510 Subject Index. Hamiltonian 33, 86, 88, 89 Hamilton operator 34, 164, 166

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1 Subject Index Ab-initio calculation 24, 122, Acentric factor 279, 338 Activity absolute 258, 295 coefficient 7 definition 7 Atom 23 Atomic units 93 Avogadro number 5, 92 Axilrod-Teller-forces 160, 331, 387 BACK model 433 BACKPF model 435, 496 Boltzmann constant 4, 93 corrected statistics 99, 107, 113 entropy relation 22, 85 factor 25, 71 Bond, intermolecular 23 Born-Oppenheimer approximation 86, 102, 105 Buckingham-Corner potential 235 Cell theories 27 Chemical potential from equation of state 6 from Gibbs potential 3 from Helmholtz potential 3 from partition function 76 ideal gas 259, 295 standard states 7 state function 2 statistical formula 81 Clebsch-Gordan coefficients 171, 244, 246, 248 Cluster integrals 260, 297 Combination rules 236, 449 Combinatorial arrangements Boltzmann 98 Bose-Einstein 99 Fermi-Dirak 99 distributions 65, 66, 67, 99 Compressibility equation 354 Compressibility factor expansion in density 258 hard sphere theory 380 Computer simulation asymmetric solution 314 correlation function 346 cut-off correction 322 equilibration 316, 320!low diagram 317, 320 importance sampling 313 Markov chain 313 minimum image convention 322 mixture 448, 471 molecular dynamics 318 Monte Carlo 311 periodic boundary conditions 321 pure fluids 323 relevance 330 Conformal solutions critical constants 466 definition 460 mean density 470 van der Waals Convex bodies 369 COR model 436 Corrections harmonic oscillator.141 heat capacity 143 molecular partition-function 142 rigid rotator 141 Correlation functions background 358 computer simulation 346 definition 341 ideal gas 345 liquid 345 real gas 345 second virial coefficient 345 solid 345 thermodynamic functions 397, 450 total 358 Correspondence principle 38, 45

2 510 Subject Index Corresponding states principle critical constants 279, 337 liquid 331 real gas 277 Critical constants 279, 337 Critical opalescence 85 Coulomb's law 164 Dalton's law 111 De Broglie duality of matter 31 wavelength 26, 31, 91 Degeneracy 94, 99 Degrees of freedom general 25 independence 104, 105 of a molecule 103 in the semi-classical approximation 87 Dispersion forces Axil rod-teller term 215 combination rule 207 non-additive three-body potential 212 pair potential 205 potential parameters 207 review 157 Dissociation energy 121, 145 Distribution of systems 64, 65, 78 Eigenvalue 365 Eigenfunction 35 Electron 23, 32, Electronic energy Born-Oppenheimer approximation 86, 102, 105 degeneracy 113 ideal gas functions 113 molecular partition function 113 Elementary charge 93 Energy external 20 free intermolecular 26 internal 1, 19, 72 molecular interpretation 19 of a molecule 102 potential 20 transfer as heat 1, 20 transfer as work 1, 20 zero 102 Ensemble averages 62 canonical 62, 63 equivalence 83 grand canonical microcanonical 62, , 85 Enthalpy free 2 formation 6 from Gibbs potential 2 vaporization 12 Entropy Boltzmann relation 22, 85 from partition function 76, 81 molecular interpretation 22 of mixing 110 standard state 6 state quantity 1 statistical formula 76 zero 6, 75, 105 Equation of state Bender equation 12 Boublik equation 363 Carnahan-Starling equation 364 excess functions 11 ideal gas 4, 106 Lee-Kesler equation 468 Redlich-Kwong equation 13, 464 thermodynamic properties 4 Twu-Lee-Starling equation 332 van der Waals equation 432 Euler angles 189, 243, 284 Excess functions definition 10 Redlich-Kister expansion 15 relation to activity coefficient 10 relation to equation of state 11 relation to partition function 447 Expectation value 50 Flexibility 434 Fluctuations dynamical variables 61 energy 84 magnitude 83 number of molecules 85 Fugacity coefficient 7, 8 definition 7 ideal gas mixture 7 relation to equation of state 7 Gas solubility 8 Gas constant 4, 93 Gaussian overlap potential 229 Gibbs fundamental relation 1, 73, 81 Helmholtz equation 2 paradoxon II 0 potential 2 Grand canonical potential 28, 82, 258 Hamiltonian 33, 86, 88, 89 Hamilton operator 34, 164, 166

3 Subject Index 511 Hanley-Klein potential definition 234 real gas data 266 Hard sphere potential definition 232 diameter from equation of state 367 diameter from perturbation theory 374 equation of state 364 mixture 452 pair correlation function 359, 365, 456 Percus-Yevick equation 359 perturbation theory 374 second virial coefficient 262 third virial coefficient 263 viscosity 367 Heisenberg's uncertainty principle derivation 53 practical relevance 58 relation to operator properties 54 in semi-classical approximation 87 Helmholtz potential 2 Henry coefficient 8, 9 Hermitian properties 34, 93 Hydrogen bonding 157 Ideal dilute solution 8 Ideal gas canonical partition function 98, 104 definition 97 equation of state 4, 97, 105, 106, 253 mixture 108, 446 significance 97 thermodynamic functions 105, 108 Ideal solution definition 10 free energy of mixing 447 vapor-liquid equilibrium 17 Indistinguishability 59, 87, Induction forces non-additive three-body potential 200, 208 pair potential 199, 201, 202 review 157 Integral equation 27 Interaction parameter,14 Intermolecular interactions attraction 159 Axilrod-Teller forces 160 Born-Oppenheimer approximation 159 combination rules 163 dispersion 157 electrostatic nature 156 energy function 158, 169 expansion in spherical harmonics 162, 393 flexible molecules 164 hydrogen bonding 157 induction 157 MPA-model 162 multipole 157 non-additive three-body forces 160, 200, 208, 212 overlap 157 pair potential 158, 161 relevance 23 repulsion 159 revtew 156 SSR-model 162 SSR-MPA-model 163 Intramolecular interactions Born-Oppenheimer approximation 102 vibration frequency 125 Joule-Thomson coefficient definition 256 source of potential information 264 Kihara potential anisotropic core 228 spherical core 234 Lagrangian multipliers 70 Lattice theories 27 Legendre function 245 Legendre polynomial Legendre transformations Leonard-Jones potential definition mixtures 448, 449 pair correlation function 451 real gas data 266 Liquid molecular interpretation 19 phenomenological difinition,309 structual theory 341 Lorentz-Berthelot rules 237, 449 Macrostate 60 Maitland-Smith-Kihara potential argon data 266, 390 definition 234 Mason-Monchick approximation 286 Mean density approximation definition 470 for integrals 487 relation to vdw1-theory Microstate 60 Mixing rules empirical mean density approximation 470 van der Waals I 462 virial coefficients 298 Moment of inertia 91 M ultipole expansion 169

4 512 Subject Index Multipole forces average effect 197 expansion 187 pair potential 187 point charge model 188 Multipole moments "ab-initio" information 173 cartesian coordinates 174 definition 172 explicit expressions 174 symmetry 173 units 176 Non-additive three-body interactions definition dispersion 212 induction 208 perturbation theory 387, 409 relevance 397, 293, 390 Nonsphericity parameter 369 Normal fluids 338 Occupation numbers 122 Overlap potential Orthogonality definition 94 expansion theorem 96 wave functions 94 Packing fraction 359 Pade-approximation 415 Pairwise additivity 160 Partial molar quantities 3 Partition function canonical , 86, 259 configurational , 259 factorization 89 generalized van der Waals 432 grand canonical 79, molecular relation to free energy 24 semi-classical approximation 25, 88 translational 106 Pauli exclusion principle 60, 156 Perc us-yevick equation 27, 357 Perturbation theory anisotropic reference 427, 499 blip-expansion 372 hard sphere reference 374, 477 ).-expansion 371 Lennard-lones reference 392, Rayleigh-Schrodinger 165 WCA-theory 374, 477 Perturbed hard chain model 435 Phase equilibria from equation of state 5 from activity coefficients 8, 9 general conditions 3 Photoelectric effect 31 Planck blackbody radiation 31 constant 25, 31, 87, 91, 92 Pressure from Helmholtz potential 2 from partition function 73 molecular interpretation 21 Polarizability bond-additivity concept 184 cartesian elements 182 definition 181 explicit expression 183 symmetry 183 Probability average over distributions 65 equal a priori 63, 65 of a distribution 65, 77 of a microstate 64, 78, 86 of a quantum state 65 Quantum effects corresponding states principle 338 diffraction effects 91 perturbation theory 389 relevance 91, 390 second virial coefficient 265 symmetry effects 91, 101 sources 87 Wigner-Kirkwood expansion 91, 389 Quantum mechanics experimental evidence 31 first postulate 33 intermolecular energy function 165 operators 33, 35 second postulate 35 Quantum numbers 87, 106, 122 Rayleigh-Schriidinger perturbation theory 165 Reaction equilibrium general conditions 3 gas phase 144 from ideal gas functions 144 Real gas definition 252 thermodynamic functions 255 virial coefficients 253 zero density limit 255 Residual state quantities 4 Rigid molecule approximation 26, 90, 160 Rotation, external characteristic temperature 120 contribution to ideal gas functions 115 degeneracy 50

5 Subject Index 513 energy values 50 kinetic energy 46, 119 linear molecule 46, 119 mode of molcular motion 103 molecular partition function 115, 120 moment of inertia 46 non-linear molecule 119 Schrodinger equation 47 semi-classical approximation 118 symmetry number Rotation, internal characteristic temperature 130 contribution to ideal gas functions 130, 151 definition 127 free 129 hindered 131 indistinguishable configurations 128 kinetic energy 129 molecular partition function 130 moment of inertia 129 potential energy 128 symmetry 128 torsional oscillation 128 Rotation matrices 171, 245 Scatchard-Hildebrandt theory 17 Schrodinger equation general 35 interacting charges 165 quantization of energy 36 Semi-classical approximation 86 Shape of molecule 23, 218 Site-site-repulsion definition 162 expansion in spherical harmonics 220 perturbation theory 413, 417 pair potential 218 parameters 219 Solid, molecular interpretation 19 Speed of light 31, 92 Spherical harmonics 161, 284 Square-Well potential definition 232 equation of state 433 second virial coefficient 264 SSR-MPA potential model 238 Statistical mechanics first postulate 62, 86 second postulate 63, 86 Stirling's formula 69, 79, 96, 109 Stockmayer potential 161, 284 Superposition approximation 414 Sutherland potential 232 Symmetry bosons 60 fermions 60 Pauli exclusion principle 60 wave function 59 Temperature molecular interpretation 21 statistical formula 73, , 319 Thermal motion 20 Translation contribution to ideal gas function 11 correspondence principle 38 degeneracy 39 energy values 37 Heisenberg's uncertainty principle 37 mode of molecular motion 103 molecular partition function 106 Schrodinger equation 37 semi-classical approximation 107 wave functions 37 Transport properties 273 Two-center-expansion 170, 239; 243 Van der Waals conformal solution theory 460 equation of state 432 generalized theory mixing rules 462 partition function 432 Vibration characteristic temperature 122 contribution to ideal gas functions 122 correspondence principle 45 degeneracy 124 diatomic molecule 121 energy values 44, 121 force constant 40 frequencies 40, 121 ground state 44 Heisenberg's uncertainty principle 44 intramolecular energy 40, 121 mode of molecular motion 103 molecular partition funciton 121 normal coordinates 124 polyatomic molecule 124 Schrodinger equation 41 semi-classical approximation 123 wave functions 44 zero energy 121 Virial equation expansions , 257 extrapolation to zero density 255 mixtures 296 relation between coefficients 253 region of validity 254, 257 statistical derivation 258 thermodynamic functions 255 Virial coefficients definition 253 source of potential information 264

6 514 Subject Index statistical formulae 261, 263 temperature dependence 255 Viscosity dilute gas 274 gas mixture 299 hard spheres 367 source of potential information 274 Wave function antisymmetric 60 concept 12 Heisenberg's uncertainty principle 33 normalization 33, 167 particle location 32 perturbation theory 166 relation to probability 33 superposition 32 symmetric 60

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