damian g. allis et al- analysis of diamondoid mechanosynthesis tooltip pathologies generated via a...

8/3/2019 Damian G. Allis et al- Analysis of Diamondoid Mechanosynthesis Tooltip Pathologies Generated via a Distributed Co

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Copyright 2011 American Scientic PublishersAll rights reservedPrinted in the United States of America

Journal of Computational and Theoretical Nanoscience

Vol. 8, 123, 2011

Analysis of Diamondoid MechanosynthesisTooltip Pathologies Generated via a

Distributed Computing ApproachDamian G. Allis1 , Brian Helfrich2, Robert A. Freitas Jr.3, and Ralph C. Merkle3

1Department of Chemistry, Syracuse University, Syracuse, NY 13244, USA2Helcorp, Maplewood, NJ, 07040, USA

3Institute for Molecular Manufacturing, Palo Alto, CA 94301, USA

The results of a combined molecular dynamics/quantum chemistry pathology study of previouslyreported organic (diamondoid) tooltips for diamondoid mechanosynthesis (DMS) are presented.

This study, employing the NanoHive@Home (NH@H) distributed computing project, produced80,000 tooltip geometries used in 200,000 calculations optimized at either the RHF/3-21G orRHF/STO-3G levels of theory based on geometries obtained from high-energy molecular dynamicssimulations to produce highly deformed starting geometries. These 200,000 calculations have beencatalogued, grouped according to energies and geometries, and analyzed to consider potentiallyaccessible defect structures (pathologies) for tooltip geometries either binding a carbon dimer (C 2feedstock or not containing the transported dimer feedstock. The transport and deposition of feed-stock and the stability of the tooltip between dimer loading cycles are important geometries thatmust be considered as part of a tooltip stability analysis. The NH@H framework is found to be a use-ful method both for the study of highly deforming covalent geometries and, using lower-temperatureMD simulations, for generating and optimizing molecular conformations (demonstrated using biotin,n -heptane, and n -octane in this study). The results of the pathology survey are discussed andgeneral considerations for the exploration of DMS tooltip usability are explored.

Keywords: BOINC Platform, Conformational Searches, Diamondoid Mechanosynthesis,Distributed Computing, Molecular Manufacturing, NanoHive@Home, TooltipPathologies.

1. INTRODUCTION

Molecular quantum mechanics (QM), classical molecu-lar dynamics (MD) simulations, and their combinationplay unique roles in the eld of molecular manufac-turing by their use as the foundational tools directingnearly all research efforts. In the sub-eld of diamondoidmechanosynthesis (DMS),1 2 initial experimental feasibi-lity studies have begun but are difcult due to the cur-rent inability to positionally control and deposit carbon (C)atoms or reactive organic fragments, although prior expe-rimental studies demonstrate the feasibility of mechanicalbond manipulation35 and the rst US patent on DMS wasissued in 2010.6 The positional-control feature of DMSdenes its many differences from (and possible advan-tages over) traditional chemosynthetic approaches for thefabrication of complex nanostructures. In the eld of

Author to whom correspondence should be addressed.

DMS, computational chemistry can be thought to serve thesame role in experimental studies and engineering effortsthat computer-aided design (CAD) performs in modernmechanical and electrical engineering, providing a frame-work for design and validation in efforts to greatly reducethe time and resource requirements of experimental stud-ies performed in the absence of these predictive tools. Theuse of computational tools for design and initial testinginuences all areas of DMS study, including the mod-eling of molecular tooltips for the delivery of feedstockto workpieces1 2 711 and of workpiece reactivity duringmechanosynthetic operations,79 13 the design of usefulDMS reaction sequences2 9 and pathways for rechargingspent tooltips,2 12 and the modeling of feedstock depositiononto workpieces for the fabrication of structured surfacesand constrained molecular fragments.2 9 Computationalstudies provide considerable information concerning thedynamics of structures, binding energies of feedstock to

J. Comput. Theor. Nanosci. 2011, Vol. 8, No. 7 1546-1955/2011/8/001/023 doi:10.1166/jctn.2011.1792 1


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Analysis of Diamondoid Mechanosynthesis Tooltip Pathologies Generated via a Distributed Computing ApproachAllis et al.

tooltips and workpieces, transition state barriers betweenpossible defect structures (pathologies), and estimates of positional tolerances8 9 12 based on the control of opera-tional conditions (such as system temperatures and com-ponent composition). The utility of these studies is limitedlargely by the quality of the calculations that can be per-formed or, more specically, the accessibility of computa-tional resources capable of handling high-level calculationson large structures.

The area of study in DMS that has received themost attention to date has been the design and valida-tion of tooltips used for the delivery of feedstock toworkpieces.1 2 712 A generic tooltip and division into itsimportant components is shown in Figure 1. These studiesconsider the stability of feedstock bound to tooltips,1 2 7 8the transfer energies of feedstock to workpieces,2 712 theoptimization of tooltip designs to limit the potential forinteractions between the tooltip framework and poten-tially reactive workpieces,1 2 8 and the potential for defect

structure formation.1 2 8 12

The formation of tooltip defectstructures either with or without bound feedstock is, afterthe identication of candidate tooltip delivery geometries,the most important area of testing. The results of post-design tooltip studies may determine the acceptability of a tooltip as an experimental candidate, either removing atooltip design from consideration based on the accessibil-ity of geometries that prohibit recharging or deposition, orinstigating the redesign of a tooltip to reduce the likelihoodof a possible route to defect formation.

Two factors limit the identication of defects and theirpossible accessibility during mechanosynthetic operations.These include(1) the number of potential defects accessible for a pro-posed tooltip and(2) the computational resources required to model whatmay be multiple accessible defect structures from whatmay be multiple candidate tooltip structures.In the interest of addressing both of these limiting fac-tors, a distributed computing study was performed using

Fig. 1. The general design of a molecular tooltip for diamondoidmechanosynthesis. A tooltip is composed of a framework that holds, e.g.,two binding atoms, a pair of binding atoms for the stable binding andcontrolled deposition of feedstock, and some feedstock (in this case, acarbon dimer) that is deposited onto a workpiece.

the NH@H project16 and a series of tooltips that hadbeen the subjects of two previous DMS studies. ThisNH@H study, known as the NH@H tooltip pathol-ogy survey, employed a combined MD/QM methodol-ogy, the Quantum Search for Minimum Alternatives inKinetically-Accessible Space (Q-SMAKAS), and com-bined the computational resources of 10,000 volunteeredPCs to identify possible defect structures for 25 tooltipsgenerated from high-temperature (highly deforming) MDsimulations and optimized (via distributed computing)using quantum chemistry calculations. The analysis of thenearly 200,000 quantum chemistry calculations coveringthe generated structures and the presentation of possibledefect structures for this set of 25 tooltips are describedin the present work. The two previous DMS studies aresummarized briey below.(1) Horizontal Ge-Substituted Polymantane-Based C 2 Dimer Placement Tooltip Motifs for Diamond Mechanosynthesis: This study1 of carbon dimers (C2

bound to two germanium (Ge) atoms within adamantaneand related frameworks considered only pathologies thatchanged the binding modes of the dimer. The 24 tooltipsfor which high-level computational studies (B3LYP/6-311 + G(2d,p)//B3LYP/3-21G* relative energies andnormal mode analyses) were performed were from anoriginal set of 53 tooltips, of which 29 were determined byan AM1-driven MD simulation (combined semi-empiricalquantum chemistry and classical dynamics) at 900 K tobe too unstable for use in mechanosynthetic operationsdue to such identied problems as dimer orientationinstability (a preference for the C2 to orient perpendicularto the Ge Ge axis to form a carbenic structure, seebelow), GeC bond strain due to the design of the Cframework, large mobility of the tooltip framework afterC2 removal, and proximity of tooltip hydrogen (H) atomsto the Ge atoms (as H migration to the C2 binding posi-tions is one form of tooltip poisoning). This study was afollow-up to the rst dimer tooltip proposal (2003) for theDCB and MCB motifs.7(2) Design and Analysis of a Molecular Tool for CarbonTransfer in Mechanosynthesis: This study8 considered asingle tooltip (named DC10c) in great detail, with theanalysis of geometry, binding energies, defect structures,and transition state calculations performed in a mannerthat models how the subsequent studies of the 24 candidatetooltips above would be performed as either a means toacceptability or removal from possible experimental con-sideration. This study determined that the C2-bound tooltipgeometry was both a stable minimum energy structureand that several potential defect structures were, despitesome that were determined to be more stable than theoperational tooltip geometry, inaccessible based on theirlarge calculated transition state barriers. The transitionstate search and defect structure analysis included bothC2 orientation and larger defects within the tooltip frame-work itself, with the generation of defects determined

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Allis et al. Analysis of Diamondoid Mechanosynthesis Tooltip Pathologies Generated via a Distributed Computing App

from strain analyses at various positions, expectationsbased on organic mechanism considerations, and chemicalintuition.

2. COMPUTATIONAL METHODS

NH@H16 was a distributed computing system based onthe Berkeley Open Infrastructure for Network Computing(BOINC) platform.17 BOINC is a system that manages thedistribution of computing jobs to participant computers onthe Internet. Participants register and donate CPU time,after which data and applications are sent to the participantmachine from a central server. After their computer hascompleted processing the data, it uploads the results to thecentral server and is then sent more data to process.

An initial geometry optimization of each tooltip, bothwith bound feedstock (loaded) and without (unloaded,see below), was performed to produce baseline structures.All energy minimizations were calculated using the opensource Massively Parallel Quantum Chemistry (MPQC)program from Sandia National Laboratory.18 The initialoptimizations were performed both in-house and with theNH@H network. The majority of the tooltips were opti-mized at a Restricted Hartree-Fock level with the 3-21GGaussian-type basis set.19 Seven of the tooltips were deter-mined to be too large for the 3-21G basis set, with thetradeoff of compute time versus chemical accuracy biasedin favor of faster optimization of more structures andaway from the more common strategy of slower but moreaccurate optimization of fewer structures. The need toaccommodate the computing power of many participantmachines (ca. FebruaryMay 2007) further argued for a

Table I. Unique geometries obtained from each molecular dynamics simulation (temperature in K as reported for each collection of structurthe loaded (L) and unloaded (U) tooltips. For each tooltip, a representative structure code from each run is provided (Struct.) and is availSupplemental Material.L n andU n labels correspond to structures provided in Figure 6. The numbers in bold within theStruct. columns are the totalnumber of successful quantum chemistry optimizations for each tooltip snapshot, with the total number of snapshots submitted to quantum choptimization provided below the tooltip label for each MD run ( n Runs ).

C100GeATD Struct. kJ/mol C100GeATSr5 Struct. kJ/mol C100GeATS Struct. kJ/molL1 1z 0.0 L1 1z 0.0 L1 1z 0.0

1250 Runs 1210 1500 K 1250 Runs 1094 1500 K 1250 Runs 1218 1500 K

L1 1t 0.0 L1 1v 0.0 L1 1t 0.0L2 928t 159.2 L2 421v 138.6 1000 Runs 331 4500 K

1000 Runs 263 4500 K L3 90v 279.11000 Runs 636 3500 K U1 5t 0.0U1 1s 0.0 U2 412t 93.6U2 59s 43.6 U1 1w 0.0 U3 626t 296.1U3 861s 165.0 U2 41w 81.2 U4 995t 372.6U4 627s 417.9 1000 Runs 711 3000 K 1000 Runs 342 4500 K

1000 Runs 121 5000 K

C100GeATSr6 Struct. kJ/molC100GeCTS Struct. kJ/mol C100GeCTS Struct. kJ/mol L1 1z 0.0

L1 1v 0.0 U1 1w 0.0 1250 Runs 1050 1500 KL2 258v 261.3 U2 970w 102.8L3 280v 326.1 1000 Runs 829 3000 K L1 1x 0.0

1000 Runs 661 3500 K 1000 Runs 711 2500 K

reduced basis set quality approach in these larger systems,resulting in the use of the STO-3G basis set.20 STO-3Ggeometries are of sufcient quality to serve as the basisfor later studies at higher levels of theory, given that thegoal of the project was to generate a selection of potentialfailure modes for subsequent work. The tooltips processedat the RHF/STO-3G level were MCB5Ge, MCB57Ge,DCB75Ge, C100GeATD, C100GeATS, C100GeCTS, andMCB75Ge (see the Results section for the geometries).

The optimized tooltip geometries served as the start-ing structures for molecular dynamics (MD) simulationsat high temperatures for 50,000 iterations, with snapshotsof the tooltip saved to a le every 40 or 50 iterations.The thermal energy provided during the high tempera-ture simulations perturbed each tooltip signicantly. Thesnapshots provided kinetically accessible deformations of tooltip geometries, which were then subjected to quan-tum chemistry optimization at either the RHF/3-21G orRHF/STO-3G levels of theory. MD simulations were per-formed with the GROMACS software package21 using theGROMOS8722 force eld with suitable modications.14 15The following parameters were employed for the simula-tions: timestep= 2 0 fs, neighbor list updated every tensteps, twin range electrostatics cut-offs with neighborlistcut-off = 0 8 nm and Coulomb cut-off = 1 4 nm, van derWaals cut-off = 0 8 nm, Berendsen-thermostat temperaturecoupling with time constant= 0 1 ps, and Berendsen pres-sure coupling.

Initially, a 50,000-iteration MD simulation at 1500 Kwas performed with each loaded and unloaded tooltipto establish a baseline level of tooltip deformation. Theroot mean square deviation (RMSD) of all tooltips at this

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temperature was around 0.02 . Quantum chemistry opti-mizations were then performed on the NH@H networkusing MPQC for each snapshot with the following conver-gence criteria and parameters: basis set= RHF/3-21G orRHF/STO-3G (as dened above), maximum energy gra-dient 0.001 Hartrees/Bohr, maximum atom displacement

0.001 , maximum optimization convergence attempts=

40, maximum energy convergence (SCF) cycles per opti-mization step attempt= 100. For this RMSD 0 02 passof calculations, no failure modes were discovered. The rep-resentative structures for this temperature are tagged with

Table II. Unique geometries obtained from each molecular dynamics simulation (temperature in K as reported for each collection of strufor the loaded (L) and unloaded (U) tooltips. For each tooltip, a representative structure code from each run is provided (Struct.) and is avaSupplemental Material.L n andU n labels correspond to structures provided in Figure 7. The numbers in bold within theStruct. columns are the totalnumber of successful quantum chemistry optimizations for each MD simulation, with the total number of structures submitted to quantum coptimization provided below the tooltip label for each MD run ( n Runs ).

DCB55AGe Struct. kJ/mol MCB55Ge Struct. kJ/mol MCB5Ge Struct. kJ/mol

L1 1z 0.0 L1 1z 0.0 L1 1z 0.01250 Runs 1088 1500 K 1250 Runs 944 1500 K 1250 Runs 1196 1500 K

L1 1t 0.0 L1 32q 0.0 L1 1y 0.01000 Runs 363 4500 K L2 682q 49.8 1000 Runs 899 2000 K

L3 816q 26.2U1 1u 0.0 L4 129q 30.2 U1 1z 0.0U2 630u 118.5 L5 161q 41.7 1000 Runs 916 2000 KU3 898u 83.8 L6 958q 100.1U4 470u 74.0 L7 839q 218.2U5 909u 1.4 1000 Runs 14 6000 KU6 3u 16.3 DCB65Ge Struct. kJ/molU7 606u 94.0 U1 1z 0.0 L1 1z 0.0U8 28u 234.7 U2 746z 63.0 1250 Runs 952 1500 K

1000 Runs 549 4000 K 1000 Runs 913 1500 KL1 1w 0.0

1000 Runs 490 3000 KDCB55CGe Struct. kJ/mol DCBIceane7Ge Struct. kJ/mol

L1 1z 0.0 L1 1z 0.0 U1 1v 0.01250 Runs 1012 1500 K 1250 Runs 1095 1500 K 1000 Runs 346 3500 K

L1 1v 0.0 L1 1v 0.0L2 225v 165.7 1000 Runs 704 3500 K

1000 Runs 401 3500 K MCB75Ge Struct. kJ/molU1 1w 0.0 L1 1x 0.0

U1 1u 0.0 U2 10w 7.4 1000 Runs 138 2500 KU2 701u 66.4 U3 431w 57.4U3 81u 126.8 U4 503w 110.2U4 424u 210.9 1000 Runs 509 3500 K

1000 Runs 485 4000 K MCB57Ge Struct. kJ/molL1 1z 0.0

DCB57Ge Struct. kJ/mol 1250 Runs 1148 1500 KDCB75Ge Struct. kJ/mol L1 1z 0.0

L1 1z 0.0 1250 Runs 987 1500 K L1 1y 0.01250 Runs 1187 1500 K 1000 Runs 827 2000 K

L1 1u 0.0L1 1x 0.0 1000 Runs 443 4000 KL2 79x 10.5L3 274x 142.1 U1 1u 0.0 DCB6Ge Struct. kJ/mol

1000 Runs 638 2500 K U2 998u 20.7 L1 1z 0.0U3 969u 55.2 1250 Runs 977 1500 K

U1 1y 0.0 U4 843u 171.5U2 381y 71.4 1000 Runs 394 4000 K L1 1v 0.0

1000 Runs 620 2000 K 1000 Runs 490 3500 K

z in the Struct. column of Tables IV. See below formore information.

A series of MD simulations were then performed foreach tooltip in increasing temperature increments of 500 Kuntil structures were produced with structural RMSDs of at least 0.04 . The nal range of temperatures for the var-ious loaded and unloaded tooltips were: 2000 K (taggedy in the Struct. column of Tables IV), 2500 K (taggedx), 3000 K (tagged w), 3500 K (tagged v), 4000 K(tagged u), 4500 K (tagged t), 5000 K (tagged s),5500 K (tagged r), and 6000 K (tagged q). For this



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Table III. Unique geometries obtained from each molecular dynamics simulation (temperature in K as reported for each collection of strucfor the loaded (L) and unloaded (U) tooltips. For each tooltip, a representative structure code from each run is provided (Struct.) and is avaiSupplemental Material.L n andU n labels correspond to structures provided in Figure 8. The numbers in bold within theStruct. columns are the totalnumber of successful quantum chemistry optimizations for each MD simulation, with the total number of structures submitted to quantum choptimization provided below the tooltip label for each MD run ( n Runs ).

C110GeS Struct. kJ/mol AdamGe22 Struct. kJ/mol AdamGe33 Struct. kJ/molL1 1z 0.0 L1 1z 0.0 L1 1z 0.0

1250 Runs 1188 1500 K 1250 Runs 1195 1500 K 1250 Runs 1200 1500 K

L1 1v 0.0 L1 1w 0.0 L1 1w 0.0L2 613v 11.6 L2 701w 22.4 L2 568w 85.2L3 558v 21.8 L3 865w 4.7 L3 409w 97.9L4 801v 97.5 1000 Runs 834 3000 K 1000 Runs 742 3000 KL5 783v 124.2

1000 Runs 698 3500 K L1 1v 0.0 U1 2z 0.0L4 787v 36.2 U2 597z 6.0

U1 1v 0.0 1000 Runs (D) 746 3500 K U3 350z 238.1U2 304v 27.6 U4 216z 277.6U3 635v 190.5 U1 1w 0.0 1000 Runs 422 1500 K

1000 Runs 322 3500 K U2 742w 45.2U3 733w 204.9 Diad3Ge22 Struct. kJ/molU4 724w 276.5 L1 2z 0.0

TwistaneGe Struct. kJ/mol 1000 Runs 354 3000 K 1250 Runs 1003 1500 KL1 1z 0.0

1250 Runs 1223 1500 K L1 1x 0.0C111Ge3 Struct. kJ/mol L2 865x 111.7

L1 1u 0.0 L1 1z 0.0 1000 Runs 670 3000 KL2 238u 58.6 1250 Runs 1037 1500 K

1000 Runs 551 4000 K U1 1w 0.0L1 1v 0.0 U2 951w 218.4

1000 Runs 584 2500 K U3 37w 37.9U4 872w 63.9

1000 Runs 506 3000 K

RMSD> 0 04 pass of calculations, failure modes werediscovered. The nal analysis of the generated structures

was performed by energy comparisons, using a 1 kJ/molcut-off for the grouping of distinct geometries. Structuresof identical geometry that differed by more than 1 kJ/molbut less than 3 kJ/mol were sorted by inspection. For theperformed tooltip calculations, defect geometries are theresult of changes to covalent frameworks and not simply

Table IV. Unique conformational geometries obtained from each molecular dynamics simulation (temperature in K as reported for each colof structures) for the loaded (L) and unloaded (U) tooltips. For each tooltip, a representative structure code from each run is provided (Structavailable as Supplemental Material.L n and U n labels correspond to structures provided in Figure 9. The numbers in bold within theStruct. columnsare the total number of successful quantum chemistry optimizations for each MD simulation, with the total number of structures submitted to chemistry optimization provided below the tooltip label for each MD run ( n Runs ).

DCB55BGe Struct. kJ/mol DCB55BGe Struct. kJ/mol DCB5Ge Struct. kJ/molL1 1z 0.0 U1 1z 0.0 L1 1z 0.01250 Runs 607 1500 K U2 681z 71.4 1250 Runs 1006 1500 K

U3 928z 1.3L1 1w 0.0 U4 860z 1.2 L1 1w 0.0

1000 Runs 141 3000 K U5 301z 8.9 L2 13w 126.2U6 441z 18.7 L3 377w 150.0U7 978z 20.6 L4 881w 159.8U8 524z 22.0 1000 Runs 561 4000 KU9 655z 24.0

U10 710z 29.8 U1 2x 0.01000 Runs 929 1500 K U2 950x 58.8

U3 237x 25.01000 Runs 663 2500 K

conformational changes. Despite this, alternate minimawere determined in a few cases to lie close in energy to the

starting geometries, thereby resulting in the small 1 kJ/molstarting structure delimiter.An additional set of calculations were performed that

only succeeded in generating conformations (and not struc-tures with altered covalent frameworks) in three famil-iar molecules. A series of 1500 K MD simulations were


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Table V. Unique geometries obtained from each molecular dynamics simulation (temperature in K as reported for each collection of structuthe loaded (L) and unloaded (U) DC10c tooltips. For each tooltip, a representative structure code from each run is provided (Struct.) and is avaSupplemental Material.L n andU n labels correspond to structures provided in Figure 10. The numbers in bold within theStruct. columns are the totalnumber of successful quantum chemistry optimizations for each MD simulation, with the total number of structures submitted to quantum coptimization provided below the tooltip label for each MD run ( n Runs ). Simulations using deuterium masses for all H atoms are identied as (D).

DC10c Struct. kJ/mol DC10c Struct. kJ/mol DC10c Struct. kJ/molL1 1v 0.0 L1 1r 0.0 U1 1q 0.0

L2 719v 3.1 L3 557r 19.3 U2 259q 14.3L6 563v 320.9 L5 798r 312.1 U3 889q 23.0

1000 Runs 880 3500 K L7 841r 322.3 U4 159q 144.5L8 776r 337.1 U5 704q 168.7

L1 1w 0.0 1000 Runs 490 5500 K U6 718q 201.9L4 193w 307.7 U7 641q 288.5

1000 Runs (D) 372 3000 K U8 901q 299.91000 Runs 952 6000 K

performed for biotin,n-heptane, andn-octane in orderto demonstrate the utility of the NH@H network as atool for conformational sampling. For each of these threemolecules, 1000 MD snapshots were generated and opti-mized with NH@H at the RHF/3-21G level of theory.

For the NH@H tooltip pathology survey, the data sent toeach participant computer were tooltip geometries (primar-ily snapshots) and MPQC. Each tooltip geometry was sentto two different computers and both results were comparedbefore acceptance as nal data. If the two results werenot in agreement, the geometry was sent to a third com-puter, and so on until a quorum of two matching resultswere received. Approximately 6,000 participants donatedtime on over 10,000 computers to perform nearly 200,000energy minimizations over a period of three months, repre-senting 2.5 million CPU hours of actual geometry opti-mization time in the present work.

3. RESULTS

3.1. Conformational Searches with NH@H: Biotin, n-Heptane, and n -Octane

The utility of the Q-SMAKAS methodology for the moregeneral quantum chemistry study of molecular confor-mation searches was tested using the biomolecule biotin(C10H16N2O3S) and the linear hydrocarbonsn-heptane(C7H16 andn-octane (C8H18 . The results of these studiesare presented below with the geometries for all calculatedstructures provided as Supplemental Material.

3.1.1. Biotin

As a test case for conformational searches, biotin isan interesting molecule on several levels beyond itsbiological signicance. There are three (two OH andone NH) H-bond donors and ve (two O, one S,and two lone pair N) H-bond acceptors responsiblefor the water-solubility of this B-complex vitamin. Asmost of these fragments are localized on the fused ure-ido/tetrahydrothiophene (U/T) rings at the head of the

biotin molecule, the presence of multiple local conforma-tional minima along the covalent potential energy surfaceare made accessible by exibility in the C4H8 taillinking the fused ring head to the carboxylic acid (COOH)pendant group. While multiple local minima have beenpredicted by previous studies,2325the two most interestingconformations of note are a cyclic form predicted in thegas phase (where a pair of H bonds are formed betweenthe U/T rings and the COOH) and the fully-extended formfound in the solid-state (where the formation of multipleintermolecular H bonds is preferred over intramolecularH-bond formation).25

Figure 2 shows a sample of the identied local minimapredicted to lie within 40 kJ/mol of the global minimum,as well as the least stable structure optimized to a mini-mum energy geometry. Among those conformations within40 kJ/mol of the global minimum, the stabilities of the

biotin molecule geometries are found to increase signi-cantly with H-bond formation between the U/T rings andthe COOH. Neglecting the small variations in C4H8 con-formations among the most stable structures, the identiedbiotin minima can be grouped according to the numberand arrangement of H bonds formed between the U/T headand COOH tail. These basic motifs are shown in Figure 2.The most stable structures are found to form two directH bonds using the entire COOH (COCOOH HNU/ Tand OHCOOH O CU/ T tail. The second group of structures forms a smaller cyclic H-bonding systemcontaining an oriented OHCOOH group that acts asboth H-bond donor (OHCOOH O CU/ T and acceptor(HOCOOH HNU/ T . The third group contains structureswith only a single directed H bond (C OCOOH HNU/ Tor OHCOOH O CU/ T . The nal group to lie within40 kJ/mol of the lowest energy structure contains noH-bonding interactions between the polar fragments of theU/T ring and COOH but may include weak CHO/NH bonds to add slight stability and diversify the numberof predicted minima in this category.

The least stable structures (of which several are foundto lie 90 kJ/mol or more above the global minimum) con-tain O COH carboxylic acid geometries where the



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Fig. 2. Representative conformational minima within 40 kJ/mol of the predicted global minimum geometry (OHtail O== Chead+ C== Otail HNheadand the highest energy conformation identied from the HF/3-21G optimizations (180COOH). Representative structure codes (top) and relative energies( ERel, in kJ/mol) are also provided.

dihedral angle around the central CO bond approaches180 degrees. This local geometry is signicant both to theanalysis of the results and to the algorithm being usedin the conformational survey. This geometry would beexpected to be highly disfavored because it places the lonepair of the OHCOOHoxygen into its closest proximity witha lone pair of the O CCOOHoxygen, a geometry that com-bines the electrostatic repulsion of these two lone pairswith the breaking of a favorable interaction between theC O lone pair and the H atom in the OH. Nevertheless,this geometry is found to be an isolatable structure accord-ing to the SCF convergence algorithm in several of thecalculated structures.Even highly strained conformations

can be trapped by a convergence algorithm in a quan-tum chemistry calculation provided that the local potentialwell is deep enough to not allow the converger to sam-ple alternate local minima that might lie much lower inenergy.

3.1.2. n-Heptane and n-Octane

The linear alkanesn-heptane andn-octane are nonpolarmolecules whose conformations are generated by rotationabout CC -bonds and are the result of a minimiza-tion of the total number of eclipsing HH geometriesfor which maximum electrostatic repulsion occurs betweenneighboring CH2CH2 fragments. In the case of n-heptane, the range of identied minima extends from thefully extended global minimum to an S-shaped max-imum 31.5 kJ/mol higher in energy. Forn-octane, thisrange extends to 41.1 kJ/mol in another highly twistedS-conformation that was only found in a single struc-ture optimization. A selection of conformations for bothmolecules is shown in Figure 3, with the nal struc-ture groupings of the 1000 starting geometries for eachmolecule determined rst by relative energies and secondlyby RMSD analysis. The approximate 3.2 kJ/mol increase

in energy with each CC rotation away from the most sta-ble geometry is reproduced in the conformational group-ings of both then-heptanes andn-octanes.

3.2. Carbon (C 2) Dimer Tooltips and Pathologies

The 25 tooltip structures considered in the NH@H studyare taken from two previous computational studies. All butone of the tooltips used were part of a larger survey byFreitas et al.,1 This rst survey identied structures thatwere predicted at the B3LYP/6-311+ G(2d,p)//B3LYP/3-21G* level of theory to bind C2 either by the bindingmode that uses the C2 to bridge two Ge atoms separated

by the organic tooltip framework or by defect modes thatinvolve rearrangement of the C2 dimer at its Ge Gebinding position. The search for additional defect struc-tures was not performed in the rst survey due to the largenumber of tooltips and the absence of a thorough com-putational procedure for automating the defect structureprocess. One additional tooltip, DC10c, was the subject of a comprehensive optimization, defect geometry, and tran-sition state analysis by Allis and Drexler.8 This tooltip isdistinct from the Ge-based tooltips in both the manner of C2 binding in the completed (loaded) tooltip and the use of

-conjugation as the means for stabilization of the tooltipin the C2 dimer-free (unloaded) tooltip the Ge tooltipsuse only the relative binding energies of the C2 to theframework Ge atoms and the stability of the frameworkCC bonds relative to potential CGe structure rearrange-ment. The tooltip structures corresponding to the opera-tional geometries (bound C2 dimer on a stable optimizedframework) for all 25 structures considered in the NH@Hstudy are shown in Figures 4 and 5.

As a means to clarify terms used generally in the pre-vious mechanosynthetic tooltip analyses but not otherwisecommon in a strictly chemical context, several terms usedin this analysis are dened below.


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Fig. 3. Relative energy groupings (energies in kJ/mol) and representative structures from then-heptane andn-octane structure optimizations.

3.2.1. Denitions

Loaded Tooltip A loaded tooltip (LT) is one binding theC2 dimer at both binding positions in the tooltip. The LTis distinct from C2 dimer binding modes that do not bindthe C2 dimer at either end in the tooltip binding position(a few examples of which are provided as pathologies inthe analysis).Unloaded Tooltip An unloaded tooltip (UT) is one inwhich the C

2dimer is not present. For use in mechanosyn-

thetic operations, rechargeable tooltips (one for which anew C2 dimer has been added) require that both the LTbe stable for positional control and the UT be stable afterC2 dimer deposition. A tooltip that undergoes any struc-tural rearrangement upon C2 dimer removal or that hasany nearby accessible potential minima that involve minorstructural changes that modify the C2 dimer binding areais not a reliable tooltip for multiple operations.Pathology A pathology , as dened in previousmechanosynthetic studies,1 2 12 is a defect structure inan operational context in the same way that a structural

isomer in a chemical context has the same molecularformula but a different atomic framework arrangement.Pathologies, like structural isomers, can appear verysimilar in geometry to the desired molecule, or can becompletely rearranged in geometry, or may possess anintermediate geometry. Ln and Un The naming convention in this study for eachtooltip and tooltip pathology is to label the base geome-try (the expected LT or UT) as L1 (loaded base geometry)and U1 (unloaded base geometry). Subsequent structurelabels are ordered from most stable to least stable pathol-ogy. In several cases, pathologies occur that are more sta-ble than the expected LT and UT structures but are stilllabeled from Ln+ 1 and U n+ 1 . In Tables IV, theseLn and Un labels are provided with a structure labeled ina N n format, whereN is the snapshot number andn

= y x w v u t s r qis a letter corresponding to thebath temperature of the MD run (see the Methods sectionabove). These codes correspond to representative geome-tries whose coordinates are provided as Supplemental



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Fig. 4. Loaded tooltip (LT) geometries used in the NH@H study. Carbon dimers (C2 are shown in red. Framework C and H atoms are shown indark grey and white, respectively. Germanium atoms (in all but the DC10c tooltip) are shown in blue. DC10c C atoms used for C2 dimer binding areshown in yellow.

Material. They do not represent the numbers of times atooltip was identied as a minimum, only one member of the set of tooltips with identical energies and geometriesafter the quantum chemistry optimization.C 2 dimer The C2 carbon dimer is a feedstock fragmentemployed for mechanosynthetic depositions. C2 has beenthe feedstock of choice for several previous computationalstudies as a predictably manageable building unit for dia-mondoid, nanotube, and graphene fabrication.2 79 The C2dimers in all images are shown in red.Framework The framework in these tooltips are theC atoms that hold the Ge atoms (or any C2-dimer bindingatom positions) in place. A change to the geometry of theframework (as occurs in some pathologies) must involvechanges to the organic framework and may or may notinvolve changes to the C2 dimer binding position (specif-ically, to the positions of the Ge atoms). A framework

defect may still serve as a proper tool for C2 dimerrecharging and mechanosynthetic operations. Hydrogen inversion The majority of all identiedpathologies are the result of one or more H atoms fromthe organic framework inserting into the three-dimensionalcage geometry of the tooltip. These structures result fromthe very high temperatures used in the MD simulations togenerate the deformed geometries and the large H-atomdisplacements that occur as a result of the combinationof H-atom momentum and long time steps. Generally,the H-inverted structures generated from the MD simu-lations are chemically inaccessible because of the signif-icant energies involved both in the insertion and in thenal H-trapped minima. As a simple procedure for remov-ing these geometries from the structure analysis, simplyplacing a 400 kJ/mol energy cut-off on acceptable tooltipsfor included structures removes all but a few H-inverted


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Fig. 5. Loaded tooltip (LT) geometries used in the NH@H study. Carbon dimers (C2 are shown in red. Framework C and H atoms are shown indark grey and white, respectively. Germanium atoms are shown in blue.

cases. Some of the tooltip structures are exible enough attheir framework bases that H inversion, while energeticallyinaccessible under normal conditions, leads to pathologieswithin the range of other pathologies, and so these struc-tures are included in the analysis for comparative purposes.This simulation issue is addressed in greater detail in theDiscussion section.

3.2.2. Ge-Tooltip Structures Optimized at the RHF/STO-3G Level of Theory

3.2.2.1.C100GeATD (Table I, Fig. 6) . A single LT pathol-ogy (L2,+ 159.2 kJ/mol) is identied from the 4500 K MDsimulation generated by the migration of a framework CHH atom onto the C2 dimer and formation of a C2 dimer-Cframeworksingle bond to produce a CCGe three-memberring. Three UT pathologies are identied from a 5000 KMD simulation, including a more stable structure gener-ated by the migration of a nearby CH H atom to a tooltipGe (U2), another structure with a broken GeC bond (U3),and another with considerable C C framework rearrange-ment and the formation of one C C double bond (U4).3.2.2.2.C100GeATS (Table I, Fig. 6). The 1500 K and4500 K MD simulations of the LT produced only the basegeometry (L1). Three pathologies of the UT are identi-ed in the 4500 K MD simulation that are less stablethan the UT base structure (U1), with the U1 optimiza-tion itself resulting in the formation of a GeGe bond (or

close contact; see below). The three pathologies all opti-mize with one or more broken GeC bonds. Pathology U2includes GeC bond breaking and the formation of oneC C double bond. Pathology U3 has an H atom insertedinto the tooltip framework and signicant displacement of one Ge from its U1 position. Pathology U4 has one brokenGeC bond and H migration. Both U3 and U4 representdefects not expected to occur in a larger tooltip frame-work, as the surface CH H atoms involved in migrationwould be replaced with additional CC framework bonds.In the isolated tooltips, the resulting H rearrangements pro-duce structures of signicantly higher energy than the basestructure (U1).3.2.2.3.C100GeCTS (Table I, Fig. 6). Two LT patholo-gies are identied in the 3500 K simulation. The rst (L2)involves the breaking of one CC framework bond and acombination of H migration and CC double bond for-mation which occurs away from the C2 dimer bindingposition. Pathology L3 similarly involves framework car-bon bond rearrangement with the preservation of the C2dimer binding geometry at the two Ge atoms. In L3, asingle GeC bond is broken and, via several small rear-rangements, a framework cyclopropyl ring is formed. TheUT base structure (U1) optimizes with the formation of a GeGe single bond. The only identied pathology fromthe 3000 K simulation (U2) combines a broken GeCbond with the formation of one C C double bond andthe migration of an H atom to one Ge atom that lies



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Fig. 6. LT and UT base geometries (L1 and U1, respectively) and identied pathologies. Carbon dimers (C2 in the LT structures are shown inred. Framework C and H atoms are shown in dark grey and white, respectively. Germanium atoms are shown in blue. The relative energies ostructures are provided in Table I.

103 kJ/mol higher in energy than U1; the source of thisH atom is the nearest C atom in the C C bond.3.2.2.4.DCB75Ge (Table II, Fig. 7). Two LT patholo-gies were identied from the 2500 K MD simulation. Therst of these (L2) is a conformational change of the twomethylene (CH2 fragments at the base of the tooltip andrepresents only a 10 kJ/mol change in energy. The sec-ond and more signicant defect (L3) is the product of anH inversion into the tooltip framework. As the DCB75Geframework is larger at the base, this H inversion occurswith a relatively small change in energy compared to otherH-inverted structures (142 kJ/mol). In both pathologies, theaddition of a larger support structure would be expected toremove these accessible defects.A single UT pathology is identied in the 2000 K MD sim-ulations. The base structure (U1) optimizes with the forma-tion of a GeGe single bond. In pathology U2, the GeGesingle bond is retained, but a single CH H atom adjacentto one Ge atom is inverted into the exible framework of the tooltip, producing a geometry only 71 kJ/mol higherthan the U1 base geometry. The addition of a larger sup-port structure might be expected to remove this accessibledefect, although the close proximity of the inverted H atomto the two Ge atoms (and, therefore, to the C2 dimer bind-ing position) makes framework addition a potentially prob-lematic solution to the potential H inversion problem.3.2.2.5.MCB5Ge (Table II, Fig. 7). The LT 1500 K and2000 K MD simulations produced no pathologies for thisstructure. The UT 2000 K MD simulations also producedno pathologies.3.2.2.6.MCB57Ge (Table II, Fig. 7). The LT 1500 K and2000 K MD simulations produced no pathologies for this

structure. Energy convergence for the UT structures wasnot achieved in the allotted time and within the 40-stepSCF limit.3.2.2.7.MCB75Ge (Table II, Fig. 7). The LT 2500 KMD simulations produced no pathologies for this struc-ture. Energy convergence for the UT structures was notachieved in the allotted time and within the 40-step SCFlimit.

3.2.3. Ge-Tooltip Structures Optimized at the RHF/3-21G Level of Theory

3.2.3.1.C100GeATSr5 (Table I, Fig. 6). Two LT patholo-gies were produced from the 3500 K MD simulations.The rst (L2) involves H inversion into the bottom of thetooltip framework which, being a more open structure,produces a pathology below the 400 kJ/mol H inversioncut-off. This pathology would not form in a larger frame-work, where this part of the tooltip would be embedded ina larger C framework. The second pathology (L3) involvesthe breaking of a GeC bond and the migration of oneH atom from the broken GeC C atom onto the brokenGeC Ge atom. The two identied UT pathologies areunique in that the geometries are similar in appearance butdiffer by 81.2 kJ/mol. The more stable structure (U1) isless symmetric than U2 with a 0.1 increase in the GeCdistances from its bound carbons and a 0.2 reduction inthe H2CGeCH2 C C separation.3.2.3.2.C100GeATSr6 (Table I, Fig. 6). The LT 1500 Kand 2500 K MD simulations produced no pathologies forthis structure. Energy convergence for the UT structures


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Fig. 7. LT and UT base geometries (L1 and U1, respectively) and identied pathologies. Carbon dimers (C2 in the LT structures are shown inred. Framework C and H atoms are shown in dark grey and white, respectively. Germanium atoms are shown in blue. The relative energies structures are provided in Table II.

was not achieved in the allotted time and within the 40-step SCF limit.3.2.3.3.C110GeS (Table III, Fig. 8). Four LT patholo-gies are identied from the 3500 K MD simulations,including one of slightly lower energy. Pathology L2 dif-fers from the base LT geometry (L1) with the rotationof the C2 dimer to form a structure with two GeCbonds to the same C2 dimer atom. While the calcu-lations here predict this geometry to lie 11.6 kJ/mollower in energy, the original study on this system (at the

B3LYP/6-311+ G(2d,p)//B3LYP/3-21G* level of theory)predicted the base L1 geometry to be 54 kJ/mol more sta-ble. Tooltip pathology L3 involves the breaking of oneGeC bond and the migration of the GeH H atom to thebroken GeC C atom. L4 is formed by the breakage of aframework CC bond, the formation of one CC doublebond at the base, and the migration of one CH H atomfrom a C C bond C atom to the framework C atomformerly bound to the C C double bond C atom. Thenal pathology (L5) features a broken GeC bond with



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Fig. 8. LT and UT base geometries (L1 and U1, respectively) and identied pathologies. Carbon dimers (C2 in the LT structures are shown inred. Framework C and H atoms are shown in dark grey and white, respectively. Germanium atoms are shown in blue. The relative energies ostructures are provided in Table III.

migration of the C2 dimer, breaking a GeC2 dimer bondto form a CframeworkC2 dimer bond. The new CframeworkC2 dimer bond in L5 also produces H migration from theframework C (Cframework to the C2 dimer.

The UT 3500 K MD simulations produced two patholo-gies, with the geometry optimization of the base structure(U1) resulting in the formation of a GeGe bond. Therst pathology (U2) shifts one GeH H atom to the otherGeH Ge atom, producing a completed GeH2 fragment,one H-vacant Ge atom, and a breaking of the GeGe bondin a structure only 27 kJ/mol higher in energy than U1.

This defect can be prevented from forming in a largertooltip framework where the GeH H atoms are replacedwith additional framework C atoms. The higher-energypathology (U3) combines the breaking of a GeC bondwith GeH CH H migration to form a stable C frame-work and a GeGeC three-member ring.3.2.3.4.C111Ge3 (Table III, Fig. 8). The LT 1500 K and2500 K MD simulations produced no pathologies for thisstructure. Energy convergence for the UT structures wasnot achieved in the allotted time and within the 40-stepSCF limit.

3.2.3.5.AdamGe22 (Table III, Fig. 8). The LT MD sim-ulations at 3000 K and 3500 K produced three patholo-gies either more stable or only slightly less stable thanthe LT base structure (L1). Pathology L2 is 22.4 kJ/molmore stable than L1, the result of a rotation of the C2dimer such that both Ge atoms are bound to the sameC atom in the C2 dimer. This geometry is similar to thatpredicted for C110GeS-L2 but is more stable relative to itsbase geometry by 11 kJ/mol. Pathology L3 shifts the C2dimer such that one dimer -bond is now directly boundto one Ge atom and the second C2 dimer C atom is shifted

towards this Ge atom to form a coordinating interaction.This structure is a small feedstock rearrangement with asmall relative energy change but is of great signicancebecause of the amount of structural exibility identiedand the potential problems associated with positional con-trol raised by the small barrier to dimer motion. Pathol-ogy L4 is a derivative of the L3 geometry, with a singleGeC bond breaking and the GeH H atom from the GeCGe atom shifting to the GeC C atom. Despite the largechange in geometry, this pathology lies only 36.2 kJ/molhigher in energy than base geometry U1.


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Three UT pathologies are identied from the 1500 KMD simulations, with the base structure (U1) optimizationproducing a GeGe bond. Pathology U2 optimizes withboth GeH H atoms shifted to the same Ge atom (retain-ing the GeGe bond but leaving one Ge with a dimin-ished valence). Pathology U3 optimizes with one GeHH atom shifted to a position between the two Ge atoms,retaining the original GeH bond and producing a longer-range GeH Ge interaction. Pathology U4 combines thebreaking of a GeC bond with migration of a CH H atomto produce one GeH2 fragment, one C C -bond, andone GeH pendant group coordinated to the new C Cdouble bond.3.2.3.6.AdamGe33 (Table III, Fig. 8). The two LTpathologies identied for AdamGe33 involve GeC bondbreaking, the results of which are signicantly deformedstructures. Pathology L2 breaks one GeC bond andmigrates the GeH H atom to the GeC C atom to producea free methyl group. Pathology L3 breaks a framework CC bond and migrates one CH H atom to complete theformation of both a free methyl group and a frameworkC C double bond. Three UT pathologies are identiedfrom the 1500 K MD simulations, with the base structure(U1) optimization producing a GeGe bond. Pathology U2is only slightly higher in energy than U1 but involves asignicant rearrangement that retains the original connec-tivity but shifts a complete methylene (CH2 group froma framework position to a bridging position between thetwo Ge atoms. Pathology U3 migrates one GeH H atomto the other Ge atom to form a complete GeH2 fragment,one H-free Ge atom, and a broken GeGe bond. Pathology

U4 is similar in geometry to U3 but shifts one local CH2H atom to the H-free Ge atom to form a Ge C doublebond and complete valences at all atoms.3.2.3.7.Diad3Ge22 (Table III, Fig. 8). A single LT pathol-ogy is identied for Diad3Ge22 from the 3000 K MDsimulations. The Ge and C atom positions in pathologyL2 are identical to those of the base tooltip (L1), withthe structure difference occurring in the orientation of thetwo GeH H atoms which now point in opposite direc-tions instead of residing on the same side of the tooltipas in L1. The three UT pathologies, all involving only thetwo GeH bonds, feature the breakage of the GeGe bondformed from the optimization of U1. Pathology U2 hasboth GeH H atoms on the same Ge atom, while U3 andU4 contain either one bridging GeHGe H atom (U3)or both GeH atoms pointing in opposite directions on thetooltip surface (U4). Defect U4 is similar in geometry tothe LT pathology L2. These accessible pathologies are H-dependent and may not occur in systems where the GeHbonds are replaced with GeCframework bonds in a largertooltip handle structure.3.2.3.8.DCB55AGe (Table II, Fig. 7). No LT patholo-gies are identied from either the 1500 K or 4500 KMD simulations. Several UT pathologies are identied that

display increasing degrees of tooltip deformation awayfrom the base geometry (U1). The lowest-energy structure(U2) combines GeC bond breaking with CH GeH H migration to form an open structure with a GeHbond and a C C double bond. Pathology U3 nds a sin-gle GeC bond broken at both Ge atoms which producestwo incomplete Ge valences and a single C C doublebond formation, with all other C valences satised withH atoms. Pathology U4 is a complete cleavage of the twoGeC bonds on one side of the tooltip with formation of a C C double bond to produce an open tooltip structure.These rst three pathologies are all signicantly more sta-ble than the base UT geometry. Pathology U5 representsa considerable change to the base framework connectivity,combining both the GeC bond cleavage and CC doublebond formation in U4 with a single H inversion into thetooltip framework, producing a structure only 1.4 kJ/molmore stable than the base U1 geometry. In contrast, pathol-ogy U6 retains much of the base tooltip geometry. Here,two GeC bonds are broken on a single Ge, forming aCC bond at this position. The result is a tooltip witha Ge bound only to one C atom but coordinated to twonearest-neighbor H atoms. Pathology U7 is a more dis-rupted arrangement of U5, combining GeC bond cleavageand C C double bond formation with H inversion at adifferent CH position in the framework. Finally, pathol-ogy U8 involves the structural rearrangement of U7 with asecond H inversion to produce a close HH interactionwithin the tooltip framework.3.2.3.9.DCB55BGe (Table IV, Fig. 9). No LT tooltippathologies are identied for L1 at either 1500 K or3000 K in the MD simulations. The UT geometries are var-ied in nature but are not properly described as pathologies.Instead, the structures from U1U10 are largely conforma-tional variations at the base of this tooltip, with the moststable geometry also involving the formation of a GeGebond (U2). Tooltip U2, as the only structure with a closeGeGe interaction, appears to be balancing the formationof this GeGe bond with a constrained framework confor-mation such that the GeGe bond formation produces astructure only 70 kJ/mol more stable than several of themore open tooltip geometries. The overlay of these struc-tures (Fig. 9) shows that the U2 geometry having the singleGeGe bond is unique in its Ge geometry from all othertooltips, which group into more open GeGe faces. Theenergy range for all 10 of these structures (100 kJ/mol)is low in comparison to the other conformation-specic tooltip series (DCB5Ge) wherein framework con-straints place the relative energies over a 160 kJ/molrange.3.2.3.10.DCB55CGe (Table II, Fig. 7). The only identi-ed LT pathology (L2) is the product of a CH2 torsionat the base of the tooltip on the opposite side of the C2dimer binding position. As a result, this defect would not



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Fig. 9. LT and UT base geometries (L1 and U1, respectively) and identied pathologies for DCB5Ge and DCB55BGe. Carbon dimers (C2 in theLT structures are shown in red. Framework C and H atoms are shown in dark grey and white, respectively. Germanium atoms are shown in blrelative energies of these structures are provided in Table IV. Overlay images are generated from RMSD alignment.

necessarily affect the C2 dimer binding in base structure

L1 if the tooltip was embedded within a larger frame-work. Three UT pathologies are predicted at higher ener-gies than the base structure (U1). The rst of these, byinspection, is the most disruptive, involving H migrationto the Ge atoms and C C double bond formation to pro-duce a greatly deformed structure at moderately higherenergy (66 kJ/mol). Pathology U3 is the result of a singleCH GeH H migration. Pathology U4 combines CCframework bond breaking with H migration to produce anopen structure containing a framework C C double bondand a nearby methyl group.

3.2.3.11.DCB57Ge (Table II, Fig. 7). No LT pathologies

are identied for the base tooltip (L1) at either 1500 Kor 4000 K in the MD simulations. Three UT pathologiesare identied, including one of lower energy. PathologyU2 combines two broken GeC bonds on the same sideof the tooltip framework with C C double bond forma-tion. Pathology U3 is similar to U2 but includes a singleinverted H atom into the tooltip framework. The openingof the frame from GeC bond breaking provides enoughspace within the tooltip to make this inverted geome-try only 70 kJ/mol higher than U2. Pathology U4 com-bines CC framework bond breaking with H migration to


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produce a free methyl group and a C atom with only twoCC -bonds to it.3.2.3.12.DCB5Ge (Table IV, Fig. 9). The three predictedLT pathologies for DCB5Ge are the result of conforma-tional differences in the free CH2CH2- fragments at thetooltip base. With the tooltip framework constraining theseCH2CH2- groups to a small separation, the conforma-tional energy differences for L2, L3, and L4 are quite largedespite the only minor apparent structural changes. Thesampling of all conformational differences and the local-ization of these differences to the base of the tooltip is bestrepresented by the overlay of all four Ln tooltips (Fig. 9).

The UT pathologies represent the extremes in observedtypes of deformations for all tooltips. Pathology U2 is theresult of breaking both GeC framework bonds and of the formation of a C C double bondthe Ge atoms donot gain H atoms from other positions to complete thevalence. Pathology U3 is a H-inverted geometry that isincluded in the tooltip summary because the DCB5Geframework is exible enough that this inverted geometryis only 25 kJ/mol higher in energy than the base structure(U1).3.2.3.13.DCB65Ge (Table II, Fig. 7). The LT 1500 Kand 3000 K MD simulations produced no pathologies forthis structure. The UT 3500 K simulations produced nopathologies for this structure.3.2.3.14.DCB6Ge (Table II, Fig. 7). The LT 1500 K and3500 K MD simulations produced no pathologies for thisstructure. Energy convergence for the UT structures wasnot achieved in the allotted time and within the 40-stepSCF limit.

3.2.3.15.DCBIceane7Ge (Table II, Fig. 7) . The LT 1500K and 3500 K MD simulations produced no pathologiesfor the base structure (L1). Three low-lying UT patholo-gies are identied for the base structure (U1), which itself optimizes with the formation of a GeGe single bond (orclose contact). Pathology U2 involves the migration of aGeH H atom to the other Ge atom, producing one Gewith a complete valence and one constrained in the RHFcalculation to a ground state singlet that lies only 7 kJ/molhigher than the base structure. Pathology U3 combinedGeC bond breaking with GeH CH H migrationbetween the same GeC atoms. Pathology U4 is a highlydeformed geometry that involves GeC bond cleavage atboth Ge atoms and GeH GeH2 H migration to formone C C double bond, one GeH2 fragment, and one Geatom bound by only one GeGe bond and one GeC bond.3.2.3.16.MCB55Ge (Table II, Fig. 7). Six alternative LTgeometries are identied for MCB55Ge but none are bestdescribed as pathologies, as all differ only by the ori-entations of the four CH2CH2- fragments bridging thetwo Ge atoms to the more constrained framework base.Tooltips L2, L3, L4, L5, and L6 all lie within a narrowenergy range. Tooltip L7 is the least stable version of MCB55Ge with all of the CH2CH2-fragments oriented

to maximize H H repulsion on the tooltip frameworksides. It is noteworthy that L2 and L7 are both of C2v sym-metry and represent the minimum and maximum in therange of energies for the CH2CH2-conformations.

A single UT pathology is identied (U2) to producea pair of structures (U1 and U2) very similar to tooltipC100GeATSr5 (Fig. 6). In MCB55Ge, the energy differ-ence for the symmetric base structure (U1) and more stableasymmetric structure (U2) is only 18 kJ/mol smaller thanthe same difference for C100GeATSr5. In both, the geom-etry of one Ge atom is more sp3-like in nature while theother Ge is more sp2-like, indicating that this differencein geometry is the result of intramolecular charge-transferin the singlet-constrained RHF wavefunction to form ananionic Ge (sp3 and cationic Ge (sp2 pair within thesame molecule. This interpretation is consistent with theMulliken charge analyses, since the Ge atom charges areidentical for the symmetric tooltips but different (approxi-mately 0.8 e in both cases) for the asymmetric structures.

3.2.3.17.TwistaneGe (Table III, Fig. 8). A single LTpathology is identied in the 4000 K MD simulation.Pathology L2 breaks one GeC2 dimer bond and migratesthe associated GeH H atom to the C2 dimer to producea valence-lled Ge-[C2 dimer]-H acetylene structure andone Ge atom with an incomplete valence. This structureis predicted to be 58 kJ/mol more stable than L1. As thedefect appears to be largely a result of H migration uponCGe bond breaking, the removal of the GeH H atoms ina larger framework might prevent this defect from form-ing. Energy convergence for the UT structures was notachieved in the allotted time and within the 40-step SCF

limit.

3.2.4. DC10c (Table 5, Fig. 10)

Seven LT pathologies are identied for the DC10c tooltip,of which two (L2 and L3) are potentially accessibledefects. Pathology L2 is the result of a symmetry-breakingof two separate CframeworkCdimer-bindingbonds and the bend-ing of the C2 dimer towards the two broken CframeworkCdimer-bindingC framework atoms to form a highly strainedfour-member ring in a slightly more open tooltip struc-ture. This defect lies only 3.1 kJ/mol lower in energy thanthe base tooltip geometry (L1). The previous B3LYP/6-31G(d,p) study on the DC10c tooltip also identied thisgeometry as a potential defect of concern, but found thetransition state barrier for this rearrangement to lie a con-siderable 243 kJ/mol higher in energy than the L1 basestructure, making it inaccessible under proposed opera-tional conditions.8 A second pathology (L3) involves thebreaking of one CframeworkCdimer-bindingbond and CframeworkH Cdimer-bindingH H migration to produce a tooltip withone Cframework C double bond and one Cdimer-binding Cdouble bond, thereby completing the valences of all atomsin a highly strained geometry. The high-energy pathology



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Fig. 10. LT and UT base geometries (L1 and U1, respectively) and identied pathologies for the DC10c tooltip. Carbon dimers (C2 in the LTstructures are shown in red. Framework C and H atoms are shown in dark grey and white, respectively. The C atoms used to bind the C2 dimer areshown in yellow. The relative energies of these structures are provided in Table V.

L4 is noteworthy for its formation of a four-member ringfrom the two C C double bonds on either side of theC2 dimer binding positions. All other pathologies (L5, L6,L7, L8) involve considerable framework deformations dueto framework CC bond breaking.

Seven UT pathologies are identied for DC10c, of which two are close in energy to the base geometry (U1).Pathology U2 involves the breaking of one [Cdimer-bindingC C] Cdimer-bindingC bond and rotation of the associatedC C double bond such that both C2 dimer binding posi-tions (yellow) are now connected to the same C atom.The binding face of the DC10c tooltip is, despite thissignicant geometry change, partially retained. PathologyU3 is the result of breaking framework CC bonds belowthe C2 dimer binding surface followed by formation of a three-member ring, nevertheless also preserving the C2dimer binding position. Pathology U4 is an interestingdefect structure as it preserves the overall UT geometrybut breaks the strained conjugation of the six-member ringin favor of two shorter C C double bonds on either sideof the dimer binding position. This defect might be consid-ered the upper-limit geometry on a ring-breathing vibra-tional mode. The high-energy pathology U7 incorporatesa C2 dimer within the framework after breaking a CCbond between the framework and one of the dimer bind-ing positions. Pathologies U5, U6, and U8 all, remarkably,completely preserve the geometry of the strained -systemat the C2 dimer binding position but involve various frame-work CC -bond rearrangements and H migrations.

4. DISCUSSION

4.1. Unloaded Tooltips and GeGe Bond Formation

Several base geometry UT optimizations (C100GeATS,C100GeCTS, C110GeS, AdamGe22, AdamGe33,Diad3Ge22, DCB55BGe, DCB75Ge, MCB5Ge,DCBIceane7Ge) produced structures with covalent GeGebonds. These structures are signicant for two reasons.First, the formation of a GeGe bond requires either thatthe tooltips be exible enough to allow for the two Geatoms to move within bonding distance of one another orthat the Ge atoms already be in close enough proximity inthe LT that the removal of the C2 dimer enables GeGebond formation without signicant motion in the tooltipframework. Second, a stabilizing GeGe bond (and thepotential motions within the tooltip to accommodate thisbond formation) increases the transition state barrier cor-responding to C2 dimer addition back onto the tooltip.While the GeGe bond may be weak due to the orien-tation of the orbitals used to form this bond in highlyconstrained tooltips, the barrier to GeGe bond insertionfor these systems is still expected to be higher by someamount than tooltips for which the framework completelyprohibits GeGe bond formation (systems which accountfor the majority of the analyzed tooltips).

The formation of a GeGe bond and the added stabil-ity it provides to a UT geometry may, for some systems,be an advantage. Any stabilizing interactions within theopen tooltip may serve to increase the barriers to structural


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rearrangement, H migration, etc. between the time a C2dimer is deposited on a workpiece and the time the tooltipis recharged with a new C2 dimer. In effect, such bondformations in the Ge-tooltip series are similar in potentialapplicability to the strained -framework on the C2 dimerbinding face of the DC10c tooltip.

4.2. More Stable Pathologies and Transition StateBarriers

The identication of tooltip pathologies in this MD-drivenquantum chemistry study indicate that alternative frame-work geometries for some cases are more stable than theLT or UT structures designed for use in mechanosyn-thetic operations. But these tooltip pathologies are similarto structural isomers in any other organic molecule. Theidentication of a more stable structure does not provideany insight into the energy barrier over which an opera-tional mechanosynthetic geometry must pass in order toconvert into a non-operational geometry. Transition statecalculations must be performed to provide any insights intothe barriers for these conversions. The original transitionstate barrier calculations for the DC10c tooltip indicatedthat, although identied pathology L2 is 1.3 kJ/mol morestable than operational tooltip geometry L1, the transi-tion state for the L1 L2 rearrangement is 51 kJ/mol atthe B3LYP/6-31G(d,p) level of theory. While some of thefailure modes predicted to lie within 100 kJ/mol of theoperational geometry for a tooltip appear to be related bya single transition state coordinate, it is clear that manyother predicted failure modes involve considerable struc-

ture rearrangement of the framework atoms and thus likelyare the result of multi-step transition state conversionsfrom one structure to the next.

The NH@H failure mode survey for the tooltips simplyprovides ground state geometries on the covalent potentialenergy surface. Identifying from among the failure modeswithin some energy range which of the operational tooltipstructures that are accessible within a thermal regime ina working system is a time-consuming but very importantsubsequent step in any continued developmental survey of these tooltips.

4.3. Hydrogen-Inverted Tooltip Geometries andLarger Tooltip Frameworks

The MD simulations for each tooltip generated multiplestructures at higher energies that have been removed fromall but a few of the tooltip summaries. These largely-ignored tooltip pathologies are the results of hydrogeninversion , a type of defect that nds one or more H atomsinserting into the cage framework as a result of a method-ological mismatch of atom momentum and classical timestep in the MD simulations. The problems associated withH motions in classical MD simulations are familiar at

all levels of simulation, from protein and DNA dynam-ics studies in aqueous media at room temperature to thesevery high temperature/high energy deformation simula-tions at up-to 4500 K. Three common workarounds forlarge H atom displacements per time step are(1) the use of smaller time steps to recalculate the forceson the H atoms,(2) the articial increase of the mass of the H atoms toreduce their net displacement over some set time step(such as re-massing H atoms to deuterium or higher), and(3) the subsuming of the H atoms into the associatedheavy atom to remove the H motion entirely from thesimulation.

A representative set of pathologies from a single tooltipis shown in Figure 11 for DCB65Ge. This tooltip is usefulas an example because the tooltip cage is reasonably widefor the small number of atoms, producing an enclosedregion within the tooltip that can expand and adjust asone or more H atoms minimize within the framework.

The seven identied H-insertion pathologies are shown inFigure 11 with their representative codes (these structuresare available as Supplemental Material) and the energiesof these structures relative to the optimized loaded tooltip(in kJ/mol). Despite large expected repulsive energies uponinsertion, three of these defects lie within 200 kJ/mol of the base structure, a range comparable to the energiesof defect geometries in several other cases among thetooltips. Furthermore, the only pathologies identied forthe DCB65Ge tooltip are those involving H insertion, indi-cating that the tooltip framework itself is otherwise quiteresistant to structural deformation.

There are two reasons why such structures are not likelyto be of benet in a pathology analysis and thus areexcluded in all but a few cases in the tooltip survey. First,the process of H inversion is a known issue of the MDmethodology and is, therefore, something better treated byemploying methods that remove the large H atom motionsacross all temperature ranges. Second, framework H atomsin these tooltip structures are, in effect, included in thequantum chemistry analysis to complete the valences of sp3 carbons that would, in a complete tooltip framework,be replaced by bonds to other atoms as a way to anchorthe tooltip onto some workpiece. An example structure isprovided in Figure 12. While an ideal tooltip might con-tain within its base some fragment of a diamondoid latticethat easily provides the means for its inclusion into a largermechanosynthetic assembly, many of the studied tooltipsare not so ideally designed, thereby requiring a connec-tive bridge that links the tooltip to some larger structure.In the hypothetical DCB65Ge bridge framework shown inFigure 12, it is seen that all but the CH H atoms clos-est to the Ge atoms have been replaced by CC bonds,removing all but one (559 w) of the predicted H-inversionpathologies from any further defect analysis.

There are a few ways to script the identication andremoval of inverted species from the tooltip survey if



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Fig. 11. Predicted H inversion structures for the DCB65Ge (four orientations shown at top) tooltip. Carbon dimers (C2 in the LT structures areshown in red. Framework C and H atoms are shown in dark grey and white, respectively. Germanium atoms are shown in blue. Inverted H ashown in green. Structure numbers ( NNN w) and relative energies (in kJ/mol) are provided for each structure.

efforts are not otherwise taken to remove large (inverting)H motions, although each has its potential drawbacks. Oneapproach is to perform H-only molecular mechanics (MM)minimizations on the tooltips before submitting them tothe quantum chemistry queue. Complete MM minimiza-tions (all atom MM) in such cases would not be expectedto be benecial because the connectivity of the atoms inthe tooltips is predened in the MM parameter assignmentprocess. In this case, structures will optimize around theircovalent connectivity and not, when the atomic positionsare sufciently different, the proximity of atoms to oneanotherwhich is the type of optimization obtained by aquantum chemistry analysis when no particular connectiv-ity is assumed. In the absence of a procedure to adjustthe H atom positions for MD time step samples where theH atoms are either within a cage framework or well withinthe sum of the van der Waals radii of a nearby atom, thequantum chemistry analysis must be performed to iden-tify a structure with a more proper geometry than theMD structure. After that, the separations between atoms

Fig. 12. The DCB65Ge tooltip within a larger diamondoid frame-work, showing how additional framework CC connections removeH atoms that underwent H inversion in the MD simulations (for the baseDCB65Ge structure, see Fig. 11).

are expected to be far more reasonable and the removalof H-inversion geometries can be performed algorithmi-cally by identifying H atoms residing within the tooltipframeworks.

The use of increased mass (deuteration) to reducethe prevalence of H-inversion geometries in the MDsimulations was tested on the DC10c LT structure at

3000 K. (A 3500 K AdamGe22 MD simulation was alsoperformed, but this structure does not contain a frame-work cage that can accommodate an inverted H atom with-out signicant structural rearrangement). While the overallnumber of H-inverted defects in LT DC10c droppedslightly, a 3000 K simulation is, unsurprisingly, disrup-tive enough to an organic framework to still producemany H inversion pathologies. If such structures are tobe avoided but not removed from the quantum chemistryanalysis, alternative approaches at the force eld or MDlevel should be considered.

4.4. The NH@H Network and Best-PracticesConsiderations

The NH@H tooltip pathology survey generated a con-siderable amount of data and, after the analysis of theresulting data, yielded a selection of tooltip pathologies toserve as the basis for subsequent studies of tooltip defectpathways. The most important benet gained from theNH@H approach was the massive distribution of the time-consuming quantum chemistry optimizations to externalresources (i.e., home computers). As only the structure dis-tribution, and not the quantum chemistry calculation, is


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distributed across the network, the success of an exami-nation is resource-dependent in a manner different from adedicated cluster, time-share, or national laboratory queue-based facility. The speed of a calculation and, ultimately,the quality of the calculation for a particular analysis aredictated by the quality of the computers owned by theparticipants. The RHF/3-21G and RHF/STO-3G calcula-tions were not selected for their accuracy, but instead wereselected because they provideab initio answers that virtu-ally any home computer (ca. 2006) would have the RAM,CPU performance, and hard drive capacity to run success-fully. While the dedicated participants in this rst NH@Hstudy may not have had any reservations about committingfull resources to these calculations, it is clear that submit-ting a tooltip the size of the C100GeATD, C100GeCTS,or any of the larger structures to a home computer forgeometry optimization at an MP2/6-311+ G(2d,p) level of theory would very likely risk depleting those machines of all storage space, since the estimated storage requirements

for such calculation range as high as 500 GB based onprevious trials. Such large runs also risk depleting par-ticipants of all patience as single geometry optimizationcycles would execute over the course of days instead of minutes. The use of a survey of representative availablecomputers at the start of a series of quantum chemistrystudies can be of great benet in identifying the constraintsa researcher must place on their investigation.

4.5. Identied Minima versus Accessible Minima

In the absence of transition state calculations or MD simu-lations on larger tooltip frameworks to remove degrees of freedom in some atoms, it is not known how many of thesetooltips can be ignored simply for energetic reasonseither due to large rearrangement barrier energies or due toone-step inaccessibility because of the presence of multiplebarriers to complete a rearrangement to a predicted min-imum. Further, as demonstrated in the calculated energydifferences for the C110GeS-L2 tooltip, the relative ener-gies of these structures may be very dependent on the levelof theory used for their calculation. While classes of defor-mation can be catalogued, these geometries only serve asa structural basis. Higher levels of theory are required forthe prediction of relative energies and, subsequently, tran-sition state barriers to rearrangements involving only a sin-gle coordinate or the modeling of multiple steps along asequence to more signicant rearrangements.

4.6. Hydrogen Migration

In most stable tooltips, H migration is assumed to bethe most accessible route to the formation of inopera-tive structures (what previous studies1 have called hydro-gen poisoning). Among the pathologies identied in theNH@H study, only two of the LT defects (C100GeATD-L2 and C100GeATSr5-L3) contain H-migrated GeH

bonds (the addition of valence electrons to the Ge atomsby H migration then affects the recharging step in anymechanosynthetic procedure). Only one of these nds theH atom bound to the C2 dimer itself (C100GeATD-L2).With the deposition of a C2 dimer, both Ge atoms ineach tooltip contain unlled valences, providing sites forpotential H migration. A number of UT pathologies arethe result of GeH H migration, including DCB55AGe-[U2], DCB55CGe-[U2,U3], DCBIceane7Ge-[U2,U3,U4],C100GeATD-[U2], C100GeS-[U2], AdamGe22-[U2,U4],AdamGe33-[U3], Diad3Ge22-[U2], and C100GeCTS-[U2]. While the GeH bonds are predicted to be weakerthan the CH bonds even in strained systems, the energydifferences need only be enough to enable fractional GeHH migration either to inuence the recharging of a tooltipwith a C2 dimer or, possibly, to enable some other struc-tural transformation in the tooltip to occur. One possiblemethod for reducing the potential for H migration to theGe atoms is to employ tooltips that, upon C2 dimer deposi-

tion, develop strained GeGe bonds as observed in severalof the tooltip structures and, therefore, increase the bar-rier to migration by requiring intramolecular GeGe bondscission before GeH H-bond formation can occur.

4.7. GeC Framework Bond Breaking

All of the tooltips in this study are designed to facilitatedimer deposition and tooltip retraction with the only mod-ication to the covalent framework of the tooltip being theloss of the C2 dimer. Among the Ge-containing tooltips,four LT pathologies (C100GeATSr5-[L3], C110GeS-[L3],

AdamGe22-[L4], AdamGe33-[L2]) are identied withonly GeCframework bond breaking (as opposed to moresignicant deformations involving additional frameworkmodication), while numerous UT structures contain thisdefect mode. The few LT forms are noteworthy for theirsmall relative energy differences from ground state geome-tries. Only C100GeATSr5-[L3] lies above 100 kJ/mol fromits ground state geometry. The UT structures run the gamutfrom signicantly more stable (e.g., DCB55AGe-[U2] is119 kJ/mol more stable than its base geometry) to signif-icantly less stable (e.g., C100GeATD-[U4] is 418 kJ/molless stable than its base geometry). These calculated ener-gies are less reliable than those computed at higher lev-els of theory and those combined with proper transitionstate barriers, but the fact that a large range is observedmakes such defect modes of considerable importance astooltip analyses are performed either to redesign or toremove candidate tooltips from consideration for perform-ing mechanosynthetic operations.

As part of the operation of a tooltip deposition process,the possibility of GeCframeworkbond breaking12 is anotherimportant issue at the point where the presumably singlecovalent bonds between the C2 dimer and the workpieceare formed and the tooltip is ready to be retracted. The



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formation of single CC bonds between the C2 dimer andworkpiece does not result in the breaking of the Ge[C2dimer]Ge GeC bonds, as the C2 dimer is itself boundto each tooltip as a strained triple-bond system and, uponworkpiece bond formation, is a less strained double-bondsystem. (One might consider it an ethene functionalizedwith tooltip and workpiece.) It is at this point in the depo-sition process that the relative strength of the GeCframeworktooltip bonds compared to the GeCdimer bonds becomesthe determining factor for whether or not GeCframeworkbond breaking is an important defect mode, as has pre-viously been observed in simulations during step 3 of aCGe tooltip retraction event during a hydrogen abstrac-tion tooltip recharge sequence.12 The defects identied inthe NH@H study with broken GeCframeworkbonds may notthemselves be accessible in isolation, but the additionalbonding modes and resulting strain in the entire system aspart of a mechanosynthetic operation makes such defectmodes important in the overall design analysis of a dia-

mondoid structure that is to be fabricated. The study of such defect modes requires the modeling of the depositionprocess, which can be performed at a considerable cost incomputational resources.12

4.8. Combined GeC framework Bond Breaking andC== C -Formation

The formation of broken GeC/CC bond pathologiesare noteworthy, both in the context of the operationalissue described above and in the manner by which asymmetric bond breaking in these tooltips can produce

very stable geometries that then require large transi-tion state barriers to be present for the mechanosyn-thetic operability of the tooltip. This class of defectmode occurs in several of the UT structures (AdamGe22-[U4], DCB55AGe-[U4,U5,U7,U8], DCBIceane7Ge-[U4],DCB57Ge-[U2,U3], DCB5Ge-[U2]) but, remarkably, didnot occur in any of the LT structures. The presence of a conjugated unit on the Ge atoms (C2 dimer) might beexpected to stabilize Ge radical formation in the symmetricbond scissions by pairing these electrons in an extended

-system, but no such structures were identied in thequantum chemistry optimizations though they may havebeen present in some form during the MD simulations.

As with the single GeCframeworkbond breaking defectsdescribed above, the paired GeC/C C pathologies maybe of greater concern during a mechanosynthetic deposi-tion than among structuresen route to deposition. In adeposited [Cworkpiece]C C[Getooltip] structure, the forma-tion of C C -system pathologies becomes possible if the [CworkpieceCdimer]Getooltip Cdimer-Ge bond is of compa-rable or greater strength than the GetooltipCframeworkGeCbonds such that the retraction of the tooltip results in thesymmetric GeC bond breaking and C C -bond forma-tion with retention of the CdimerGetooltip bonds.

4.9. GeGe Bond Formation

This class of structures is described in sectionDiscussion I above. As noted in the Hydrogen Migration section, theformation of these strained bonds in the UT structures maynot be detrimental to tooltip operation but may, by increas-ing the barrier to other defect modes, serve as a form of stabilization during the time between deposition and C2dimer recharging.

4.10. C 2 Positional Variation

Remarkably, despite the high temperatures and other-wise large deformations identied in many of the tooltipstructures, specic structural deformations at the Ge[C2dimer]Ge position were identied in only a few casesfrom the MD-based quantum chemistry optimizations.These structures include C100GeATD-[L2], C100GeS-[L2,L5], AdamGe22-[L2,L3,L4] and TwistaneGe-[L2],among which only those for C110GeS and AdamGe22were considered as part of tooltip pathologies in theoriginal analysis.1 The results of the RHF/3-21G opti-mizations for the carbene pathologies in C100GeS andAdamGe22 are noteworthy for the reversal in their rel-ative energies to the base structures compared to theoriginal B3LYP/6-311+ G(2d,p)//B3LYP/3-21G* survey,which placed C100GeS-[L2] 54 kJ/mol higher in energythan its base structure and AdamGe22-[L2] 44 kJ/molhigher than its base structure. Here and generally, boththe quality of the basis set and the inclusion of electroncorrelation (by way of the B3LYP density functional) areexpected to make a considerable difference in the accuracy

of the estimated relative energies.

4.11. Conformational Differences

In most rigid tooltip designs, the identication of confor-mational minima is interesting but otherwise not of signif-icance, as conformational exibility at the tooltip base is,like H inversion, removed from all structures as a resultof embedding the structure within a larger and more con-straining tooltip framework. Nevertheless, the results of theDCB55BGe UT simulations are noteworthy for the pre-dicted changes to Ge Ge separation in the many confor

damian g. allis et al- analysis of diamondoid mechanosynthesis tooltip pathologies generated via a...

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