josh@cs.rutgers.edu (04/20/91)
+---------------------------------------------------------------------+ | The following material is reprinted *with permission* from the | | Foresight Update No 11, 4/15/91. | | Copyright (c) 1991 The Foresight Institute. All rights reserved. | +---------------------------------------------------------------------+ Modeling Molecular Machines by K. Eric Drexler Molecular mechanics software can be used to model molecular machines, and a suitable product is now available for the Macintosh computer. The following gives a brief sketch of molecular mechanics and its applicability, then reviews the program Chem3D Plus from Cambridge Scientific Computing. If you have the right computer for the job, an interest in molecular machinery, and donUt already have access to modeling software, you may want to buy it. Molecular mechanics As chemists know, molecular mechanics models describe atoms as soft, elastic spheres subject to mutual attraction and repulsion. Bonded pairs of atoms overlap, and stretching of the bond is described by a spring constant. Bonded triplets of atoms define an interbond angle, and the angular degree of freedom has an associated spring constant. A series of four bonded atoms defines a dihedral angle, which is associated with a set of sinusoidal potentials. Further energy terms can be added (and are, in the more accurate models), resulting in a potential energy function of considerable flexibility. This function relates energy to molecular shape, thereby defining forces, accelerations, stiffnesses, and so forth. If the potential function is good, it describes real molecules with reasonable accuracy. For the design of future molecular machinery, the best potential energy function in general use today is MM2, developed by Norman Allinger and colleagues (MM2 was discussed in Update No. 10 in connection with Ted Kaehler's project to develop a library of nanoscale bracket designs). It describes the structure and energy of a wide range of organic molecules with enough accuracy to be useful to chemists; since chemical equilibria are sensitive to energy differences that are negligible in many nanomechanical engineering contexts, this indicates that it gives a sufficiently accurate picture of reality for many purposes--if the user knows enough chemistry to know when MM2 is lying. Among the lies are these: bonds (described with both quadratic and cubic terms) break too easily unless a quartic bond-stretching term is added (but with it, they donUt break at all). Amine nitrogen atoms cannot undergo inversion, because the pseudo-atom representing the electron lone pair stays on one ! side; this and other situations c Chem3D Plus Cambridge Scientific Computing has implemented a graphical molecular modeling system with an interface that enables rapid and easy construction of three-dimensional molecular structures, enabling control of rotation and viewing: this is Chem3D. More recently, Cambridge Scientific has implemented an extension which includes a version of the MM2 potential, enabling the user to turn on simulated molecular forces and watch the molecule settle into a minimum-energy configuration: this is Chem3D Plus. Alternatively, the user can set a target temperature, turn on molecular forces and dynamics, and observe the molecules in motion. For large structures (hundreds of atoms) each step takes many seconds, but the results can be reviewed after letting the computer crunch by itself for as long as necessary (all speeds here are on a Mac IIci, which includes a math coprocessor). Chem3D Plus is powerful enough to enable the design of small nanomechanisms, and with the caveats above, its mathe! matical model is accurate enough Chem3D Plus 3.0 will be an impressive package even if no improvements are made from the late beta-test version now in hand. It adheres closely to the standard features of the Macintosh user interface, making it easy to learn and use. Operations including dragging and atom-type-changing can be performed on large sets of atoms using selection rectangles and shift-clicking. Display modes include wireframe (fast), ball and stick (moderately fast, easy to work with), and space-filling (slow, but offering a better representation of the final molecular shape). Parts can be rotated around bonds or rotated as a whole by several convenient methods. Selected molecules can be rotated in precise 0.5 degree increments around coordinate axes or axes defined by pairs of selected atoms, and pairs and triples of atoms can be aligned with Cartesian axes or planes by menu commands. These capabilities make it possible to align components and rotate them with respect to one anotherQfor example, to study the smoothness of the rotational potential energy function of a bearing like that in Figures 1 and 2. Structures can be built by clicking, dragging, copying, and pasting with a variety of options for automatic clean-up of the resulting object. Energy minimization can be performed with a quick and dirty potential or with MM2 itself. Selection can be used to restrict energy minimization or dynamics to a chosen subset of atoms; this enables the user to calculate the elastic properties of components by moving a set of anchored atoms to several different positions and comparing the energies of the resulting deformed structures. The potential energy function can be customized or extended: when needed parameters are missing from MM2, Chem3D Plus prompts the user; it will open to the appropriate locations in the parameter file while highlighting the offending parts of the structure. In addition to reporting the total energy (and its division into several MM2-defined components), the interface makes it easy to analyze the geometry of the structure. Pointing, or pointing and clicking, pops up a small window giving relevant atom types, bond types, distances, angles, and the like. A preferences window (which can generate a saved preferences file) keeps track of a huge number of options for the geometry reports, display options, and much else. On the input and output side, files can be read from or written to many different standard formats, permitting interchange with other programs, including quantum-mechanical modeling systems such as MOPAC. Molecules can be saved or copied to the clipboard in Encapsulated Postscript form, and print as crisp ball-and-stick or intersecting-spheres images (with options for controlling atom sizes, colors, depth cuing, and so forth). In its user interface, modeling capabilities, flexibility, and overall quality, Chem3D Plus bears comparison to packages costing tens of thousands of dollars. Indeed, is so surprisingly good (and has improved so much since version 2) that I am willing to believe that its remaining warts will be removed. At the moment, these include some bugs in support of foreign file formats, and serious performance problems in drawing and manipulating what are (unfortunately) precisely the sorts of structures of most interest in a nanomechanical context: large, polycyclic molecules with a family resemblance to bits of diamond. The program gives special attention to ring structures at inappropriate times (e.g., when cutting and pasting structures, and even when selecting atoms), and that special attention can consume minutes to hours of CPU time with no visible result beyond what a conventional drawing program would accomplish in a fraction of a second. It is wise to have reading material o! n hand. On the positive side, Che Chem3D Plus can handle several hundred to a thousand or so atoms in 3 megabytes of RAM: enough to design a variety of struts, gears, bearings, and shafts, and to calculate their mechanical properties. To do so in a reasonable time, however, will require either great patience or a Macintosh with a floating-point chip, although any machine able to support System 6.0.4 or later can run the program (warning: upgrade to 6.0.5 or later: Chem3D Plus does not presently tolerate the bugs in System 6.0.4). On a IIci, it is a rewarding tool for nanomechanical design and analysis. On machines that are slower or have less RAM it should still be, at the very least, an excellent almost-hands-on introduction to the mechanical properties of molecules as objects. Several years ago, Roger Gregory predicted that molecular modeling on personal computers would enable widespread participation in nanomechanical design on a serious-hobby basis, years before advances in positional synthesis enable the designs to be built (Foresight Update No. 2). This design-ahead process can speed understanding of the potential of nanotechnology, and can substitute concrete detail for earlier abstract arguments. The software and hardware are available today. Availability Chem3D Plus is available from Cambridge Scientific Computing, 875 Massachusetts Avenue, Suite 41, Cambridge, MA 02139, 617-491-6862. The single-copy price is $895 for corporations and $595 for academic institutions. Cambridge Scientific is interested in the possibility that a new, non-institutional market may exist among Foresight members interested in molecular nanotechnology; please call the Foresight office (415-324-2490) for current information on pricing policy for Foresight members. K. Eric Drexler does exploratory molecular engineering. He is a Visiting Scholar at Stanford University's Dept. of Computer Science and serves as president of the Foresight Institute. +---------------------------------------------------------------------+ | Copyright (c) 1991 The Foresight Institute. All rights reserved. | | The Foresight Institute is a non-profit organization: Donations | | are tax-deductible in the United States as permitted by law. | | To receive the Update and Background publications in paper form, | | send a donation of twenty-five dollars or more to: | | The Foresight Institute, Department U | | P.O. Box 61058 | | Palo Alto, CA 94306 USA | +---------------------------------------------------------------------+