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APPENDIX: UNITS

This appendix explains some of the abbreviations1•2 used for units in this book and gives conversion factors to SI units and atomic units:

1 a0 = 1 bohr = 0.5291771 X 10-10 m 1 A= 1 Angstrom= lo-10 m = 1.889727 ao

1 me = 1 atomic unit of mass = mass of an 9.109534 X 10-31 kg = 5.485803 X 10-4 U

1 u 1 universal atomic mass unit = one twelfth the mass of a 12c 1.6605655 x lo-27 kg = 1822.887 me

1 t Eh 1 = 1 atomic unit of time = 2.418884 x l0-17 s

1 s = 1 = 4.134137 x 1016 t/Eh

1 K = 1 Kelvin

1 mol = 1 6.022045 x 1023 , molecules, or formula units

1 cm-1 = 1 wavenumber 1 kayser 1.986477 x lo-23 J 4.556335 x 10-6 Eh

857 858 APPENDIX: UNITS

1 kcal/mol = 1 kilocalorie per mole 4.184 kJ/mol = 1.593601 x 10-3 Eh

1 eV 1 electron = 1.602189 x lo-19 J 3.674902 X 10-2 Eh

1 Eh 1 = 4.359814 x lo-18 J

Since so many different energy units are used in the book, it is helpful to have a conversion table. Such a table was calculated from the recommended values of Cohen and Taylor3 for the physical censtants and is given in Table 1.

REFERENCES

1. "Standard for Metric Practice", American Society for Testing and Materials, Philadelphia (1976). 2. D. H. Whiffen, Expression of results in quantum , Pure Appl. Chem. 50: 75 (1978). 3. E. R. Cohen and B. N. Taylor, The 1973 least-squares adjustment of the physical constants, J. Phys. Chem. Ref. Data 2: 663 (1973). )> "'tl "'tlm z 0 X c z Table 1 Energy conversion factors. uJ

cm-l kJ/mol kcal/mol eV E h

1 cm- 1 = I 1.0 1.196266 X 10-2 2.859144 X 10-3 l_. 239852 X 10-l; 4, 556335 X 10-G

1 kJ/mol = 83.59347 1.0 2, 39005 7 X ]_0-l 1. 036436 X 10- 2 3.808798 x Jo- 1+

1 kcal/mol = 349.7551 4.184a 1.0 4. 336445 x 10-2 1.593601 X Jo-3

1 eV = 8065.479 96.48455 23.06036 1.0 3.674902 x 1o-2

1 Eh = 219474.7 2625.500 627.5095 27.21161 1.0 a. exactly (by definition)

CXlc, '() INDEX action-angle variables, 8, 21, effect of inelastic events, 292, 293, 640, 793, 794 835-839, 849 activation energy, 3, 139, 142- optical potential calculations, 146, 153, 155, 156, 162, 835-839 170, 172-175, 177, 179, average ~-labelling of CS, 718, 180, 248, 249, 255, 311, 719, 722, 723 332, 351, 353, 359, 434, 441-445, 447, 448, 469, basis set effe~ts, 169, 172-176, 478, 485, 487, 523-526, 186-190, 194, 245, 248, 253, 531, 599, 653, 654, 658 344, 540, 544, 654, 662, 663, activation energy, state• 665-667, 776-778 selected, 448, 469, 478, bimolecular rate constants, 39, 40, 485 289, 290, 294, 296-300, 331, active orbitals, 333 332, 338-340, 345-347, 371, adiabatic energy transfer, 692, 432, 438, 439, 441-445, 456, 693, 696 469, 477, 478, 556, 587-631 adiabatic theory of reactions, bond-energy-bond-order (BEBO) 366, 593 model, 294-297, 595, 597 alkyl radical dissociations, bond strengths, calculated, 141- 37-69 144, 153-155, 176-179, 351, angular momentum effects on 557, 665, 666, 675 unimolecular decay, 24, bottleneck region of potential 46, 62, 64, 225-227, 570 energy surfaces, 2, 24, 273- anharmonic oscillators, 19, 20, 278, 587-631 107, 236, 237, 292, 332, branching reactions, 11, 24, 27, 449, 775, 793, 794 146, 156-161, 519, 520, 522- anharmonic state counting, 19, 531, 551-584, 600, 601, 606, 20, 26, 27, 51, 52, 595, 609, 610, 619, 626, 627, 850 596, 604, 613 bulge effect, 753 anharmonicity effects on unimolecular decay, 19, capture cross sections, 232-234 20, 236, 237 carbene insertions, 170, 177 apse quantization axes, 719, carbene rearrangements, 185, 251 731, 733 catalysis, 639, 654, 676-681, 813 Argand diagrams, 388-391 centrifugal sudden approximation, atom-surface scattering, 290, 291, 298-300, 376, 692, accurate calculations, 831-839 717-733 attractive hard-wall classical cross sections, 741, 744- calculations, 832-835 746, 753, 754

861 862 INDEX classical model for laser, 639- double mass spectrometer system, 641 536, 538-540 combustion, 139, 294, 330, 331, 359 edges of microcrystallite, 844 contour diagrams of potential effective core potentials, 261, energy surfaces, 109, 119, 662 126, 204, 208, 211, 361, effective cross sections, 435, 362, 401, 409, 411, 501, 436 527-530, 541, 542, 557- eigenphase-shift analysis, 394- 560' 688 397 Coriolis coupling, 21, 267, Einstein model, 711 268, 313 ejection yields, 844-851 coupled-cluster methods (CCM electron correlation, 132-156, and CCD), 133-139 161, 162, 169, 171-180, 187-189, 194, 245, 248, decay rates of quasibound 253, 535-538, 653, 656, clusters, 223-232, 577 663-675, 772-779 decoupling approximations, 476, electronic excitation , 692, 693 133, 147-155, 161, 162, degeneracy-averaged differential 187-194, 337, 763, 779-783 cross sections, 722-724 electronic-field representation, derivatives as input in inter• 759-762 polation, 204, 205 electronic representations, 687 detailed balance, 438, 440 electronically nonadiabatic diatomics-in-molecules (DIM) processes, 193, 293, 297, method, 294-297, 315, 486, 488, 548, 639-641, 359-363, 367-371, 520- 646-649, 686-688, 691-693, 531, 553-559, 688 695, 713, 763-768, 853 DIM-3C method, 522 energy minimization pathway, 654, differential cross sections 655, 657 (differential in scat• energy partitioning, tering angle), 312, 314, in products of surface reactions, 319, 320, 327, 413-415, 809-812 421-429, 450, 451, 496, in unimolecular reactions, 40, 570-576, 704, 707, 710, 41, 57-67, 86, 192 711, 714, 720-724, 737- experimental reaction cross 755, 808, 811, 812, 846, sections, 535, 536, 546-548 850-853 dissociation reactions, 2, 15, factorization of the CVT recrossing 140-145, 152-156, 179, coefficient, 613-631 249, 287, 431-433, 445, Fermi resonance, 121-127 456, 466-469, 548, 564- filtering techniques, 422-428 570, 686, 694, 695 Fourier series expansion, 421-425 distinguished coordinate, 655, Franck-Condon model of electronic 658 energy transfer, 693 distorted wave approximation, Franck-Condon structure, 11, 106, 291, 298-300, 463, 495, 107, 115-121, 291, 640, 642, 496' 692' 693 643, 645, 650 INDEX 863 fundamental dynamical assumption laser-induced chemistry, 639-651, of TST, 588, 596, 603 759-768 laser inhibition of reaction, generalized relaxation cross 640, 645-648, 650 sections, 721, 723-728 local modes, 20, 22, 106, 123, generalized valence bond wave• 126-128 functions, 24, 253, 331, London-Eyring-Polanyi-Sato (LEPS) 333, 334, 340, 341, 347- and extended LEPS potential 350, 464, 552, 560, 662- energy surfaces, 294-296, 681 359, 370, 371, 376, 422- gradient method, 172, 243-261, 429, 520, 551, 560, 597, 265, 595 600, 601, 618-629, 641, 645, 807 Hammond's postulate, 615 lifetimes of collision complexes, bond, 76, 79-81, 89, 11, 48, 391-394, 415, 552, 90 560, 571, 572, 576-578 impulse model, 704, 708, 714, magnetic transitions, 320-324, 733 693, 718, 719, 730-733 inactive orbitals, 334 many-body approach to atom• information-theoretic methods, molecule collisions, 687, 287, 301, 568, 569, 691, 694-696, 703, 704 795-797, 811 many-body expansion, 772, 785-793 interpolation of derivatives, many-body perturbation theory 204, 205 (MBPT) of electronic interpolation of potential structure, 133-139, 161, energy surfaces, 206-210, 772-779 294, 361 minimum-energy path (MEP), 43, intramolecular vibrational 243, 250, 330, 405, 409, energy redistribution, 1, 513, 590, 591, 595, 598, 7, 10-23, 40, 42, 49-57, 604, 606, 607, 612-615, 620 121-128, 230, 251, 255, molecular beam experiments, 10, 259, 572, 577, 584 40, 249, 415, 495, 496, intrinsic reaction coordinate 703, 753, 806, 811-813 (IRC), 243, 250-259, 265, M~ller-Plesset theory, 171 590 moments of final-state distri• isotopic selectivity via laser butions, 59, 301, 323-325, field, 639, 649, 650 421, 449-453, 455, 456, inversion problem, 687, 694, 691, 795-797 754 multicenter potentials, 688, 689, 704, 706-708, 710, 713, kinetic isotope effects, 249, 845, 846 291, 298-300, 547, 548, multi-configuration-self• 606-611, 623, 624, 626, consistent-field (MCSCF) 627, 630, 639, 640 method, 206, 244, 331, 656-658, 663 Langevin equation, 278-284, 808 multiple-collision expansion, laser effects on collision 694, 708 processes, 287, 639-651, multivalued interpolation, 205 686, 725, 759-768 864 INDEX natural collision coordinates, quantal reaction probabilites, 251, 497, 498 289-291, 297-300, 360, negative ion-neutral reactions, 363-369, 375-383, 405, 536, 538-549 406, 411-413, 432, 437, non-RRKH lifetimes, 4, 11-20, 438, 467, 589, 596, 612, 49-57 630 number states, 759 quantal scattering wavefunction, 398-400, 405, 495, 499- orbital concepts for chemical 503, 509-513 reactions, 188-192, 333, quasibound clusters, definition 334, 340, 341, 347-350 of, 221, 222 orbital phase continuity quasibound states of diatomics, principle, 333 433, 455, 456, 468 organic radical processes, 37, quasiclassical trajectory 179, 185 calculations, 287-293, osculating complex model, 570- 296-302, 311-327, 359, 575, 578 370, 379, 380, 421-429, 431-469, 479-482, 484-487, partial retention of diatomic 495, 551-584, 597, 639-650, differential overlap 690, 703, 704, 753, 793-800 (PRDDO) method, 620 quasiperiodic trajectories, 7, 9, periodic orbits, 121-128, 294, 21, 51, 53-56, 292, 793 366 photoabsorption, 10, 11, 104, R-matrix propagation method, 506, 105, 107-111, 649, 650, 507' 691, 765 725 rainbow scattering, 737-755 photodesorption, 98 atoms from atoms, 694, 741-743 photodissociation, 108-110, 173, atoms from diatomic molecules, 185-195, 251-255 693, 694, 744-751 photon angular momentum, 762 atoms from polyatomic molecules, polarization CI method, 294- 751' 752 297, 331, 335-338, 341- from surfaces, 807 345, 350-353, 359 light from drops, 738-741 polynomial root interpolation, rainbows, 199-212 double, 751, 752 product state and energy supernumerary, 739, 741, 743 distributions, 4, 10, 11, Raman scattering, 106, 113-115, 23-26, 41, 48, 57-69, 192, 725 255, 257-259, 298-302, rate constant, state-selected and 311-327, 346, 347, 448- state-to-state, 289, 298- 456, 463-466, 469, 496, 300, 433, 438, 439, 445- 513, 514, 556, 569, 572, 447, 469, 477-482 691 reaction coordinate and reaction propagation of scattering wave• path, 173, 189, 194, 231, function, 503-509 247, 250-259, 265-272, 284, 330, 334, 351, 352, 548, quadruple excitations, 136-139, 588-592, 597, 615, 630, 654, 175, 667-674, 773 655, 657 INDEX 865 reaction mechanisms, 653, 658, rotational distribution of products 676, 681, 850 products, 10, 57-59, 62-67, reactive lOS approximation, 290- 291, 316-318, 320-324, 448- 291, 298-300, 475-488, 450, 455, 463-466, 469, 477, 496 556, 581-583 reaction threshold energies, 42, rotational excitation, non• 139, 173, 175, 190-194, reactive, 434-438, 440, 456- 230, 231, 336, 337, 344, 466, 469, 718-733, 737, 744- 362-371, 375, 437, 438, 755 485, 536, 593-595, 603, rotational predissociation, 82 604, 640 Rydberg states, 185-195 reagent-excitation effects and mode specificity, 10, 11, S matrix, reactive scattering, 16, 22, 23, 38, 47, 63, 289, 388-397, 414, 502, 503, 64, 235-237, 298-302, 311, 508, 509 312, 317, 318, 324-326, secondary ion mass spectrometry, 346, 431, 438, 445-464, angle-resolved, 843, 851-853 813 semiclassical eigenstates or eigen• recombination rates, 156-161, values, 8, 105, 291, 292, 227-229, 232, 233 300, 302, 313, 432, 691 resonance theory of atom• shock-tube studies, 653, 654 surface scattering, 821- short-time expansion, 709 827 skew angle, 406, 408, 606-611, resonances, 51, 375-416, 495, 616, 617, 619, 621 496, 513, 514, 807, 822- solid-surface scattering, 689, 839 693, 695, 703-705, 711-714, experimental detection of reac• 805-813, 817-840, 843-853 tive, 414-416, 496 solvation effects, 679 lifetime analysis of, 391-394 spectroscopic constants, 3, 4, 44, retention of bondedness, 666, 45, 145, 150, 159, 175, 245- 675 247, 335, 342, 350, 351, 787 Rice-Ramsperger-Kassel-Marcus spectroscopy, 103-129, 146, 193, (RRKM) method, 2, 4, 10, 410, 411, 805-807 12-14, 18-20, 25,27, 37- sputtering, 843-853 40, 49-53, 56, 60, 61, square-well potential, 382, 384- 255 388 Rice-Ramsperger-Kassel (RRK) stability map, 122 theory, 230, 231, 234- state-to-state chemistry at 237, 273 surfaces, 805, 806 rotated-Morse bond-energy-bond• statistical models and theories, order (~ffiEBO) method, 10-14, 18-27, 37, 38, 40, 595, 597-599, 612, 615- 41, 230, 231, 257, 259, 272- 618, 620-629 278, 284, 287-289, ~02, 331, rotated-Morse-oscillator-spline 560, 568-570, 580-583, 690, (RMOS) method, 294-297, 692, 805, 806, 808-811 361-366 stochastic trajectory techniques, rotational adiabaticity, 448, 808, 809 449, 469 866 INDEX sudden approximations, 290, 291, unrestricted Hartree-Fock, 135, 298-300, 475-477, 692, 138, 140, 161, 171, 244, 693, 696, 717-733, 753, 249, 332, 772-779 754, 772, 797-799 surface fitting, 5, 6, 199-212, valence-configuration interaction 259, 288, 289, 294-297, (VCI), 536-538, 540-544 312, 360, 361, 376, 432, van der Waals molecule structures, 597, 601, 612, 785-793, 80, 81, 98, 654 801 van Hove correlation function, 708 variational transition state time-correlation functions, 705, theory, 2, 290, 294, 332, 706, 709, 714 587-631 total cross sections, 428, 477 vibrational adiabaticity, 139, transition state properties, 257, 259, 332, 345, 346, 44, 173-175, 245, 248, 362-371, 375, 378, 398, 252, 257, 294-297, 300, 402-405, 441, 448, 469, 334, 336-338, 341-345, 590-599, 604, 606-611, 615, 360, 363, 423, 523-526, 618, 642, 643 531, 540, 603, 606-608, vibrational excitation, 82, 448- 616, 619-622, 624-629, 466, 536, 540, 686, 687, 639, 658 691-695, 709-711, 714, 777- transition state theory, 2, 4, 801 10, 19, 39, 139, 156-158, vibrational predissociation, 82- 179, 180, 249, 272, 273, 98, 190 287-290, 294, 299, 300, 331, 332, 340, 345, 359, wavepacket dynamics, 7, 23, 107-121 360, 365, 371, 441, 442, Wigner correction, 296, 297, 332, 444, 547, 587-631 340, 345, 346, 360, 592, tunneling, 81, 126-128, 175, 593, 595, 630 191, 255, 266, 289, 291, 293, 294, 296, 297, 331, 332, 340, 345, 346, 360, 362, 365, 367, 441, 442, 444, 589, 592-596, 615, 630 unified statistical model, 272- 278, 284 unimolecu1ar classical trajec• tory studies, 1, 7-9, 37- 69, 214, 217-238, 570-583 unimolecular decomposition, 1, 10, 37, 98, 169-180, 255, 551, 570-584, 597 unimo1ecu1ar rate constants, 11-20, 39-42, 49, 84-97, 156-160, 179, 180, 223- 232, 234-238, 266