Atomistic Design and Simulations of

Nanoscale Machines and Assembly

Sponsoring Agency: NASA

Principal Investigators

Project Objectives

  • to use large scale molecular dynamics (MD) to study and simulate the dynamics of nanomachines and of molecular assemblers

  • to use quantum mechanics (QM) to study and develop diamond mechano synthesis tools and to develop force fields (FF) for use in MD and MC.

  • to use MD and Monte Carlo (MC) techniques to examine self-assembled monolayers (SAM) strategies for constructing components of nanoscale systems.

  • The Caltech software for these processes will be optimized for the NASA parallel computers in order that they be available for this and other NASA computational nanotechnology projects.

  • These projects will be in collaboration with industrial groups at Xerox and at Hughes Electro/Optical systems.


    In the first year the project milestones are:

    The second and third years will build upon these activities, including strategies in which self assembly of supramolecules is used to obtain components nano devices.

    Nanoscale Machines

    In order to lay a foundation for creating a technology for manufacturing at the nanoscale, Drexler, Merkle, and collaboratorsl,2 have been analyzing designs for mechanical systems at the nanoscale (1 to 100 nm) that could in principle be manufactured. At the nanoscale one can no longer think of the material as a continuum whose properties change continuously as it is cut and shaped. Rather one has to consider that it is formed from discrete atoms. Thus at the nanoscale one has a supermolecule rather than a finely divided solid. This requires one to analyze how the elements of normal macromaterials design change as the scale is reduced from mm to micron to nanometers. The differences are dramatic. For a macrosystem a long alkane molecule or a flake of MoS2 might serve as a lubricant, but for a system built on the scale of nm, such molecules may serve as dirt that would clog and disable the nanosystem. Similarly the scaling of vibrations, electrical forces, thermal expansion, magnetic interactions, and surface tension with size can lead to phenomena very different at the scale of atoms than at the macroscale. Indeed in Nanosystems2, Drexler considered many aspects of how the scaling of familiar macroscopic concepts changes as one goes to the nanoscale.

    In order to make progress here it is necessary to consider specific nanoscale supermolecular systems which could in principle be manufactured. Without worrying about the practical aspects of synthesizing the system, can one make supermolecular assemblies that would function as useful nanoscale machines? Can one design synthetic procedures that could in principle manufacture these machines? Again it is not essential to have a practical cost-effective design. It is sufficient to demonstrate the existence theorem, that sequences of steps involving real atoms with the properties of real molecules can indeed lead to processes that would manufacture nanoscale machines with useful functionality. If the goal is achievable, then we can focus on ways to achieve the design in a practical fashion.

    Of course we know that nanoscale machines are possible. Nature has figured out methods of synthesizing quite remarkable nanoscale machines that function reliably, are synthesized cheaply and reliably (often self correcting) from readily available materials and energy sources, and are environmentally benign (biodegradable). Indeed modern science is finding ways to manipulate these systems to manufacture modified molecules and systems with predesigned properties and functionalities. However, the complex chemistry and biology involved in such systems limits the applications and flexibility to modify these systems for dramatically different applications. Thus it is important to determine the feasibility of designing and making nanoscale machines with new functionality and characteristics.

    Along these lines Merkle and Drexler3 have designed a nanoscale planetary gear with eight moving parts (see Fig. 1) using molecular mechanics force fields4 to ensure that the bond lengths, bond angles, van der Waals distances, and strain energies are reasonable. Based on their design we carried out and reported at the 1995 Nanotechnology conferences a molecular dynamics simulation to test the properties of this gear. Using somewhat extreme conditions (rapid accelerations and high frequency rotations), we found significant instabilities in this designs (see Fig. 2). In response Merkle and Drexler improved their designs (see Fig. 3) to achieve much more stable motions. We find that this new design is more stable; however, it also has too much slip.7 That is the actual distances between the atoms for the specific set of atoms in this supermolecular system leads to spacings between the gear teeth and the opposing gear faces that are easily stripped. The problem is that a careful balance must be achieved between:

    It is possible to balance these in the static system, but the dynamical motions lead to fluctuations (vibrations) that allow slippage.7 This is not a calamity and does not mean that nanotechnology will not work. It means that we have a lot of hard work to do in designing prototype systems and testing them.

    The problem here is the discreteness of the atoms. A macroscopic system is treated as a continuum. To make a gear one can design the shape of the gear teeth and the shape of the opposing teeth of the face to have exactly the same spacing as the gears turn. It is then only necessary to design the casting or injection molding system with appropriate tolerances to achieve good performance. The discreteness of the atoms plays no role when these tolerances are 0.0001 inch = 2.54 103 urn. We propose to continue developing and testing designs for nanoscale machines with the goal of determining designs that would indeed work if synthesized. We imagine that the eventual design would have the functionality of a planetary gear but might have an appearance completely different than the macroscopic systems. Thus because a gear tooth in the xy plane cannot be atomically smooth in the z direction, we may develop a Vee design so that the Vee shape of the gear tooth in the z direction nestles within a Vee notch in the race to keep stability in the z direction as the teeth contact in the xy plane. This design would make no sense for a macroscopic gear system since the gear could never be placed inside the race. However for a molecular system one could imagine that the gear is constructed and that the race is constructed all except for a last joining unit. The parts could be assembled and then the final connections on the face made to complete the design. This is a little like the ZARBI system of Rebek.8 We propose to investigate such systems, using accurate force fields3,9,l0 and massive molecular dynamics simulations to test and refine the concepts.

    More recently Drexler and Merklel3 have designed a nanomachine (Fig. 4) which in one mode could served as a pump for Ne and in another could serve to convert Ne pressure to rotary power. We propose to investigate this system using accurate force fields and molecular dynamics simulations to test and refine the concepts.

    The key part of this proposal is to find creative solutions to the difficult problems involved in developing viable nanosystems. Our team of collaborators is uniquely suited for this. They have been involved since 1991 in presenting invited lectures at the biannual Nanotechnology conferences sponsored by the Foresight Institute. They interact frequently and publish with Ralph Merkle one of the leaders in developing the new concepts. They have been involved with forming a nanotechnology study group among the graduate students at Caltech.

    Dynamic tests of a molecular assembler

    Ultimately we need a programmable synthetic system to make a real device. Even though we may not have tools for all the chemical steps and may not have designs for all the pumps, and engines, and transmissions needed, we propose to study the dynamics of simplified prototype assemblers. In these studies we anticipate having

    1. a reservoir or supplies area for providing the various building units (atoms and fragments) required

    2. a work area in we construct the nanomachine device (initially we will consider assembling the structure on top of a diamond surface).

    3. a molecular scale nanohand which will extract the atoms from 1 and carry them to 2

    We will then use extensions of our MPSim massive molecular dynamics program12 to operate the system: moving the tip from reservoir to work area, moving it to contact the appropriate surface site, moving it to regenerate the active tip, and then moving it back to add new atoms and molecules. This will include proper temperature effects, molecular vibrations, energy release upon the various chemical steps, etc.

    The ground rules here are that a realistic FF be used and that all pieces be treated at the atomic level (but some might be semi-rigid). This will use the FF developed for nanosynthesis. The purpose of these simulations is to examine issues of vibration cause by chemical forces as the tool picks up and delivers atoms to the growing surface. Also we want to consider the effect of energy release in the chemical steps on the thermal fluctuations in these systems (which may cause displacements and vibrations).

    Diamondoid Mechanosynthesis

    In addition to testing the design of nanomachines, it is necessary to develop procedures that could in principle be used to synthesize them. Can we design a tip for a device having the control of an Atomic Force Microscope (AFM) or Scanning Tunneling Microscope (STM) which would have chemical properties suitable for deliberately adding or subtracting atoms from a nanopart to synthesize the desired molecule? Along these lines we carried out quantum chemical calculations on a tool (the nanohand) that would be able to pluck off selected hydrogen atoms from a diamondoid-like tool.14 We also showed how this H could be eliminated (using light) from the nanohand to reactivate the nanohand tip.14 We have also investigated the mechanism of CVD growth of diamond38 from H2 + CH4, including the effect of Cl and F on this growth. We have also investigated the mechanism of growth for isolated nanotubes.39 These studies provide lessons about the chemistry of such systems which may be useful in developing practical nanotools.

    More recently we initiated the study of adding C, C2, or C3 units with new nanohands.36 It is important that these designs be such that the nanotools can be continually recycled on site. Probably the current designs would not be practical for constructing nanomachines having 10,000 to a million atoms (length scales of 5 to 30 nary). However they may be needed to activate specific sites that would serve to catalyze particular steps or lead to joining of particular units. We propose to continue developing nanotips capable of delivery particular units. Eventually we want to consider atoms such as O. S. Cl, F. and small molecular units such as OH, NO2, SO2, HCO, etc.) that might be useful for subsequent chemistry.

    One goal of mechanosynthesis tool development is to use quantum mechanical calculations at the appropriate level of theory to determine the FF to be used to model larger systems. Some of the systems to be studied include models of diamond mechanosynthesis with inclusion of surface reconstruction and molecular dynamics simulations of reactions at surfaces and mechanical systems such as gears, bearings etc. The electronic structure calculations will be used to model detailed chemistry which might not be well described by the usual FF. An example of a system where the usual potentials might fail is the reaction of a carbene with a diamond surface. Here potentials derived from experimental and ab initio data might not reproduce the non-least-motion pathways characteristic of these systems. In this work we have used density functional theory (DFT) methods, since we have found that they are the most cost-effective means of obtaining accurate results on the reactions that we need to consider. For example, we have made detailed comparisons of ab initio and density functional theory for the reaction of vinylidene with acetylene, which has some of the features of the reaction of the carbene tool with a diamond surface.

    We have considered36 the interaction of the carbene tool and C2 tool with the unreconstructed diam~ond (111) surface. We found36 that for the unreconstructed surface, where adjacent surface radical sites are separated by the second nearest neighbor distance, the carbene tool prefers an on-top site to a bridged site and this tool is not useful for adding a single carbon atom to this surface. However, the C2 tool is found to be effective at adding a bridged C2 molecule. The bond length in the bridged C2 molecule is closer to the nearest neighbor distance and also the remaining ~ bond in the C2 is highly strained, since it is strongly bent. Thus, the bridged C2 molecule is reactive to the carbene tool and this reaction ultimately provides a means to generate a three-fold coordinated C3 on the (111) surface. Thus, this sequence of steps can be used to build up a step on the diamond (111) surface.

    An extension of the calculations on unreconstructed diamond (lllj is to examine ways of adding additional C atoms to the developing step. This could occur in several ways. One possibility is to add another C atom across a CC bond of the bridged C3. This leaves a C perpendicular to the surface and activation of the adjacent surface layer carbon (by removal of H) could lead to a four-fold coordinated C4. An alternative is to add a C2 to the three-fold coordinated C3. The bonds to the added C2 would make an angle of about 120 deg. with the surface. By activating three adjacent surface layer carbons, the added C2 could form bonds to the surface leading to a flat Cs structure. One question is whether there would be a barrier to the latter process. By the time this many atoms have been added to the surface, reconstruction effects involving the surface and sublayer atoms along with the added atoms might become important. We propose to test this using FF in conjunction with the QM.

    The diamond (111) surface is atypical since it has adjacent surface radical sites separated by the next-nearest neighbor distance. At temperatures above about 120bK the (111) surface undergoes a (2x1) reconstruction. The reconstructed surface exhibits rows of dimers. Similarly, the (110) surface has rows of dimers, and the reconstructed (100) surface has rows of dimers. Thus, the bridged C2 model typifies the diamond surface elements expected to be important in diamond mechanosynthesis. It is probable that the carbene tool could be used effectively on these surfaces in the same way that the carbene tool could be used to add a carbon to a C2 bridged on diamond (111). However, we propose to test this on clusters which model the reconstructed (111) and (100) surfaces and the unreconstructed (110) surface.

    The C2 tool could also be used to add a C2 in a four-fold coordinate site across a pair of dimers. This is relevant for the reconstructed diamond (100). We propose to test some of the steps illustrated in that mechanism.

    Another reaction is the addition of acetylene to a radical site followed by insertion of the other carbon of acetylene into a CH bond. This behavior was shown in MNDO calculations by Huang et al. The implication is that the intermediate structure, which would usually be drawn as a vinyl radical like structure i.e. a double bond and a radical orbital, might be more appropriately represented as a radical adjacent to a singlet carbene. An alternative to carbene insertion, is a two step process, in which the vinyl radical abstracts a H leaving a surface radical site, which adds to the CC ~ bond of the acetylene in a second step. We propose to study the reaction pathways for this process to determine whether it is concerted or two step.

    Self Assembled Supramolecular Systems

    The alternative strategy to mechano synthesis of nanosystems is to design molecules that self assemble to automatically form structures at the nanoscale. A recent review of work in this field is given by John Marie Lehn.43 The MSC has several activities in this area. 44~45 Thus we have determined the first detailed structure for a SAM on Au(111), which leads to xray diffraction patterns in excellent agreement with experiment.46 In addition we have designed a modified system in which the presence of amide groups substantially increases the cohesive energy (and stability). We have also developed Monte Carlo (MC) techniques for examining the phase diagrams for these systems. The difficulty with making machines with self assembled systems is that the SAM's stability tends to be temperature dependent and it is difficult to combine them into heterogeneous systems. We believe that surface modifications, say on diamond, to provide specific surface active sites that encourage SAM formation in particular regions may be possible. We plan to initiate such studies the second year, after examining the progress in projects 1, 2, and 3.

    Micro Electro Mechanical Systems (MEMS)

    There has been a great deal of activity with developing micron sized electro mechanical sensors in recent years. A spectacular success has been with accelerometers. However machines need moving parts and the current generation of Si based MEMS has very high friction, leading to very rapid wear. 47 As a result other materials must be found. We have begun a collaboration with Dr. Mike Gardos of Hughes who has shown that polycrystalline diamond48 surfaces lead to low wear suitable for MEMS materials. There are many issues having to do with surface preparation. We believe that there will be overlap of the advances in projects 1, 2, and 3 with the MEMS projects and Dr. Gardos has agreed to participate in the Caltech based nanotechnology meetings.

    Calculational Considerations

    The computational part of this proposal involves 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). The principle investigators are uniquely positioned to carry out these calculations. They have been involved with developing state-of-the-art software in all of these areas, software that is critical to making rapid progress. In addition they have the capability to extend this software as new needs arise in computational nanotechnology.

    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. The principle investigators have significant qualifications in this area. They have been involved in developing and using many of the modern methods of quantum mechanics (GVBl5, PS-GVB16, MR-CI4l, GDSDFTl7). These methods will be primarily needed for the synthetic steps and Dr. Walch will be primarily responsible for these studies. Given the quantum mechanical results we will develop force field (FF) descriptions to provide the energetics needed for the simulations of the molecular assembler. These FF will be adjusted to obtain the proper energy differences (it is difficult to obtain a FF that is accurate in the transition state region).

    Force Fields

    Most important in atomistic modeling of nanotechnology systems is to use force fields which faithfully represents the 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. Our force fields technology effort over the last few years was developed to achieve such reliability.

    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 a FF suitable for molecular dynamics (MD) simulations. To obtain a FF that accurately describes the properties of a specific class of molecules or polymers, we use the Hessian-Biased FF (HBFF)10 approach which is incorporated in the FFOPT code developed at the MSC and used in conjunction with the PolyGraf commercial software. This combines normal mode eigenstate information from HF theory with eigenvalue information from experiment. This HBFF approach has been used to develop accurate FF for many industrially interesting polymers (e.g., PE18, PVDF20, nylon,19 POM21, PSiH22), ceramics (e.g., Si3N423, C3N424), semiconductors (all group IV25, III-V26, and II-VI27, systems), and metals (e.g. the fcc metals28,29). We will use the FFOPT software10 developed at Caltech for obtaining HBFF from quantum mechanics to develop new FF for particular applications.

    For rapidly considering new systems it is also useful to use generic force fields suitable for general classes of molecules. Thus the DREIDING FF4 has been used for constructing many nanosystems and the Universal force field (UFF)9 is suitable for any inorganic, organometallic, or organic molecule (any element of the periodic table). In addition charge equilairation42 (QEq) allows accurate charges to be predicted rapidly. The only parameters in UFF are atomic parameters; thus with UFF and QEq one can predict structures for any combination of elements from H to Lr (element 103). '

    Standard FF use 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 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 possible20 to use pseudoelectrons in the FF to properly describe the polarization for polymers, metals, ceramics, and organometallics. 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.

    In order to predict the piezoelectric and dielectric properties20~30 of poly(vinylidene fluoride) (PVDF), we developed the covalent shell model (CSM)20 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 HF calculations on model systems. The FFOPT software includes the ability to develop general CSM parameters for predicting of polarization properties, by fitting to molecular polarizabilities from quantum mechanics.

    Massive Molecular Dynamics

    Nanosystem simulations may require 1 million to 100 million atoms considered explicitly. This has required major improvements in molecular dynamics (MD) methodologies.

    The biggest bottleneck obstructing atomic-level simulations on super-large systems is accurately summing the Coulomb interactions, which decrease slowly with distance and could lead to N2/2=0.5 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 transforms31 which scale as N15, totally impractical for a million atoms.

    Because of this need to simulate millions of atoms, we developed methods and optimized parallelized computer programs efficient for high capacity MD [simulation of 10,000 to 1,000,000 atoms for finite molecules or 10,000 to 1,000,000 atoms per unit cell for PBC]. Important recent developments include:

    1. The Cell Multipole Method32 (CMM) which dramatically reduces the cost of long-range Co~ilomb and van der Waals interactions while retaining high accuracy. The cost scales linearly with size, allowing atomic-level simulations for million atom systems.32 1l~l2

    2. The Reduced Cell Multipole Method33 (RCCM) 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 semi-crystalline 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) method34~35 for internal coordinate dynamics (e.g., torsions only). This 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. Semi-rigid dynamics. The current MPSim9712 allows some units to be treated as rigid bodies, others to be described semi-flexibly (with bonds and angles fixed, but torsions free), and other to be treated semi-rigidly (with torsions fixed relative to each other but allowed to move as a unit, wiles others parts of the same unit are semi- flexible)

    6. A focus has been toward developing the algorithms and methods suitable for massively parallel high performance computers (Intel Paragon, CRAY T3D, J Machine, etc.) and to develop optimal software for exploiting such computer environments. 11,12

    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. The MPI version for the Intel Paragon and CRAY T3D version is completed. These parallel programs scale quite well through 500 processors.


    1. Drexler Engines of Creation 1986
    2. Drexler Nanomachines 1992
    3. Drexler and Merkle, first generation planetary gear
    4. DREIDING: A Generic Force Field for Molecular Simulations, S. L. Mayo, B. D. Olafson, and W. A. Goddard III, J. Phys. Chem. 94, 8897 (1990)
    5. G. Gao, T. Cagin, W. A. Goddard III, "MD Simulation of the Drexler-Merkle Nanoscale Planetary Gear". to be published. Presented by WAG at the 1995 Nanotechnology Conference sponsored by the Foresight Institute, Oct. ? 1995.
    6. Drexler and Merkle, second generation planetary gear. Presented at the 1995 Nanotechnology Conference sponsored by the Foresight Institute, Oct. ? 1995
    7. G. Gao, T. Cagin, W. A. Goddard m, "MD Simulation of the second generation Drexler-Merkle Nanoscale Planetary Gear". to be published.
    8. J. Rebek Jr. Scientific American, July 1994, p 48
    9. ''UPP, a Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynam ics Sim ulation," A. K. Rappe, C. J. Casewit, K. S. Colwell, W. A. Goddard m, and W. M. Skiff, J. Am. Chem. Soc 114, 10024 (1992)
    10. The Hessian Biased Singular Value Decomposition Method for Optimization and Analysis of Force Fields S. Dasgupta, T. Yamasaki, and W. A. Goddard m, J. Chem. Phys. 104, 2898 (1996)
    11. Molecular Dynamics for Very Large Systems on Massively Parallel Computers K-T. Lim, S. Brunett, M. Iotov, R B. McClurg, N. Vaidehi, S. Dasgupta, S. Taylor, and W. A. Goddard m, J. Comp. Chem., submitted
    12. G. Gao, M. Iotov, T. Cagin, and W. A. Goddard m, "MPSim97 A tool for massive molecular dynamics simulations", in preparation
    13. Drexler and Merkle the Ne nanopump
    14. Theoretical Studies of Hydrogen Abstraction Tool for Nanotechnology C. B. Musgrave, J. K. Perry, R. C. Merkle, and W. A. Goddard m, Nanotechnology 2, 187 (1991)
    15. Generalized Valence Bond Description of Bonding in Low-Lying States of Molecules W. A. Goddard III, T. H. Dunning Jr., W. J. Hunt, and P. J. Hay, Accts. Chem. Res. 6, 368 (1973)
    16. New Pseudospectral Algorithms for Electronic Structure Calcualtions: Length Scale Sep-aration and Analytical Two-Electron Integral Corrections B. H. Greeley, T. V. Russo, D. T. Mainz, R. A. Friesner, J-M. Lantlois, W. A. Goddard m, R. E. Donnelly, and M. N. Ringnalda, J. Chem. Phys. 101, 4028 (1994). Accurate First Principles Calculation of
    17. Molecular Charge Distributions and Solvation Energies from Ab Initio Quantum Mechanics and Continuum Dielectric Theory D. J. Tannor, B. Marten, R. Murphy, R. A. Friesner, D. Sitkoff, A. Nicholls, M. Ringnalda, W. A. Goddard III, and B. Honig J. Am. Chem. Soc. 116, 11875 (1994)
    18. Dual-Space Approach for Density-Functional Calculations of Two- and Three- Dimen-sional Gystals Using Gaussian Basis Functions X. J. Chen. J-M. Langlois, and W . A. Goddard m, Phys. Rev . B 52, 2348 (1995)
    19. Mechanical Properties and Froce Field Parameters for Polyethylene Crystal N. Karasawa, S. Dasgupta, and W. A. Goddard m, J. Phys. Chem. 95, 2260 (1990
    20. Crystal Structures and Properties of Nylons Polymers from Theory S. Dasgupta, W. B. Hammond, and W. A. Goddard III, J. Am. Chem. Soc., accepted
    21. Force Pields, Structures, and Properties of Poly(vinylidene fluoride) Crystals N. Karasawa and W. A. Goddard m, Macromolecules 25, 7268 (1992)
    22. Polyoxymethylene: The Hessian Biased Force Field for Molecular Dynamics Simulations S. Dasgupta, K. A. Smith, and W. A. Goddard m, J. Phys. Chem. 97, 10891 (1993)
    23. Hessian Biased Force Field for Polysilane Polymers C. B. Musgrave, S. Dasgupta, and W . A. Goddard m, J. Phys. Chem. 99, 13321 (1995)
    24. The Hessian Biased Force Field for Silicon Nitride Ceramics; Predictions of Thermodynamic and Mechanical Properties for a- and ~ Si3N4 J. A. W endel and W . A. Goddard m, J. Chem. Phys. 97, 5048 (1992)
    25. Is Carbon Nitride Harder than Diamond? No, but its Girth Increases When S~etched (Negative Poisson Ratio) Y. Guo and W. A. Goddard m, Chem. Phys. Lett. 237, 72 (1995)
    26. The MSXX Force Field for Group IV Materials (IV = C, Si, Ge, Sn) C. Musgrave, J. Hu, and W. A. Goddard m, J. Vac. Sci. Tech.
    27. The MSXX Force Field for m-v Semiconductors (III = Al, Ga, In; V = P. As, Sb) C. B. Musgrave, J. Hu, and W. A. Goddard III J. Vac. Sci. Tech.
    28. The MSXX Force Field for II-VI Semiconductors (II = Zn, Cd, Hg; VI = S. Se, Te) J. Hu, C. B. Musgrave, and W. A. Goddard III, Phys. Rev.
    29. Phenomenological Many-Body Potentials from the Interstitial Electron Model. I. Dynamic Properties of Metals M. Li and W . A. Goddard III, J. Chem. Phys. 98, 7995 (1993)
    30. Properties of FCC Metals from Many-Body Force Fields Y. Kimura, T. Cagin, and W. A. Goddard III, Phys. Rev. B1, submitted
    31. Dielectric Properties of Poly(vinylidene fluoride) From Molecular Dynamics Sim ulations N. Karasawa and W. A. Goddard III, Macromolecules 28, 6765 (1995)
    32. Acceleration of Convergence for Lattice Sums N. Karasawa and W. A. Goddard m, J. Phys. Chem. 93, 7320 (1989)
    33. Atomic Level Simulations on a Million Particles: The Cell Multipole Method for Coulomb and London Nonbond Interactions H. Q. Ding N. Karasawa and W. A. Goddard m, J. Chem. Phys. 97, 4309 (1992)
    34. The Reduced Cell Multipole Method for Coulomb Interactions in Periodic Systems with Million-Atom Unit Cells H. Ding N. Karasawa, and W. A. Goddard m, Chem. Phys. Lett. 196, 6 (1992)
    35. 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 A. M. Mathiowetz, A. Jain, N. Karasawa, and W. A. Goddard III Proteins 20, 227 (1994)
    36. Constant Temperature Conskained Molecular Dynamics: The Newton-Euler Inverse Mass Operator Method N. Vaidehi, A. Jain, and W. A. Goddard m, J. Phys. Chem. 100, 10508 (1996)
    37. S. Walch and R. Merkle "Theoretical Studies of Diamond Mechanosynthesis Reactions", to be published
    38. Ab initio Quantum Chemical Studies of Hydrogen and Halogen Migration on the Diamond (110) Surface M. S. Melnik, D. G. Goodwin, and W. A. Goddard III Proc. Mat. Res. Soc. (1994)
    39. The Surface-Radical Surface-Olefin Recombination Step for CVD Growth of Diamond. Calculation of the Rate Constant from Frist Principles C. B. Musgrave, S. J. Harris, and W. A. Goddard III Chem. Phys. Lett. 247, 359 (1995)
    40. Polyyne Ring Nucleus Growth Model for Single-Layer Carbon Nanotubes C-H. Kiang and W. A. Goddard III, Phys. Rev. Lett. 76, 2515 (1996)
    41. The MSX)C Force Field for Molecular Dynamics Simulations of Si (111) Surfaces C. B. Musgrave, S. Dasgupta, and W. A. Goddard m, Surf. Sci.
    42. Correlation-Consistent Configuration Interaction: Accurate Bond Dissociation Energies from Simple Wavefunctions E. A. Carter and W. A. Goddard III, J. Chem. Phys. 88, 3132 (1988)
    43. Charge Equilibration for Molecular Dynamics Simulations A. K. Rappe and W . A. Goddard III, J. Phys. Chem. 95, 3358 (1991)
    44. Supram olecular Chem istry. Concepts and Perspectives. J-M. Lekn. VCH, Weinheim 1995
    45. Atomic Structure for Self-Assembled Monolayers to Alkanethiols on Au(111) Surfaces J. J. Gerdy and W. A. Goddard m, J. Am. Chem. Soc. 118, 3233 (1996)
    46. Functionalized Alkane Thiol Self-Assembled Monolayers on the Au (111) Surface C. F. Fan, J. J. Gerdy, S. Dasgupta, and W. A. Goddard m
    47. P. Penter, A. Eberhardt, and P. Eisenberger, Science 266, 1216 (1994).
    48. Tribological Behavior of Polycrystalline and Single-Crystal Silicon, M. N. Gardos, Tribiology Letters, in press
    49. Surface Chemistry-controlled triobological behavior of silicon and Diamond, M. N. Gardos, Tribology Letters, 2, 173 (1996)