Subject Index Acid catalysis 244, 245, 247, 249, 252 Bonds-pairs 177, 178, 184, 185, 190, 191, Activation 207, 208 202-204 Activation barrier 160, 233, 242, 249 Bottleneck 291, 299, 307, 323-325, 336, Activation energy 233, 246, 247, 306, 357, 359, 360 307, 312, 314, 331, 332-339 Butane 5, 14, 17-24 Adiabatic potential, vibrational-rotational CASMCSCF 148, 158 309, 314-317, 319-323, 325, 338 CASSCF 150 Adiabatic states, electronic 312 Adiabatic states, vibrational 312, 314, 322 Adiabatic surface 147, 279 Allowed and forbidden pathways 205, 206 Allowed reactions 110 Allyl 180, 183 AM1381 Analytic expansion 8, 10 Analytic gradient 33-35, 45, 49, 348, 349 Anchor state 202, 203 Angular momentum 349, 352, 353 Concerted 151 Catalysis 231, 242, 244, 245, 249, 251 Catchment regions 59-61, 70-72 Cation-anion recombinations 208 Cavity 223, 380 CHj transfer 197 Charge exchange 261 Charge transfer 114, 130, 133-136, 158, 160, 200, 203, 232, 235, 237, 240, 249, 251, 276, 277, 279 Chemical reactivity 147 Clausius-Mossoti equation 380 Collision integrals 281 Antibonding 166, 174, 176, 177, 182, Concerted transition structure 156, 245, 188, 189 247 Asymptotic expansion 271 Asynchronous 151, 204 Atom abstractions 193 Avoided crossing 193, 194, 196-198, 200, 205-207, 210, 279 Configuration interaction 190, 198, 207 Conformational rearrangements 340, 374 Continuum 223, 231, 232-234, 244, 379 Contour surfaces 77, 79, 80, 81, 83, 84, 89, 91, 93, 96, 325, 318-321 Barrier 165, 166, 193, 196 Coriolis coupling 352, 356 Betti numbers 13-15, 17, 18, 28 Correlation 194, 201 Bifunctional catalysis 231, 242, 244-247, Coulomb parameters 149 249, 252 Counting 295 Binomial coefficients 13, 17 Coupling functions 351, 352, 357 Biradical intermediate 204, 206 Covalent bond 166, 173, 177, 202 Bond distortions 207, 208 Covalent curves 196, 198-200 Bond-diagram 167, 177, 178, 184, 190, Covalent determinants 173, 177, 180 205 Critical point relations 64-66 387
388 Critical points 33-35, 48-49, 311 Crossing point 199, 205, 207, 208 Cumulative reaction probability 358, 359 Curvature coupling 319, 322, 352, 353, 355, 362, 363 Electrostatic interaction energy 219 Elimination reaction 203 Energy first derivatives 33-35, 45, 49 Energy second derivatives 34, 45, 57, 49-50 Curvature of reaction path 304, 318-323, Energy third derivatives 34 327-329, 335, 339, 352 Entropic effects 232, 245, 292, 307, 325, Curvature properties 77, 82 326, 334-339 Curve crossing diagrams 165, 166 Enumeration of internal coordinates 39- Cycloaddition 102, 131, 149, 152, 156, 40 203-206, 244, 378 Ethane 11, 14, 15 Cyclobutane 205 Ethylene hydrogenation 245-247 Cyclopropenyl 180, 182 Exchange integral 106, 117, 155 Deflection function 264, 265, 266 Exchange parameters 149 Deformation energy 207-210 Exchange reaction 202 Density of states 294-299, 358 Excited state 177, 196, 199, 201, 207, Determinant-mixing 171, 174, 177, 183 208 Diabatic surface 101, 102, 117, 125, 127, Feynman path integral 365, 366 129, 133, 140-144, 147-148, 150, 160- Flux 356-359, 366 161 FO-VB diagrams 184, 185, 190, 202 Diels Alder Reaction 147, 158, 206, 378 Forbidden reaction 152 Differential cross section 257-261, 263, Force constant 5, 6, 8, 329 270, 274, 282 Force constant matrix 34, 45, 47, 49-50, Diffusion coefficients 283 348, 350, 351, 364 Discrete 231, 233, 235, 379 Free energy of activation 232, 245, 306, Dispersion energy 219 307,312,313,331,334-339 Displacement reactions 197 Friction 308, 333, 334, 365 Dividing surface 304 Friedel-Crafts reaction 247-249 Dummy atoms 38-44 Gaussian 86, 33, 36-37, 51. 376 Dynamic shape properties 93 Generalized Langevin equation 232, 333, Effective Hamiltonian 155 365 Electric field 231, 244, 249-252 Generalized transition state 299, 381 Electric permittivity 221 GEOMO 380 Electron transfer 176, 203, 237-241 Global analysis of PES 56-58, 63 Electrophile 203 Gradient 5, 6, 8-10, 33-35, 45, 49, 376 Electrophilic substitution 226, 247, 251 Gradient length 7
H-atom transfer 318-321, 323-331, 334, Maxima 5-9, 11, 13-18, 20, 23, 24, 312 335, 338, 339, 348, 353, 354, 368 MCSCF 110, 112, 116, 120, 126, 140, Heisenberg Hamiltonian 101, 117-121, 143, 152, 154, 377 125, 131, 133, 136, 140, 143, 147, 149, Menschutkin reaction 208 155, 158, 160, 169, 180 Minima 2, 5-11, 13-18, 20, 22, 24, 26, Heitler-London 174, 177-180, 182, 183, 28, 33-35,48-49 185, 193-195, 198-200 Minimum energy path 48, 49, 51, 304, Hessian 34,45,47,49-50,376,378 305, 309-311, 315-323, 326-328, 331, HOMO 226,378 335,348,349,353,355,357,368, 382 HOMO-LUMO 204-206 Mixed-valence species 185 Homology groups 83 MNDO 380 Homotopy group 62-63 Mobius 182, 185, 186 Huckel 181, 185 Molecular beams 263, 269 Hydrocarbons 17, 329-331 Molecular body vs. molecular skeleton Ideal surface 1, 29 78,79 Image state 201-206 Molecular Dynamics 231, 240, 380 Index of critical point 5-12, 14-20, 27, Monte Carlo 231,233,234,237,238,380 311 Induction energy 219 Internal coordinates 36-45, 49-50 Intersection curves 194 Ionic exchange 197 Jahn-Teller mechanism 184, 190 Kekule structures 182, 183, 186-191 Ketoenolic tautomerism 242-244 Kinetic measurements 210 Knots and chirality polynomials 84, 85 Lewis structures 167, 178 Linear free energy relations 208-210 Linear reaction path 348, 353, 357, 364, 368 Long bond 167, 189, 198 LUMO 226, 378 Marcus theory 208 Matrix elements 167,171,172,176,180, 186-190, 200, 213-215 Multiconfiguration TDSCF 367 Multipoles 220, 225 Newton-Raphson optimization step 35-36 Nodal properties 205 Non-ideal surface 1, 29 Non-linear Schrodinger equation 367 Nonbonded interactions 207 Normal coordinates 311, 314, 330, 350, 353, 356, 357 Normal mode 162 Nucleophile 203 Nucleophilic substitution 208, 226 Optimization 33-51, 304-308 Orbital interactions 210 Orbital symmetry 206 Oriented relative convexity 82 Overlap repulsion 170, 171, 186, 189 Parallel algorithm for quasi global optimization 55, 64-65 389
390 Partition functions 293, 299-306, 309- Recrossing 232, 240, 241, 298, 299, 323, 312, 331, 335 325, 333 Pericyclic reaction 206 Reference cluster approach 70-72 Permutations 211-213 Regiochemical pathways 204 Perturbation language 177, 196 Relative convexity 82 Phase space 292-303, 307, 308, 332 Relaxation times 222, 235, 308, 332-334 Polarizability 220 Resonance 170, 177, 183, 192, 207, 208 Polyrate 381 Rotation-inversion 4 Potential Energy Surfaces 34, 193, 231, Rotational excitation 261, 275, 308 249, 250, 291, 292, 294, 304-323, 347, Rumer functions 160 348, 354, 355, 368, 374 Rumer spin functions 162 Propane 14-16, 20 Saddle point 2, 5, 7-10, 13, 15-18, 20, QMRE 207, 210 22-24, 26,33-35, 45-46,48-49, 304,305, Quadratic expansion 5, 8, 35-36, 317 318-321, 324, 326, 329 Quasi-Newton methods for optimization 34-36 Radical anion 200 Radical attacks 293, 323-331, 335, 338, 339 Radical reactions 193, 204-206 Reaction barriers 148 Reaction coordinate 160, 197, 201, 233, 235, 236, 241, 244, 247, 249, 251, 252, 292, 296-307, 309-323, 331-335, 352, 360, 361, 364, 365 Saddle point optimization 33-51 SCD 165, 194, 196-198, 200-202, 204-209 SCF 226 Second derivative 5, 7, 8 Semiclassical approximation 264, 266, 308-331, 334-339, 360, 362-364 Shape groups 77, 80, 81, 83, 84 Singlet-pairing 174, 175, 177, 181 SN2 reaction 35,192,197,208,209,231-237, 240, 241, 249-252, 380 Reaction Field 225, 231, 252 Solute-solvent interactions 221 Reaction mechanism 55-56, 59, 62-63 Solvation 221, 231 Reaction path 48-51, 300-304, 307, 311, Solvation free energy 332 314-323, 327-329, 335, 337 Solvation parameter 235-237 Reaction path Hamiltonian 292, 297, 300, Solvent 221 348, 351, 352, 355, 360, 362, 364, 368 Solvent dynamic effect 231, 240, 331- Reaction profile 162, 232, 233, 249, 250, 334, 339 300-307, 309-312, 314-323, 331, 350 Solvent effects 231, 232, 241, 379, 293, Reactive flux 291-303, 312, 319, 324 308, 331-335 Reactivity patterns 165, 193 Solvent fluctuations 237, 238, 241
Solvent reorganization 232, 233, 237, Transition state 33-35,45-46,48-49, 108, 238, 242 126, 129, 142, 147-150, 158, 162, 192, Solvent static effect 231, 232, 235, 331, 196, 197, 199, 200, 205-210, 242-248, 332 291-312, 324-326, 331, 332, 336-339, Space-orbitals 211 348, 349, 353, 355, 361, 376 Spin correspondence 214 Transition state optimization 33-51 Spin transfer 192, 193, 197, 202, 203 Transition state theory 222, 232, 241, Spin-eigenfunction 167, 194 291,298,356-360, 381 Spin-orbital 167-173, 175, 195, 211-213, Translation 301-303 215 Transmission coefficient 240, 241, 309, Spin-pairing 174, 177, 178, 181, 193, 313,317,323,335,347-339 198, 201, 203, 205 Triionic structures 198 Stationary points 33-35,48-49,234,249 Triplet state 173,174,177,180,186-188, Statistical approximations 294, 306, 308, 190, 194, 196, 205, 207 312, 333, 356, 360 Tunneling 291, 292, 308, 309, 313-324, Stereochemistry I, 5, 14, 17 326-332, 336-337, 355, 362, 363, 382 Strong coupling of internal coordinates Valence Bond 102, 111, 112, 116-118, 40-44 120, 121, 125, 133, 136-138, 143, 144 Substituent effects 209 165-167, 179, 191, 193, 194, 196, 197, Supra-antara 204, 205 200, 203, 207-210, 213 Supra-supra 204, 205 Van Vleck method 379 Symmetry 245, 247, 376, 303, 311, 325 Variational transition state theory 292, Symmetry and dummy atoms 38-39 381 Symmetry and optimization 34-35 VB determinants 165, 167-175, 178, 180, Symmetry and transition vectors 3 185, 211, 215 Symmetry constraints on PES 70, 72 VB-mixing diagram 173, 176, 179, 181- Synchronous 151 183, 185-190, 195, 199 Synthesis design on PES 54, 57, 63 VBCM 165 TDSCF 366 Vertical excitations energies 208-210 Testing stationary points 48-49 Yamanouchi-Kotani 121-123, 126 Thermal conductivity 280 Z-matrix 36-44, 46-47, 376 Thermal diffusion 280 Zwitterionic determinants 173, 175, 177- Topological periodicity 11, 13, 14, 26 179, 194-196 Topology 1.. 5, 10, 11, 13-20, 24-29 Total cross section 261, 274 Torus 11-13 391