# Book Index

### A

$A b$ initio quantum chemistry, $40-42$

Absorption of light, 151

Abstraction reactions:

models of mechanochemical, 226-229

of nonhydrogen atoms, 247

potential energy surfaces, 62-63, 226, 228

by radicals, 215

Acceleration, 25, 349

Accommodation coefficients, 182, 183, 358

Acenaphthyne, 214

Acoustic noise, 91

Acoustic power and control, 472-476

Acoustic radiation:

and energy dissipation, 162-168

equal-speed approximation, 163

moving disturbances, 166

oscillating force at a point, 163

oscillating pressure, 166

oscillating torque at a point, 165

in sleeve bearings, 290

in sliding of irregular objects, 283

uniform medium assumption, 162

Acoustic transmission lines, 363

Activation energy, see Potential barriers

Activation length, 202

Activation volume, 201

Actuation time, 197

Actuators, electrostatic, 335

Adamantene, 214

Adhesive interfaces, 270-271, 412,413-414

Agoric open systems, 371

Alignment bands:

and acoustic radiation, 167

and dislocations, 173

phonon scattering, 173-175, 292

thermoelastic drag, 181

Alkene reagents, 213-215, 229-232

Alkylidenecarbene, 242

Alkyne reagents 213-215, 241-243

Alkynyl radical, 216-217, 227, 232-233

Allenes, 214

Aluminum, 149, 153

AMBER force field, 43

Amines and lone pairs, 45

AM1 semiempirical method, 41

Anharmonicity, 179

Antibodies, 265, 374, 375, 448, 462, 466

Anti-Morse function, 62

Approximation, role of, 11, 23-24, 497

Assembler, see Mechanosynthesis;

Molecular manufacturing

Atmosphere, model of probability gas, 77

Atomic-point bearings, 303

Atoms, see also names of elements

generation of free, 9,195

MM2 properties, table of, 44

radii of, under load, 44, 60-61

### B

Band flutter, 173, 175, 292

Band-stiffness scattering, 174, 292

Barrier heights, see Potential barriers

Barth, Phillip, 150, 429

Basis functions, in quantum chemistry, 40

Bearings, see also Sleeve bearings

atomic point, 303

bonded, 303

dry $v s$. lubricated, 27

as example of nanomachine, 2-5

interfacial structures, 294-295

interfacial stability, 296

roller, 308

Belt and roller systems, 309-310, 386-390

Benzyne, 214

Bevel gears, 308-309

Binding sites, see Receptors

Biochemistry, 10, 510-511

Boltzmann factor, 75

Bonaventura, Joseph, 482

Bond angle-bending, 45, 47, 51, 205

Bond cleavage:

by applied tension, 221-225

cage effect, 139

energy dissipation in, 222-224, 237

Lippincott potential for, 54, 56, 223

and molecular orbital methods, 61

Morse potential for, 51-56, 223

photochemical, 151

rates of thermal, 138

solid cage effect, 139

by stress and tunneling, 142

and support stiffness, 222

thermal, $138-140$

thermomechanical, 140-143

Bonded bearings, 303

Bonds:

allowable stresses, 142

metal-ligand, 219-220, 234-237

properties, table of, 52

weakness of nitrogen-nitrogen, 298

Bond stretching, 44, 45, 51, 54

Bond torsion, 47, 48. See also Pi-bond torsion

Born-Oppenheimer approximation, 39-40

Boron-nitrogen compounds, 232, 270

Bounded continuum models, 12, 257

of logic rods, 346

and molecular mechanics, 67-69

and nanomechanical design, 318

Brittleness, and cracks, 254

### C

Cage effect, 139,148

Cams, 172, 310, 374, 388-389

Capacitance, scaling of, 30

Capacitative time constant, scaling of, 32

Carbanions, 213

Carbenes, 195, 217, 218, 232, 242-243

Carbon, 195. See also Diamond; Diamondoid structures; Graphite

Carbonium ions, 213

Carry chains, 365

Casimir-Polder equation, 64

Catalysis and mechanosynthesis, 204

Chaos and statistical mechanics, 75

Charge distribution, molecular, 41, 48, 264

Charging, electrical, 150, 337-338

CHARMM, 43

Chemical synthesis, see Mechanosynthesis; Organic synthesis

Chemistry, see also Mechanosynthesis; Organic synthesis; Reactions

contrasts between machine and solution phase, 6, 88, 135-137, 152, 196-207

Classical continuum models and scaling laws, 23-35. See also Bounded continuum models

Classical electromagnetic systems, 28-32

Classical dynamical models, 73,74

Classical statistical mechanics, 73, 75-80

Clocking of CPUs, 367-369

Clutches, 314

Col, 36. See also Transition states

Combinational logic, 359-362, 364

Compression, see Nonisothermal compression

Computation, see also Nanocomputers agoric open systems, 371

computer as a hierarchical system, 12

cost of molecular modeling, 40, 41, 42

and entropy, 83

logically reversible, 83

Computer-aided design, 434-441

chemical $v s$. nanomechanical, 319

of components, 271

of dislocations, 269

of irregular structures, 265

Kaehler bracket approach, 266

of mechanochemical syntheses, 249

of strained shells, 268

Concentration, 5

Conditional repetition, 210, 388, 396

Conductors, electrical, 333

Configuration interaction, 40

Configuration space, 77-80

and chemical reactions, 194

and the PES, 36,77

probability densities in, 76

Conformations, 86

Conjugated bonds in MM2, 49

Conservative assumptions, list of, 13

Constraints, list of, 3

Contact potentials, 337

Continuum models, 12

Cooling systems, 330-332, 370

Cope rearrangements, 146

Correspondence principle, 76

Coulomb energy, 38

Coupled sites, 283

CPUs, 361, 367-370. See also Computation; Nanocomputers

Critical angular velocity, 339

Cubane, 88, 195

Cubene, 214

Cumulenes, 214, 245

Current density limits, 334

Curved-shell structures, 268

Cycle times for reactions, 208

Cyclo[18]carbon, 195

Cycloadditions, mechanochemical, 233

Cyclobutene, 148

Cyclopentyne, 214

Cyclopropane, 195, 217

### D

Damage, see also Thermomechanical damage

dominance of radiation damage, 157

energy sources, 120

mechanisms of, $120,135,379$

photochemical damage, $150-154$

Dampers, 314

Damping, 91

Darcy-Weisbach formula, 327

Debye model, 169,170

Deformation, scaling of, 25

Density, table of values, 256

Design, see also Computer-aided design and approximation, 23, 497

computer support for, 434-441

errors in, 89

Detailed balancing, principle of, 78

Detents, 314

Diamond, see also Diamondoid solids; Diamondoid structures

chemical vapor deposition, 241

Debye temperature, 170

hexagonal, 246, 262

modulus and surface effects, 262

surfaces, 150, 239

synthesis as model, 238

theoretical tensile strength, 142

Diamondoid structures, 13, 255

vs. biological structures, 10

mechanosynthesis of, 238-248

number of, 263

stiffness and predictability, 87

$v s$. protein, for receptors, 375

Dielectric constant, 64

Diels-Alder reactions:

for adhesive interfaces, 270

mechanochemical forcing, 233

and molecular orientation, 136

in molecular processing, 386

piezochemistry of, 214

Diffusion, 139, 149, 329

Digital logic, 8, 36. See also Computation; Nanocomputers

Dipolar bonds for adhesive interface, 270

Dipoles, 48, 201

Dirac, P. A. M., and quantum theory, 37

Dislocations, 166, 254, 268

Dispersion force, see van der Waals force

Dissociation constants for antibodies, 374

DNA, 446-447

as structural material, 510

synthesis of, 196

Dodecahedrane, 195

Double bonds, torsional stiffness of, 48

Drag, see Energy dissipation

Ductility of metals, 254

E

Effective concentration, 198, 199

Effective volume, 124

Efficiency, scaling of mechanical, 27

Elastic springs vs. entropic springs, 118

Electrical current, scaling of, 29

Electrical switches, 335

Electric fields, 203, 320, 334

Electrochemistry, 203

Electromagnets, scaling of, 31

Electromechanical devices, 333-341

Electromechanical power, scaling of, 30

Electromechanical power density, 30

Electromigration, 29, 334

Electron correlation, 39, 40, 61

Electronegativity in MM2, 49

Electronic transitions, 29, 39 Electron relaxation time in metals, 31

Electrostatic actuators, 335, 366

Electrostatic energy, scaling of, 30

Electrostatic fields, 29, 200

Electrostatic force, scaling of, 29

Electrostatic generators (DC), 336-341

Electrostatic interactions in MM2, 48

Electrostatic motors, 336-341, 370

Elimination reactions and pyrolysis, 146

Ene reactions, 147

Energy, see also Potential energy; Potential energy surfaces; Power

mean value, 75

and nonbonded force, 59

and partition function, 75

release in adhesion, 271

units for molecular phenomena, 11

Energy barriers, see Potential barriers

Energy dissipation, 161

acoustic radiation, 162-168

band-flutter scattering, 175

band-stiffness scattering, 174

in bond cleavage, 222

dislocations as model, 166

in electrostatic motors, 339

free expansion losses, 188

in gears, 307

interfacial sliding, 273

and intersystem crossing, 224

in logic rods, 348

in mechanochemistry, 221

in molecular mills, 395

moving disturbances, 166

moving harmonic oscillators, 172

nonadiabatic quantum processes, 168

nonisothermal compression, 181-186

phonon-phonon scattering, 179

phonon scattering drag, 170

phonon viscosity, 180

radiating alignment bands, 167

in registers, 358

in roller bearings, 172

scaling with speed, 162

shear-reflection drag, 177

sleeve bearings, $290-293$

in sliding of irregular objects, 282-283

in sorting rotors, 378

thermoelastic damping, 179

time-varying potential wells, 186-189

Entropic springs, 111-113, 118

Entropy:

defined in terms of probability, 82

of fusion, 263

and information, 82-83, 523

and partition function, 75

in quantum statistical mechanics, 75

Enzymes and mechanosynthesis, 200

Equilibrium, 80, 121

Error rates, see also Damage; Failure rates equilibrium model, 132

instantaneous-onset model, 133 in logic rods, 352

in mechanosynthesis, 197, 205

models for placement, 131

in molecular assembly, 130

worst-case decoupling model, 134

Errors:

in design, 89

in mechanochemical modeling, 192

in placement, $130-134$

in radical addition, 229

sinusoidal well model, 132

switched coupling model, 132

Ethyne, 385, 391

Eutactic, definition, 6

Evolution and nanomechanical systems, 10

Exciton for "photochemistry," 203

Excluded-volume, 66

Exoergic $v$ s. endothermic, 196

Exothermic vs. endoergic, 196

exp-6 potential, 49,274

Experimentation, role of, 89, 137, 438, 480$481,485,495,496-497$

### F

Fail-stop systems, 393

Failure, single-point assumption, 15, 156

Failure rates, $74,157,158$. See also

Damage; Error rates

False-negative errors, acceptability of, 16

False-positive errors, avoidance of, 16

Fan-in and fan-out, 362

Fatigue, 157, 317

Fault-tolerant systems, 390

Feedstocks, 373

Feynman, Richard, 27, 37, 83, 511-512

Field emission, 28

Field emission current, scaling of, 30

Field-ion microscope, 203

Field strength, limits to electrostatic, 28

Finite-state machines, 359-363

Flexibility of devices, 200

Fluid mechanics, 326

Fluids, 27, 328, 329. See also Liquids

Flywheels, 370

Follower and cam, 310

Force, see also Bond cleavage; Molecular mechanics

measurement of, 322

in mechanochemistry, 201

in molecular mills, 386

and nonbonded contact radii, 60

and nonbonded energy, 59

and nonbonded stiffness, 59

scaling of, 24

Foresight Institute, 513

Fourier transforms, 274-277

Fragmentation reactions, 146

Framework structure, 259

Free energy:

and gas in cylinder problem, 112

and information, 82 and mean-force potential, 85

and partition function, 75

Frequency, scaling of, 25, 32

Friction, 27, 80, 316

Fullerenes, 247

### G

Gases, 326, 328, 329-330. See also Fluids

Gates, 343-355, 364

Gears:

barrier heights for rotation, 304

bevel, 308

energy dissipation, 307

helical, 308

planetary, 311

rack and pinion, 308

spur, 304-308

worm, 309

Generators, see Electrostatic generators

Graphite, 184, 256

Gravitation, effects of, 25,409

Grignard reagents, 219

Grüneisen number, 179

### H

Hagen-Poiseuille law, 327

Hall, J. Storrs, 400

Hamaker constant, 63, 64

Harmonic drives, 323

Harmonic oscillators:

and classical mechanics, 71

and classical uncertainty, 91

damping by acoustic radiation, 164

damping of torsional, 165

energy of quantum mechanical, 93

Gaussian PDF, 91

graph of rms displacements, 95

mean energy, 93

mean square displacement, 93

phonon scattering, 172

quantum mechanical uncertainty, 92

and quantum mechanics, 71

thermally excited, 91

total vs. classical variance, 94

Heat, waste, 397. See also Energy dissipation

Heat capacity, scaling of, 33

Heat flow, 33

Helical gears, 308

Helium and seals, 328

Hexagonal diamond, 246, 262

Hydrocarbons, thermal stability of, 147

Hydrogen bonding, 270

Hydrogen and seals, 328

### I

Independent electron approximation, 40

Inductance, scaling of, 31

Inductive time constant, scaling of, 31

Information, 82

Infrared spectroscopy, 71

Institute for Molecular Manufacturing, 513

Instrumentation, 87

Insulation (electrical), 334

Interfaces in bearings, 294

Interfacial sliding, see Sliding

Intersystem crossing:

and energy dissipation, 224

in pi-bond torsion, 231

radical coupling, 215

rates of, 197, 216

and reaction reliability, 210

Intramolecular reactions, 122 . See also Rearrangement reactions

Ion(s), 198, 200, 328

Ionic bonding, 270

Ionic solids as materials, 255

Ionic species, reactions of, 212

Ionization, 150, 151

Ionization energies, 41

Irregular objects, sliding of, 277-284

Isotopes, 373

### J

Jahn-Teller effect, 39

### K

Kaehler brackets, 266, 436

Kinetic decoupling in error models, 132

Knudsen number, 326

Krummenacker, Markus, 467

### L

Latching, 321, 356

Least common multiple, 286

Lennard-Jones potential, 58

LEPS potential, see

London-Eyring-Polanyi-Sato potential

Lifetimes, $156-160$

Lifshitz theory, 64

Ligands for mechanochemistry, 235

Light, see Photochemistry

Linear systems, 77

Lippincott potential, 54, 62, 223

Liquids, 27, 326, 379. See also Fluids

Lithography, 9

Logic rods, 343-355

alignment knobs, 345

applied forces, 347

bounded continuum model, 346

drivers, 345

drive springs, 345

dynamics, 348-352

electronic analogies, 343

energy dissipation, 348-352

energy per switching cycle, 354

error rates, 352

gate knobs, 345

geometry, 346

housing structure, 345

input rods, 345 interlocks, 345

mass, 348

nonthermal vibrations, 351

output rods, 346

probe knobs, 345

reset springs, 346

sliding-interface drag, 350

stiffness, 348

stored energy, 352

thermoelastic losses, 351

vs. transistors, 354

vibrational excitation, 349

volume, 354

London-Eyring-Polanyi-Sato potential, 62,226

Lone pairs, 45

Lubricants, 26, 316, 329

### M

Machine-phase systems, 6, 14, 122, 135

Magnetic field energy, scaling of, 31

Magnetic fields, 31,320

Magnetic force, scaling of, 31

Maitland and Smith potential, 58

Manufacturing processes, 397 . See also Molecular manufacturing

Margins of safety and reliability, 16

Materials, survey of, 254-256

Mean-force potentials, $84,85,112,125$

Mean free path in gas, 326

Measurement:

devices, $320-322$

and equilibrium, 84

error models, 130

iteration and reliability, 322

Mechanical energy, thermalization of, 81

Mechanical engineering, 7,24

Mechanochemistry, 191-192. See also Mechanosynthesis

comparisons, 192

energy dissipation in, 221

forcible processes, $220-238$

as power source, 397

theoretical modeling, 192

Mechanosynthesis, 1, 191,197-207. See also Mechanochemistry

and catalysis, 204

cluster-based strategies, 246

competing reactions, 204

of diamondoid structures, 238-248

electrochemistry, 203

electrostatic effects, 200

error rates in, 205. See also Error rates

flexible components, 200

handle structures, 197

highly active reagents, 206

ionic reactions, 200

ions in, 198

large effective concentrations, 198

limited reagents, 197

for molecular manufacturing, 207-211

natural parallelism, lack of, 197

nondiamondoid structures, 248

and photochemistry, 198, 203

radicals in, 198

reaction cycle times, 208

reagent preparation $v s$. application, 208

sensitivity to modeling errors, 88

in solution, 14

vs. solution-phase synthesis, 196-207

solvation, lack of true, 198

summary of comparison, 211

temperatures in, 198

Melting point, table of values, 256

Memory, 365

Merkle, Ralph C., 246, 268, 269, 286, 296, $299,311-312,371,419,459,470$

Merkle buckling logic, 354

Metals:

electron relaxation time in, 31

as materials, 254,430

optical transmittance, 153

surface instability, 149

Microtechnology, 8

Miller, Mark Samuel, 369

Misreaction rates, 209, 229

MM2 model, 44-51

accuracy of, 42

atom types, 44

bond angle-bending, 45, 50

bond stretching, 44, 45

bond torsion, 47,48

collision data, comparison to, 58

conjugated bonds, 49

conservatism of designs, 50

electronegativity correction, 49

electrostatic interactions, 48

errors in modulus prediction, 262

at high bond stresses, 51

and interfacial sliding, 274

and MM3, 43, 50

nonbonded interactions, 44,48

poor fit of vibrational frequencies, 50

stretch-bend interactions, 49, 50

van der Waals force, 48

MM3, 43, 50

MNDO, 41

Modeling errors as perturbations, 87

Modulus of slim rods, $260-262$

Molecular beam experiments, 72

Molecular biology, 10

Molecular dynamics, 72-74

Molecular machinery, 253. See also Nanomachines

Molecular manufacturing, 1. See also Mechanosynthesis

mill and manipulator approaches, 207

misreaction rates, 209

omitted-reaction rates, 209

reagent stability for, 210

and reliability constraints, 207

resemblance to digital logic, 8 vs. solution-phase chemistry, 5

Molecular mechanics, 42-61

combined with quantum methods, 61

experimental basis, 42

as a level of approximation, 12

limitations of, 43

Molecular mills, 386-398

belt and roller systems, 386

conditional repetition, 388,396

energy dissipation, 395

error detection, 394

error rates, 393

fail-stop systems, 393

fault tolerance, 390

interfacing mechanisms, 390

mass, 391

pallets, 390

radiation damage, 394

reactive encounters, 386

reagent application, 391

for reagent preparation, 391

size, 391

waste heat generation, 397

Molecular nanotechnology, 1. See also Mechanosynthesis; Molecular manufacturing

Molecular orbital methods, 12, 40-42

Molecular ordering, 383-386

Molecular reaction dynamics, 61

Molecular solids as materials, 255

Molecular structures, geometry of, 86

Molecules, sorting and ordering, 373-386

Monte Carlo analysis, 278

Morrison, Philip, 503

Morse potential, 51, 52

and bond cleavage, 61

and bond stability limits, 54

in the LEPS potential, 62

in tensile bond cleavage, 223

and thermomechanical bond cleavage, 141

Motion, mechanical $v s$. thermal, 80

Motors, see Electrostatic motors

Murray's law, 331

### N

Nanocomputers, see also Computation; CPUs; Finite-state machines; Gates; Logic rods; Memory; Nanomachines; Registers

cooling of large arrays, 370

electronic analogies, 342

interfaces, 366

material properties, 343

signal transmission, 342

why mechanical, 14

Nanoelectronic devices, 14, 29

Nanomachines, 2-5. See also Molecular machinery; Nanocomputers

Nanomechanical engineering: compared to chemistry, 51 vs. macromechanical engineering, 315-318

and mechanical engineering, 24

and PES requirements, 51,87

problem of positional uncertainty, 90

stability vs. sensitivity, 87

stiffness and error tolerance, 87

Nanomechanical systems:

vs. biological, 253

nanoelectronics, contrasted to, 14

relatively simple PES, 80

thermal vs. mechanical motion, 80

uncertainty in, 83

Neutrinos and radiation damage, 156

Nonblocking merging junctions, 390

Nonbonded interactions:

and collision data, 58

continuum models of, 63-67

effective mean stiffness, 172

and interfacial sliding, 274

Lennard-Jones potential, 58

Maitland and Smith potential, 58

in MM2, 44, 48

Nonisothermal compression:

harmonic wells, 184

in measurement, 321

multidimensional systems, 185

in registers, 358

and thermoelastic losses, 179-180

square wells, 181

Nonlinear effects, 71

Nuts, 301

### O

Objectives, limitations in this volume, 15

Omitted reactions, 209

Orbital symmetry, 234

Organic synthesis, 193-196

Organometallic reagents, 219

Ostwald, Wilhelm, 191

Overlap forces, 63

Overlap repulsion in MM2, 49

### P

Partition functions:

classical harmonic oscillator, 125

classical theory, 76

and entropy, 75

and free energy, 75

and mean energy, 75

and pressure, 75

in quantum statistical mechanics, 75

quantum transition state theory, 126

ratios of quantum and classical, 127

transition state theory, 122

Partitioning of wells, 321

PDF, see Probability density function

Peroxide, 139

PES, see Potential energy surfaces

Phonons:

and ballistic heat transport, 33 energy density of, 169

optical modes, 170

phonon viscosity, 180

transmission coefficient, 175

Phonon scattering:

and energy dissipation, 169-179

harmonic oscillators, 172

phonon-phonon scattering, 179

in sliding of irregular objects, 282

Photochemistry, 151

avoidance via shielding, 15,153

as damage mechanism, 150-154

design for stability, 152

and mechanosynthesis, 203

Pi-bond torsion, 230-232, 387

Piezochemistry, 201

Pipe, fluid flow in, 327

Piston and cylinder, 111-113

Placement, error rate models, 131

Planetary gear systems, 311

PM3, 41

Poisson's ratio, 163,166

Polar groups, 150

Polarizability, 41

Polymeric solids as materials, 255

Polymer pyrolysis, 145

Polyynes, 214

Position, measurement of, 322

Positional uncertainty, 90,92, 118

Potential barriers:

for abstraction of hydrogen, 226

and applied force, 220

for cleavage of stressed bond, 141

and compressive load, 226

gear rotation, 304

in interfacial sliding, 274, 277

Monte Carlo analysis, 278

quantum corrections, 126

and reaction rates, 86

and reaction reliability, 209

reduction by compensation, 312

tunneling transmittance, 129

vector model, 278

Potential energy, 76, 93

Potential energy surfaces:

accuracy requirements, $85-89$

basis for nanomechanical design, 36

chemical accuracy, 85

and conformations, 86

errors and later correction, 89

errors as perturbing forces, 87

and mechanosynthesis, 88

of nanomechanical systems, 80

perturbed by thermal bath, 80

physical accuracy, 85

sensitivity of designs to errors, 87

of a solution-phase system, 79

time dependent, 130

Potential wells, 36, 186, 321

Power:

electrostatic motors, 336-341 mechanochemical sources, 397-398

scaling of mechanical, 26,30

supply for CPUs, 370

Pressure, 75, 201, 202, 320

Probability density, 76

Probability density function, 38, 91

Probability gas, 77-78, 122

Probability of states, 75

Propellane, 195

Proteins, 86, 196, 380. See also Antibodies

Pumps, 329

Purification cascades, 380-383

Pyrolysis, 145-148

### Q

Quality factor, scaling of, 32

Quantum chemistry, 192

Quantum electrodynamics, 37

Quantum electronics, 14, 29

Quantum interference, 85

Quantum theory and the PES, 37-42

Quantum uncertainty, 83

Quasiclassical approximation, 72

### R

Rack-and-pinion gears, 308

Radiation, 33, 154. See also Acoustic radiation; Radiation damage

Radiation damage, 154-156

classical target theory, 154

dominance of, 157

in molecular mills, 394

shielding from, as difficult, 156

simple lifetime model, 155

track-structure lifetime model, 155

Radicals:

abstraction reactions, 215

addition reactions, 215, 229, 386

coupling, 62, 215

displacement, 232, 388

mechanochemical displacement, 232

in mechanosynthesis, 198

as reagents, $215-217$

sigma, 216

stabilization by delocalization, 215

Random-access memory, 365

Random-walk model, 277

Ratchets, 315, 474-476

Reaction coordinate, 121

Reaction(s), see also Mechanosynthesis; Potential barriers; Rearrangement reactions; Transition state theories

bond breaking $v$ s. rearranging, 135

as cause of damage, 134, 144-149

elementary $v s$. nonelementary, 144

intramolecular, 137

and molecular mechanics, 61

potential energy functions, 61-63

rate of, and effective concentration, 198

rate of, and electrostatic effects, 200

rate of, and PES accuracy, 85 sensitivity to small energies, 41

Reaction cycle, 230

Reactive encounter mechanisms, 387

Reactive intermediates, 149

Reactive species, 212-220

Reagent(s):

application of, 208, 391

highly reactive, 206

multiply-bonded noncarbon atoms, 247

preparation of, 208, 391

stability of, 210

Reagent devices, 149, 200

Rearrangement reactions:

of carbenes, 218

of ionic species, 213

photochemical, 151

and pyrolysis, 146

radicals, 217

of unsaturated hydrocarbons, 215

Receptors:

antibodies as models, 374

diamondoid structures, 265, 375

rotor with modulated, 374

for selective transport, 373-380

specificity, 376

tight-receptor mechanism, 377

Reconstruction of surfaces, 149, 239-240

Redundancy, 159. See also Reliability

Refractive index, 64

Registers, 355-359

Relativistic effects, 37

Relaxation of vibration, 81

Reliability, 16,36,159, 207. See also Damage; Error rates; Failure rates

Resistance, scaling of, 29

Resistive power density, scaling of, 30

Resonance effects, 129

Reynolds number, 327

Ribosomes, as machine tools, 10

Rods:

approximate total longitudinal uncertainty, 101

classical longitudinal uncertainty, 96

as entropic springs, 113

longitudinal positional uncertainty of, 94-101,113-117

quantum mechanical longitudinal uncertainty, 97

signal transmission, 342

sliding in sleeves, 302

thermally excited bending, 104-110

transverse vibrational effects, 113-117

Roller bearings, 172, 308

Rollers and belts, 309

$S$

Safety, 16. See also Reliability

Scaling, 35

of capacitance, 30

classical laws, 27, 28, 33

of classical mechanical systems, 24-28 constant electric field assumption, 28

constant shape and stress, 24

of deformation, 25

of electric current, 29

of electromagnets, 31

of electromechanical power, 30

of electrostatic energy, 30

of electrostatic force, 29

of energy dissipation with speed, 162

of field emission current, 30

of force, 24

of frequency, 25,32

of heat capacity, 33

of inductance, 31

of inductive time constant, 31

of magnetic fields, 31

of mass, 25

of mechanical efficiency, 27

of mechanical power density, 26

of positional variance with temp., 118

of quality factor, 32

of resistance, 29

of resistive power density, 30

of shear stress, viscous, 26

of skin depth, 31

of speed, 26

of stiffness, 25

of strength, 24

of temperature elevation, 33

of thermal conductance, 33

of thermal speed, 28

of thermal systems, 32-33

of thermal time constant, 33

of wear, 27

of reaction yield, 204

Schrödinger, Erwin, 38

Schrödinger equation, 12, 38-39

Schwinger, Julian, 37

Screws, 301

Second law of thermodynamics, 83

Semiconductors, reconstruction of, 150

Semiempirical methods, 41

Shape, 262-266, 320, 322

Shear, 327

Shear-reflection drag, 177, 291

Shear stress, scaling of viscous, 26

Shielding, 153,156

Signal transmission, 342, 343, 363

Singlet states and bond formation, 62

Size and surface effects, 258

Skin depth effects, 31

Sleeve bearings, 284-301

acoustic radiation in, 290

construction-simplifying asymmetry, 300

load-compensating asymmetry, 300

loaded, 288

rotational symmetries, 285

shear-reflection drag in, 291

small bearing designs, 298

spatial frequencies, 285

stiffness, 289 strained-shell design, 297

unloaded, 286

Sliding, 277-284, 312

Software, see also Computer-aided design for large systems, 371

automated design-rule checking, 160

Solution-phase systems, PES of, 79

Solvation, eutactic analogue, 200

Solvents, 138, 144

Soreff, Jeffrey, 168, 174, 175, 177, 178, 324, 340,436

Sorting rotors, $374,378,379$

Spectral density, 275

Speed, scaling of, 26

Sphere, fluid drag, 327

Spin and energy dissipation, 224

Spin-orbit coupling, 37, 216

Stability, 137, 296. See also Reliability

States in configuration space, 78

Static friction, 283

Statistical mechanics, 73-85

applicability of classical, 77

assumption of equilibrium, 74

classical partition function, 76

classical and quantum uncertainty, 83

classical theory, 75

departures from equilibrium, 80

vs. detailed dynamics, 74

equilibrium assumptions, 80

and estimated failure rates, 74

mean energy, 75

nonequilibrium conditions, 80

partition function, 75

and probabilistic descriptions, 74

probability of quantum state, 75

quantum theory of, 75

of single molecules, 74

uncertainty and equilibrium, 84

Steric crowding and piezochemistry, 203

Stewart platform, 476-477

Stiffness:

and bond cleavage, 222

of bond stretching, 44

and effective concentration, 199

and error rate in radical addition, 230

under large loads, 51

and mechanosynthetic errors, 205

in molecular mills, 386

and nonbonded force, 59

scaling of, 25

and sensitivity to modeling errors, 87

of sleeve bearings, 289

of surface atoms, 225

torsional, 47

of transition metal bonds, 237

Stokes's law, 327

Storage systems, 365

Strain, see also Bond stretching

in diamondoids $v s$. steel, 317

in MM2, 42

and reaction rates, $140-143$ relief by dislocations, $268-269$

in shell surfaces, 267-268

Strength, 24, 221, 256

Stretch-bend interactions, 49, 50

Surface(s):

atomic stiffness of, 225

forces between, 63

interaction forces in vacuum, 66

softness relative to macroscale, 316

stability of, 149

Surface effects, 13, 257, 258-262

Symmetrical structures, $267-270$

Synthesis, 3. See also Organic synthesis; Mechanosynthesis

### T

Taylor, Dean, 476

Temperature, operating, 15

Temperature elevation, scaling of, 33

Temperature of single molecule, 74

Tensile loads and bond PESs, 51

Thermal bath, 72, 80

Thermal bond cleavage, 138-140

Thermal conductance, scaling of, 33

Thermal equilibrium, 72

Thermal expansion, 179, 181

Thermal gradients, 80

Thermalization of mechanical energy, 81

Thermal motion, 28,77-80, 92

Thermal speed, scaling of, 28

Thermal systems, scaling of, 32-34

Thermal time constant, scaling of, 33

Thermodynamics, see also Energy; Entropy

of molecular manufacturing, 426

second law, 83,505

and statistical mechanics, 73-77

third law, 82

Thermoelastic damping, 179, 181, 283, 292

Thermomechanical damage, 134-150

Time, scaling of mechanical motion, 26

Time-dependent PES, models of, 130

Tomonaga Shini'chirō, 37

Toroidal worm drives, 323

Torsional stiffness, magnitude of, 47

Transformation time, 197

Transistors, 12, 354

Transition metals and complexes, 219

bond stiffnesses in complexes, 237

ligands for mechanochemistry, 235

mechanochemical processes, 234

in molecular processing, 386

multiply bonded complexes, 234

pi-bond torsion in complexes, 232

and power generation, 397

Transitions, forced, 81

Transition rate, 224

Transition states, 121, 122, 205

Transition state theories, 121-128

classical, 121-126

equilibrium assumption, 121 and error rate models, 131

partition function, 122

probability gas, 122

quantum rate constant, 128

quantum theories, 126

and time-dependent potentials, 131

transition rate, 122

transmission factors, 126

variational theories, 125

Wigner tunneling correction, 127

Transverse-continuum approximation, 289

Tribble, Eric Dean, 253

Triplet states, 62

Tube, fluid flow in, 327

Tunneling:

and bond cleavage, 142

charge neutralization reactions, 213

corrections to transition state theory, 126

and electrical contact, 334

and electrical insulation, 334

of electrons $v s$. atoms, 29

resonance effects, 129

transition rates, 128

Tunneling junctions, 335,366

Turbomolecular pumps, 329

### U

Ultraviolet light, 151, 153

Uncertainty, quantum and classical, 83.

See also Positional uncertainty

Unsaturated hydrocarbons as reagents, 213

### V

Vacuum pumps, 329

van der Waals force:

and adhesive interfaces, 270

continuum models of, 63-66

interactions between objects, 64

in MM2, 48

Vibration, 71, 351

Vibrational excitation of logic rods, 349

Viscosity, 27, 326

### W

Waste heat, 397. See also Energy dissipation

Wave function, 38,129

Wear, 27, 157, 316

Wentzel-Kramers-Brillouin, 128

Wigner correction factor, 127

WKB approximation, 128

Work of compression, 84

Work functions, 337

Worm drives, toroidal, 323

Worm gears, 309

### X-Z

Xenon, as a solvent, 482

Yield, scaling with size, 204

Young's modulus, table of values, 256

Zero-point energy, 52, 126

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