Binding sites for use in a simple assembler

by

Ralph C. Merkle
Xerox PARC
3333 Coyote Hill Road
Palo Alto, CA 94304
merkle@xerox.com
http://www.merkle.com/

Copyright 1995 by Xerox Corporation. All Rights Reserved.

This paper has been published in Nanotechnology 8, No. 1, March 1997 pages 23-28. It can be found on the WWW at: http://www.zyvex.com/nanotech/bindingSites.html. The web version may differ in some respects from the published version.

Abstract

Machines, both macroscopic and molecular, are made from parts. The initial orientation and positioning of those parts is usually random. To facilitate subsequent parts handling and assembly steps, it is convenient to position and orient the parts. At the molecular scale, this corresponds to binding feedstock molecules dissolved in solvent. In the system design process, the binding site and the feedstock molecule can be designed together, simplifying the design of both. Simple linear molecules (e.g., acetylene, butadiyne, cyanogen) could be bound by simple tubular binding sites (e.g., bucky tubes). Planar rectangular molecules could be bound by simple "box" binding sites. This paper examines several such feedstock-molecule/ binding-site combinations to illustrate that the combined design process is feasible and often relatively straightforward.

Introduction

Molecular manufacturing should let us inexpensively fabricate most structures that are consistent with physical law. One approach for accomplishing this objective is to design and build self-replicating assemblers, devices able to precisely position reactive molecular species and construct complex atomically precise structures by a series of site-specific molecular reactions. Design proposals for assemblers often include a barrier which prevents the entry of contaminants and impurities from the outside environment into the very precise and highly controlled internal environment. This is the approach taken in the design of a "simple" diamondoid assembler (Merkle, 1996), to name but one example.

If assemblers build things, and the machinery for building things is protected behind a barrier, this raises the obvious question of how the raw materials for construction are transported through the barrier. The purpose of this paper is to begin to address this question.

Binding site design

The function of a binding site is to (a) bind desired feedstock molecules from the external solvent, (b) transport those bound molecules into the interior of the assembler (through a presumably diamondoid wall), (c) block the entry of undesired molecules and (d) reliably make the bound feedstock molecule available in a controlled orientation inside the assembler for further processing.

The general proposal in Nanosystems (Drexler, 1992) includes multiple stages of filtration with counter flow. At each stage, desired molecules have a high probability of moving forwards to the next stage and a low probability of moving backwards to the previous stage, while undesired molecules have a high probability of moving backwards to the previous stage and a low probability of moving forwards to the next stage. As a consequence, the final stage will consist almost exclusively of the desired molecules with an impurity level that can be made arbitrarily low by adding enough stages. The illustration shows a single selective transporter; many of these devices would be required for a multi-staged cascade.

For the simple diamondoid assembler, we will assume that the cost of the feedstock can be relatively high (and therefore that the feedstock molecules themselves can be relatively exotic, if this should prove desirable), and that the primary objective is to simplify the design of the binding site and associated transport machinery.

Linear feedstock molecules

Perhaps the simplest binding site would be nothing more than a tube. For linear feedstock molecules, such tubes should form good to excellent binding sites. Bucky tubes form a large class of tubes of varying diameter. For any arbitrary bucky tube, it would be possible (conceptually) to cut the tube along its axis and flatten the tube. The resulting graphitic sheet could then be described by two parameters. Specific definitions of these two parameters will vary, but possibilities are the width of the strip (the circumference of the bucky tube) and its angle with respect to a graphitic sheet; or two indices giving the end point of the straight line which defines the circumference (assuming that the starting point of this line is at (0,0)).

Another way of viewing this is to start with a point on a graphitic sheet, take an integral number of steps along one crystollographic axis, followed by another (and typically different) integral number of steps along the second crystollographic axis, reaching an endpoint. The straight line connecting the start point and the end point is then defined as the circumference of some bucky tube, while the two integers provide a succinct name for that bucky tube.

The corresponding bucky tube is obtained by drawing two parallel lines at right angles to the circumferential line and passing, respectively, through its start and end points, and then (a) deleting all atoms not between the two straight lines and (b) curling up the flat sheet until the two newly formed edges can be joined.

Clearly, we are most interested in bucky tubes whose circumference is such that the tube will bind simple linear molecules. A computer program to generate the indices for all bucky tubes whose circumference (or radius) lies in a given range was written, and a range of tubes surrounding the estimated best binding radius was generated. The resulting circumference, radii, index values (which define the circumference of the bucky tube) and the binding energy are given.

Circumference (nm)  radius (nm)    indices     Binding energy
                                             to acetylene (maJ, (kcal/mole))

      1.9608          0.3121        (8,0)          28 ( 4.06)
      2.0062          0.3193        (7,2)          56 ( 8.07)
      2.0941          0.3333        (8,1)          96 (13.78)
      2.1226          0.3378        (5,5)         118 (16.96)
      2.1367          0.3401        (6,4)         118 (16.93)
      2.1785          0.3467        (7,3)         120 (17.20)
      2.2059          0.3511        (9,0)         125 (18.00)
      2.2464          0.3575        (8,2)         123 (17.69)
      2.3381          0.3721        (6,5)         115 (16.57)
      2.3381          0.3721        (9,1)         121 (17.41)
      2.3637          0.3762        (7,4)         114 (16.40)
      2.4140          0.3842        (8,3)         119 (15.89)
      2.4510          0.3901        (10,0)        108 (15.48)

Table 1. Radii of bucky tubes approximately suited as binding sites for linear molecules.

The maximally binding bucky tube for this particular potential energy function is the 9-fold symmetric bucky tube (an index of (9,0)) as illustrated here:

The binding energies shown were computed using the Universal Force Field (Rappe et al., 1992) implemented by MSI in Cerius 2. The method used was to minimize a segment of the specified bucky tube, then minimize a segment of the same bucky tube with acetylene in it. Solvation and entropic factors were not computed. While these clearly must be considered to determine the effectiveness of these structures as binding sites in any particular solvent, the point being illustrated here is not the specific values but the fact that the binding energies form a fairly broad basin. This implies that, even if our current potential energy functions are somewhat in error, that we can still select a bucky tube which provides a "good" binding site for a linear molecule.

Some error was likely introduced because a segment of bucky tube of finite length and with an irregular hydrogenated termination was used, rather than an infinite length of bucky tube. Typical bucky tube lengths were on the order of 20 angstroms, but this varied from tube to tube. In the (7,3) and more visibly in the larger tubes, the axis of the acetylene molecule was misaligned from the axis of the tube after minimization. This is likely caused by the relatively small van der Waals radius of the hydrogen atoms at the ends of the acetylene molecule. This might have contributed to the irregular fluctuations in energy seen in the larger tubes. Some misalignment appeared to be present in tubes of smaller radius.

Calculations on C4H2, , showed that (in accordance with expectations) it has a significantly higher binding energy than C2H2. For the (8,2) bucky tube, the binding energy of C4H2 was 210 maJ (30 Kcal/mole), about 60% larger than the binding energy of C2H2 for the same bucky tube. The selective transport of larger molecules should in general be more reliable (in the sense that the probability that the correct feedstock molecule has been selected can be made much higher, while the probability that some incorrect molecule has been selected can simultaneously be made much lower).

The use of a solvent which is unable to enter the binding site (e.g., neopentane) might also prove useful. In combination with increased pressure this would be an effective method of increasing the affinity of the binding site for the desired feedstock molecule.

(1/9/97) As an aside, experimental work by (Thess et al., 1996) shows that production of (10,10) bucky tubes is feasible. While the (10,10) bucky tube has a larger diameter than optimal for linear feedstock molecules, there should be many bulkier polymers that find it a congenial fit. This suggests, in particular, that a large "end cap" that could not enter the (10,10) buckytube could be covalently bound to a polymeric "tail" that would. An open ended (10,10) buckytube, when exposed to this hybrid, would bind to its tail but would leave the end cap exposed. This might be advantageous in AFM work when buckytubes are used as nanoprobes, as there are many possible end caps which (a) could be covalently linked to a suitable polymeric tail and (b) would have desirable properties as a probe tip.
Several linear molecules exist. To quote the abstract from (Lagow et al., 1995):
A carbon allotrope based on "sp" hybridization containing alternating triple and single bonds (an acetylenic or linear carbon allotrope) has been prepared. Studies of small (8 to 28 carbon atoms) acetylenic carbon model compounds show that such species are quite stable (130 degrees to 140 degrees C) provided that nonreactive terminal groups or end caps (such as tert-butyl or trifluoromethyl) are present to stabilize these molecules against further reactions. In the presence of end capping groups, laser-based synthetic techniques similar to those normally used to generate fullerenes, produced thermally stable acetylenic carbon species capped with trifluoromethyl or nitrile groups with chain lengths in excess of 300 carbon atoms. Under these conditions, only a negligible quantity of fullerenes is produced. Acetylenic carbon compounds are not particularly moisture or oxygen sensitive but are moderately light sensitive.
The nitrile terminated chains are of most interest here, as bulky end caps would not fit into simple tubular binding sites of constant diameter. An example of a short nitrile-terminated linear molecule is cyanogen, . (Safety should also be considered: cyanogen is highly poisonous, which is one motivation for our later consideration of somewhat more complex but less lethal feedstock molecules). The closing sentence of the article says "We believe that most organic end groups and perhaps many inorganic end groups will stabilize linear carbon."

Another useful property is solubility: "...capped linear carbon chains are very soluble in most organic solvents, producing rich amber colored solutions at lower molecular weights and concentrated dark brown solutions at carbon chain lengths of about 300." Solvation of feedstock molecules is obviously important in the system proposal being advanced.

Finally, linear forms of carbon "...should be under appropriate conditions an excellent precursor for diamond synthesis..." This is consistent with the observation in Nanosystems (Drexler, 1992, page 245) that cumulene strands represent promising precursors for the mechanosynthesis of diamond.

Many short linear compounds involving only first row elements are well known including:

N2:

O2:

CO2:

C3O2:

C2H2:

C2N2:

C2HF:

etc. etc.

Other candidates might include isoelectronic variants of known compounds (e.g., CO is isoelectronic with N2).

We can increase the number of linear compounds by including second row elements, but at the cost of creating a molecule with a non-uniform radius.

Planar feedstock molecules

The number of linear feedstock molecules is relatively modest. By contrast, the number of flat feedstock molecules, though still small in comparison with the enormous range of possible molecules, represents a much larger class. A classic example is the binding between the two DNA bases cytosine and guanine.

While the feedstock molecule is constrained to be one that can be readily synthesized in bulk, the binding site will be made using molecular manufacturing techniques, and in particular using mechanosynthesis. We are therefore not constrained to consider only binding sites that can be synthesized by present methods, but are free to consider binding sites whose synthesis would, with present synthetic methods, be considered either challenging or actually impossible. As might be appreciated, this greatly simplifies the task of designing the binding site.

Rectangular feedstock molecules are a particularly simple subset of the planar feedstock molecules. As an example, if the selected feedstock molecule is anthracene a binding site need be little more than a simple box with open ends into which the anthracene can slide.

One such box is illustrated here:

This binding site consists of an upper and lower sheet of graphite that sandwich the anthracene between them, and two graphite strips with fluorinated edges that should have good affinity for the hydrogens along the edge of the anthracene. All four graphitic components of the binding site would have to be held in place by further structural elements (not shown). The placement of the four graphitic components was determined by minimizing the whole structure.

The binding energy computed with HyperChem's MM+ potential energy function (an extension of MM2), and again not considering entropic or solvent effects, is 285 maJ (41 kcal/mole). For comparison, the heat of sublimation of anthracene from 25 degrees centigrade is 172 maJ (24.7 kcal/mole) (Dean, 1979). Anthracene is "slightly soluble" (Lide, 1995) in several organic solvents (sufficient for our purposes). It seems likely, therefore, that the binding site considered here will be energetically preferable to both the solid and dissolved state of anthracene.

A more complete design for an anthracene binding site is:

This binding site was designed by positioning two slabs of hexagonal diamond above and below the anthracene, determining an appropriate vertical gap, and then fitting in two end pieces which hold the two primary hexagonal slabs in the right position. The horizontal gap was adjusted by selecting among various negative groups until an acceptable fit was found. Note that the relative insensitivity of the binding site to minor changes in dimension (on the order of a few tenths of an angstrom) permitted the design of a site with a reasonable binding affinity without requiring extreme precision in the design. It seems very likely that better binding sites can be designed. The reader might note that the anthracene is somewhat misaligned in the site -- this is likely caused by an inability to precisely adjust the horizontal gap. This binding site has a predicted binding energy (again using HyperChem's MM2+ potential energy function) of about 320 maJ (46 kcal/mole).

As the binding energy is sensitive both to the particular well depth chosen for the van der Waals energy and to the particular method of computing electrostatic interactions (particularly between the F or O and H), it is likely that different potential energy functions will produce different results. For example, the Universal Force Field (UFF) (Rappe et al., 1992) implemented by MSI in Cerius 2, combined with their algorithm for computing electrostatic interactions, produces a significantly higher binding energy for both binding sites. While we can reasonably conclude that a binding site able to bind anthracene is feasible, and more broadly that the design of binding sites for a wide range of other rectangular molecules is likewise feasible, further research is required to establish the actual binding energy of any particular binding site with confidence.

The graphitic binding site was minimized with the anthracene in it, and then minimized again after the anthracene had been removed. During the second minimization, atoms around the edge of the binding site were immobilized to prevent the binding site from collapsing.

It would be theoretically possible for the anthracene to be caught in a minima after only partially entering the binding site. For both binding sites, minimizations started with the anthracene outside the binding site (but oriented appropriately to enter the site) resulted in the anthracene entering the binding site and eventually adopting a central position in the binding site. While this procedure suggests that any minima other than the principal minimum are either small or nonexistent, it does not guarantee their absence.

These binding sites are based both on the general attraction of one molecule for another (van der Waals forces) and on the principle that opposite charges attract. By placing a region of positive charge (hydrogen) in the feedstock molecule close to a region of negative charge (fluorine, oxygen) in the binding site, the affinity of the binding site for the feedstock molecule can be increased.

The major conclusion to be drawn from this example is that binding sites with relatively high affinity for chosen rectangular feedstock molecules can be fairly easily designed given that mechanosynthesis greatly relaxes the synthetic constraints that would otherwise limit the range of binding site designs that could be considered. By increasing the size of the feedstock molecule the binding energy of the binding site can be increased. If the binding site has a sufficient affinity for the feedstock molecule it should be feasible to design a "one pass" binding site and trans-barrier transport system that would reliably bind to the chosen feedstock molecule and reliably reject undesired molecules. While there would be some probability of error, this probability could be made small enough that it could be neglected.

There are a reasonably large number of generally rectangular molecules. There are fluorinated variants of anthracene, such as:
Substitution of N for CH results in molecules like:

Many more variations are possible.

Perylene is another rectangular structure with many possible variations:


The final six membered ring of anthracene could be changed to a five membered ring. Many five membered rings are possible. Two examples are indole and benzofuran.

The use of five membered rings at the end allows rectangular molecules which consist of two regions joined in the middle. One such structure is indigo:

Another example is the joining of two indoles by a single bond:

This has the further advantage that structures similar to this might be used as radical precursors. The two ends of the structure would be "gripped," mechanical force applied, and the relatively weak C-C bond in the middle should break, yielding two radicals.

Beyond applying force to the two ends via repulsive overlap interactions (pushing), it is also possible to bind to appropriately designed molecules with reasonable strength. One possibility in a vacuum environment would be to use boron "grippers" that form dipolar bonds to exposed oxygen or nitrogen (and possibly fluorine). The dipolar bonds formed between boron on the one hand and nitrogen or oxygen on the other have the convenient property that they are significantly weaker than the covalent bonds that typically hold a molecule together, but can be much stronger than thermal noise at room temperature. In a vacuum environment, dipolar bonds could reversibly bind to small molecules without disrupting those molecules. This is somewhat reminiscent of "post-it" notes.

Calculations using the 6-311+G(2d,p) basis set with B3LYP (no zero point correction) suggest the N -> B bond in HCN -> BH3 is about 19 kcal/mol (see the Gaussian output for HCN -> BH3, HCN, and BH3 for details). One possible use would be a nitrile group on a diamond (111) surface with a facing (111) surface in which a boron had been substituted for a surface C-H. As this would prevent the boron from assuming a planar configuration, it would tend to increase the strength of the N -> B dipolar bond.

The generation of radicals (perhaps using the approach suggested above) would then permit further reactions. For example, Nanosystems (Drexler, 1992) proposed the use of an acetylenic radical to perform selective abstractions of hydrogen, as illustrated below:

This proposal has been further studied by (Musgrave et al., 1991) and (Sinnott et al., 1994) If such a tool is to be used more than once, then the hydrogen must be removed from its tip. A proposal in Nanosystems to do this is to use two weaker radicals (as might be generated by the mechanism suggested above) to simultaneously attack the C-H bond.

A possible structure for a hydrogen abstraction tool might be similar to an anthracene whose end had been modified to resemble the following:

Prior to use, this structure would have to be activated by removal of the terminal hydrogen.

A more direct method of generating a hydrogen abstraction tool would be to use a molecule like theone illustrated below:

Chem3D Pro's implementation of MM2 predicts that this molecule will have a slight preference for the planar configuration. It can reasonably be considered a rectangular molecule and the design of a relatively high affinity binding site, using the approach outlined above, should be feasible. The solubility of this molecule would have to be considered, and variants that had appropriate solubility might have to be substituted.

Once such a molecule had entered the simple diamondoid assembler, one anthracene could be rotated 90 degrees with respect to the other and mechanical force applied, pulling the two anthracenes apart. While this procedure should rupture one of the two single bonds, it's not clear exactly which one. A positionally controlled transition metal might be useful in preferentially weakening one bond. Other mechanisms should also be feasible. Without such a mechanism, it would be necessary to conditionally select one or the other of the two anthracenes (as appropriate) in order to get the desired hydrogen abstraction tool.

A variant is

Conclusion

Existing design proposals for diamondoid assemblers (Merkle, submitted to Nanotechnology) require binding sites able to to bind to feedstock molecules in solution outside the assembler, and then move the bound molecule into the assembler for further processing. The use of planar rectangular feedstock molecules seems to offer a sufficient range of structures, while at the same time sufficiently constraining both the search space and the design issues for the binding sites, that it is worth further investigation.

References