NANOSCALE THEORY AND SIMULATION:

A Critical Driver for and a Critical Challenge to Commercial Nanotechnology

William A. Goddard III

Introduction

Nanotechnology is concerned with the structures, properties, and processes involving materials having organizational features on the spatial scale of 1 to 300 nm. This is bigger than simple molecules but smaller than the wavelength of visible light. At these scales there are new phenomena that provide opportunities for new levels of sensing, manipulation, and control. In addition, devices at this scale may lead to dramatically enhanced performance, sensitivity, and reliability with dramatically decreased size, weight, or cost. From the experimental point of view, the fundamental problem in nanoscale technology is that the units are too small to see and manipulate and too large for single-pot synthesis from chemical precursors; consequently, most synthetic nanotechnologies focus on self-assembly of molecules. Most presentations at the May 1997 WTEC workshop focused on the challenges and strategies required to synthesize and copy at the nanoscale and to characterize the systems experimentally.

Another critical challenge in developing successful nanoscale technology is development of reliable simulation tools to guide the design, synthesis, monitoring, and testing of the nanoscale systems. This is critical for nanotechnology because we cannot "see" the consequences of experiments at the nanoscale. Thus we believe that it is essential to build fast computational software that reliably predicts the chemistry and physics (structures and properties) as a function of conditions (temperature, pressure, concentrations) and time. Such software must also predict spectroscopic signatures (IR, Raman, UV, NMR) and properties (density, color, surface tension) that can enable experimentalists to gauge the progress in the reactions and processes.

The difficulty from the theory point is that such systems are too large for standard atomistic approaches -- a cube of polyethylene 100 nm on a side contains about 64 million atoms. This requires a level of description coarser than atomic that must still contain the atomistic information responsible for the chemical properties. This nanoscale regime is also referred to as the mesoscale; it lies between the molecular or atomistic scale (where it is convenient to describe molecules in terms of a collection of bonded atoms) and the continuum or macroscale (where it is convenient to describe systems as continuous with a finite element mesh basis for a digital description). The relationships between various scales in the hierarchy of materials modeling approaches is illustrated in Figure 9.10.

We do not yet have sufficient fundamental understanding of the theory and methods required to adequately describe the mesoscale regime, just as we do not yet have all the experimental technology and strategies to synthesize, copy, and manipulate nanoscale systems. Predicting the structure, dynamics, and properties of mesoscale systems on the required time scale (minutes or preferably seconds) demands substantial improvements in

• theory -- we require a better basic understanding of the connection between structure and properties at the mesoscale
• methods -- we require new algorithms to carry out calculations of mesoscale phenomena
• graphical representations -- we require improved ways to communicate mesoscale information in appropriate graphical representations where the relevant elements for designing new systems can be visualized and manipulated

Simulation theory and software that meet these requirements are likely to be both drivers toward nanotechnology and challenges to the development of commercially successful nanotechnology.

Fig. 9.10. The California Institute of Technology Materials and Process Simulation Center (MSC) hierarchy of materials simulation. It is necessary to predict reliable properties prior to synthesis and experiment. The foundation is quantum mechanics (QM). This allows prediction in advance, but it is not practical for time and distance scales of engineering. Thus, it is necessary to extend from QM to engineering design by a succession of scales, where at each scale, the parameters are determined by averaging over the finer scale. This allows first-principles simulations for engineering problems.

The development of these kinds of computational tools for nanotechnology has for several years been a goal of the Materials and Process Simulation Center (MSC) at the California Institute of Technology. Progress has been slow due to a lack of direct funding for this area, which has certainly impeded progress. Recently NASA has established a mechanism for seed funding in this area, which although quite small, has helped significantly.

Computational Nanotechnology: Design, Characterization, Operation, Analysis, and Optimization of Nanoscale Systems

Nanoscale device design involves four stages:

1. predicting the physical and chemical properties of the materials components
2. modeling and characterizing the fabrication and assembly processes
3. analyzing the simulated device under operational conditions
4. controlling and optimizing simulated device operation

The components of a nanoscale device may be in the vapor/gas, liquid, or solid phase (or all three phases may be present and interacting through vapor-liquid, solid-liquid, vapor-solid interfaces) at various stages of fabrication assembly and operation.

Our objectives are to

• develop and validate the computational tools and algorithms required to predict from first principles the materials properties (structural, mechanical, electrical, thermal, rheological, and interface properties) of nanoscale devices as a function of time, pressure, and temperature
• apply these tools to design, characterize, analyze, and optimize devices for various applications
• improve computational performance by porting and optimizing these computational tools into multi-processor environments using emerging parallelization tools
• make these computational tools useful by assembling them into an engineering workbench that allows a designer to construct a nanoscale system on a computer and then test computationally the properties of the resulting system
• aid the iterative design of nanoscale systems by providing graphical analysis tools that allow the engineer to modify parts of the nanostructure and then measure the change in properties

Our goal is to develop accurate, robust, and efficient physics-based and chemistry-based computational and analytical tools and assemble them as a nanoengineering design and simulation workbench, NanoSim. These tools should be useful in enhancing the performance, reliability, and affordability of nanoscale devices, making them valuable for use in advanced technology applications.

Research and Development Scope

Challenges that the MSC team is addressing in its work on NanoSim include the design and simulation of the following kinds of nanoscale systems (NSS):

• memory systems with nanoscale elements
• nanoscale chemical sensor arrays (e.g., electronic noses)
• quantum dot arrays
• nanoscale fuel cells
• nanoscale batteries
• nanoscale springs
• vibration isolators
• nanoscale diodes and transistors

Ultimately, these various units would be integrated into nanodevice systems, which may include internal power sources (e.g., nano fuel cells); energy storage (e.g., nano batteries); controllable switches (combining nano memory); and switches controlled by light, heat molecules, electric, and/or magnetic fields, etc.

Elements of the nanoscale systems might include those shown in Table 9.1, and properties that need to be predicted with the NanoSim computational tools include those shown in Table 9.2.

Table 9.1
Elements of Nanoscale Systems



Table 9.2
Properties to be Predicted with NanoSim Computational Tools

Nanoscale System Design and Simulations: Electrons to Atoms and Beyond

The nanoscale device design computations involve various levels of theory: quantum mechanics; force field development; massive molecular dynamics on all atoms of large systems; and long term molecular dynamics with semi-rigid systems (high frequency modes fixed).

Quantum Mechanics

It is important to use quantum mechanics to describe systems in which bonds are being broken and formed. Only then can we be sure to obtain accurate barrier heights and bond energies. There are a number of developments that are improving and extending the modern methods of quantum mechanics: generalized valence bond, GVB (Goddard et al. 1973); psuedospectral GVB (PS-GVB) (Greeley et al. 1994; Tannor et al. 1994); multireference configuration interaction, MR-CI (Carter and Goddard 1988); and Gaussian dual space density functional theory, GDS-DFT (Chen et al. 1995). These methods are needed to establish the fundamental parameters for new systems. Given the quantum mechanical results we develop force field (FF) descriptions to predict the structures, energetics, and dynamics of the nanoscale systems. The research requirements in this area are to obtain more accurate descriptions for periodic boundary conditions that include many-body effects and accurate forces sufficiently quickly to be used directly for molecular dynamics (MD) without force fields.

Force Fields

Despite the progress in first principles electronic structure theory, the calculations remain far too slow for studying the dynamics in nanotechnology applications. Thus, it is essential to replace the electrons with an FF suitable for MD simulations. Most important in atomistic modeling of nanotechnology systems is to use force fields that faithfully represent the structures and properties of real materials. This is necessary because there may be few experimental tests of the predictions in the early years, requiring that the theory be validated and well founded. In recent years, new force field technologies have been developed to achieve such reliability.

The Hessian-biased force field (HBFF) (Dasgupta et al. 1996) combines normal mode eigenstate information from Hartree Fock (HF) theory with eigenvalue information from experiment. This HBFF approach has been used to develop accurate FF for many industrially interesting polymers such as PE (Karasawa et al. 1990), PVDF (Karasawa and Goddard 1992), nylon (Dasgupta et al. n.d.), POM (Dasgupta et al. 1993), and PSiH (Musgrave et al. 1995); ceramics such as Si₃N₄ (Wendel and Goddard 1992) and C₃N₄ (Guo and Goddard 1995); all semiconductors in group IV, III-V, and II-VI systems (Musgrave 1995); and metals such as the face centered cubic (fcc) metals (Li and Goddard 1993; Kimura et al. n.d.).

For rapidly carrying out calculations on new systems it is also useful to have generic force fields suitable for general classes of molecules. Thus the DREIDING FF (Mayo et al. 1990) has proved quite useful for constructing many nanosystems from main group elements (e.g., C, N, O, F, Si, S, P, Cl). The Universal force field (UFF) (Rappé et al. 1992) is defined for any combination of elements from H to Lr (element 103) and is suitable for any inorganic, organometallic, or organic. To obtain the charges required for accurate calculations, we find that charge equilibration (QEq), which is defined for any combination of elements from H to Lr, allows fast but accurate predictions (Rappé and Goddard 1991). Thus, with UFF and QEq one can predict structures for any combination of elements from H to Lr (element 103).

Standard FF uses springs to average over the electrons of quantum mechanics in describing structures and vibrations of molecules. However, there are many systems where the instantaneous response of the electron (polarizability) is essential in describing the properties. Rather than using quantum chemistry to describe polarization effects (which would be too expensive for most simulations), we have found it possible to use pseudoelectrons in the FF to properly describe the polarization for polymers, metals, ceramics, and organometallics (Karasawa and Goddard 1992). We believe that force fields suitable for accurate prediction of the temperature behavior of moduli and other mechanical, dielectric, and optical properties will require use of such pseudoelectrons.

Thus to predict the piezoelectric and dielectric properties (Karasawa and Goddard 1992; 1995) of poly(vinylidene fluoride) (PVDF), we developed the covalent shell model (CSM) (Karasawa and Goddard 1992) in which each atom is described with two particles: one possesses the mass and is connected to the valence springs of the standard FF theory; the other is light (zero mass) and attached only to its nucleus with a spring constant related to the charge and polarizability. These atomic polarizabilities are obtained by fitting to the polarizability tensor from quantum mechanics calculations on model systems.

Massive Molecular Dynamics

Nanosystem simulations may contain explicit descriptions of 1 million to 1 billion atoms. To make such calculations practical has required major improvements in MD methodologies.

The biggest bottleneck obstructing atomic-level simulations on superlarge systems is accurately summing the Coulomb interactions, which decrease slowly with distance and could lead to N²/2 = 0.5 x 10¹⁶ terms for a 100 million particle system. The standard approach to simplifying such calculations for finite systems has been to use nonbond cutoffs with spline smoothing; however, this leads to an enormous nonbond list for one million particles and also leads to errors two orders of magnitude too large. The only reliable previous procedure (Ewald) for summing the Coulomb interactions for a periodic system requires Fourier transforms (Karasawa and Goddard 1989), which scale as N^1.5, totally impractical for a million atoms.

Because of the need to simulate millions of atoms, we developed methods and optimized parallelized computer programs efficient for high capacity MD (simulation of 10,000 to 10,000,000 atoms for finite molecules or 10,000 to 1,000,000 atoms per unit cell for periodic boundary conditions). There have been a number of important developments:

1. The Cell Multipole Method (CMM) (Ding et al. 1992b), which dramatically reduces the cost of long-range Coulomb and van der Waals interactions while retaining high accuracy. The cost scales linearly with size, allowing atomic-level simulations for million atom systems (Ding et al. 1992b; Lim et al. n.d.; Gao 1997).
2. The Reduced Cell Multipole Method (RCMM) (Ding et al. 1992a), which handles the special difficulties with long-range Coulomb interactions for crystals by combining a reduced unit cell plus CMM for interaction of the unit cell with its adjacent cells. The cost scales linearly with size while retaining high accuracy, allowing simulation of crystals having a million atoms per unit cell (the major use is for models of amorphous and semicrystalline materials).
3. Hierarchical internal coordinates for molecular dynamics, in which some regions (e.g., an alpha helix) are treated as rigid, while others (e.g., an alkane block) are treated with only the torsional degrees of freedom, and others are allowed full Cartesian freedom.
4. The Newton-Euler Inverse Mass Operator (NEIMO) method (Mathiowetz et al. 1994; Vaidehi et al. 1996) for internal coordinate dynamics (e.g., torsions only), which allows the solution of the dynamical equations for internal coordinates without inverting the mass tensor (moment of inertia tensor). The cost of NEIMO is linear in the number of degrees of freedom and small compared to other costs for million atom systems.
5. A semi-rigid body dynamic, MPSim (Gao 1997; Iotov 1997), which allows some units to be treated as rigid bodies, others to be described semi-flexibly (with bonds and angles fixed, but torsions free), and others to be treated semi-rigidly (with torsions fixed relative to each other but allowed to move as a unit, while other parts of the same unit are semi-flexible).
6. A focus has been to develop the algorithms and methods suitable for massively parallel high performance computers and to develop optimal software for exploiting such computer environments (Lim et al. n.d; Gao 1997; Iotov 1997).

The new MPSim program was written and optimized for parallel supercomputers. MPSim is now being used for production simulations on million atom systems using the SGI Power Challenge and HP-Convex systems. These parallel programs scale quite well through 500 processors, as illustrated in Figures 9.11 and 9.12.

Nanoscale System Design and Simulations at the MSC

Examples of nanosystem simulations recently performed at the MSC include the following:

1. structures and binding properties of dendritic polymers; these have substantial potential for the design of tailored hyperbranched structures for use in molecular nanotechnology applications (Miklis et al. 1997)
2. molecular mechanics and molecular dynamics to determine the structure and properties of alkali-doped single-walled nanotubes (Gao et al. 1997b)
3. moduli and pseudo-plasticity of single-wall nanotubes (SWNTs) from accurate force fields, using molecular mechanics (Gao et al. 1997a)
4. molecular dynamics and molecular mechanics simulations of nanomachines (Musgrave et al. 1991; Cagin et al. 1997)
5. QM studies of diamond mechano-synthesis (Walch et al. 1997)
6. development of nanodevice and nanomachine simulation tools in a molecular modeling environment (Che et al. n.d.)
7. incorporation and extension of bond-order-dependent force fields (BOD-FF) for carbon nanotechnology into MPSim, and PolyGraf¹

Fig. 9.11. The scaling behavior of massively parallel evaluation of energy and forces using Cell Multipole Method in MPSim as a function of number of CPUs and atoms.

Fig. 9.12. The scaling behavior of molecular dynamics step in MPSim as a function of number of CPUs and atoms. Recent Developments

Among several new projects related to computational nanotechnology started during 1997 are the following:

1. BOD-FF for description of wear and tribology of microelectricalmechanical systems (MEMS). A key problem is developing BOD-FF with terms to represent long range tube-tube interactions in a continuous manner to address nano and micro tribology problems for nanomechanical and micromechanical devices. The problems of wear and friction are especially important in the design of nano- or micro-mechanical devices for long term space missions. The preliminary results of this investigation will be presented at the American Physical Society March 1998 meeting (Che, Cagin, and Goddard n.d.).
2. Molecular self-assembly. Researchers at the MSC have made substantial progress in investigating the role of molecular self-assembly of Langmuir-Blodgett (LB) films on gold (Gerdy and Goddard 1996) and of corrosion inhibitors (Ramachandran et al. 1996) and wear inhibitors (Jiang et al. 1997) on metals and ceramics. At present, we are investigating the tribology of molecularly thin self-assembled layers and their influence on device operations. These systems involve heterogeneous systems composed of surfaces (mostly hard materials), physisorbed or chemisorbed organic molecularly thin layers on these surfaces and fluid interfaces. Preliminary results of this initiative will be presented at the American Physical Society March 1998 meeting and the ACS 1998 August meeting (Zhou et al. n.d.).
3. Supramolecular assembly of dendritic polymers. We have initiated a subproject to understand the self-assembly of dendrimers on surfaces as possible nano- or microscale sensor applications.
4. Transport properties of carbon nanotubes. Nanotubes as nanoelectronic device components are being studied at several laboratories. An important issue here is the thermal transport properties of the carbon nanotubes. Over the past two years Cagin and Goddard have developed nonequilibrium molecular dynamics techniques to study the transport properties of materials by employing synthetic fields to generate currents and measure the response of materials. Until recently, most of the applications have centered on mass transport and flow properties (Qi et al. n.d.) such as diffusion constants of gases in polymers (Iotov et al. n.d.; Iotov 1997) and viscosity of fluids (metal alloys and hyperbranched organics) (Qi et al. n.d.). Recently we have focused on thermal transport using a synthetic Hamiltonian approach. Next we plan to study the thermal conductivity of nanotubes using nonequilibrium molecular dynamics (NEMD) techniques.

New Initiatives

In addition to continuing the projects listed in the previous section, we have initiated two subprojects:

1. Inherent tribological properties of nanoscale materials. At present, silicon forms the basis of microelectronic and MEMS devices; however, silicon has inherently less desirable wear properties when compared to diamond and polycrystalline diamond (PCD). The promising developments in carbon nanotube synthesis and application make carbon-based materials attractive for device design. Using advanced quantum mechanical techniques, we will investigate the wear phenomena at the electronic level.
2. Failure mechanisms in nanotubes. Using steady state molecular dynamics techniques and BOD-FF, we plan to investigate the yield, fracture, and failure of nanotubes as a function of strain rate and strain profiles. The steady state molecular dynamics technique differs from standard equilibrium molecular dynamics techniques in the sense that the system is not at equilibrium, but it is maintained under a steady state by the presence of various thermodynamic baths. The thermodynamic baths include heat, pressure, and stress for which a constant gradient is maintained.

Notes

References

Cagin, T., A. Jaramillo-Botero, G. Gao, and W.A. Goddard III. 1997. Molecular mechanics and molecular dynamics analysis of Drexler-Merkle gears and neon pump. Paper presented at the Fifth Foresight Institute Conference on Nanotechnology, Palo Alto, Nov. 7. To be published in Nanotechnology.

Carter, E.A., and W.A. Goddard III. 1988. Correlation-consistent configuration interaction: Accurate bond dissociation energies from simple wave functions. J. Chem. Phys. 88: 3132.

Che, J.W., T. Cagin, and W.A. Goddard III. N.d. Work in progress.

Che, J.W., G. Gao, T. Cagin, and W.A. Goddard III. N.d. Comparison of various force fields for describing the properties of carbon nanotubes and nanotori. Work in progress.

Chen, X.J., J.-M. Langlois, and W.A. Goddard III. 1995. Dual-space approach for density-functional calculations of two- and three-dimensional crystals using Gaussian basis functions. Phys. Rev. B 52: 2348.

Dasgupta, S., W.B. Hammond, and W.A. Goddard III. N.d. Crystal structures and properties of nylons polymers from theory. J. Am. Chem. Soc. Accepted.

Dasgupta, S., K.A. Smith, and W.A. Goddard III. 1993. Polyoxymethylene: The Hessian biased force field for molecular dynamics simulations. J. Phys. Chem. 97: 10891.

Dasgupta, S., T. Yamasaki, and W.A. Goddard III. 1996. The Hessian biased singular value decomposition method for optimization and analysis of force fields. 1996. J. Chem. Phys. 104: 2898.

Ding, H., N. Karasawa, and W.A. Goddard III. 1992a. The reduced cell multipole method for Coulomb interactions in periodic systems with million-atom unit cells. Chem. Phys. Lett. 196: 6.

_____. 1992b. Atomic level simulations on a million particles: The cell multipole method for Coulomb and London nonbond interactions. J. Chem. Phys. 97: 4309.

Gao, G. 1997. PhD Thesis, Physics, Caltech (December).

Gao, G., T. Cagin, and W.A. Goddard III. 1997a. Energetics, structure, mechanical and vibrational properties of carbon nanotubes and nanofibers. Paper presented at the Fifth Foresight Institute Conference on Nanotechnology, Palo Alto, Nov. 7. To be published in Nanotechnology.

_____. 1997b. Where the K are in doped single walled carbon nanotube crystals. Phys. Rev. Lett. Submitted for publication.

Gerdy, J.J., and W.A. Goddard III. 1996. Atomistic structure for self-assembled monolayers of alkanethiols on Au(111) surfaces. J. Am. Chem Soc. 118: 3233.

Goddard, W.A., III, T.H. Dunning, Jr., W.J. Hunt, and P.J. Hay. 1973. Generalized valence bond description of bonding in low-lying states of molecules. Accts. Chem. Res. 6: 368.

Greeley, B.H., T.V. Russo, D.T. Mainz, R.A. Friesner, J.M. Langlois, W.A. Goddard III, R.E. Donnelly, and M.N. Ringnalda. 1994. New pseudospectral algorithms for electronic structure calculations: Length scale separation and analytical two-electron integral corrections. J. Chem. Phys. 101: 4028.

Guo, Y., and W.A. Goddard III. 1995. Is carbon nitride harder than diamond? No, but its girth increases when stretched (negative Poisson ratio). Chem. Phys. Lett. 237: 72.

Iotov, M. 1997. PhD thesis, Caltech (Dec.).

Iotov, M., S. Kashihara, S. Dasgupta, and W.A. Goddard III. N.d. Diffusion of gases in polymers. To be submitted.

Jiang, S., R. Frazier, E.S. Yamaguchi, M. Blanco, S. Dasgupta, Y. Zhou, T. Cagin, Y. Tang, and W.A. Goddard III. 1997. The SAM model for wear inhibitor performance of dithiophosphates on iron oxide. J. Phys. Chem. B 101: 7702.

Karasawa, N., S. Dasgupta, and W.A. Goddard III. 1990. Mechanical properties and force field parameters for polyethylene crystal. J. Phys. Chem. 95: 2260.

Karasawa, N., and W.A. Goddard III. 1989. Acceleration of convergence for lattice sums. J. Phys. Chem. 93: 7320.

_____. 1992. Force fields, structures, and properties of poly(vinylidene fluoride) crystals. Macromolecules 25: 7268.

_____. 1995. Dielectric properties of poly(vinylidene fluoride) from molecular dynamics simulations. Macromolecules 28: 6765.

Kimura, Y., T. Cagin, and W.A. Goddard III. N.d. Properties of FCC metals from many-body force fields. Phys. Rev. B1. Submitted for publication.

Li, M., and W.A. Goddard III. 1993. Phenomenological many-body potentials from the interstitial electron model. I. Dynamic properties of metals. J. Chem. Phys. 98: 7995.

Lim, K.T., S. Brunett, M. Iotov, R.B. McClurg, N. Vaidehi, S. Dasgupta, S. Taylor, and W.A. Goddard III. N.d. Molecular dynamics for very large systems on massively parallel computers. J. Comp. Chem. Submitted.

Mathiowetz, A.M., A. Jain, N. Karasawa, and W.A. Goddard III. 1994. Protein simulations using techniques suitable for very large systems: The cell multipole method for nonbond interactions and the Newton-Euler inverse mass operator method for internal coordinate dynamics. Proteins 20: 227.

Mayo, S.L., B.D. Olafson, and W.A. Goddard III. 1990. DREIDING: A generic force field for molecular simulations. J. Phys. Chem 94: 8897.

Miklis, P., T. Cagin, and W.A. Goddard III. 1997. Dynamics of Bengal rose encapsulated in the Meijer dendrimer box. J. Am. Chem. Soc. 119: 7458.

Musgrave, C.B. 1995. PhD thesis in Materials Science, Caltech.

Musgrave, C.B., S. Dasgupta, and W.A. Goddard III. 1995. Hessian based force field for polysilane polymers. J. Phys. Chem. 99: 13321.

Musgrave, C.B., J.K. Perry, R.C. Merkle, and W.A. Goddard III. 1991. Theoretical studies of hydrogen abstraction tool for nanotechnology. Nanotechnology 2: 187.

Ramachandran, S., B.L. Tsai, M. Blanco, H. Chen, Y. Tang, and W.A. Goddard III. 1996. Self-assembled monolayer mechanism for corrosion inhibition of iron by imidazolines. Langmuir 121: 6419.

Rappé, A.K., and W.A. Goddard III. 1991. Charge equilibration for molecular dynamics simulations. J. Phys. Chem. 95: 3358.

Rappé, A.K., C.J. Casewit, K.S. Colwell, W.A. Goddard III, and W.M. Skiff. 1992. UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulation. J. Am. Chem. Soc. 114: 10024.

Tannor, D.J., B. Marten, R. Murphy, R.A. Friesner, D. Sitkoff, A. Nicholls, M. Ringnalda, W.A. Goddard III, and B. Honig. 1994. Accurate first principles calculation of molecular charge distributions and solvation energies from ab initio quantum mechanics and continuum dielectric theory. J. Am. Chem. Soc. 116: 11875.

Vaidehi, N., A. Jain, and W.A. Goddard III. 1996. Constant temperature constrained molecular dynamics: The Newton-Euler inverse mass operator method. J. Phys. Chem. 100: 10508.

Walch, S., and R. Merkle. N.d. Theoretical studies of diamond mechano-synthesis reactions. To be published.

Walch, S.P., W.A. Goddard III, and R.M. Merkle. 1997. Theoretical studies of reactions on diamond surfaces. Paper presented at the Fifth Foresight Conference on Nanotechnology, Palo Alto, Nov. 7. To be published in Nanotechnology.

Wendel, J.A., and W.A. Goddard III. 1992. The Hessian biased force field for silicone nitride ceramics: Predictions of thermodynamic and mechanical properties for (- and (-Si₃N₄. J. Chem. Phys. 97: 5048.

Qi, Y., T. Cagin, Y. Kimura, and W.A. Goddard III. N.d. Shear viscosity of a liquid metal alloy from NEMD: Au-Cu. To be submitted.

Zhou, Y.H., T. Cagin, and W.A. Goddard III. N.d. Work in progress.