Quantitative parts closure

In this section we analyze the global use of the proposed molecular tools to make another set of tools. We do this to make sure we don't have a net negative production of some molecular tool, despite a superficial ability to synthesize that tool.

To start the analysis, we note that we can generate as many hydrogen abstraction tools (ethynl radicals) as desired. We start with a set of "spent" hydrogen abstraction tools (i.e., tools with a terminal hydrogen). We also require one functional hydrogen abstraction tool, one spent hydrogen deposition tool (the tin radical) and two silicon radicals. Using reaction 15, we transfer the hydrogen from the tip of the hydrogen abstraction tool to the hydrogen deposition tool. This consumes one hydrogen abstraction tool and one tin radical. We then use a reaction similar to reaction 8 to separate the two hydrogen abstraction tools. This produces two refreshed hydrogen abstraction tools, and leaves the two silicon radicals unchanged.

The net result of these reactions is to transfer a hydrogen from an abstraction tool to a deposition tool, while leaving the rest of the tool count unchanged. Of course, this reaction consumes a tin radical. As we are assuming that the hydrogen deposition tool will be discharged when we manufacture a structure which needs an additional hydrogen, and are further assuming that we can manufacture hydrogen rich structures if this is needed, we will not run out of tin radicals. Put another way, we can get rid of hydrogen by making hydrogen rich structures. When we do this, we remove hydrogens from hydrogen deposition tools. As these tools are simply hydrogen bonded to tin, removing the hydrogen creates tin radicals. This lets us produce as many tin radicals as might be desired.

As we can now refresh the hydrogen abstraction tool at will, we can freely use this tool in the manufacture of other tools. In particular, all other radicals can be generated from their hydrogenated precursors by applying the hydrogen abstraction tool.

Conversion of butadiyne into a bound polyyne (reaction 1 and 2) uses two hydrogen abstraction tools and two silicon radicals. Two additional silicon radicals are used in the production of two C#C dimers able to reload the dimer deposition tool (reaction 21). Loading of the dimer deposition tool results in the bonding together of two silicon radicals. However, these radicals can be regenerated simply by pulling them apart. As a consequence, the net effect of these reactions is to reload two dimer deposition tools with no net decrease in the number of silicon radicals. The two hydrogen abstraction tools used to remove the two hydrogens from butadiyne can be regenerated as discussed earlier.

Generation of carbenes from butadiyne uses only hydrogen abstraction tools, transition metals, and silicon radicals (reactions 9 through 14). The hydrogen abstraction tools are not limiting, and there is no net loss of silicon radicals in this process.

As a consequence, we can freely use all of these tools without concern that they cannot be refreshed. The manufacture of new hydrogen abstraction tools is shown in reactions 3 and 4, while creation of a new carbene insertion tool can be done by attaching a long cumulene to a diamond surface (such as the (100) surface) followed by severing the cumulene as in reactions 12 and 13.

We do not show the detailed synthesis of the positionally controlled transition metal(s), silicon radical or tin radical. As we now have an existing set of tools which we can freely use without concern that they will be irreversibly "used up," the synthesis of the other tools should be feasible. A detailed set of reactions for this process (which would require a specific proposal for the "vitamin" molecule) is needed, but is beyond the bounds of this paper.