Rogers Computational Chemistry Using the PC

INDEX

Matrix, 31 addition, 31 algebra, 31

as operator, 207 complex, 42 diagonalization, 51 element, 31

formalism for two masses, 138 inversion, 51

inversion and diagonalization, 51 mechanics, 39

multiplication, 33 powers and roots, 35 rank, 38 transformation, 41

Maxwell Boltzmann distribution, 20 Median speed, 21

Medical statistics, 17 Methane, 89

Method of least squares, 60 Methylenecyclopropene, 226 Methylenepentadiene, 225 Minimal, 100, 108

basis, 242 Minimization, 63, 99, 105

parameter, 63 minimize, 150, 154

MM3, 100 ff, 107, 117, 148, 154, 157, 162 parameters, 117 ff

MM4, 147 MMFF94, 112, 127 MNDO, 279 Molality, 78, 79

Molecular energies, 301 mechanics, 93, 98, 131 orbital, 175, 299 speeds, 19

Moment of inertia, 106, 108 MOPAC, 281, 283

MP2, 313

MP4, 313 Multivariate, 45

least squares analysis, 80

Naphthalene, 226, 290, 291 NDDO, 279 Newton-Raphson

generalization, 144 method, 7

Nitrogen, 284

Nodes, 171

Nonhomogeneous vector, 46, 185 Nonsingular matrix, 51

347

Normal

coordinates, 136, 285, 288 curve, 15

equations, 64, 82 modes, 137

modes of motion, 136 Normalized, 16

Number density, 3 Numerical integration, 9, 24

Odd function, 120 Operator, 173

Optimization, 99, 143, 292, 300, 308 Orbital, 179, 323

approximations, 176, 237, 265 Orthogonal matrix, 40 Orthonormal transform, 206 Orthonormality, 184

Output file, 103 Overdetermined set, 81 Overlap integral, 183, 220

PALA, 91 Parameterization, 113, 280

semiempirical, 281 Parameters, 97, 117, 251 Partial molal volume, 77

of ZnCl2, 77

Partial molar volume, 78, 79 Particle in a box, 170 Partition function, 146

contribution, 146 Pauli principle, 255, 267

PCMODEL, 112, 127, 149, 155, 283 Permutations, 271

Peroxide complexes, 52 Phenantherene, 291 Photoeolectron spectruma, 323 Photon, 2, 3

Pi electron calculations, 155 Planck radiation law, 4 PM3, 279

Polarized functions, 311 Polarographic reduction, 225 Polyatomic molecules, 97, 288 Polynomial, 8, 68

equations, 36 higher degree, 68

POP, 151

Pople, J. A., 306 Population, 14, 215

energy increments, 151 Postmultiplication, 33

348	COMPUTATIONAL CHEMISTRY USING THE PC

Potassium fluoride, 74

Potential energy, 97, 120,122, 126, 174 function, 123

well, anharmonic, 302 well, harmonic, 302

Powers and roots of matrices, 35 PPP, 248

-SCF, 248, 249, 256 Premultiplication, 33 Primitives, 242, 310 Principal axes, 43 Prismane, 326 Probability density, 23 Propene, 111, 316, 325 Pyridine, 228

QCISD(T), 312

QMOBAS, 194 QSIM, 18

Quadratic functions, 65 Quadrature, 9

Quantum mechanics, 23 number, 171

Radiation density, 3 Rank, 37, 38 Rayleigh frequency, 3 Reduced mass, 95 Regression, 70 Reliability

of fitted parameters, 70

of fitted polynomial parameters, 76 Residual, 69, 86

Resonance, 155 energy, 157, 217

of benzene, 157 integral, 185

Root, 6, 7, 139, 187, 234, 254, 274 Roothaan Hall equations, 278 Rotamers, 128

Rotation matrix, 188, 191 Row operations, 51 Rydberg equation, 76

Sample, 14

Scalar, 33

Scale factor, 306 SCF, 231, 236, 241

ultraviolet spectral peaks, 256 dipole moments, 258

energies of first row atoms and ions, 240 matrix, 252

Schroedinger equation, 169

approximate solutions, 172 exact solutions, 170

Secular determinant, 6, 186, 203, 274 equations, 134, 185, 203

matrix, 7, 186 elements of, 232

Semiempirical, 248, 263

small molecules HF to HI, 284 methods, 248

model, 97 approximations, 279

SHMO, 223, 225

Sigmaplot, 25 Significant figures, 84 Similar matrices, 42, 192

Similarity transformation, 287 Simpson’s rule, 9, 10 Simultaneous analysis, 52

analysis by visible spectroscopy, 83 equations, 51, 64

probabilities, 60 spectrophotometric analysis, 52

Singular matrix, 38, 46 Slater determinant, 255, 269 Slater orbital, 221 Slater-type orbital, 237, 238 Slope, 65

matrix, 83 Solvation, 73 Space, 3 Span, 44

Special matrices, 39 Spectrophotometry, 52

transitions, 197, 253 Spectrum, blackbody, 3 Speed, 19

Spin, 268 correlation, 273

Spinorbital, 255, 268 Spline fit, 27 ff

Split valence basis sets, 310 Spreadsheet, 25

Standard deviation, 14, 72 of the regression, 77

Standard hydrogen electrode, 68 Statement number, 5

Stationary point, 300, 308

Statistical criteria for curve fitting, 69 Statistics, 14

Steric energy, 98 104, 161 STO-1G ‘‘Basis Set’’, 243 STO-2G, 245

STO-3G, 241 247, 300

INDEX

Stochastic search, 159, 166 STO-xG, 240, 242

Strain energy, 158 Strainless

bond energies, 145 parameters, 145

Stretching mode, 115 Styrene, 168, 225

Sums in the energy equation, 115 Superpositions, 135

Symmetric matrix, 40 Symmetry, 305 Synchronous mode, 137 System, 13

TableCurve, 24, 69, 70, 71 Taylor

series, 141 expansion, 115

THC, 322

Thermodynamic functions, 319 TINKER, 108 ff, 148 TMOBAS, 194

Tobacco smoke, 291 TORS, 151 Torsion, 118

modes of motion, 153 Total energy (GAMESS), 325 Trace, 40, 221 trans-But-2-ene, 148 Transformation matrix, 41 Transpose, 39

Triangular matrix, 40 Tridiagonal matrix, 40 TrueBASIC, 6, 196 Tryptophan, 88 Two-Mass Problem, 95 Tyrosine, 88

TZV, 317, 319

349

Uncertainty, 87

Uncoupled equations, 136

Unit matrix, 34

Unitary matrix, 42

Unitary transformation, 42

Upper bound, 309

Upper triangular matrix, 48

Valence bond approximation, 177 van der Waals Energy, 122 Variance, 86

Variational calculation, 236 method, 178, 181

treatment of the hydrogen atom, 181 VB, 177

Vector, 40 space, 44, 201

Velocity, 19

VESCF, 156 Vibration

of nitrogen, 284 Vibrational spectrum, 301, 302 Virtual orbitals, 256

Wave function, 22

mechanics, 39

What’s going on here?, 42

Why so much fuss about coupling?, 143 Wien’s law, 4, 6

Zero point energy, 162, 303

ZPE, 303

Z-Score, 18

b, 198, 257 gij, 257 p-electron, 176