concise physical chemistry (rogers/concise physical chemistry) || index

P1: OSOind JWBS043-Rogers September 24, 2010 12:57 Printer Name: Yet to Come

INDEX

1s STO and a Gaussian approximation,324

6-31G basis functions, 332

Ab Initio methods, 324Absorption wavelengths, 293

of conjugated polyalkenes, 293Acetic acid, 69Acetone, 196, 200Acetonitrile, 159Acidity constant, 209, 215Activated complex, 350, 355

enthalpy level diagram, 157structure, 355

Activation, 351activation barrier, 156, 157, 351

Activation energy, 344Activity, 97, 186

activity coefficient, 98, 186Additive extrapolations, 339

the G3(MP2) scripted method,339

Additive methods, 305Adenosine 5′-triphosphate ATP, 105Adiabatic work, 50

ADP, 107Ag ions, 212, 216–217Alkane conformers, 308Allinger MM method, 308Allinger, 64Ammonia, 82, 195, 201AMP, 107Amperostat, 215–216Amplitude function, 238, 249Anode, 223Antioxidants, 347Antisymmetric wave functions, 239Antisymmetrized orbitals, 240Arclength, 40Arrhenius law, 158, 349Atomic units, 243ATP, 103–104, 107Aufbau principle, 280Autooxidation, 346Avogadro, 3Azeotrope, 138

Bar (unit), 13BASIC, 83Basis function, 245, 320

Concise Physical Chemistry, by Donald W. RogersCopyright C© 2011 John Wiley & Sons, Inc.

369


370 INDEX

Battery, 221Benzene, 342Benzoic acid, 68Bimembrane, 167Bimolecularity, 155Binary solutions, 184Body-centered cubic cell, 180Bohr, 236, 264Boiling point elevation, 188Boltzmann 101, 108Boltzmann constant, 9Boltzmann distribution of molecular speeds,

158Bond additivity, 306Bond breaking, 350Bond dissociation energies (BDE), 348,

355, 358Bond energy, 65Bond enthalpies, 306Bond length, 292, 299Bond making, 350Bond moments, 296

dichloroethene isomers, 296Bond strength, 292, 299Born probability postulate, 252Born, 237Born-Haber cycle, 178–179Bosons and Fermions, 278Boyle, 1Bragg’s law, 173Bravais crystal systems, 176Bravais lattices, 176Breaking degeneracy, 259

Cadmium half-cell, 232Calculated ionization potentials,

281Calomel electrode, 229Calorie, 54Calorimeter, 104Calorimetry, 56Capacitance, 294Capillary rise, 167Carbon dioxide, 34, 86

free energy of formation, 87Carbon disulfide, 91, 92Carnot, 71Carnot’s engine, 72Cartesian space, 330

Cathode, 217, 223Cell diagrams, 223Cell reaction, 223Central field approximation, 239Cerium, 234Chain reaction, 153, 345–346

initiation, 346propagation, 346termination, 346

Charge distribution, 241Charles, 1Chemical kinetics, 144Chemical potential, 87

nonideal systems, 100, 102pressure dependence, 87temperature dependence, 88–89

Chemical reactions, 78, 79Chloroform, 200Clapeyron equation, 128Classical harmonic oscillator, 288Classical molecular modeling, 305Clausius, 71Clausius–Clapeyron equation, 128Close packing, 171Closed system, 41Coexistance curve, 127Colligative properties, 187, 194Collision theory, 158Combined gas law, 2, 12Combined or scripted methods, 338Combining enthalpy and entropy, 84Combustion of C(gr) and CO(g), 59Combustion, 92

free energy of, 92of methane, 92

Components, 124Components, phases, and degrees of

freedom, 124Compound phase diagrams, 137Compressibility factor, 20, 21, 28

calculated from the van der Waalsconstants, 28

Computational chemical script, 338Computational geometries, 177Computational kinetics, 159Computational statistical thermodynamics,

119GAUSSIAN 03 C©, 119

Computational thermochemistry, 100


INDEX 371

Computed partition functions, 120for molecular and atomic sodium, 120

Computer files, 273Concentration cells, 225Concentration units, 184Conductance cell, 206Conductance, 205, 211Conductivity, 203, 205Conservation laws, 35

exact differentials, 35Conservtive systems, 238Contracted Gaussian orbitals CTGO, 328Conversion of a Liquid to Its Vapor Without

Boiling, 25Copper electrode, 221Correlation energy, 337Corresponding states, 23, 27Coulomb (unit), 224Coulombs, 212Coulometry, 203Covalent bond radii, 176Critical density, 26Critical point, 25, 127Critical temperature, 24Cross term, 310Crystal forces in MM, 312Crystals, 170CTGO, 328Cubic (crystal) cell, 175Cubic equation, 28, 29Cubic real gas behavior, 34Curve-fitting software, 21

Dalton’s Law, 5Daniell cell, 220de Broglie, 235Debye-Huckel law, 213Degeneracy, 257

and equilibrium, 109Degenerate two-level equilibrium, 110Degree of dissociation, 208Degree of ionization, 208Degrees of freedom, 4, 124Density functional theory (DFT), 338Density ρ curves, 26

for liquid and gaseous oxygen, 26Dependent variables, 4Detailed balance, 152Determinantal wave functions, 240

Deviations from Raoult’s law, 185Dewar, 323Diatomic molecules, 290Dielectric constant, 294Dielectric, 294Diethyl ether, 196Different paths of transformations, 38Differential scanning calorimetry, 66Digression on “Space”, 9Dipole moments, 294, 301, 303Dipole, 294Discontinuous energy levels, 8Disorder, 74, 109, 183Distortion polarization, 295Distribution, 110DSC, 66

Early atomic theory, 235Early quantum theory, 236Ebullioscopic constant, 190Effective molecular weight (molar mass), 28Effective nuclear charge, 240Effective quantum number, 282Egyptian tomb, 163Eigenfunction postulate, 252Eigenvalues and eigenvectors, 250Einstein, 247Einstein’s law, 344Electrical potential, 203, 204Electrical work, 224Electrochemical cells, 220Electrochemical potential, 221Electrolyte, 203Electromagnetic spectrum, 235Electron spin resonance, 299Electronic promotion in alkenes, 293Electronic spectra, 292Empirical equations, 18Empirical gas laws, 1Energy and enthalpy, 44Energy equations, 308, 309Energy of formation, 57

indirect, 59Engine, 72Ensemble, 6, 7Enthalpies of formation of n-alkanes, 306Enthalpies of reaction, 60Enthalpy level diagram for an activated

complex, 157


372 INDEX

Enthalpy of activation, 351Enthalpy of formation, 57, 64

from classical mechanics, 64indirect, 59of hydrogenation, 61, 65–66

Enthalpy of fusion, 92, 200Enthalpy of vaporization, 129Enthalpy, 305Entropy, 71, 99, 113

and probability, 113and the second Law, 71from the van’t Hoff equation, 99

Entropy changes, 74chemical reactions, 78expansion, 75heat transfer, 77heating and expansion, 75heating, 74mixing, 77of transition, 75

Entropy of activation, 354Entropy, enthalpy, and Gibbs free energy

changes for mixing, 183Equations of state, 4Equilibrium, 93, 94, 108

and free energy, 99Equilibrium constant Keq , 73, 97

as a quotient of quotients, 88statistical approach, 117

sodium vapor, 117variation with temperature, 97

Equilibrium, 108Equilibrium, 94, 108

general formulation, 94Euler’s reciprocity relationship, 36,

76Eutectic mixture, 137Exact differentials, 36Excluded volume, 29Expectation value, 17Experimental determination of molecular

structure, 287Experimental determination of the rate

equation, 154Extensive variable, 6Extent of reaction, 96Extrapolation to E◦, 226, 227Eyring reaction path, 350Eyring theory of reaction rates, 349

Failure of perpetual motion, 39Faraday (unit), 211Faraday, 205Faraday’s laws, 211Favorable and unfavorable orbital overlap,

263First law of thermodynamics, 35–36First-order radioactive decay, 146First-order rate laws, 144–145Flash photolysis, 154Fluid, 25Fluorescence, 160–161, 345

mechanism of, 346Force constants and parameters, 308Force fields, 308, 310Frankenstein, 220Free electron model, 292Free energies of formation, 85Free energy and equilibrium, 102

in biochemical systems, 102Free energy, 87

of reaction, 87of formation, 90of methane, 90

Free solvent, 194Freezing point of water, 195Fugacity, 97

coefficient, 98Fundamental thermodynamic identities,

86Further basis set improvements, 336

G3(MP2), 338Gain medium, 348Galvani, 220GAMESS, 330, 340

calculation of methane, 340control lines, 341file for the hydrogen molecule, 330

Gas constant, 13Gaussian approximation, 272Gaussian basis set, 324Gaussian distribution, 7

in hyperspace, 10Gaussian distribution, 7Gaussian gen input, 273

for the hydrogen atom, 273energies, 273

GAUSSIAN C© input for hydrogen, 330


INDEX 373

Gaussian probability density distributions,10

Gaussian, 69GAUSSIAN C©, 69, 244

HF calculation of E , 273Gibbs chemical potential, 133, 192Gibbs free energy, 84, 112

and the partition function, 112of water, 126

Gibbs thermodynamic function, 76Gibbs–Helmholtz equation, 89Glass electrode, 230Glucose, 69Gordon, 323Graham’s Law of effusion, 6

molecular weight (molar mass)determination, 6

Group additivity, 62, 306hydrogen atom counting, 63

n-octane, 69GUI, 310

Half cells, 221Half-cell potentials, 222Half-time, 146Hamiltonian operator, 237, 251Harmonic oscillator, 287Hartree (unit), 272Hartree and Fock, 239Hartree equations, 242Hartree independent electron method, 240Hartree product, 263Hartree-Fock limit, 336Heat capacities and γ for selected real

gases, 48Heat capacity, 44, 48, 70

as a function of temperature, 50, 168of an ideal gas, 48

Heat capacity of liquids and solids, 168Heat death, 73Heat transfer, 77Heisenberg, 237Heitler and London, 238, 239Helium, 81, 243, 274Hemolytic cleavage, 348Henry’s law, 186Hermitian operators, 269Hess’s law, 61Heteroatoms: oxygen, 332

Hexa-1,3,5,-triene, 81Hey, Let’s Make a Perpetual Motion

Machine!, 38HF, 329Higher molecular orbital calculations, 322Hittorf cell, 211, 216HOMO, 285, 292Hooke’s law, 289Hooke’s potential well, 289Huckel, 271Hydrogen atom, 244, 258, 325Hydrogen emission spectrum, 236Hydrogen half-cell, 222Hydrogen molecule ion, 319

bonding and antibonding orbitals, 321,322

Hydrogen molecule, 329Hydrogen spectrum, 235Hydrogen-like atoms, 260

for an electron in the 3s orbital, 262higher exact solutions, 260radial probability density, 262roots of the radial 3s wave functions, 261the first six wave functions for hydrogen,

261the first three s wave functions for

hydrogen (simplified form), 261Hyper space, 3-, 4-, etc., 10

Ideal gas laws, 1Ideal solutions, 182Independent variables, 4, 125–126

coexistence curves, 125Influence of temperature on rate, 156Intensive variable, 6Intermolecular attraction at an air–water

interface, 166Internal and Cartesian coordinates, 334Interplanar (crystal) distances, 173Invasive crabs, 163Inversion of optical activity, 352Inversion temperature as a function of

pressure, 47Iodine vapor, 122, 123Ion activities, 213Ion mobilities, 209, 210, 211Ion speed, 210Ionic character, 297Ionic strength, 214


374 INDEX

Ionization potential IP, 274of helium, 284

Ion-permeable membrane, 204Irreversible change, 72Isobar, 26Isodesmic reactions, 349, 356Isolated system, 41Isotherm, 24

of a van der Waals gas, 24Iterative procedure, 241

Joule and Joule–Thomson experiments, 46Joule (unit), 42Joule, 46, 50

KCl, 62Kinetic energy, 7Kohlrausch’s law, 206

L-(dihydroxyphenyl)alanine, 218Laplace transforms, 149Lasers, 348Lattice energies, 177Law of corresponding states, another view,

27LCAO, 320L-Dopa, 218Le Chatelier’s principle, 99Lead, 83Length of an Arc, 40Limiting law, 214Line integrals, 39, 52–53Line spectrum, 235, 246Linear and angular momentum vectors, 283Linear combination, 270Linear combinations of atomic orbitals

LCAO, 322Lipid peroxidation, 346Liquids and solids, 165Liquid–vapor coexistence curve, 127Logarithmic decay of a radioactive element,

147LUMO, 285, 292

Magnetic resonance imaging (MRI), 299Making ATP, the cell’s power supply, 103Many-electron atomic systems, 263Mathcad C©, 52, 246Maxwell, 108

Maxwell-Boltzmann distribution, 7, 8, 13Mean activity coefficient of HCl, 232Mean ionic activity coefficients, 229Membrane potential, 203Methane, 331Methanol, 332

finding the enthalpy of formation,334–336

Methyl isocyanide, 159Microstates, 112Microwave spectroscopy, 292Mixing, 77MKS system, 2, 213MM series, 309

input file for water, 314thermodynamic properties, 311

MM4, 315geometry output for water, 315input geometry for methane, 316output geometry for methane, 316

Mobility, 211Models, 307Moeller-Plesset energies, 337Molality, 184, 197, 198Molar conductivity, 206

at infinite dilution, 207Molar heat capacities, 48Molar mass of a nonideal gas, 28Molar volume, 16, 33, 129Molarity, 198Mole fraction, 6, 184Molecular enthalpies of formation, 58Molecular mechanics, 309Molecular modeling, 310Molecular orbitals, 328Molecular quantum chemistry, 238Molecular variational method, 318Molecular velocities, 12Molecular weight (molar mass)

determination, 6Moles, 3Momentum, 15Moving boundary method, 210

NaCl conductivity, 219Naphthalene, 68NDDO and related approximations, 323Nernst equation, 224Newton’s second law, 14


INDEX 375

Nitric oxide, 358Nitrogen, 21, 222Nitrogen dioxide, 148Nitrogen tetroxide, 105NMR spectrum of ethanol, 299Nodes, 254

three wave functions, 254Born probability densities, 255

Nonideal binary solutions, 131Nonideal systems, chemical potential, 100Nonvolatile solute, 189Normalization, 257NSTP new standard temperature and

pressure, 16Nuclear magnetic resonance (NMR), 297,

304

Occupation number, 11Open system, 41Operator, 237Optical activity, 352Optical inversion, 352Optimizing the Gaussian function, 272Orbitals, 257Order and molecularity, 155Orientation polarization, 295Orthogonality, 262, 264

and overlap, 262Osmotic presure, 191, 192, 202Oxygen bomb calorimetry, 68Ozone depletion, 347Ozone hole, 156, 347Ozone, 155

Packing fraction, 174Parabola, 52Parabolic potential well, 290

of the harmonic oscillator, 290Parallel plate capacitor, 294Parametric curve fit, 19Partial GAUSSIAN G3(MP2) output, 339Partial ionization, 208Partial MM4 enthalpy output for ethane,

311Partial molar thermodynamic functions, 133

the general case, 133Partial molar volume, 129

as a slope of V vs n, 131the general case, 132

Partial pressure, 5, 6, 186, 195Particle in a cubic box, 255

the first excited state, 257Particle in a one-dimensional box, 253

energy, 265fundamentals and overtones, 254

Partition function, 10, 108, 111, 114, 118for different modes of motion, 116Gibbs free energy, 112rotational, 116vibrational, 115

Path independence, 38Path, 38Pauling, 239Perturbation, 337pH meter, 226Phase change, 84

water, 84Phase diagram, 127

water, 128Phase plane, 127Phase rule, 124Phases, 124Phosphorescence, 345

mechanism of, 346Photochemistry, 344Photoinduction, 345Physical equilibrium, 126Pitzer, 92Polar molecule, 297Polarizability, 295, 303Polarized basis functions, 332Pople, 323Population inversion, 348Population, 8Post-Hartree–Fock calculations, 336Potential drop, 204Potential energy surface, 350Potential enrgy, 42Pressure fraction, 5Primitives, 326Principle of detailed balance, 152Priogine, 42Probability “shells”, 258Probability, 12, 113

entropy and, 113Probability density, 8, 12, 241Probability factor, 159Pythagoras, 40


376 INDEX

QCISDT, 337Quadratic least squares, 21, 22Quadratic real gas behavior, 32Quantum mechanical systems, 251Quantum molecular modeling, 318Quantum numbers, 249, 277Quantum rigid rotor, 290

energy levels, 291Quantum yields, 345

experimental quantum yields, 345

Radial equation, 258Radial node of the 2p atomic orbital,

262Radiative decay, 161Radioactive decay, 144Raoult’s law, 183Rate controlling step, 155Ratio γ , 50–51, 55Reaction coordinate, 73, 351Reaction diagram, 88Reaction mechanisms, 154Reaction order, 149Reaction molecularity, 155Real gases, 18, 30Real solutions, 185Reciprocity relationship, 36Redox, 234Reduced variables, 27Reduction potentials, 223Reference states, 307Regression wizard, 31Reservoir, 72Resistivity, 205Resonance frequency, 291Reversible expansion, 43

of an ideal gas, 43Reversible processes, 42

path independence, 42Reversible reactions, 151RHF, 329Roothaan, 322Rotational symmetry, 171Route section, 329

Salt bridge, 223Saturated calomel electrode SCE, 229,

233Scalar, 251SCF Energies of atoms and ions, 281

SCF variational ionization potential forhelium, 275

Schrodinger equation, 64, 250GAMESS, 64Schrodinger, 237Second law of thermodynamics, 39Second virial coefficient, 22

as a function of temperature, 22Second-order reactions, 147–148Secular determinant, 268, 270Self consistent field (SCF), 243, 275,

277Semiempirical equation, 19Semiempirical methods, 323Semipermiable membrane, 191Separable equations, 256Sequential reactions, 150Shell structure, 331Shelley, 220Shielding constant, 280Shielding, 240Silver, standard entropy, 80, 81Silver–Silver chloride electrode, 227, 231,

234Sin(x), sin(2x), and sin(3x) [0, π ], 249Single-component phase diagram, 128Slater determinants, 279, 286Slater orbital, 276Slater, 282Slater’s rules, 282Slater-type orbitals (STO), 279, 282

oxygen, 284nitrogen, 285

Sodium vapor, 117Software, curve fitting, 21Solubility product constant, 228Solubility product, 228, 231Solute, 184Solution chemistry, 182Solvent, 184Space, 9

hyperspace, 3-, 4-, etc., 10spherical velocity space, 12velocity space, 12

Speed, 7Spherical polar coordinates, 259Spin, 278Spin–orbit coupling, 283Spin–spin coupling, 298Split valence basis sets, 331


INDEX 377

Spontaneous processes, 77chemical reactions, 78expansion, 75heating and expansion, 75heating, 74mixing, 77

Stability products, 228Standard hydrogen electrode SHE, 233Standard state, 103Standard states, 58State function, 237State functions (variables), 41, 45State of a System, 19State vector, 241State, 19Statistical approach to thermodynamics,

108Statistical thermodynamic functions

(Irikura, 1998), 114Statistical thermodynamic functions,

113Statistical thermodynamics, 108Steady-state approximation, 153Steady-state equilibrium, 353Stewart, 323STO-2G of hydrogen, 325

basis set, 325, 326STO-3G calculations on methanol, 333Stoichiometric coefficient, 96Stored parameters, 328

STO-2G basis for the 1s orbital ofhydrogen, 326–328

Strainless molecule, 307Stretching a two-dimensional membrane,

166Strong electrolytes, 208Structure, 307Subcritical fluids, 25Sucrose, 199Sulfur dioxide, 82Sum-over-states, 10Supercritical fluid, 25Surface tension, 165Surroundings, 41Symmetry, 340System, 19, 41

Temperature dependence of the Gibbs freeenergy, 88

Ternary phase diagrams, 138

Thermal protein denaturation, 67Thermal reaction, 67Thermal wavelength, 118, 120, 123

electronic, 116dissociation, 117translational, 116, 118

Thermochemical cycle, 60Thermochemistry, 56Thermodynamic cycles, 37Thermodynamic functions, 37, 41Thermodynamic property, 41Thermodynamic states and systems, 41Thermodynamics of simple systems, 35

the first law, 35Third law, 78Tie line, 137, 139Time’s arrow, 73Tocopherols, 347Total volume of an ideal binary solution,

130Transition states, 313Transition, 42Translational levels, 119Translational motion, 118

quantum number, 118thermal wavelength, 118

Transport number, 209, 211Triple point, 127

benzene, 143Trouton’s rule, 91Two-component phase diagrams, 134

Type 1, 135Type II, 136Type III, 137

Two-level equilibrium, 109, 111

UHF, 329Uncertainty principle, 238Unit cell, 174, 180Units, 2Universal gas constant, 13, 17Universe, 41, 73

Valence bond theory, 239van der Waals equation, 18van’t Hoff equation, 98Vapor pressure, 184, 187, 196

depression, 190Raoult’s law, 184


378 INDEX

Variation of enthalpy of formation with T ,65

Variation of the equilibrium constant withtemperature, 97

Variational method, 243, 267Variational treatment of the hydrogen atom,

271the energy spectrum, 271

Vector space, 268, 320Vector, 241Velocities of ideal gas particles, 8Velocity space, 11, 12Vibration-rotation band, 300, 302Vibration–rotation spectrum of CO, 302Virial equation, 19Virtual orbitals, 337Viscosity of liquids, 169

laminar flow, 169Poiseulle equation, 170viscosity coefficient, 170viscous drag, 169

Visualization, 310the ethane molecule via PCModel 8.0 C©,

310Vitamin E, 347Volta, 220Voltage, 203, 221Volume behavior of a nonideal binary

solution, 131Volume increase (or decrease) upon adding

solute, 130

Water, 84, 125, 128dissociation constant, 125enthalpy of vaporization, 139–140phase diagram, 128

Wave equations, 249two dimensions, 250three dimensions, 250

Wave function vector, 251Wave mechanics of simple systems, 248Wave motion, 248

amplitude, 249fundamental, 248overtone, 248

Weak electrolytes, 207, 208Work, 43

adiabatic, 50

x-Component, 13X-ray crystallography, 172X-ray diffraction, 173x-Space, 7

Z = f (p) Curve, 23for the same gas at two different

temperatures, 23for two different gases, 23

Zero point energy, 289Zinc electrode, 221z-Matrix format, 328, 329z-Matrix input file for methane, 340

concise physical chemistry (rogers/concise physical chemistry) || index

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