Foresight Update 10 Page 3

Molecular Carpentry

by Ted Kaehler

On his sabbatical from Apple Computer, Ted Kaehler worked with the Foresight Institute on molecular systems design and modeling:

In the everyday world, we work with building materials that can be cut to size. When you are building a structure out of wood, you measure the raw material and cut it to the proper dimensions. Designs in the everyday world commonly use fixed 90 degree angles, but variable lengths. Nanomechanical designs operate under a different set of rules: bond lengths are virtually fixed, but angles can be varied substantially. Designing a nanomechanical structure is thus different from designing with a material that can be cut to any desired size.

During the summer of 1990, I worked with Eric Drexler to develop a system for designing molecular "parts" with arbitrary length or angle requirements. Here is a typical problem we considered: a designer has a nanometer scale device that needs to be supported and held firmly in place (the required rigidity varies with the application). Suppose the surrounding matrix is a diamond crystal lattice (Fig. 1). For convenience, the designer has chosen hexagonal carbon rings to serve as a standard interface. Every piece, including the diamond lattice, has a triangle of three bonds coming straight out of a hexagonal carbon ring which serves as its attachment point. The problem is this: what arrangement of atoms will bridge from the diamond crystal to a mounting ring on the device and hold it firmly? Within the diamond, there are only four distinct bond directions available, and at a limited set of points in space. If we extend the crystal right up to the mounting ring, it is unlikely that any of the bonds will closely match it in angle or location. Thus we need a new arrangement of atoms which will form a strong and stiff bridge from the crystal to the device.

Figure 1. A diamond surface with a six-membered ring attached.
The upper three carbon atoms (dark gray) are shown with missing
bonds where the bracket would be extended. The lower carbon atoms
are shown likewise, where the diamond crystal would be extended.
The free surfaces are terminated with hydrogen atoms (white) save
for three embedded nitrogens (light gray) included to avoid the
need for crowded hydrogens. The illustrated structure was minimized
using the MM2 potential energy function (Chem3D Plus implementation).

Three methods for designing the bridge come to mind. The first is to build the bridge atom by atom and "search" for the proper configuration. This is much like a computer program for playing chess. Placing an additional atom on the end of the structure is like making a move in chess. One wants it to be a step toward the solution, but one can't tell if it is the right step, except by trying it. Only after more atoms are added (more chess moves are made), can we tell whether the bridge matches up at the far end (whether these moves lead to a better chess position). If not, one must take back those moves and try others. In the absence of a good predictive theory, this kind of search takes a tremendous amount of computation, just as chess playing programs do. Without this, designing a new bridge from scratch every time one has a specific need does not look like such a good idea.

The second method is to design a "universal" structure that has length and angle adjustments. This would be a flexible structure with many two-position adjustment points. These might be chains that could be shortened by one atom, or atoms with different bond lengths that could be substituted. By changing which adjustment points were set to "long" and which were "short," the length of the whole structure could be varied by small amounts. Such a structure might have some disadvantages. It would have to be large in order to get sufficient variability. It is unlikely that it could be made very stiff without being so large as to dwarf the device it was meant to hold. We have not been able to think of any good structures that avoid these problems, and this area is still open for innovation.

The third method is to design hundreds of short, strong molecular brackets and then classify them by offset and angle. After each arrangement of atoms is designed, a program computes its detailed shape, and the results are stored in a dictionary. The designer uses the dictionary to choose the proper bracket to support the device in its proper place. To choose the right bridge from the catalog, we first imagine the diamond crystal extended up past the mounting ring we are trying to secure. For the "number one" atom on the mounting ring, we find its location within a unit-cell of diamond crystal. We also note the angle in 3-space of a vector that expresses the orientation of the ring. We then look up the position and angle in the dictionary to find the closest match. We find an entry for a known bracket and the (x,y,z) offsets to each of its three attachment points in the diamond lattice. The dictionary tells the designer what bracket to use and where in the diamond lattice it will attach. The bracket is free standing, attaching to the diamond crystal with just three bonds (Fig. 1). In the final design, the diamond only comes as close to the device as the offset says to, and the bracket spans the remaining distance.

To design a family of brackets, we begin with a stack of six-membered carbon rings. Such stacks are found within the structure of hexagonal diamond (lonsdaleite) and are a strong, compact structure (Fig. 2). Each ring has three covalent bonds to the ring below and three to the ring above. This gives good stiffness. A barrel-like stack of six-membered rings is straight, so we must introduce some variation to make it bend. One way is to use seven-membered rings. Each seven-membered ring has three attachments above and three below. The seventh atom distorts the ring in some direction. A second seven-membered ring on top of the first has six different places where the seventh atom can interrupt the ring. The many combinations of seventh atoms on different levels give a range of combined twists, bends, and offsets from the normal lattice. All extra carbon bonds that hang out of the structure are capped with hydrogen.

Figure 2. A stack of four six-membered carbon rings. 'D' indicates the three bonds to the diamond substrate. The top ring attaches to the device being supported. Hydrogen atoms attached to the two middle rings are not shown. (The structure appears to be curving slightly to the left. It should be completely straight, and we are looking for the bug in our software.)

Figure 3 shows a typical two-layered bracket with a hexagonal mounting ring on each end. Even a structure of just two layers can have quite a bit of twist and offset. The structure is compact and stiff, with three or more covalent bonds at each cross-section. Here are the major ways that a normal stack of six-membered carbon rings can be varied to make brackets for cataloging:

Add a seventh atom in one of six places on a given ring.

Add another layer to the structure. Try both six-membered and seven-membered rings in the new layer.

Substitute silicon for any of the carbon atoms. Silicon has longer bonds and distorts the structure.

Substitute nitrogen for carbon. Substitute oxygen or sulfur for carbon at the seventh atom (it is only bonded to two other atoms).

Use a C=C double bond instead of a single bond. This only works at certain places in the structure, and is strained.

A side view of the stack shows six-membered rings facing outward. When there is a seventh atom in a layer, the side view shows a seven-membered ring. When two seven-membered layers have their extra atom above each other, the side view shows an eight-membered ring. That ring can be split in two by adding a fourth bond between the layers. The side view now shows two five-membered rings. The extra bond between the layers changes the shape of the bracket.

Similarly, a six-membered ring facing outward can be bridged in a direction along the axis by adding a carbon, oxygen, sulfur, or silicon (along with any needed hydrogen atoms).

The computer program to build the catalog proceeds as follows: Enumerate all the possible brackets using the above rules, starting with the shortest first. For each bracket, compute its shape using a molecular mechanics program. The most important aspect of its shape are the three bonds coming out of the mounting ring on each end. With one end attached to a diamond lattice, we compute the offset and angle of the ring on the other end, and enter it into the catalog. Since computing the shape of the bracket is the hard part, we save time by making catalog entries for the mirror image of the bracket, the bracket upside down, and the bracket attached to a vertical face of the diamond crystal.

Figure 3. The same structure with a seventh atom inserted in two of the rings. The top ring is rotated, displaced sideways, and tilted. Thousands of such variations will be be classified in a catalog according the location of their top ring. The designer selects the bracket that matches the location of the part he wishes to support.

Not every structure we compute will become an entry in the catalog. When many brackets reach the same place and angle, we only want the shortest and stiffest one. The catalog will be made to a certain spatial and angular resolution. If we try to find one entry for every 0.154 Å (a tenth of a carbon-carbon bond length), then number of position points in a unit will be around 1029. For each of these, we need a variety of angles. Since bonds can bend much more easily than they can change length, an angular accuracy of plus or minus 10 degrees may suffice. Accounting for all the spherical symmetries, we need 66 different angle entries per approximate position, derived from as few as 4250 bracket designs. (A single bracket may be entered into the table in as many as 16 different ways.) The shape of many more than 4250 brackets will have to be computed to get a sufficient variety of angles and locations. It will be interesting to see how clumpy the distributions of brackets is, and to see if there are any regularities that will allow us to predict the shape of an as-yet-uncomputed bracket.

It is possible that reaching the full diversity of the catalog will require putting too many layers in the bracket. Such a bracket would be too long and floppy to be of much use. If this is true, all brackets with more than a certain number layers will be designed with thick bases. Imagine the thick base as a short bracket made from three parallel hexagonal tubes. It is short and stiff. On top of this is a normal one-tube bracket. The richer structure of the thicker bracket allow it to have many more variations per layer, making a diverse set of shapes easier to generate.

If the designer is not happy with the spatial and angular resolution he finds in the catalog, he can pull a few tricks. The device he is building is likely to be anchored at several places. If one of those anchors is at a slightly wrong place, he can pick the other anchors to push the structure back in the right direction. Likewise, slightly wrong angles can be pitted against each other to give a correct final position. Such a mildly strained structure should work just fine.

To begin the project, we selected an existing molecular mechanics program. Programs that compute the shapes of molecules come in a variety of speeds. The structures we are simulating contain nothing but the atoms and bonds of locally-unremarkable organic molecules. We are not studying unstable transition states in chemical reactions, so we don't need "molecular orbital" programs that model the quantum mechanics of electron clouds. Instead we used a "molecular mechanics" program that treats each chemical bond as a spring with a certain resting length. Additional springs handle the desire of an atom to keep its bonds at certain angles to each other. By using only forces between the centers of atoms, this program can go very fast. The program we selected is STRFIT3 by Martin Saunders and Ronald Jarret of Yale University, which gives results closely approximating those of the classic MM2 program . Around this we are building programs to generate the brackets and enter them in the catalog after their shape is known.

This system is implemented in Digitalk Smalltalk/V Mac on an accelerator-assisted Macintosh II. After we have verified that STRFIT3 is producing shapes that agree with known molecules, we intend to run the system every night and build a catalog of nanomechanical brackets.

The interesting thing about this project is considering design problems in a world in which angles can be varied but lengths cannot, with lengths and flexible angles like those found in real molecules. The catalog we build now will probably not be the one used when nanostructures are actually built. By the time fabrication technology is available, designers will want to use the latest modeling programs and the fastest computers to rebuild the catalog with high accuracy. By creating the tools to build a catalog today, we can get a glimpse of the techniques and pitfalls of designing mechanical structures in which 'every atom is in its place.'

Reference

Martin Saunders and Ronald Jarret, "A New Method for Molecular Mechanics," Journal of Computational Chemistry, Vol. 7, No. 4, 578-588 (1986).

Ted Kaehler is a computer scientist who spent his sabbatical from Apple Computer working with the Foresight Institute. He and Foresight would like to thank Martin Saunders of Yale for allowing us to use the program STRFIT3 and for his additional help. Ted's participation was funded by the Restart Program of Apple Computer, Inc.

[Editor's note: For current information, visit Ted Kaehler's home page at http://www.webPage.com/~kaehler2/.]

From Foresight Update 10, originally published 30 October 1990.

Foresight thanks Dave Kilbridge for converting Update 10 to html for this web page.

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Foresight Update 10

page 3

Molecular Carpentry

by Ted Kaehler

Reference