8.3.3 Postscript

3-21G and 3-21G(*) basis set, 214, 216, 219–20, 222–5, 230–1, 233, 255, 260, 423

6–31G* basis set, 216, 221, 225–6, 231, 246, 307, 398, 400, 406

A

ab initio calculations, 159–337, 297 illustration, 192–209

summary of steps in a calculation, 209–10 strengths, 322

weaknesses, 322–3

ab initio energies, 262–89 ab initio frequencies, 289–96 ab initio geometries, 253–62

ab initio method, applications, 253–322 ab initio methods, 2–4, 237, 253, 312, 322,

339–40, 346–7, 362, 364–5, 369, 375, 377, 385, 422, 436–7

activation energies, 33–4, 242, 263, 347, 353, 355, 362–4, 377, 407, 410–12, 435

ab initio, 267, 281–7 DFT, 411–13 semiempirical, 362–4

adiabatic connection method (ACM), 400, 408

AIM see atoms-in-molecules analysis Allinger, N. L., 45, 254

Alzheimer’s disease, 452

AM1, 352–3, 359–60, 362–3, 365, 370, 406, 417

AMBER, 58–9, 63

angle bending term, 46, 48

applications of ab initio method, 253–324 energies, 262–89

frequencies, 289–96 geometries, 253–62

properties arising from electron distribution: dipole moments, charges, bond orders, electrostatic potentials, atoms-in-molecules, 296–312

miscellaneous properties – UV and NMR spectra, ionization energies, and electron affinities, 312–16

visualization, 316–22

applications of density functional theory, 399–436

energies, 406–13 frequencies, 413–14 geometries, 400–6

properties arising from electron distribution: dipole moments, charges, bond orders, atoms-in-molecules, 414–19

miscellaneous properties – UV and NMR spectra, ionization energies, and electron affinities, electronegativity, hardness, softness and the Fukui function, 419–36

visualization, 436

applications of molecular mechanics, 57–72 frequencies, 68–72

geometries and energies, 57–61 geometries, 64–8

MM in organic synthesis, 61–3 molecular dynamics and Monte Carlo

simulations, 63–4

applications of SCF semiempirical methods, 355–77

energies, 361–4 frequencies, 364–8 geometries, 355–61

properties arising from electron distribution: dipole moments, charges, bond orders, 368-73

miscellaneous properties – UV spectra, ionization energies, and electron affinities, 373–5

visualization, 375–6

applications of simple Hückel method, 122–33

applications of extended Hückel method, 149 aromatic molecules, 128

aromaticity, 128, 453–5 Arrhenius, 89

Arrhenius activation energies, 263, 267, 411 Atkins, P, 33, 37

atomic orbitals (AOs), 95, 151–2, 162–4, 176, 178, 211, 217, 223, 324, 342, 346 and hybridization, 96

and LCAO, 111

as one-electron functions and overlap matrix, 115 and orthogonality, 116

atomic units, 161

464 Index

atomization method (for heat of formation), 276–8

atoms-in-molecules (AIM) analysis, 296, 308–12, 369, 414, 418–19, 452

B

Bader, R. F. W., 308 Baker.J., 412 banana bonds, 100

basic principles of ab initio method, 160–210 basic principles of density functional theory,

387–400

basic principles of molecular mechanics, 45–57

basic principles of SCF semiempirical methods, 340–55

basis functions, 111,141, 342

basis sets, 111, 140–2, 177–9, 211–31, 341–2, 353–4, 395

preliminaries, 211–16 types and uses, 216–31

basis set superposition error (BSSE), 251–3 Bauschlicher, C. W., 404, 410, 413 Berzelius, J. J., 424

Binkley, J. S., 238

blackbody radiation, 82–5, 151 Bohr, N., 89

Bohr atom, 82, 89–91 Bohr model, 151, 161 Boltzmann, L., 87

bonds and electronic structure calculations,

44

bond energies, 265

bond length, 1, 9, 10, 43, 50–1, 58, 64, 141, 208–9, 253–1

bond orders, 131, 300–7, 312, 344, 371, 416 bond path, 311

bond stretching term, 43, 45, 75 bond stretching parameters, 73 books, 455–7

Born, M., 20–3, 38, 44, 69, 81

Born interpretation of the wavefunction, 95,

97

Born–Oppenheimer approximation, 20–2, 38, 44, 81, 113, 168

Boyd, R., 418 Brownian motion, 88 Brown, S. W., 413 Busch, D. H., 424

C

calculating heats of formation, 275-89 calculating the Fock matrix, 198–201 calculating the Hückel c’s and energy levels,

determinant method, 135–9 calculating the integrals (ab initio), 194–7 calculating the orthogonalizing matrix,

143-5, 197-8

calculation of entropies, 266, 281 canonical molecular orbitals, 98, 167 Cayley, A., 101

CHARMM, 58–59 CNDO, 344–6

complete active space SCF (CASSCF), 247–8, 251, 451

complete basis set methods, 229, 260, 274–5 complete neglect of differential overlap see

CNDO

computational chemistry, 1-2, 58, 81 outline of, 1–7

quantum mechanics in, 81-153 configuration interaction (CI), 237, 242-8,

251

correlation energy, 233-5

coulomb integral, 117–18, 152, 169-70, 177, 398

Coulson, C. A., 111, 263, 340

coupled cluster method (CC), 237, 247, 248, 251, 261, 411, 436, 437

cyclobutadiene, 126, 130 cyclobutadiene dication, 130–1 cyclopropylidene, 286

D

Dalton, J., 87

de Broglie, L., 92

de Broglie equation, 92 delocalization energy, 130 Democritus, 87

density functional calculations (density functional theory, see too DFT), 3, 385–445

strengths, 436 weaknesses, 436

summary of steps in a calculation, 394–5 density functional transition states, 412 density matrix, 188–9, 203, 205 derivatives on potential energy surface, 11,

16–17

determinant method of calculating simple Hückel c’s and energy levels, 135–9

determinants, 101–9 some properties of, 109

Dewar, M. J. S., 217, 340, 347, 352 DPT energies, 406–13

DFT frequencies, 413–14 DFT geometries, 400–6

DFT method, applications, 399–436 DFT, miscellaneous properties – UV and

NMR spectra, ionization energies, and electron affinities, electronegativity, hardness, softness and the Fukui function, 419–36

DFT, properties arising from electron distribution: dipole moments, charges, bond orders, atoms-in-molecules, 414–19

DFT, visualization, 375–6 Diels-Alder reaction, 61, 248, 451 differential overlap, 342–3

dipole moments,

from ab initio calculations, 297–300 from DFT calculations, 414–16

and MM, 69, 73, 75

from SCF semiempirical calculations, 369–71

and the simple Hückel method, 133 Dirac, P. A. M., 87

and Fermi-Dirac statistics (re DFT), 387 Dirac braket (bra-ket) notation, 141, 186, 392 Dirac equation, 94, 230

Dirac integral notation, 141, 168, 186 direct SCF, 215

double bond and hybridization, 99–101 Doering, W. E., 128

Domeniciano, A., 254 double-zeta basis set, 226–6

E

ECP see effective core potentials effective core potentials (ECP), 229–30 EHM see extended Hückel method eigenvalue equation, 110

Einstein, A., 85 and atoms, 5

and photoelectric effect, 85 and relativity, 87

Eksterowicz, E. J., 59

El-Azhary, A. A., 404

electron affinities, 315–16, 374–5, 423–4 electron correlation, 231–7

configuration interaction (CI) approach to, 242–53

coupled cluster (CC) approach to, 248 Møller-Plesset (MP) approach to, 237–42 and post-HF calculations, 231–53

electron density function, 308–12, 385–7

Index 465

electron diffraction, 98,253–4, 386 electron population, 302–4, 431–5 electron repulsion matrix, 200 electronegativity, 303, 306, 424, 426, 428 electronic structure calculations and bonds,

44

electrophile, 2, 320, 431, 433–5 electrostatic potential (ESP), 307–8 electrostatic potential charges, 307, 372, 416 energy-levels matrix, 115

enthalpy, 263

enthalpy and bond energies, 265 enthalpy change, 265

enthalpy differences, 263

enthalpy of formation (heat of formation), 275

enthalpy surface, 17 entropy, 263,266–7 entropy difference, 263, 266

equilibrium geometry (equilibrium structure), 9, 58, 290

ESP see electrostatic potential ethene

bond order in neutral and anion, 131–2 hybridization, 99–101

neutral, energy levels, 125 radical anion, energy levels, 125 radical cation, energy levels, 125

exchange correlation potential, 393 exchange-correlation energy functional, 394,

396

exchange integrals, 170

extended Hückel calculation, illustration, 146–9

extended Hückel method (EHM), 140–58, 159

applications, 149 strengths, 149–50 theory, 140–6 weaknesses, 150–1

Eyring, H., 17

F

Fermi hole, 233 Fermi–Dirac statistics, 387

Fermi–Thomas model, 387–8

flux density (blackbody radiation), 83 Fock, V., 115

Fock matrix

ab initio, 183, 187, 189 DFT, 395

extended Hückel method, 140–1 semiempirical SCF, 341

simple Hückel method, 115

466 Index

forcefield, 43

developing a forcefield, 45 parameterizing a forcefield, 50 sample calculation with, 54

Foresman, J. B., 249, 288

“formation” method (for heat of formation),

279

four-center integrals, 211 free energy, 74, 263

frequencies, vibrational see infrared spectra, also ab initio frequencies; applications of ab initio method, frequencies; applications of density functional theory; applications of molecular mechanics; applications of SCF semiempirical methods; DFT frequencies.

Frisch, Æ., 249, 288 frontier orbitals, 425 “frozen-nuclei” energy, 17 Frurip, D. J., 263

Fukui, K., 425

Fukui function, 425, 431–6 functional, 388

G

gas-phase unimolecular reactions, 283 Gaussian 94, 274, 412

Gaussian 94 workbook, 249 Gaussian 98, 274, 420

Gaussian functions, 192–3, 211–12 contracted, 212–13

Gaussian programs, 292 Gaussian-2 (G2) methods, 273 Gaussian-3 (G3) methods, 273 Gázquez, J. L., 433

Geerlings, P., 433

generalized-gradient approximation (GGA),

397

geometry coordinate matrices, 28 geometry optimization, 2, 22–9, 33, 38, 57,

64

German Physical Society in Berlin, 84 Gill 1996 (G96) functional, 398 global hardness, 434

global softness, 434

gradient (first derivative) matrix, 27 gradient vector field, 311 gradient-corrected functionals, 397

H

Hall, G.G., 178

Hamilton, W. R., 110

Hammond postulate, 60 hand-held model, 61 hardware, 459 Hargittai, I., 254

harmonic approximation, 290 Hartree, D., 160 Hartree–Fock see too HF

Hartree–Fock calculation (SCF calculation), 160, 164–210

summary of steps, 188, 209

and electron correlation, 232–7, 447

and variation theorem (variation principle),

171

Hartree product, 162 Hartree SCF method, 160–4 heat (enthalpy) of formation

from ab initio calculations, 275–81 from density functional calculations, 411 from molecular mechanics calculations,

58,74

in semiempirical procedure, 348–9 heat of hydrogenation, 454

Hehre, W. J., 230, 260, 268, 289, 399, 415 Hertz, H., 85

Hermitian matrix, 105 Hess, B. A., 135 Hesse L. O., 28

Hessian, 28, 29, 30–2, 61, 230, 310–11, 364, 376, 413

HF determinant, 244–5

HF electronic configuration, 245 HF electronic energy, 190

HF equations, 164–77 meaning, 176–7

Roothaan–Hall treatment, 177–210 example of calculation with, 192–210

HF method

and SCF procedure, 185

re closed shell molecules, 262

HF wavefunction, 171, 179, 242, 244, 246,

248

highest occupied MO (HOMO), 123, 124,

181, 315, 316, 320, 373, 374, 375, 376,

420, 424, 425, 427, 428, 430, 431, 434, 436, 438

Hilbert,D., 107

Hoffmann, R., 123, 124, 140, 146, 147, 149, 150, 152

Hohenberg–Kohn theorem, 388–9, 393, 437 Holder, A. J., 353

Holthausen, M., 387

homoaromaticity, 453–4 homodesmotic reactions, 454

homolytic bond dissociation, 235–7, 271, 407–8

Houk, K. N., 59

Hückel, W., 82, 95, 96, 159, 339 Hückel delocalization energy, 130 Hückel method, extended (EHM) see

extended Hückel method

Hückel method, simple (SHM) see simple Hückel method

Hückel’s rule, 128 Hückel–Fock matrices, 119 Hughes, E, D., 45 Hund,F., 111

hybrid functionals, 398 hybridization, 96–101

I

icosahedral symmetry

imaginary frequencies, 32, 39, 68, 69, 231, 260, 281, 282, 286, 289, 318-19

in-vacuo optimized conformations, 73 inductive effects, 452

infrared (IR) spectra

calculation of, 1, 2, 3, 23, 24, 28, 29, 31, 33, 50, 73, 133, 289–96, 317–18, 364–6, 368, 413

frequencies, factors affecting, 289–92 frequencies, corrections to, 291–2, 364–5,

413

intensities of bands, 292, 366, 368, 413 samples of calculated, by ab initio, 293–4 samples of calculated, by DFT, 414–17 samples of calculated, by molecular

mechanics, 70–1

samples of calculated, by SCF semiempirical methods, 367–70

Ingold, C. K., 45

intermediate neglect of differential overlap (INDO), 346

intrinsic reaction coordinate (IRC) see reaction coordinate

ionization energies, 315, 374–5,423–4 IR spectra see infrared spectra

IR spectrum of 1-propen-2-ol, 23 IRC (intrinsic reaction coordinate) see

reaction coordinate Irikura, K. K., 263

isodesmic reactions, 268, 270–2, 280–1, 410 isoozone, 14–15

Index 467

J

J integrals (coulomb integrals), 169 Jacobi (rotation method) matrix

diagonalization, 107, 118 Jahn–Teller effect, 126

K

K integrals (exchange integrals), 170 Kekulé structures of benzene, 130 kinetics, 281–7, 362–4, 411–13 Knox,L. H., 128

Koch, W., 387, 391

Kohn, W., 346, 386

Kohn-Sham (KS) approach, 388–99, 437 Kohn-Sham energy, 390–3

Kohn-Sham energy and equations, 389–94 Kohn-Sham equations, 393–4, 437

solving, 394–6

Koopman’s theorem, 315–16, 423 Kronecker, L., 116

Kronecker delta, 116, 143, 344 KS Fock matrix elements, 395 KS operator, 394

L

Lagrange, J. L., 109

Lagrange expansion of determinants, 109 Lagrangian multipliers, 171–2

Laplacian operator “del squared”, 94

LCAO (linear combination of atomic orbitals), 111, 139, 143,151–2,178, 183, 185, 190, 201, 209, 211, 223, 247

Lenard, P., 85 Lennard-Jones, J. E., 111

Levine, I. R., 33, 37, 82, 165, 210, 230, 341, 355, 387, 388, 394, 399, 456, 457

Lii,J.-H., 69 Lipkowitz, K. B., 61,73 Literature, 447–62

local density approximation (LDA), 396–7 local spin density approximation (LSDA),

397

Lou,L., 399, 415

Löwdin, P.O., 144 Löwdin method

for charges and bond orders, 307 for bond orders, 308, 416

Löwdin orthogonalization, 144

lowest unoccupied MO (LUMO), 124,181, 315, 320, 322, 323, 373, 420, 424, 425, 427, 428, 430, 431, 434, 436, 438

Lummer–Pringsheim curve, 84

468 Index

M

Mach, E., 5, 87

macroscopic balls and springs model, 9–10 many-body problem, 162

Marcelin, R., 20

Marcus, R., 20 Martell, J. M., 408 matrices, 101–8

some important kinds of, 104

matrix diagonalization, 30, 107, 116, 118,

135, 139

matrix orthogonalization, 150

Maxwell’s equations of electromagnetism, 89 Maxwell’s laws, 89, 151 Maxwell-Boltzmann kinetic theory, 87 mechanical calculators, 208

Méndez. F., 433

Merck Molecular Force Field (MMFF), 58,

69

Merrill, G. N., 406, 412 metal binding ability, 61

microwave spectroscopy, 253–4 minimal basis set see STO-3G minimal valence basis set, 141 minimization of energy, 172 minimum-energy geometry, 43, 205 model-building program, 28 modern ab initio programs, 210

molecular dynamics methods, 3, 5, 282 molecular dynamics and Monte Carlo

simulations, 63–4

molecular mechanics calculations (see too MM), ix, 2, 3, 4, 5, 9, 28, 37, 43–79, 81,

132, 231, 253, 283, 322, 339, 340, 351, 355, 361, 385, 399, 411, 456, 457 strengths, 72–3

weaknesses, 73–4 MM, applications, 57–72

forcefields, 61 frequencies, 68–72 geometries, 64–8

geometries and energies, 57–61 in organic synthesis, 61–3

MM programs, 45, 69, 73 MNDO, 349–52, 363 MNDOC, 363

“molecular basis set” (Dewar), 351 molecular dynamics, 63–4 molecular energy, 167

molecular geometries (determination, problems with), 253–4

molecular Hamiltonian, 110

molecular orbitals, ix, 73,107,151–2 basis function expansion of, 177–85, 211 canonical, 167

and electron density function, 387 delocalized, 98, 167

Kohn-Sham, 390, 392, 424

as linear combinations of AOs (LCAO),

111

localized, 167, 355

minimizing energy with respect to, 167,

171–5

nodes in, 122–4

as one-electron functions, 283 orthogonality of, 116

and photoelectron spectra, 115 SHM, pattern from, 127–9

as Slater determinants, 164–7 as vectors in Hilbert space, 107 virtual, 223, 238, 240–1, 244–8 visualization of, 320–1, 375–6

molecular orbital method (vs. valence bond),

95

Møller-Plesset approach, 237–241 Monte Carlo methods, 63–4 Mortier, W. J., 431–2

MP calculations see Møller-Plesset approach Mulliken, R. S., 111

Mulliken bond order, 304 Mulliken charges, 304 Mulliken electronegativity, 427

Mulliken population analysis, 301–7 multiconfigurational SCF (MCSCF), 247 multireference CI (MRCI), 248

N

N6, 450

natural atomic orbitals (NAO), Weinhold population analysis, 307

NDDO-based methods, 346–8 NDO methods, 344

Newton’s laws of motion, 63, 89 Nguyen, L. T., 434–5

Nichols, J., 216

nitrogen pentafluoride, 449 NMR shielding, 455

NMR, ix, 1, 99, 313–15, 318, 373,422, 455 nodal properties of MOs, 122–4 nonbonded interactions, 48–50, 52–3, 54,

56, 75

nonbonding orbital, 126 noninteracting reference system, 390 nonmonochromatic radiation, 83

normal-mode vibrations, 29–30, 38, 289 nuclear atom, 82,87–9, 151

O

orbitals (see too atomic, molecular orbitals), as an approximation, 95

Oppenheimer, R., 21

optimization (geometry) algorithm, 25–9, 38 organic synthesis, 61, 75

origins of quantum theory, 82–6 orthogonal matrices, 106–7, 144, 148 orthogonalization, 144

orthonormal matrix, 106 Ostwald, W. F., 5, 88

overlap integrals, 115, 134, 140, 143, 146–7, 150, 171,194,197, 209, 302, 304, 342–5, 350, 378

overlap matrix, 115–7, 140, 143–7, 151–2, 184, 197, 301, 304, 341, 342–5, 350, 394

overlap population (Mulliken), 302–4 oxirene, 447–9

ozone, 14–15, 261–2

P

parameterizing (parametrizing)

DFT functionals 386, 388, 397, 399, 400, 406, 408, 437–8

re extended Hückel method, 150, 153 a molecular mechanics forcefield, 50

SCF semiempirical methods, 340, 343–55, 373, 376–8

Pariser–Parr–Pople method, see PPP Parr, R.G., 387, 392, 424, 431 Pauli, W., 94

“Pauli correction”, 177

Pauli exclusion principle, 166, 170, 176, 244 Pauling, L., 96

Pearson, R. G., 424, 428 penetration integral, 346 Perrin, J., 87

perturbational DFT method, 414 perturbational theory, re (MP)

calculations, 237

PES see potential energy surface Peterson, M. A., 61

photochemical processes and orbitals symmetry, 123–4

photoelectric effect, 82, 85–6, 151 photoelectron spectroscopy, 98 Planck, M., 84

Planck equation, 84, 92

Index 469

Planck’s constant, 84, 86, 89–90, 159, 161, 283, 339

Plesset, M. S., 237

“plum pudding” model, 88

PM3, 353, 359, 360–4, 365, 370, 406, 417 Polanyi, M., 20

polar coordinates, 94

polarization functions, 224, 240, 291 polarization, of carbonyl group, 452 Pople, J. A., 216, 238, 260, 346 positivist school of Ernst Mach, 5, 87 post-HF calculations, 231–53

potential energy surface (PES), concept, 9–41

potential energy hypersurface, 11 PPP, 341, 343–4

probability density function see electron density function

properties arising from electron distribution ab initio methods, 296–312

DFT methods, 414–19

SCF semiempirical methods, 368–73 pseudopotentials see effective core potentials pyramidane, 449–50

Q

quadratic CI (QCI) method, 247–8 quantitative structure-activity relationships

(QSAR), 59 quantum chemistry, 81

quantum mechanical calculations, 75, 117 quantum mechanical methods, 3–4, 95,159

R

radioactivity, 82, 86–7, 151 Radom, L., 260, 291 Raman spectra, 292

reaction coordinate (intrinsic reaction coordinate, IRC), 14–16, 281

reaction energies

and potential energy surface, 33–4 ab initio, 263–7, 268–72 (see too

thermodynamics; high-accuracy calculations, also thermodynamics; calculating heats of formation)

DFT, 407–11 semiempirical, 362–4

relativistic effective core potentials, 230 relativity, 82, 87, 151, 258

resonance effects vs. inductive effects, 452

470 Index

resonance energies (simple Hückel method), 129

“resonance structures” 130

restricted Hartree-Fock (RHF) method, 210 restricted open-shell Hartree-Fock (ROHF)

method, 210 Roothaan, C. C. J., 178 Roothaan-Hall equations

deriving, 177–83

using for ab initio calculations – the SCF procedure, 183–210

using for ab initio calculations – an example, 192–209

summary of steps in an SCF calculation using, 209–10

Rutherford, E., 88

S

saddle point, 16, 18–20 St. Amant, A., 401, 408 Salzner, V., 424

SAM1 (semi ab initio method number 1), 354 SCF procedure, 150, 163–4, 183–210

and semiempirical methods, 340

basic principles in semiempirical methods, 340–55

semiempirical energies (vs. ab initio energies 361–2)

semiempirical calculations, SCF, 339–83, 385

energies, 361–4 frequencies, 364–70 geometries, 355–61

miscellaneous properties – UV and NMR spectra, ionization energies, and electron affinities, 373–5

properties arising from electron distribution: dipole moments, charges, bond orders, 368–73

strengths, 377 summary, 378 visualization, 375–6 weaknesses, 377

semiempirical calculations, non-SCF (simple Hückel and extended Hückel), 95–158 simple Hückel method (SHM), 82, 95–139

theory, 109–22 applications, 122–33 determinant method, 135–9 strengths, 133–4 weaknesses, 134–5

Schaad, L. J., 135 Schaefer, H. F., 447

Scheiner, A. C., 400, 408 Schleyer, P. v. R., 45, 260 Schoenfliess point groups, 33

Schrödinger equation, 2–4, 21,81–6, 87, 91, 93–5, 109–10, 151, 161, 175, 177, 211, 323–4, 339, 385–6, 419–20

Schrödinger equation for one-dimensional motion, 93

Scott, A. P., 291

second-derivative matrix (Hessian), 28 secular equations, 114, 136

Sham, L.J., 391

Simons, J., 216

simple harmonic motion, 290

single determinant wavefunction, 235–6, 246 single point calculation, 241–2

Slater, J., 164

Slater determinants, 164–7, 168, 170, 177, 179, 210, 244, 262, 323–4, 398, 424

Slater functions (Slater orbitals), 192, 211, 342, 349

software, 457–9 orbitals, 99–100 orbitals, 99–100 SPARTAN, 58, 413 special relativity, 87

time dilation principle, 92 spin-orbit coupling, 258

split valence basis sets, 222–6

stabilization energy (simple Hückel method), see resonance energy

“stable species”, 268 “standard” geometry, 57

stationary points, 13–20, 29–33, 38 minima, 16–17

saddle point, 16–17, 18–20 Stephens, P. J., 406

STO-1G, 213, 216, 238 STO-3G, 212–13, 216–22 Storch, D. M., 217 Stowasser, R., 424

strain energies, 74 Streitwieser, A., 452–3

stretching and bending terms, 56 supercomputer performance, 460 symmetric matrix, 105 symmetry axes, 34

symmetry elements, 35–6 symmetry, 33–8

T

tetrahedral symmetry, 37 “the HF energy”, 191

theory of atoms-in-molecuies (AIM), 308 thermodynamics, 263, 265, 268, 272, 275,

287, 362, 407

thermodynamics; calculating heats of formation, 275–81

thermodynamics; high accuracy calculations, 272–5

Thiel.W., 355 Thomas, L. H., 387

Thomas–Fermi model, 388 Thomson, J. J., 88 three-center integrals, 211

time-dependent density functional theory (TDDFT), 95, 419–29

time-dependent Schrödinger equation, 95, 419–20

time dilation principle of special relativity, 92 time-independent Schrödinger equation, 95 torsional term, 47, 52

transition state, 1, 14–15, 17, 29, 32, 59, 73, 265–6, 405

from ab initio calculations, 242–3, 260, 263–4, 267, 281–6, 289, 318–19, 322, from DFT calculations, 404–7, 411–13,

436

from MM calculations, 59–61

from semiempirical calculations, 355, 360–1, 363–5, 377

vs. transition structure, 17 transition structure, 17

two-electron repulsion integrals, 186

U

unimolecular reactions, 267, 281–7 unrestricted Hartree-Fock (UHF) method,

210

UV spectra

from ab initio calculations, 313 from DFT calculations, 419–21

from semiempirical calculations, 373–4

V

valence bond (VB) method, 95 van der Waals radii, 99

van der Waals surface of molecule, 21,132 vibrational frequencies see infrared spectra, also ab initio frequencies; applications of

ab initio method, frequencies; applications of density functional theory; applications of molecular mechanics; applications of SCF semiempirical methods; DFT frequencies

Index 471

virtual molecular orbitals, 223, 238, 240–1, 244–8

visualization, 316–22, 375–6, 436

W

wave mechnical atom, 82, 91–5 wave mechanics, 91–2

see too LCAO and molecular orbitals

as depending on coordinates and parameters, 95

as Hartree product, 162, 164 meaning of, 94

normalized, 139, 149

theory vs. density functional theory, 385–6, 423–4

“wave-particle duality”, 92 Weinhold, F., 307 Westheimer, F. H., 45

Wien blackbody equation, 92 Wolff rearrangement, 63 Wolfsberg, M., 140 Woodward, R. B., 124

Woodward–Hoffmann orbital symmetry rules, 123–4, 150

Worldwide Web, 457

X

X-ray diffraction

Y

Yang, W.J., 387, 392, 424, 431–2

Z

ZDO (zero differential overlap), 343 Zeeman effect, 91

zero matrix, 105

zero point energy (ZPE, zero point vibrational energy, ZPVE), 9, 31–4, 69, 191–2, 235–6, 251, 263–4, 266, 268–70, 273–4, 277, 283–4, 287–8, 349, 361–4, 405, 408–9, 413, 435

corrections to, 291–2 ZINDO/S, 376

Z-matrix (internal coordinates), 25