EnergyCover illustrations: TOP LEFT: Ordered lubricants confined to nanoscale gap (Peter Cummings). BOTTOM LEFT: Hypothetical spintronic quantum computer (Sankar Das Sarma and Bruce Kane). TOP RIGHT: Folded spectrum method for free-standing quantum dot (Alex Zunger). MIDDLE RIGHT: Equilibrium structures of bare and chemically modified gold nanowires (Uzi Landman). BOTTOM RIGHT: Organic oligomers attracted to the surface of a quantum dot (F. W. Starr and S. C. Glotzer).Theory and Modeling in Nanoscience Report of the May 10–11, 2002, Workshop Conducted by the Basic Energy Sciences and Advanced Scientific Computing Advisory Committees to the Office of Science, Department of Energy Organizing Committee C. William McCurdy Co-Chair and BESAC Representative Lawrence Berkeley National Laboratory Berkeley, CA 94720 Ellen Stechel Co-Chair and ASCAC Representative Ford Motor Company Dearborn, MI 48121 Peter Cummings The University of Tennessee Knoxville, TN 37996 Bruce Hendrickson Sandia National Laboratories Albuquerque, NM 87185 David Keyes Old Dominion University Norfolk, VA 23529 This work was supported by the Director, Office of Science, Office of Basic Energy Sciences and Office of Advanced Scientific Computing Research, of the U.S. Department of Energy.Table of Contents Executive Summary.......................................................................................................................1 I. Introduction..............................................................................................................................3 A. The Purpose of the Workshop..............................................................................................3 B. Parallel Dramatic Advances in Experiment and Theory......................................................3 C. The Central Challenge .........................................................................................................5 D. Key Barriers to Progress in Theory and Modeling in Nanoscience.....................................6 E. Consensus Observations ......................................................................................................7 F. Opportunity for an Expanded Role for the Department of Energy......................................7 G. Need for Computational Resources and Readiness to Use Them........................................8 H. Summary of Specific Challenges and Opportunities...........................................................9 Giant Magnetoresistance in Magnetic Storage .......................................................................11 II. Theory, Modeling, and Simulation in Nanoscience ............................................................12 A. Nano Building Blocks........................................................................................................14 Transport in Nanostructures: Electronic Devices ..............................................................14 Optical Properties on the Nanoscale: Optoelectronic Devices ..........................................15 Coherence/Decoherence Tunneling: Quantum Computing...............................................15 Soft/Hard Matter Interfaces: Biosensors............................................................................15 Spintronics: Information Technology................................................................................16 Implications for Theory and Modeling..............................................................................16 B. Complex Nanostructures and Interfaces ............................................................................17 C. Dynamics, Assembly, and Growth of Nanostructures.......................................................21 III.The Role of Applied Mathematics and Computer Science in Nanoscience......................24 A. Bridging Time and Length Scales......................................................................................26 B. Fast Algorithms..................................................................................................................31 Linear Algebra in Electronic Structure Calculations.........................................................32 Monte Carlo Techniques....................................................................................................33 Data Exploration and Visualization...................................................................................34 Computational Geometry...................................................................................................35 C. Optimization and Predictability.........................................................................................35 Optimization ......................................................................................................................35 Predictability......................................................................................................................37 Software .............................................................................................................................37 Appendix A: Workshop Agenda ................................................................................................39 Appendix B: Workshop Participants.........................................................................................41Executive Summary On May 10 and 11, 2002, a workshop sence of quantitative models that describe entitled “Theory and Modeling in Nano- newly observed phenomena increasingly science” was held in San Francisco to iden- limits progress in the field. A clear consen- tify challenges and opportunities for theory, sus emerged at the workshop that without modeling, and simulation in nanoscience new, robust tools and models for the quan- and nanotechnology and to investigate the titative description of structure and dynam- growing and promising role of applied ics at the nanoscale, the research community mathematics and computer science in meet- would miss important scientific opportuni- ing those challenges. A broad selection of ties in nanoscience. The absence of such university and national laboratory scientists tools would also seriously inhibit wide- contributed to the workshop, which included spread applications in fields of nanotechnol- scientific presentations, a panel discussion, ogy ranging from molecular electronics to breakout sessions, and short white papers. biomolecular materials. To realize the un- mistakable promise of theory, modeling, and Revolutionary New Capabilities in Theory, simulation in overcoming fundamental Modeling, and Simulation challenges in nanoscience requires new human and computer resources. During the past 15 years, the fundamental techniques of theory, modeling, and simula- Fundamental Challenges and tion have undergone a revolution that paral- Opportunities lels the extraordinary experimental advances on which the new field of nanoscience is With each fundamental intellectual and based. This period has seen the development computational challenge that must be met of density functional algorithms, quantum in nanoscience comes opportunities for re- Monte Carlo techniques, ab initio molecular search and discovery utilizing the ap- dynamics, advances in classical Monte Carlo proaches of theory, modeling, and simula- methods and mesoscale methods for soft tion. In the broad topical areas of (1) nano matter, and fast-multipole and multigrid al- building blocks (nanotubes, quantum dots, gorithms. Dramatic new insights have come clusters, and nanoparticles), (2) complex from the application of these and other new nanostructures and nano-interfaces, and (3) theoretical capabilities. Simultaneously, ad- the assembly and growth of nanostructures, vances in computing hardware increased the workshop identified a large number of computing power by four orders of magni- theory, modeling, and simulation challenges tude. The combination of new theoretical and opportunities. Among them are: methods together with increased computing • to bridge electronic through macroscopic power has made it possible to simulate sys- length and time scales tems with millions of degrees of freedom. • to determine the essential science of Unmistakable Promise of Theory, transport mechanisms at the nanoscale Modeling, and Simulation • to devise theoretical and simulation ap- The application of new and extraordinary proaches to study nano-interfaces, which experimental tools to nanosystems has cre- dominate nanoscale systems and are ated an urgent need for a quantitative under- necessarily highly complex and hetero- standing of matter at the nanoscale. The ab- geneous 1of finer scales), to new numerical algo- • to simulate with reasonable accuracy the rithms, like the fast-multipole methods that optical properties of nanoscale structures make very large scale molecular dynamics and to model nanoscale opto-electronic calculations possible. Some of the mathe- devices matics of likely interest (perhaps the most • to simulate complex nanostructures in- important mathematics of interest) is not volving “soft” biologically or organi- fully knowable at the present, but it is clear cally based structures and “hard” in- that collaborative efforts between scientists organic ones as well as nano-interfaces in nanoscience and applied mathematicians between hard and soft matter can yield significant advances central to a successful national nanoscience initiative. • to simulate self-assembly and directed self-assembly The Opportunity for a New Investment • to devise theoretical and simulation ap- The consensus of the workshop is that the proaches to quantum coherence, deco- country’s investment in the national nano- herence, and spintronics science initiative will pay greater scientific • to develop self-validating and bench- dividends if it is accelerated by a new in- marking methods vestment in theory, modeling, and simula- tion in nanoscience. Such an investment can The Role of Applied Mathematics stimulate the formation of alliances and teams of experimentalists, theorists, applied Since mathematics is the language in which mathematicians, and computer and compu- theory is expressed and advanced, develop- tational scientists to meet the challenge of ments in applied mathematics are central to developing a broad quantitative under- the success of theory, modeling, and simu- lation for nanoscience, and the workshop standing of structure and dynamics at the nanoscale. identified important roles for new applied mathematics in the above-mentioned chal- The Department of Energy is uniquely lenges. Novel applied mathematics is re- situated to build a successful program in quired to formulate new theory and to de- theory, modeling, and simulation in nano- velop new computational algorithms appli- science. Much of the nation’s experimental cable to complex systems at the nanoscale. work in nanoscience is already supported by the Department, and new facilities are being The discussion of applied mathematics built at the DOE national laboratories. The at the workshop focused on three areas that Department also has an internationally re- are directly relevant to the central challenges of theory, modeling, and simulation in nano- garded program in applied mathematics, and much of the foundational work on mathe- science: (1) bridging time and length scales, matical modeling and computation has (2) fast algorithms, and (3) optimization and emerged from DOE activities. Finally, the predictability. Each of these broad areas has Department has unique resources and expe- a recent track record of developments from the applied mathematics community. Recent rience in high performance computing and algorithms. The combination of these areas advances range from fundamental ap- of expertise makes the Department of En- proaches, like mathematical homogenization ergy a natural home for nanoscience theory, (whereby reliable coarse-scale results are made possible without detailed knowledge modeling, and simulation. 2I. Introduction A. The Purpose of the Workshop On May 10 and 11, 2002, a workshop enti- participants from the DOE labs. This report tled “Theory and Modeling in Nanoscience” is the result of those contributions and the was held in San Francisco, California, sup- discussions at the workshop. ported by the offices of Basic Energy Sci- This workshop report should be read in ence and Advanced Scientific Computing the context of other documents that define Research of the Department of Energy. The and support the National Nanotechnology Basic Energy Sciences Advisory Committee Initiative. Those documents describe a broad and the Advanced Scientific Computing range of applications that will benefit the Advisory Committee convened the work- principal missions of the Department of En- shop to identify challenges and opportunities ergy, ranging from new materials and the for theory, modeling, and simulation in energy efficiencies they make possible, to nanoscience and nanotechnology, and addi- improved chemical and biological sensing. tionally to investigate the growing and Key among those reports is the one from the promising role of applied mathematics and Office of Basic Energy Sciences entitled computer science in meeting those chal- “Nanoscale Science, Engineering and Tech- lenges. The workshop agenda is reproduced nology Research Directions” (http://www. in Appendix A. sc.doe.gov/production/bes/nanoscale.html), A broad selection of university and na- which points out the great need for theory tional laboratory scientists were invited, and and modeling. Other nanoscience documents about fifty were able to contribute to the from the Department of Energy can be workshop. The participants are listed in Ap- found at http://www.er.doe.gov/production/ pendix B. There were scientific presenta- bes/NNI.htm, and a number of reports from tions, a panel discussion, and breakout ses- other agencies and groups are linked to the sions, together with written contributions in Web site of the National Nanotechnology the form of short white papers from those Initiative, http://www.nano.gov/. B. Parallel Dramatic Advances in Experiment and Theory The context of the workshop was apparent ated new capabilities for characterizing at the outset. The rapid rise of the field of nanostructures. The invention of atomic nanoscience is due to the appearance over force microscopy produced not only a tool the past 15 years of a collection of new ex- for characterizing objects at the nanoscale perimental techniques that have made ma- but one for manipulating them as well. The nipulation and construction of objects at the array of experimental techniques for con- nanoscale possible. Indeed, the field has trolled fabrication of nanotubes and nano- emerged from those new experimental tech- crystals, together with methods to fabricate niques. quantum dots and wells, produced an en- tirely new set of elementary nanostructures. Some of those experimental methods, Combinatorial chemistry and genetic tech- such as scanning tunneling microscopy, cre- niques have opened the door to the synthesis 3of new biomolecular materials and the • New mesoscale methods (including dis- creation of nano-interfaces and nano- sipative particle dynamics and field- interconnects between hard and soft matter. theoretic polymer simulation) have been Nanoscience arose from the entire ensemble developed for describing systems with of these and other new experimental tech- long relaxation times and large spatial niques, which have created the building scales, and are proving useful for the blocks of nanotechnology. rapid prototyping of nanostructures in multicomponent polymer blends. Over the same 15-year period, the fun- damental techniques of theory, modeling, • Quantum Monte Carlo methods now and simulation that are relevant to matter at promise to provide nearly exact descrip- the nanoscale have undergone a revolution tions of the electronic structures of that has been no less stunning. The advances molecules. of computing hardware over this period are • The Car-Parrinello method for ab initio universally familiar, with computing power molecular dynamics with simultaneous increasing by four orders of magnitude, as computation of electronic wavefunctions can be seen by comparing the Gordon Bell and interatomic forces has opened the Prizes in 1988 (1 Gflop/s) and 2001 (11 way for exploring the dynamics of mole- Tflop/s). But as impressive as the increase in cules in condensed media as well as computing power has been, it is only part of complex interfaces. the overall advance in theory, modeling, and simulation that has occurred over the same The tools of theory have advanced as period. This has been the period in which: much as the experimental tools in nano- science over the past 15 years. It has been a • Density functional theory (DFT) trans- true revolution. formed theoretical chemistry, surface science, and materials physics and has The rise of fast workstations, cluster created a new ability to describe the computing, and new generations of mas- electronic structure and interatomic sively parallel computers complete the pic- forces in molecules with hundreds and ture of the transformation in theory, model- ing, and simulation over the last decade and sometimes thousands of atoms (Figure 1). a half. Moreover, these hardware (and basic software) tools are continuing on the • Molecular dynamics with fast multipole Moore’s Law exponential trajectory of im- methods for computing long-range inter- provement, doubling the computing power atomic forces have made accurate cal- available on a single chip every 18 months. culations possible on the dynamics of Computational Grids are emerging as the millions and sometimes billions of next logical extension of cluster and parallel atoms. computing. • Monte Carlo methods for classical The first and most basic consensus of the simulations have undergone a revolu- workshop is clear: Many opportunities for tion, with the development of a range of discovery will be missed if the new tools of techniques (e.g., parallel tempering, theory, modeling, and simulation are not continuum configurational bias, and ex- fully exploited to confront the challenges of tended ensembles) that permit extraordi- nanoscience. Moreover, new investments by narily fast equilibration of systems with the DOE and other funding agencies will be long relaxation times. 4required to exploit and develop these tools for effective application in nanoscience. This consensus is not merely specula- tion, but is based on recent experience of the role of theory in the development of nano- technology. Perhaps no example is more celebrated than the role of calculations based on density functional theory in the develop- ment of giant magnetoresistance in magnetic storage systems. The unprecedented speed with which this discovery was exploited in small hard disk drives for computers de- pended on a detailed picture from theoretical simulations of the electronic structure and electron (spin) transport in these systems. Figure 1. Nanotubes break by first forming a bond Some details of this remarkable story are rotation 5-7-7-5 defect. An application of density given in a sidebar to this report (page 11). functional theory and multigrid methods by Buongiorno Nardelli, Yakobson, and Bernholc, Phys. Rev. B and Phys. Rev. Letters (1998). C. The Central Challenge The discussions and presentations of the workshop identified many specific funda- mental challenges for theory, modeling, and simulation in nanoscience. However, a cen- tral and basic challenge became clear. Be- cause of the rapid advance of experimental investigations in this area, the need for quantitative understanding of matter at the nanoscale is becoming more urgent, and its absence is increasingly a barrier to progress in the field quite generally. The central broad challenge that emerged from discussions at the workshop can be stated simply: Within five to ten years, there must be robust tools for quan- titative understanding of structure and dy- Figure 2. Calculated current-voltage curve for a namics at the nanoscale, without which the novel memory-switchable resistor with 5µµ ×× 5µµ µµ ×× µµ scientific community will have missed many junctions. (Stan Williams, Hewlett-Packard) scientific opportunities as well as a broad devices based on molecular electronics, even range of nanotechnology applications. when they can be built, unless they are thor- The workshop audience was reminded in oughly understood (Figure 2) and manufac- the opening presentation that the electronics turing processes are made predictable and industry will not risk deploying billions of controllable. The electronics industry must 5have new simulations and models for nano- The fundamental theory and modeling technology that are at least as powerful and on which industry will build those tools does predictive as the ones in use today for con- not exist. While it is the province of industry ventional integrated circuits before it can to provide its own design tools, it is the role chance marketing molecular electronics de- of basic science to provide the fundamental vices for a myriad of applications. It can be underpinnings on which they are based. argued that biological applications of nano- Those fundamental tools for quantitative technology will require the same level of understanding are also necessary to the pro- quantitative understanding before they are gress of the science itself. widely applied. D. Key Barriers to Progress in Theory and Modeling in Nanoscience Much of the current mode of theoretical science arises because theoretical efforts in study in nanoscience follows the traditional separate disciplines are converging on this separation of the practice of experiment intrinsically multidisciplinary field. The from the practice of theory and simulation, specific barrier is the difficulty, given the both separate from the underpinning applied present funding mechanisms and policies, of mathematics and computer science. This is undertaking high-risk but potentially high- not a new observation, nor does it apply payoff research, especially if it involves ex- only to theory, modeling, and simulation in pensive human or computational resources. nanoscience. Nonetheless, it is a particularly At this early stage in the evolution of the problematic issue for this field. field, it is frequently not at all clear what techniques from the disparate subdisciplines By its very nature, nanoscience involves of condensed matter physics, surface sci- multiple length and time scales as well as ence, materials science and engineering, the combination of types of materials and theoretical chemistry, chemical engineering, molecules that have been traditionally stud- and computational biology will be success- ied in separate subdisciplines. For theory, ful in the new context being created every modeling, and simulation, this means that week by novel experiments. The traditional fundamental methods that were developed in degree of separation of the practice of ex- separate contexts will have to be combined periment from the practice of theory further and new ones invented. This is the key rea- intensifies the challenge. son why an alliance of investigators in nano- science with those in applied mathematics For these reasons, opportunities will be and computer science will be necessary to missed if new funding programs in theory, the success of theory, modeling, and simu- modeling, and simulation in nanoscience do lation in nanoscience. A new investment in not aggressively encourage highly specula- theory, modeling and simulation in nano- tive and risky research. At least one experi- science should facilitate the formation of mentalist at this workshop complained that such alliances and teams of theorists, com- high-risk and speculative theoretical and putational scientists, applied mathemati- computational efforts are too rare in this cians, and computer scientists. field, and that sentiment was echoed by a number of theorists. A second impediment to progress in theory, modeling, and simulation in nano- 6E. Consensus Observations A broad consensus emerged at the workshop lectual and computational challenges on several key observations. that must be addressed to achieve the full potential of theory, modeling, and • The role of theory, modeling, and simu- simulation. lation in nanoscience is central to the success of the National Nanotechnology • New efforts in applied mathematics, Initiative. particularly in collaboration with theo- rists in nanoscience, are likely to play a • The time is right to increase federal in- key role in meeting those fundamental vestment in theory, modeling, and challenges as well as in developing simulation in nanoscience to accelerate computational algorithms that will be- scientific and technological discovery. come mainstays of computational nano- • While there are many successful theo- science in the future. retical and computational efforts yield- ing new results today in nanoscience, there remain many fundamental intel- F. Opportunity for an Expanded Role for the Department of Energy The time is ripe for an initiative in theory ties have begun training a new generation of and modeling of nanoscale phenomena not computational scientists who understand only because of the magnitude of the poten- scientific issues that bridge disciplines from tial payoff, but also because the odds of physical principles to computer architecture. achieving breakthroughs are rapidly im- Advances in extensibility and portability proving. make major investments in reusable soft- ware attractive. Attention to validation and Computational simulation is riding a verification has repaired credibility gaps for hardware and software wave that has led to simulation in many areas. revolutionary advances in many fields repre- sented by both continuous and discrete mod- Nanotechnologists reaching toward els. The ASCI and SciDAC initiatives of the simulation to provide missing understanding DOE have fostered capabilities that make will find simulation technology meeting new simulations with millions of degrees of free- challenges with substantial power. However, dom on thousands of processors for tens of theorists and modelers working on the inter- days possible. National security decisions face of nanotechnology and simulation tech- and other matters of policy affecting the en- nology are required to make the connec- vironment and federal investment in unique tions. facilities, such as lasers, accelerators, toka- The workshop focused considerable at- maks, etc. are increasingly being reliably tention on the role of applied mathematics in informed by simulation, as are corporate de- nanoscience. In his presentation, one of the cisions of similar magnitude, such as where scientists working on molecular dynamics to drill for petroleum, what to look for in studies of objects and phenomena at the new pharmaceuticals, and how to design nanoscale expressed the sentiment of the billion-dollar manufacturing lines. Universi- 7workshop effectively by saying that the role cussed in Section 3 of this report. But this of applied mathematics should be to “make discussion is not (and cannot be) fully com- tractable the problems that are currently im- prehensive due to the breadth of nanoscience possible.” As mathematics is the language in and the unknowable paths that modeling will which models are phrased, developments in follow. applied mathematics are central to the suc- The Department of Energy is uniquely cess of an initiative in theory and modeling situated to build a successful program in for nanoscience. A key challenge in nano- theory, modeling, and simulation in nano- science is the range of length and time scales science. Much of the experimental work in that need to be bridged. It seems likely that nanoscience is already supported by the De- fundamentally new mathematics will be partment, and new facilities are being built. needed to meet this challenge. The Department also has an internationally The diverse phenomena within nano- regarded program in applied mathematics, science will lead to a plethora of models and much of the foundational work on with widely varying characteristics. For this mathematical modeling and computation has reason, it is difficult to anticipate all the ar- emerged from DOE activities. Finally, the eas of mathematics which are likely to con- Department has unique resources and expe- tribute, and serendipity will undoubtedly rience in high performance computing and play a role. As models and their supporting algorithms. The conjunction these areas of mathematics mature, new algorithms will be expertise make the Department of Energy a needed to allow for efficient utilization and natural home for nanoscience theory and application of the models. These issues and modeling. some significant areas of activity are dis- G. Need for Computational Resources and Readiness to Use Them The collection of algorithms and computa- full range of resources, from massively par- tional approaches developed over the last 15 allel supercomputers to workstation and years that form the basis of the revolution in cluster computing. The sentiment that not modeling and simulation in areas relevant to enough resources are available to the com- nanoscience have made this community in- munity, at all levels of computing power, tense users of computing at all levels, in- was nearly universally acknowledged. This cluding the teraflop/s level. This field has community is ready for terascale computing, produced several Gordon Bell Prize winners and it needs considerably more resources for for “fastest application code,” most recently workstation and cluster computing. in the area of magnetic properties of materi- A significant amount of discussion in the als. That work, by a team led by Malcolm breakout sessions focused on scalable algo- Stocks at Oak Ridge National Laboratory, is rithms, meaning algorithms that scale well only one example of computing at the tera- with particle number or dimension as well as scale in nanoscience. with increasing size of parallel computing The workshop did not focus much dis- hardware. The simulation and modeling cussion specifically on the need for compu- community in nanoscience is one of the tational resources, since that need is ubiqui- most computationally sophisticated in all of tous and ongoing. The presentations showed the natural sciences. That fact was demon- computationally intensive research using the strated in the talks and breakout sessions of 8the workshop, and is displayed particularly algorithms and well characterized nano in the sections of this report devoted to fast building blocks. H. Summary of Specific Challenges and Opportunities The sections that follow identify a large are often composed of dissimilar classes number of challenges in theory, modeling, of materials. and simulation in nanoscience together with • To simulate complex nanostructures in- opportunities for overcoming those chal- volving many molecular and atomic spe- lenges. Because an assembly of 50 scientists cies as well as the combination of “soft” and applied mathematicians is too small a biological and/or organic structures and number to represent all the active areas of “hard” inorganic ones. nanoscience and related mathematics, the list compiled at the workshop is necessarily • To devise theoretical and simulation ap- incomplete. However, a summary of even proaches to nano-interfaces between the partial catalog accumulated during the hard and soft matter that will play cen- workshop and described briefly in the fol- tral roles in biomolecular materials and their applications. lowing sections should make a compelling case for investment in theory, modeling, and • To address the central challenge of simulation in nanoscience. The challenges bridging a wide range of length and time and opportunities include: scales so that phenomena captured in atomistic simulations can be modeled at • To determine the essential science of transport mechanisms, including electron the nanoscale and beyond. transport (fundamental to the functional- • To simulate self-assembly, the key to ity of molecular electronics, nanotubes, large-scale production of novel struc- and nanowires), spin transport (funda- tures, which typically involves many mental to the functionality of spintron- temporal and spatial scales and many ics-based devices), and molecule trans- more species than the final product. port (fundamental to the functionality of chemical and biological sensors, mo- • To devise theoretical and simulation ap- lecular separations/membranes, and proaches to quantum coherence and de- coherence, including tunneling phenom- nanofluidics). ena, all of which are central issues for • To simulate with reasonable accuracy using nanotechnology to implement the optical properties of nanoscale quantum computing. structures and to model nanoscale opto- electronic devices, recognizing that in • To devise theoretical and simulation ap- confined dimensions, optical properties proaches to spintronics, capable of accu- of matter are often dramatically altered rately describing the key phenomena in from properties in bulk. semiconductor-based “spin valves” and “spin qubits.” • To devise theoretical and simulation ap- proaches to study nano-interfaces, which • To develop self-validating and bench- are necessarily highly complex and het- marking methodologies for modeling erogeneous in shape and substance, and and simulation, in which a coarser- grained description (whether it is 9atomistic molecular dynamics or meso- breakout sessions. Three of them focused on scale modeling) is always validated nanoscience directly: against more detailed calculations, since • Well Characterized Nano Building appropriate validating experiments will Blocks often be difficult to perform. • Complex Nanostructures and Interfaces For each entry in this list, and the many that can be added to it, there is an estab- • Dynamics, Assembly, and Growth of lished state of the art together with an array Nanostructures of specific technical issues that must be Three others focused on the role of ap- faced by researchers. For all of the chal- plied mathematics and computer science: lenges listed, there is also an array of fun- damental questions to be addressed by re- • Crossing Time and Length Scales searchers in applied mathematics. • Fast Algorithms This report is a brief synthesis of the • Optimization and Predictability effort of approximately 50 experts in the nanosciences, mathematics, and computer There were, of course, other possible science, drawn from universities, industry, ways to organize the discussions, but the and the national laboratories. Following the outcome would likely have been the same no matter what the organization of the top- scientific presentations and a panel discus- sion on the roles of applied mathematics and ics. Nevertheless, the structure of this report computer science, the principal recommen- reflects this particular selection of categories dations of the workshop were developed in for the breakout sessions. 10Giant Magnetoresistance in Magnetic Storage The giant magnetoresistance (GMR) effect was discovered in 1988 and within a decade was in R R R R R R pa pa par r ra a al l ll l le e el l l a a an n nti ti tipa pa par r ra a al l ll l le e el l l i i i i i i wide commercial use in computer hard disks p p p a a a (Figure 3) and magnetic sensors. The technol- ogy significantly boosted the amount of informa- Figure 5. Schematic of GMR indicating change in tion that could be recorded on a magnetic sur- resistance accompanying magnetization reversal upon sensing an opposing bit. (IBM) face (Figure 4). The unprecedented speed of application (less than 10 years from discovery to (up or down). In fact, the magnetic moment itself deployment) resulted largely from advances in theory and modeling that explained the micro- results from an imbalance in the total number of electrons of each spin type. Modern quantum- scopic quantum-mechanical processes respon- sible for the GMR effect. mechanical computational methods based on density functional theory (for which Walter Kohn was awarded the 1998 Nobel Prize) then pro- vided a detailed picture of the electronic struc- ture and electron (spin) transport in these sys- tems. Indeed, some unexpected effects, such as spin-dependent channeling, were first predicted on the basis of first-principles calculations and Figure 3. GMR and MR head structures. (IBM) were only later observed experimentally. In fact, GMR is only one aspect of the rich physics associated with the magnetic multilayers now used in read heads. Equally important are oscillatory exchange coupling (which is used to engineer the size of the magnetic field required to switch the device) and exchange bias (which is used to offset the zero of the switching field in order to reduce noise). In exchange coupling, a detailed understanding of the mechanisms re- sponsible has been obtained on the basis of first-principles theory. Less is known about ex- change bias, but significant progress has been made on the basis of simplified models and with first-principles calculations of the magnetic struc- Figure 4. Magnetic head evolution. (IBM) ture at the interface between a ferromagnet and an antiferromagnet. The effect is observed in a pair of ferromag- netic layers separated by a (generally) nonmag- Impressive as these advances in theory and netic spacer. It occurs when the magnetic mo- modeling have been, their application to nano- ment in one ferromagnetic layer is switched from magnetism has only just begun. New synthesis being parallel to the magnetic moment of the techniques have been discovered for magnetic other layer to being antiparallel (Figure 5). When nanowires, nanoparticles, and molecular mag- a read head senses a magnetic “bit” on the stor- nets; magnetic semiconductors with high Curie age medium, it switches the magnetic moment temperatures have been fabricated; and spin- on one layer and measures the resistance, thus polarized currents have been found to drive sensing the information on the disk. magnetic-domain walls. When understood through theory and modeling, these findings also Soon after the discovery of GMR, the phe- are likely to lead to technological advances and nomenon was seen to be related to the different commercial applications. “resistances” of electrons having different spins 11II. Theory, Modeling, and Simulation in Nanoscience The challenges presented by nanoscience pharmaceutical industries in the design of and nanotechnology are not simply re- new products, the design and optimization stricted to the description of nanoscale sys- of manufacturing processes, and the trouble- tems and objects themselves, but extend to shooting of existing processes. However, the their design, synthesis, interaction with the exquisite dependence on details of molecu- macroscopic world, and ultimately large- lar composition and structures at the nano- scale production. Production is particularly scale means that attempting to understand important if the technology is to become nanoscale systems and control the processes useful in society. Furthermore, the experi- to produce them based solely on experi- ence of the participants in the workshop mental characterization is out of the ques- from the engineering community strongly tion. suggests that a commercial enterprise will The field of nanoscience is quite broad not commit to large-scale manufacture of a and encompasses a wide range of yet-to-be- product unless it can understand the material understood phenomena and structures. It is to be manufactured and can control the pro- difficult to define nanoscience precisely, but cess to make products within well-defined a definition consistent with the National tolerance limits. Nanotechnology Initiative is: For macroscopic systems—such as the The study of structures, dynamics, products made daily by the chemical, mate- and properties of systems in which rials, and pharmaceutical industries—that one or more of the spatial dimen- knowledge is often largely or exclusively sions is nanoscopic (1–100 nm), empirical, founded on an experimental char- thus resulting in dynamics and acterization over the ranges of state condi- properties that are distinctly differ- tions encountered in a manufacturing proc- ent (often in extraordinary and un- ess, since macroscopic systems are intrinsi- expected ways that can be favora- cally reproducible. Increasingly, however, bly exploited) from both small- this characterization is based on molecular molecule systems and systems mac- modeling, including all of the tools relevant roscopic in all dimensions. to modeling nanoscale systems, such as Rational fabrication and integration of electronic structure, molecular simulation, nanoscale materials and devices offers the and mesoscale modeling methods. Indeed, promise of revolutionizing science and tech- the report Technology Vision 2020: The U.S. 1 nology, provided that principles underlying Chemical Industry has identified molecular their unique dynamics and properties can be modeling as one of the key technologies that discovered, understood, and fully exploited. the chemical industry needs to revolutionize However, functional nanoscale structures its ability to design and optimize chemicals often involve quite dissimilar materials (for and the processes to manufacture them. example, organic or biological in contact Molecular modeling already plays a with inorganic), are frequently difficult to major role in the chemical, materials, and characterize experimentally, and must ulti- mately be assembled, controlled, and util- 1 ized by manipulating quantities (e.g., tem- American Chemical Society et al., 1996, http:// perature, pressure, stress) at the macroscale. membership.acs.org/i/iec/docs/chemvision2020.pdf. 12This combination of features puts un- • The focus of the third session was dy- precedented demands on theory, modeling, namics, assembly, and growth of nano- and simulation: for example, due to nano- structures, and so was concerned with scale dimensionality, quantum effects are the dynamical aspects of complex nano- often important, and the usual theories valid structures. Hence, transport properties either for bulk systems or for small mole- (such as electron and spin transport and cules break down. Qualitatively new theo- molecular diffusion) of complex nano- ries are needed for this state of matter inter- structures, as well as the dynamic proc- mediate between the atomic scale and a esses leading to their creation, particu- large-enough scale for collective behavior to larly self-assembly, were central to this take over, as well as methods for connecting session. the nanoscale with finer and coarser scales. The reports presented below are summa- Within the context of this definition of ries drafted by the session chairs. Given the nanoscience and the need for significant ad- ostensibly different charges presented to vances in our understanding of the nano- each group, there is remarkable unanimity in scale, three breakout sessions on theory, their conclusions with respect to the out- modeling, and simulation in nanoscale sci- standing theory, modeling, and simulation ence considered three broad classes of nano- needs and opportunities. Among the com- systems: mon themes are: • The first class consisted of nano building • the need for fundamental theory of dy- blocks (such as nanotubes, quantum namical electron structure and transport dots, clusters, and nanoparticles), some • algorithmic advances and conceptual of which can be synthesized quite repro- understanding leading to efficient elec- ducibly and well characterized experi- tronic structure calculations of large mentally. numbers of atoms • The second class consisted of complex 2 • new theoretical treatments to describe nanostructures and nano-interfaces, nano-interfaces and assembly of nano- reflecting the importance of nano- structures interfaces in a wide variety of nanoscale systems. This session was specifically • fundamentally sound methods for asked to consider steady-state properties bridging length and time scales and their of complex nanostructures and nano- integration into seamless modeling envi- interfaces. ronments • commitment to an infrastructure for community-based open-source codes. These common themes have been incor- 2 We can distinguish between interfaces in general porated into the recommendations and chal- and nano-interfaces as follows: Typically, an inter- lenges outlined in Section I of this report. face separates two bulk phases; we define, consistent with the above definition, a nano-interface as one in which the extent of one or more of the phases being separated by the interfaces is nanoscopic. In nano- interfaces we include nano-interconnects, which join two or more structures at the nanoscale. For nano- interfaces, traditional surface science is generally not applicable. 13A. Nano Building Blocks Well characterized building blocks for nano- units come to mind which range from clus- science need to be created and quantitatively ters less than 1 nm in size to nanoparticles, understood for a number of crucial reasons. such as aerosols and aerogels much larger A key aspect of construction, whether at the than 100 nm. However, we believe the best- macroscopic or microscopic scale, is the no- characterized and most appropriate building tion of a “building block.” Office buildings blocks are: are often made from bricks and girders, • clusters and molecular nanostructures molecular components from atoms. Just as knowledge of the atom allows us to make • nanotubes and related systems and manipulate molecular species, knowl- • quantum wells, wires, films and dots. edge of bricks and mortar allows us to con- These blocks are well defined by ex- struct high-rise buildings. periment and frequently tractable using Well-characterized nano building blocks contemporary theory. Moreover, they have will be the centerpiece of new functional been demonstrated to hold promise in exist- nanomechanical, nanoelectronic, and nano- ing technology. We believe that building magnetic devices. A quantitative under- blocks would have an immediate impact in standing of the transport, dynamics, elec- the five areas described below. tronic, magnetic, thermodynamic, and me- chanical properties is crucial to building at Transport in Nanostructures: the nanoscale. As an example, current theo- Electronic Devices retical approaches to nanoelectronics often Any electronic device needs to control and cannot accurately predict I-V curves for the manipulate current. At the nanoscale, new simplest molecular systems. Without a co- phenomena come into play. Classical de- herent and accurate theoretical description scriptions become inoperable compared to of this most fundamental aspect of devices, quantum phenomena such as tunneling, progress in this area will necessarily be lim- fluctuations, confined dimensionality, and ited. the discreteness of the electric charge. At Theoretical studies for these systems these dimensions, the system will be domi- will necessarily have to be based on ap- nated entirely by surfaces. This presents proximate methods; the systems are simply further complications for electronic materi- too large and too complex to be handled als, which often undergo strong and com- purely by ab initio methods. Even if the plex reconstructions. Defining accurate problems are tractable, we will make much structure at the interface will be difficult. greater progress with well-validated ap- However, without an accurate surface proximate models. Thus a variety of bench- structure, it will be even more difficult to marking methodologies and validation test- compute any transport properties. Moreover, ing are needed to establish the accuracy and current-induced changes within the structure effectiveness of new models and approxi- may occur. This situation will require the mate theory. complexity, but not intractable approach, of a careful self-consistent solution in a non- At the nanoscale, what are the nano equilibrium environment. building blocks that would play an analo- gous role to macro building blocks? Several 14

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