Keywords
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A
ab initio molecular dynamics → CPMD
absolute electrode potential
alternative definitions (relationship) 268
and derivative solvation parameters 274
Boltzmann vs. Fermi-Dirac statistics 269
cold- vs. warm-electron convention 268
determination 399
intrinsic → intrinsic absolute electrode potential
introduction 263
real → real absolute electrode potential
standardization 264
vacuum 264, 401, 403
vs. other key quantities 320, 321, 399, 424
vs. Volta potential differences 399
absolute molar entropy
introduction 147, 165
Sackur-Tetrode → Sackur-Tetrode equation
using spectroscopy-based statistical mechanics 191, 212
using temperature-scaled heat capacity integration 190
absolute solvation properties 36
ACA → atomistic-consistency assumption
acidity constant → deprotonation/constant
activity
approximations 177
coefficients 177, 178
combined activity coefficients 178
Debye-Hückel approximation → Debye-Hückel/theory
definition 177
dissolved species 177
gas-phase species 177
introduction 177
real vs. intrinsic 178
advance parameter → reaction/advance parameter
aggregation → electroneutrality
AGZF → characteristic situations/air gap at zero field
air gap
at zero field 254
introduction 254
air-liquid interface
definition 21
introduction 18
potential → air-liquid interfacial potential
preferential adsorption 437
air-liquid interfacial potential from QM
from CPMD 539
introduction 138
air-liquid interfacial potential in AT
boundary conditions 121
confinement potential 121, 122, 134
interface geometry 120
introduction 61, 120
Lennard-Jones wall 121
M-integration 122
mean-field treatment of polarizability 134, 526
methodology 122
numerical example 124
P-integration 122, 123
problems 132
air-liquid interfacial potential
and surface polarization 22
comparison with dielectric response mechanisms 22
contribution from water autoprotolysis 437
determination 425
electrolyte solutions 22
electrostatic interface characteristics → surface potential
experimental estimates for water (table) 435, 438, 471
experimental estimates for water 424
from AT simulations → air-liquid interfacial potential from AT
molecules without net dipole 22
non-aqueous solvents 24
QM calculation 288
solute concentration dependence 428, 430
solutions of neutral organic molecules 22
surface aging 431
temperature dependence 426
theoretical evaluation 433
alchemical
boundary condition 42
cavitation free energy 107
charging free energy 107
free-energy change in AT 102
free-energy change in CPMD 537
free-energy change in QM/MM 535
modification 103
alkali and halide
atomization (table) 367, 470
atomization 364
conventional single-ion solvation (table) 416, 420, 470, 471
conventional single-ion solvation 412
dissolved salt formation (table) 358
dissolved salt formation 353
element properties (table) 327, 470
element properties 326
gas-phase ion pairs (table) 331
gas-phase ion pairs 331
intrinsic single-ion solvation (table) 461, 462, 465, 477, 478
intrinsic single-ion solvation 440
ionic radii (table) 339, 340
ionic radii 332
ionization (table) 367, 470, 471
ionization 366
real single-ion solvation (table) 409, 410, 471
real single-ion solvation 407
redox potentials (table) 347, 348, 470
redox potentials 346, 349
reticulation (table) 374, 470
reticulation 373
salt dissolution (table) 362, 363
salt dissolution 361, 362
salt formation (table) 352, 470
salt formation 350
salt properties (table) 330, 470
salt properties 328
salt solvation (table) 381, 385
salt solvation 378
work functions (table) 396, 470
work functions 395
angular-momentum degeneracy
alkali and halides 364, 366
introduction 191
apparent molar quantities 354
approximate electrostatics
air-liquid interfacial potential in AT 133
correction terms in AT 501
solvation free energy in AT 128
asymmetric solvation
in Born model 60
introduction 60
partitioning of salt data 443
specific ion-solvent interactions 52
AT → atomistic simulations
atomistic simulations
approximate electrostatics → approximate electrostatics
basic methodology 62
extra-thermodynamic assumption for electric potential 549
finite sampling → finite sampling
finite-size effects → finite-size effects
interactions 63
introduction 43
potential-energy function 63
resolution 63
surface effects → surface effects
vs. QM computations 128
atomistic-consistency assumption
derived ionic radii 336, 337, 338
extra-thermodynamic assumption 523
introduction 523
prospects 548
atomization
halogen dissociation 365
parameters 196
autoprotolysis of water
and surface potential 437
introduction 437
B
BA → Barker-Watts reaction field
background charge → lattice-sum/background charge
Barker-Watts reaction field
applicability 77
definition 77
excluded-sites term 78
physical justification 77
self-term 78
surface-term 78
barostat
molecular dynamics 67
Monte Carlo 67
basis-set expansion 136
BFH cycle → Born-Fajans-Haber cycle
BM → Barker-Watts reaction field
boiling → vaporization
Boltzmann statistics
electrode potentials 269
electron and proton 192, 194
intramolecular partition function 191
ionization 369
bond-length constraint
constraint enforcement 63
metric-tensor effects 104
rigid molecules 63
Born model
and surface tension model 47
Born-Bjerrum equation → Born-Bjerrum equation
charging free energy 46
corrections 60, 488
effective ionic radius 45
enthalpies 55
entropies 55
errors 48
introduction 45
ionic radii 336
ionic radius ambiguity 53, 493
neglect of dielectric saturation 51, 491
neglect of electrostriction 50, 491
neglect of specific ion-solvent interactions 52, 492
qualitative nature 55, 61
surface tension coefficient ambiguity 54, 493
two-sphere model 337
volume 58
Born-Bjerrum equation 56
Born-Fajans-Haber cycle
definition 200
equation 201
history 201
relevance 201
reticulation 377
Born-Haber cycle → Born-Fajans-Haber cycle
Born-Landé
lattice energies 375
potential 335
Born-Mayer-Huggins function 63
Born-Oppenheimer approximation 135, 534
Born-Oppenheimer molecular dynamics 536
BO+ST → Born model and surface tension model
boundary conditions
alchemical 42
experimental 42
fixed → fixed boundary conditions
geometric 42
hard 42
non-periodic → non-periodic boundary conditions
periodic → periodic boundary conditions
soft 42
spatial 42, 68
thermodynamic 42
box → computational box
Buckingham exp-6 function 63
buffered-14-7 function 63
BW → Barker-Watts reaction field
C
CA → straight cutoff truncation
calomel electrode
non-saturated 299
saturated 299
calorimetry
equivalent calorimetric procedure 14
flow microcalorimetry 354
for temperature-scaled heat capacity integration 190
nanocalorimetry → nanocalorimetry
reaction calorimetry 14, 213
salt solutions 354
capacitance measurements 310
Car-Parrinello → CPMD
cavitation
alchemical 107
in AT simulation 108
in Born model 47
scaled-particle theory 54
soft-core → soft-core coupling
surface-tension model 47
cavity
formation → cavitation
interface polarization 48, 60, 488
interfacial potential 48
potential at cavity → potential at cavity
CC water model 83
CE → continuum-electrostatics calculations
CFF water model 83
chaotropic
ambiguity 483
introduction 482
characteristic situations
air gap at zero field 254
introduction 250
isolated phase with homogeneous surface polarization 250
non-polarizable interface at equilibrium 251
polarizable interface after charge equilibration 253
polarizable interface at zero charge 253
potentiostat 255
charge density
bound interfacial charge distribution 223
bound surface charge density 224
free interfacial charge distribution 223
free surface charge density 223
free 45
total interfacial charge distribution 232
charge distribution → charge density
charge enhancement
air-liquid interfacial potential 134
mean-field representation of polarizability 82, 526
water models 82
charge on spring → polarizability/charge on spring
charging free energy
alchemical 107
Born model 46
in AT simulation 109
CHARMM
shifting function 79
switching function 79
chemical potential
definition 148, 149, 156
electrochemical → electrochemical potential
intrinsic 257
introduction 256
real 257
closed system 145
cluster methods
cluster-pair approximation 449
cluster-pair correlation approximation 450
convergence of the surface potential 546
extrapolation scheme 449
for real absolute electrode potentials 401
introduction 447
cluster-ion → ion-solvent clusters
clusters → ion-solvent clusters
CM → straight cutoff truncation
cold-electron convention
definition 210
electrode potentials 268
electron and proton 194
introduction 167
ion convention 194
relevance 194
work functions 261
combination rules
geometric-mean 84
introduction 82, 85
Lorentz-Berthelot 85
Waldman-Hagler 85
compensating potential difference
definition 293
electrocapillary cells 307
introduction 16
Voltaic cell experiments 231, 301
composition variables 145
compressibility → volume-compressibility
compressimetry
introduction 212
salt solutions 355
computational box 71
conductor
perfect 225, 226
permittivity 11, 226
poor 226, 227
water 228
configuration generation
introduction 66
sampling 41, 67
searching 41
simulating 41, 66, 67
confinement potential
fixed boundary conditions 70
constraints
bond length → bond-length constraint
hard 42
metric-tensor effects → metric-tensor effects
soft 42
continuous-medium approximation
introduction 46
neglect of solvent structure 52
continuum-electrostatics calculations
applicability 55
Born model → Born model
effective ionic radius 42
errors 48
introduction 42
conventional scales
alternative conventional scales 315
aqueous-proton conventional scale 316
gaseous-proton conventional scale 316
redox conventional scale 316
standard conventional scale 313
conventional solvation parameters
and dissolved salt formation 353
conventional scales → conventional scales
definition 313
introduction 36, 311
vs. other key quantities 320, 321
vs. redox potentials 316, 348, 350
correction terms
AT charging free energies 116, 131, 498, 522
Born charging free energies 60
standard-state conversions (table) 210
Coulomb
interaction 1, 8
screened interaction 10
coupled
process 152, 185
system at equilibrium 185, 213
covalent
character of ion-solvent interactions 52
interactions in AT 63
cpd → compensating potential difference
CPMD
air-liquid interfacial potential 539
deprotonation constants 540
free-energy techniques 537
hydration free energies 537
introduction 536
redox potentials 540
structure and dynamics of ion solvation 537
crystal → salt
CT → cutoff truncation
cutoff truncation
cutoff distance 71, 72
cutoff noise 77
M-truncation 71
modified → modified cutoff truncation
molecular center 71
P-truncation 71
reaction field → Barker-Watts reaction field
schemes → cutoff truncation schemes
straight → straight cutoff truncation
truncation function 71
cycles → thermodynamic cycles
D
damping
function in modified cutoff truncation 78
of the polarizability 528
Wolf damping → Wolf damping
Debye model
dielectric permittivity 12
heat capacity 190, 376
Debye screening length → Debye-Hückel
Debye temperature 376
Debye-Hückel
inverse screening length 228
limiting law 178
theory 178
densimetry
introduction 212
salt solutions 354
density-corrected variant
activity 179
and dissolved salt formation 356
and salt dissolution 362
and salt solvation 381
conversion to standard variant 173
definition 172
derivatives (thermodynamic operator) 169
experimental approaches 175, 176
experimental vs. theoretical data 174
formation parameters 189
hypothetical non-interacting and volume-free particle 173
introduction 167
reaction parameters 181
relevance 176
standard-state corrections 203
deprotonation
cation hydration 52
constant by QM 540
reaction 540
diaerg 145
diatherm 145
dielectric permittivity
Born model 45
conductor 226
electrolyte solution 12
introduction 10, 11
spectroscopic measurement → dielectric spectroscopy
dielectric response
and air-liquid interfacial potential 22
electrolyte 12
interfacial charge densities 225
introduction 11
measurement 11
metal 12
dielectric saturation
effect on permittivity 51
neglect in Born model 51, 491
dielectric screening
Debye screening length 228
in water 12
introduction 10
screened Coulomb interaction 10
dielectric spectroscopy 12
dilatometry
introduction 212
salt solutions 355
dipolar potential → surface potential
dipole
induced dipoles → London
inducible dipoles in AT → polarizability/inducible dipoles
interaction with charge 9
moment of water around ions 527
dispersion
electron correlation 50
London → London
neglect in CE 50, 490
Slater-Kirkwood → Slater-Kirkwood
double-layer → electric double-layer
driving force
enthalpic component 155
entropic component 155
introduction 152, 154
redox potential 300
droplet → fixed boundary conditions
dropping mercury electrode → Kenrick cell/dropping mercury electrode
Drude model
dispersion effects 64
Dulong and Petit law 328, 329
dummy-atom 103
E
effective core potentials → pseudo-potentials
effective
electron numbers 86
ionic radius → ionic radius
Ehrenfest molecular dynamics 536
EIM → electrostatic interface model
Einstein model 190, 376
Einstein-Sutherland equation 336
electric double-layer
Gouy-Chapman model → Gouy-Chapman model
introduction 221
Quincke-Helmholtz model → Quincke-Helmholtz model
Stern model → Stern model
electric response 225
electric work 153
electrified interface
double-layer 221
introduction 221
electrocapillary
cell 292
compensating potential difference → compensating potential difference
curve 309
history 309
measurements 254, 307
polarizable interface 307
vs. Voltaic cell 307
electrochemical cell
definition 289
equilibrium measurements 291
electrochemical equilibrium
definition 289
electroneutrality 16
Galvanic cell → Galvanic cell/zero-current condition
half cells 294
introduction 152, 185
Nernst equation → Nernst equation/electrochemical equilibrium
non-polarizable interface 221
redox reaction 270, 296
reversibility 213
Voltaic cell → Voltaic cell/zero-current condition
electrochemical potential
definition 257
electrochemical series → redox potential/electrochemical series
electrochemistry
equilibrium → electrochemical equilibrium
introduction 289
non-zero current 217
potential difference 290
electrodynamics 45
electrolyte solution
air-liquid interfacial potential 22
finite-concentration effects 2
permittivity 12
electromotive force
definition 293
Galvanic cell experiments 231, 293
introduction 16
electron affinity
introduction 193, 197
measurement 369
vs. ionization parameters 197, 369, 370
electron convention → warm-electron convention
electron correlation
dispersion effects 50
in QM computations 136
Lennard-Jones dispersion term 64
electron spillout 219
electron
Boltzmann vs. Fermi-Dirac 194
complex solvation 484
formation parameters 196
standard state → standard state/electron
electroneutrality
as local constraint 217
constraint 8
gas-phase ions 9
in electrochemistry 16
ion aggregation 9
electrostatic artifacts
solvation free energy correction terms → correction terms
solvent structure 131, 132
electrostatic interface characteristics
bound interfacial charge distribution 223, 229
bound surface charge density 224
bound surface polarization 224
definition 221
free interfacial charge distribution 223, 228
free surface charge density 223
free surface charge polarization 223
total interfacial charge distribution 232
electrostatic interface model
definition 233
Poisson equation 233
electrostatic
limit 45
potential 45
electrostriction
neglect in Born model 50, 491
elusive → experimentally elusive
emf → electromotive force
endosmotic measurements 309
energy → internal energy
ensemble
configurational 41
open ensembles in MC 67
open ensembles in MD 67
enthalpy
at phase transition 151, 186
Born model 55
definition 147
entropy-enthalpy compensation 55, 57
pseudo entropy-enthalpy partitioning 106
relevance 154
using spectroscopy-based statistical mechanics 192
entropy calculation
finite-temperature difference 106
introduction 105
pseudo entropy-enthalpy partitioning 106
entropy
at phase transition 151, 186
Born model 55
calculation → entropy calculation
definition 146
entropy-enthalpy compensation 55, 57
molar → absolute molar entropy
pseudo entropy-enthalpy partitioning 106
relevance 154, 156
solvent structuring 52
vs. free energy 154
enveloping distribution sampling 105
equilibrium
chemical 153, 185
constant 183
electrochemical → electrochemical equilibrium
quasi-equilibrium electrochemistry 153
thermodynamic 145
equivalent calorimetric procedure → calorimetry/equivalent calorimetric procedure
ergostat
Monte Carlo 67
Euler theorem 149, 158
Ewald method 75
excluded-neighbors → excluded-sites term
excluded-sites term
fixed boundary conditions 70
introduction 63, 66
lattice-sum 73
Lennard-Jones 72
modified cutoff truncation 79
reaction-field scheme 78
straight cutoff truncation 76
exclusion potential
and quadrupole moment trace 113, 284
definition 279
QM estimates 288
QM vs. AT estimates 284
significance 118
exp-6-8 function 63
expansibility → volume-expansivity
expansivity → volume-expansivity
experimentally elusive
elusiveness 37, 545, 551, 552
fundamental problem 546
introduction 30
extent variables 146
extra-thermodynamic assumption
appearance in AT 549
appearance in QM 549
introduction 33, 35
Maxwell's equations 550
ultimate 550
F
Fajans' principle of lowest solubility 483
Faradaical equilibrium → non-polarizable interface/Nernstian equilibrium
Faraday cage 226
fast growth 105
fast-Fourier Poisson methods 75
fast-multipole methods 75
FBC → fixed boundary conditions
FDR cycle → formation-dissolution-reformation cycle
Fermi-Dirac statistics
electrode potentials 269
electron and proton 194
finite sampling
air-liquid interfacial potential in AT 133
solvation free energy in AT 130
finite-size effects
air-liquid interfacial potential in AT 133
and lattice-sum 75
correction terms in AT 505
fixed boundary conditions 71
in AT simulations 69
solvation free energy in AT 128
vs. macroscopic system 68
first law
definition 146
fixed boundary conditions
computational cost 70
confinement → confinement potential
droplet 70
finite-size effects 71
implementation 70
introduction 70
modifications 70
surface effects 71
flow microcalorimetry → calorimetry/flow microcalorimetry
fluctuating charges → polarizability/fluctuating charges
FMM → fast-multipole methods
force field
approximate representation 129, 133
electrostatic interactions 63, 68
improvement 526
ion-solvent parameters → ion-solvent interaction parameters
non-bonded interactions 63
parameters 102
polarizable → polarizable force field
potential-energy function 63
solvent models → solvent models
spectroscopic force field 103
unphysical potential-energy function 103
van der Waals interactions 63
formation reaction
electron 188
Hess law 188
introduction 188
parameters 188
real vs. intrinsic parameters 189
solute standard-state variant 189
standard parameters 188
formation-dissolution-reformation cycle
definition 200
equation 201
relevance 201
FPP → fast-Fourier Poisson approaches
free energy
at phase transition 151
calculation → free-energy calculation
change → free-energy change
definition 147
relevance 152
free-energy calculation
Born charging free energy 46
coupling parameter 103
coupling scheme 103
dummy atom 103
enveloping distribution sampling → enveloping distribution sampling
fast growth → fast growth
lambda-dynamics → lambda-dynamics
methodology 102
potential-energy function 103
replica exchange → replica-exchange
single-ion solvation free energy from AT 102, 107
single-ion solvation free energy from CPMD 537
single-ion solvation free energy from QM/MM 536
slow growth → slow growth
soft-core → soft-core coupling
thermodynamic cycles 103
thermodynamic integration → thermodynamic integration
free-energy change
alchemical in AT 102
alchemical in CPMD 537
alchemical in QM/MM 535
conformational 102
semi-adiabatic 193
thermodynamic 102
frontal
definition 245
reference interface characteristics 245
fugacity 178
G
Galvani potential
difference (measurement) 292
external in liquid 117, 279
internal in liquid 117, 279
internal vs. external 274, 275, 288, 549
introduction 234
vs. other key quantities 320, 321
Galvanic cell
electromotive force → electromotive force
example 295
experiments 231, 252, 293
introduction 16, 292
zero-current condition 292
galvanometer 290
gas-phase radius → ionic radius
generalized force shifting function 79
generalized reaction field 79
geometric-mean combination rule → combination rules
Gibbs adsorption equation 22
Gibbs equation
finite process 154
formation parameters 189
heat-up parameters 187
interpretation 155
introduction 151
partial molar variables in standard variant 170
reaction parameters 180
solute standard-state variants 173
Gibbs phase rule 145
Gibbs phase rule 145
Gibbs-Duhem equation 149
Gibbs-Helmholtz equation 150, 181
Gibbs' fundamental equation
introduction 148
spontaneity condition 148
Goldschmidt radii 346
Goldschmidt-Ahrens radii 346
Gourary-Adrian radii 346
Gouy-Chapman model 228
H
half-cell
equilibrium condition 294
introduction 16, 293
Hamiltonian → force field
hard-sphere radius → ionic radius
heat capacity
at phase transition 151
definition 147
experimental determination 212
integration → temperature-scaled heat capacity integration
isobaric 147
isochoric 148
relevance 156
using spectroscopy-based statistical mechanics 192, 212
heat-up reaction
enthalpy 187
entropy 187
free energy 187
introduction 187
parameters 194
Helmholtz model for interfacial potential 22
Hertz-Knudsen-Langmuir equation 365
Hess law
for formation parameters 188
for thermodynamic cycles 200
introduction 182
relevance 211
Hofmeister series
alkali-halides 483
and dissolved salt formation 356, 357
experimental observations 484
history 482
introduction 482
Huggins-Mayer potential 335
hydration
solvation → solvation
water → water
hydrogen bonding
anion hydration 52
hypothetical solvation process
hypothetical nature 20
introduction 18
physical 18, 39
standard-state corrections 202
unphysical 19, 39
I
ideal behavior 160
ideal gas
behavior → ideal-gas behavior/ideal gas
molar properties 193
ideal-gas behavior
ideal gas 160
ideal-mixture behavior
definition 161
gas mixtures 161
solutions 162
ideal-molal-solution behavior
definition 163
ideal-solution behavior
definition 162
IHSP → characteristic situations/isolated phase with homogeneous surface polarization
in-crystal radius → ionic radius
in-solution radius → ionic radius
inner potential → Galvani potential
insulant
introduction 225
non-perfect 226, 227
perfect 226
integral-equation methods 496
interface effects
dielectric response 225
electrified interface → electrified interface
phase interfaces 214
solvation 2
internal energy
definition 146
intrinsic absolute electrode potential
and formation parameters 273
and solvation parameters 268, 271
definition 267
experimental estimate 407
hydrogen electrode vs. solvation parameters 273
physical interpretation 272
recommended data 471
intrinsic solvation free energy
process 19
intrinsic solvation parameters
Born model 47
determination 442, 452
from theory 40, 117
intrinsic solvation free energy 21
introduction 19, 35, 318
recommended data 470
relevance 36
standard-state contribution 24
vs. electrode potentials 271, 272
vs. other key quantities 320, 321, 424
inverse Debye screening length → Debye-Hückel
ion compression 49, 332, 489
ion convention → cold-electron convention
ion-formation-solvation-reformation cycle
definition 201
equation 201
relevance 201
salt solvation 378
ion-solvent clusters
cluster methods → cluster methods
in quasi-chemical theory 532
introduction 2
ion-solvent interaction parameters
ambiguity in parameter choice 130
combination rules → combination rules
isotropic quadrupole 276
Lennard-Jones 81, 82
ion
aggregation → electroneutrality
alkali 2
definition 1
gas-phase ions → electroneutrality
halide 2
in nature 1
ion-solvent clusters → ion-solvent clusters
ionic crystals 2
ionic liquids 2
ionic melts 2
ionic radius
adjustment in Born model 53, 493
alkali-halide → alkali and halide
ambiguity in Born model 53, 493
ambiguity 332, 333
Born model 45
compression → ion compression
determination 334
gas-phase 332, 338
hard-sphere 333
in-crystal 332, 334
in-solution 332, 336
introduction 332
other ions 345
soft-sphere 333
temperature dependence 493
thermochemical 335
ionic strength 179
ionization potential
introduction 193, 197
measurement 369
vs. ionization parameters 197, 369, 370
ionization
parameters 193, 196
potential → ionization potential
semi-adiabatic 193
ionizing probe method 303
IQ → isotropic quadrupole
irreversible
process 146
isobaric expansion coefficient → isobaric expansivity
isobaric expansivity
vs. volume-expansivity 147, 148
isothermal compressibility
vs. volume-compressibility 147, 148
isothermal temperature derivative of redox potentials
definition 300
experimental data 346
relevance 300
ISR cycle → ion-formation-solvation-reformation cycle
K
Kapustinskii equation 335, 375
Kelvin probe method 302
Kenrick cell
dropping mercury electrode 305
example 304
history 309
introduction 304
Kihara function 63
Kirchhoff equation 150, 182
kosmotropic
ambiguity 483
introduction 482
L
lambda-dynamics 105
lateral
definition 245
reference interface characteristics 245
Latimer method 493
lattice energy
and reticulation enthalpy 376
Born-Landé model → Born-Landé
Born-Mayer model 375
hard-sphere model 373
introduction 373, 377
Kapustinskii equation → Kapustinskii equation
Madelung summation → Madelung summation
lattice formation → reticulation
lattice types (alkali-halides) 328, 329, 330
lattice-sum
adjusted boundary conditions 74
background charge 72, 73
computational cost 75
Coulombic limit 72
excluded-sites term 73
finite-size effects 75
function 72
implementation 75
introduction 72
self-term 73
surface effects 75
surface term 74
tinfoil boundary conditions 74
vacuum boundary conditions 74
Lennard-Jones
12-6 function 63
9-6 function 63
collision diameter 64
combination rules → combination rules
cutoff 71, 72
dispersion term 64, 86
ion-ion parameters 81, 102
ion-solvent parameters → ion-solvent interaction parameters
minimum 64
physical justification 86
radius 64
solvent-solvent parameters 81
tail correction 80
linear-response approximation
cavity potential 109
dielectric saturation 51, 491
introduction 46
Lippmann's equation 308
liquid-junction potential 298
local interface properties
homogeneous 218
interface curvature 217
introduction 217
local physical interface characteristics 217
surface characteristics 217
London
dispersion 50, 63, 64
equation 50, 64
induced dipoles 50
Lorentz-Berthelot combination rule → combination rules
LS → lattice-sum
M
M-averaging → potential in liquids
M-integration → air-liquid interfacial potential from AT
M-summation → potential at cavity
M-truncation → cutoff truncation
Madelung summation 373
Maggs method 75
many-body terms 63
Maxwell's equations
applicability 55
implicit extra-thermodynamic assumption 550
introduction 45
MC → Monte Carlo sampling
MD → molecular dynamics simulation
mean-spherical approximation 496, 497
melting
alkali-halide salts 328, 330
introduction 186
methodology dependence
charging free energy calculation 110, 111
metric-tensor effects 68, 104
MG → multigrid approaches
microscopic surface tension coefficient
estimates 54
introduction 47
vs. macroscopic coefficient 54
Mie potential 65
minimum-image 71
modified cutoff truncation
damping function → damping/function in modified cutoff truncation
definition 78
excluded-sites term 79
self term 79
shifting function → shifting function
surface term 79
switching function → switching function
molality
definition 158
reference molality 4, 164
molar entropy → absolute molar entropy
mole fraction
definition 158
molecular center 71
molecular dynamics simulation
introduction 42
molecular model
boundary conditions 42
choices 40
configuration generation 41
for ionic solvation 42
interaction function 41
resolution 41
molecular-beam spectroscopy 331
Monte Carlo sampling
introduction 42, 67
Morse function 63
MSA → mean-spherical approximation
MT → modified cutoff truncation
multigrid methods 75
N
nanocalorimetry 401
Nernst equation
electrochemical equilibrium 185, 296
equation 185
relevance 213
Nernstian equilibrium → non-polarizable interface/Nernstian equilibrium
Newtonian equations of motion 66
non-Faradaical equilibrium → polarizable interface/electrostatic equilibrium
non-periodic boundary conditions
fixed → fixed boundary conditions
introduction 68
non-polarizable interface
at equilibrium → characteristic situations/non-polarizable interface at equilibrium
definition 251
introduction 16, 236
Nernstian equilibrium 221
redox reaction 270
NPBC → non-periodic boundary conditions
NPIE → characteristic situations/non-polarizable interface at equilibrium
O
ODL → orientational disorder limit
Onsager model 48, 78
orientational disorder limit
air-liquid interfacial potential 125
introduction 115, 119
outer potential → Volta potential
oxidant 300
P
P vs. M convention
air-liquid interfacial potential 124, 133
correction terms in AT 507
debate 115, 126
intrinsic solvation free energies 114
potential at uncharged cavity 113
real solvation free energies 125
vs. quadrupole moment trace 125, 275
P-averaging → potential in liquids
P-integration → air-liquid interfacial potential from AT
P-summation → potential at cavity
P-truncation → cutoff truncation
P3M → particle-particle particle-mesh
pair → salt
partial molar variables
additivity 159, 169
compressibility (ambiguous) 157, 158
definition 157
derivatives 159
expansivity (ambiguous) 157, 158
introduction 156
real vs. intrinsic variables 159, 169
partial pressure 161
particle-mesh ewald 75
particle-particle particle-mesh 75
partition function
intramolecular 191
Pauli repulsion
introduction 63
Lennard-Jones potential 64, 65
Pauling radii 346
Pauling-Ahrens radii 346
PBC → periodic boundary conditions
periodic boundary conditions
definition 71
introduction 70
permittivity → dielectric permittivity
phase interface
definition 216
dielectric response 225
interfacial region 216
introduction 214
properties → local interface properties
phase transition
introduction 185
parameters 186
reaction 151, 185
phase
bulk 218
definition 215
Gibbs phase rule 145
phase interface → phase interface
phase transition → phase transition
standard-state specification 168
surface region 218
system of phases → system of phases
photo-electron spectroscopy 369
PICE → characteristic situations/polarizable interface after charge equilibration
PIZC → characteristic situations/polarizable interface at zero charge
plagues in ionic thermodynamics 552
plasma state 14
plate capacitor 12
PME → particle-mesh ewald
point-to-point solvation parameters
introduction 24, 202, 477
relevance 477
point-to-point solvation process
and standard-state variants 31
derivative parameters 28, 203
formation parameters in solution 29
partial molar variables 29
Poisson's equation 45, 46
polarizability
charge on spring 528
computational cost in AT 528
explicit representation 528
fluctuating charges 528
force field → polarizable force field
force field for alkali-halide ions 102
inducible dipoles 528
London equation 64
mean-field representation 82, 134
neglect in CE 49, 490
relevance in AT simulation 529
specific ion-solvent interactions 52
volume 64
polarizable force field
alkali-halide Lennard-Jones parameters 102
polarizable interface
definition 253
electrocapillary experiments 307
electrostatic equilibrium 221
introduction 236
thermodynamic studies 308
polarization catastrophe 528
polyatomic ions
in CE calculations 48
POT → characteristic situations/potentiostat
potential at cavity
intrinsic 113, 114
introduction 109, 110
M-summation 113, 129
numerical example 114
P-summation 113, 129
recalculation of potential at cavity 111, 113
potential difference
at liquid junction → liquid-junction potential
compensating potential difference → compensating potential difference
measurement → electrochemistry/potential difference
measurement 292
potential energy
discontinuities in AT 68
function 65
in AT simulations → force field
potential in liquids
external 117
implications for extra-thermodynamic assumptions 549, 550
internal 117
introduction 117
M-averaging 117
Maxwell's equations 550
notation 118
numerical example 119
P-averaging 117
potential of zero charge
and air-liquid interfacial potential 432
and maximal interfacial tension 309
definition 307
relevance 308
potentiometer
definition 217, 290
introduction 231, 255, 290
potentiostat
definition 217, 290
introduction 231, 255, 290
preferential adsorption → air-liquid interface/preferential adsorption
pressure
fugacity → fugacity
partial pressure → partial pressure
reference pressure 4, 164
thermodynamic variable 145
proton
and surface potential → air-liquid interfacial potential
Boltzmann vs. Fermi-Dirac 194
complex solvation 289
formation parameters 196
hydration free energy (popular values) 460
intrinsic partial molar variable (table) 461, 465
intrinsic partial molar variables (recommended) 471
intrinsic solvation parameters (recommended) 471
intrinsic solvation parameters (table) 461, 462
intrinsic solvation parameters 440
real solvation parameters (recommended) 411, 471
real solvation parameters (table) 409, 410
real solvation parameters 407
recommended data 470
protonation
anion hydration 52
constant by QM 540
problem in electrochemistry 300
pseudo-potentials 135
pzc → potential of zero charge
Q
QM → quantum-mechanical computations
QM/MM
deprotonation constants 542
free-energy techniques 535
hydration free energies 536
introduction 135, 534
redox potentials 542
structure and dynamics of ion solvation 535
quadrupole-moment trace
and exclusion potential 113, 284
irrelevant in AT solvent models 287
P vs. M-schemes 125, 275
quantum-mechanical calculations
air-liquid interfacial potential → air-liquid interfacial potential from QM
approximate interactions 135, 137
Car-Parrinello methods → CPMD
computational cost 135
deprotonation constants 540, 542
extra-thermodynamic assumption for electric potential 549
finite sampling 136, 138
hybrid methods → QM/MM
hydration free energies 536, 537
introduction 44, 134
limitations in level of theory 136
limitations in system size 136, 137
quasi-chemical theory → quasi-chemical theory
redox potentials 540, 541, 542
solvation free energies → solvation free energies from QM
quasi-chemical theory
cluster cycle 532
introduced 532
monomer cycle 532
Quincke-Helmholtz model 228
R
radius
cutoff → cutoff truncation
ionic → ionic radius
reaction field
potential in fixed boundary conditions 70
truncation scheme → Barker-Watts reaction field
reaction
advance parameter 184
formation → formation reaction
heat-up → heat-up reaction
limiting factors 184
parameters 180
phase transition → phase transition
quotient 183
rate 153
real vs. intrinsic parameters 180, 183
solute standard-state variants 181
standard reaction parameters 181
real absolute electrode potential
and formation parameters 273
and solvation parameters for hydrogen electrode 273
and solvation parameters 268, 271
definition 266
of reference hydrogen electrode 398
physical interpretation 271
recommended data 471
vs. lateral Volta difference 306
real solvation free energy
process 19
real solvation parameters
definition of the surface term 19, 21, 29
introduction 18, 317
real solvation free energy 21
recommended data 470
relevance of the surface term 19, 29
standard-state correction 24
vs. electrode potentials 271
vs. other key quantities 320, 321, 399, 424
vs. Volta potential difference 270, 306
recommended data
absolute real potential of hydrogen electrode 404, 406
air-water interfacial potential 436, 471
atomization 470
dissolved salt formation 355
element properties 470
gas-phase atom properties 470
gas-phase ion properties 471
intrinsic electrode potential 471
intrinsic solvation parameters 471
real electrode potential 471
real proton solvation 411, 471
real solvation parameters 471
reticulation 470
salt partial molar variables 470
salt solvation 381, 393
summary 470
redox potential
computational study 540
electrochemical series 298
experimental data 346
introduction 264, 298
isothermal temperature derivative → isothermal temperature derivative of redox potentials
measurement for alkali metals 346
relevance 300
standard 299
thermal temperature derivative → thermal temperature derivative of redox potentials
vs. conventional parameters 316, 348, 350
redox
conventional scale 316
equilibrium constant 296
Nernst equation 296
non-polarizable interface 270
potential → redox potential
reaction quotient 296
reducer 300
reference electric potential
electrode potentials → absolute electrode potential
standard-state definition 167
reference hydrogen electrode
intrinsic absolute potential 471
intrinsic electrode potential vs. solvation parameters 273
introduction 270, 298
real absolute potential (table) 404, 405, 471
real absolute potential 398, 406
real electrode potential vs. solvation parameters 273
Volta potential difference 306
relative electrode potential → redox potential
relative permittivity → dielectric permittivity
relativistic effects 136
replica-exchange
free-energy calculation 105
reticulation
and BFH 377
and TLC 377
energy → lattice energy
enthalpy 376
experimental data 350
parameters 196
recommended experimental data 470
reversible
conditions 213
interface crossing 21
process 146
real solvation free energy 18, 21
work of cavitation in scaled-particle theory 54, 496
work of cavitation in surface tension model 47
work of charging in AT 61
work of charging in Born model 46
RF → Barker-Watts reaction field
ROW water model 83
RXC → reaction calorimetry
S
Sackur-Tetrode equation 191
salt bridge 297
salt dissolution
parameters 197
process 10
salt solvation parameters
introduction 35
salt solvation
and ISR 378
optimal partitioning 385
parameters 35
salt
crystal 2
dissolution → salt dissolution
solvation → salt solvation
saturation
concentration 10, 361
dielectric → dielectric saturation
solubility product → solubility product
SBS → spectroscopy-based statistical mechanics
SC → straight cutoff truncation
scaled-particle theory
cavitation 54, 496
second law
definition 146
second-law method 214, 365
self-energy
AT simulation → self-term
unphysical solvation process 39
self-term
fixed boundary conditions 70
introduction 66
lattice-sum constant for cubic box 73
lattice-sum 73
Lennard-Jones 72
modified cutoff truncation 79
reaction-field scheme 78
straight cutoff truncation 76
semi-adiabatic
free-energy change 193
work function 395
semi-atomistic approaches 496
semi-empirical methods 136
semi-standard solvation parameters → point-to-point solvation parameters
Shannon-Prewitt radii 346
shifting function
charge-neutralized Ewald shifting → Wolf damping
CHARMM shifting → CHARMM shifting function
generalized force shifting → generalized force shifting
generalized reaction field shifting → generalized reaction field
introduction 78
silver-chloride electrode 299
single-ion solvation parameters
conventional values → conventional solvation parameters
interconnection 310, 321
introduction 18
theoretical determination 487
Slater-Kirkwood
equation 50, 64
slow growth 105
smooth particle-mesh ewald 75
soft-core coupling 108
soft-sphere radius → ionic radius
solubility product 361
solvation free energy from AT
methodology 61
problems 126
solvation free energy from QM
introduction 138
solvation process
interface crossing 39
physical process → hypothetical solvation process/physical
point-to-point → point-to-point solvation parameters
unphysical process → hypothetical solvation process/unphysical
solvation structure
chaotropic → chaotropic
CPMD studies → CPMD/structure and dynamics of ion solvation
introduction 2
kosmotropic → kosmotropic
QM/MM/ studies → QM/MM/ structure and dynamics of ion solvation
structure breaker 482
structure maker 482
solvation thermodynamics
alkali and halide 325
derivative properties 2
experimental problems 8
free energy from AT → solvation free energy from AT
free energy problem 2
intrinsic → intrinsic solvation parameters
non-aqueous solvents 325
other ions 325
real → real solvation parameters
salt → salt solvation parameters
single-ion → single-ion solvation parameters
standard-state corrections 202
theoretical problems 39, 45, 126
solvation
asymmetric solvation effects → asymmetric solvation
CPMD studies → CPMD/structure and dynamics of ion solvation
dynamics 2
finite-concentration effects 2
important reactions 196
process → solvation process
QM/MM/ studies → QM/MM/ structure and dynamics of ion solvation
salt → salt solvation
saturation → saturation
structure → solvation structure
thermodynamics → solvation thermodynamics
solvent models
CC → CC water model
CFF → CFF water model
flexible 63
parameterization 82
rigid 63
ROW → ROW water model
SPC → SPC water model
SPC/E → SPC/E water model
ST2 → ST2 water model
TIP3P → TIP3P water model
TIP4P → TIP4P water model
TIP4P/EW → TIP4P/EW water model
TIP5P → TIP5P water model
TIP5P/EW → TIP5P/EW water model
TIPS → TIPS water model
TIPS2 → TIPS2 water model
TIPSmod → TIPSmod water model
water 81
SPC water model 83
SPC/E water model 83
specific ion-solvent interactions
asymmetric solvation effects → asymmetric solvation effects
characterization 52
ion polarization 52
neglect in Born model 52, 492
spectroscopy-based statistical mechanics
atomization 191
enthalpies 192
entropies 212
heat capacities 190, 192, 212
ideal gas 193
introduction 17, 190
ionization 191
spectroscopy 190
work function 191, 193
spectroscopy
for spectroscopy-based statistical mechanics 190
ionization parameters 193
work function 194
SPME → smooth particle-mesh ewald
spontaneous
process 146, 154
ST2 water model 83
standard state
alternative conventions 205
ambiguity 8, 164
convention in this book 163, 170, 171
correction terms (table) 210
corrections to solvation process 202
dissolved 164
electron 165, 167
element 164
extrapolation 166
free-energy correction term 47, 107
gas-phase 164
liquid 164
phase specification 168
real 168
recommendation 170
reference electric potential 167
reference temperature 168, 169
solid 164
solute standard-state 171
solvent 164
virtual 168
standard variant
activity 179
and dissolved salt formation 356
and salt dissolution 362
and salt solvation 381
conversion to density-corrected variant 173
definition 172
derivatives (thermodynamic operator) 169
experimental approaches 175, 176
experimental vs. theoretical data 174
formation parameters 189
introduction 167
reaction parameters 181
relevance 176
standard-state corrections 204
standard
conventional scale → conventional solvation parameters/standard conventional scale
state → standard state
variant → standard variant
state function 146
state variables 146
Stern model 228
stoechiometric equation 180
Stokes law 336
Stokes-Einstein-Sutherland equation 336
straight cutoff truncation
computational cost 76
effective interaction function 75
excluded-sites term 76
introduction 75, 76
M-truncation 75
P-truncation 75
self term 76
surface effects 76
surface term 76
truncation function 75
sublimation
alkali metals 365
introduction 186
surface alteration
definition 218
electron spillout → electron spillout
liquids and gases 219
local multipole expansion 220
solids 219
surface effects
cutoff truncation 76
electrostatics 214
fixed boundary conditions 71
in AT simulations 69
lattice summation 75
real vs. intrinsic parameters 214
solvation process 39
surface polarization
and air-liquid interfacial potential 22
definition 21
electrostatic interface characteristics → electrostatic interface characteristics/surface polarization
introduction 18
surface potential
external 279
frontal difference 247
frontal 246
internal vs. external 274, 275, 288, 549
internal 279
introduction 238, 239
lateral 246
liquids → air-liquid interfacial potential
perturbation through contact 308
vs. other key quantities 320, 321, 424
surface tension
ambiguity in Born model 54, 493
combination with Born model 47
macroscopic coefficient 47, 54
microscopic coefficient → microscopic surface tension coefficient
model for cavitation 47
surface term in AT
fixed boundary conditions 70
introduction 66
lattice-sum 73
Lennard-Jones 72
modified cutoff truncation 79
reaction-field scheme 78
straight cutoff truncation 76
surface term
in AT simulations → surface term in AT
real solvation parameters → real solvation parameters
switching function
CHARMM switching → CHARMM switching function
introduction 78
system of phases
at equilibrium 215
definition 215
interfacial region 216
T
tail correction → Lennard-Jones/tail correction
TATB → tetraphenylarsonium-tetraphenylborate assumption
TCI → temperature-scaled heat capacity integration
temperature-scaled heat capacity integration
absolute molar entropies 190
calorimetry 190
definition 190
introduction 14, 147, 190
temperature
reference temperature 4, 164, 169
thermodynamic variable 145
tetraphenylarsonium-tetraphenylborate assumption 443
thermal temperature derivative of redox potentials
definition 300
experimental data 346
relevance 300
thermocell 453
thermochemical radius → ionic radius
thermodynamic cycles
closure 200
free-energy calculation 103
relevance for ionic solvation 199, 211
thermodynamic derivative
for finite processes 152
formation parameters 189
free-energy derivatives 150
notation 146
operator 151
reaction parameters 181
standard partial molar variables 171
standard-state corrections 203
vs. electrode potential derivatives 274
thermodynamic equilibrium 145
thermodynamic integration
cumulant expansion 105
ensemble average 104
introduction 104
quadrature scheme 104
thermodynamic variables
enthalpy 145
extensive variables 145
extent variables 146
free energy 145
heat capacity 145
intensive variables 145
internal energy 145
introduction 145
partial molar → partial molar variables
pressure 145
state variables 146
temperature 145
volume-compressibility 145
volume-expansivity 145
thermodynamics 144
thermostat
molecular dynamics 67
third law
definition 146
third-law cycle → third-law cycle
third-law entropy 147
use in temperature-scaled heat capacity integration → temperature-scaled heat capacity integration
third-law cycle
definition 202
introduction 14
reticulation 377
third-law method 214, 365
Thole damping 528
threshold spectroscopy 369
TI → thermodynamic integration
TIP3P water model 83
TIP4P water model 83
TIP4P/EW water model 83
TIP5P water model 83
TIP5P/EW water model 83
TIPS water model 83
TIPS2 water model 83
TIPSmod water model 83
TLC → third-law cycle
Tolman equation 494
transfer properties 325
truncation → cutoff truncation
U
ultrasonic wave propagation
introduction 355
ultrasonic vibration potentials 456
uncoupled
process 152
reactions in uncoupled systems 184
system at equilibrium 213
V
van de Graaff generator 231
van der Waals
functional forms in AT 63
in potential-energy function for AT 63
vapor pressure of metals
Hertz-Knudsen-Langmuir equation → Hertz-Knudsen-Langmuir equation
introduction 365
vaporization 186
variance 145
vibrating condenser → Kelvin probe method
virtual sites 63
Volta potential
and reference hydrogen electrode 306
difference 231
frontal difference 247
frontal 246
introduction 16, 238, 239
lateral 246
vs. other key quantities 320, 321
vs. real absolute electrode potential 306
vs. real solvation parameters 270, 306
Voltaic cell
compensating potential difference → compensating potential difference
dropping mercury electrode → Kenrick cell/dropping mercury electrode
equilibrium constraints 292
example 301
experiments 231, 254, 301
introduction 16, 292
ionizing probe → ionizing probe method
Kelvin → Kelvin probe method
Kenrick → Kenrick cell
relevance 301, 306
zero-current condition 292
volume-compressibility
at phase transition 151
definition 147
experimental determination 212
extensive quantity 148
ideal gas 193
relevance 156
vs. isothermal compressibility 147, 148
volume-expansivity
at phase transition 151
definition 147
experimental determination 212
extensive quantity 148
ideal gas 193
relevance 156
vs. isobaric expansivity 147, 148
volume
Born model 58, 59
definition 146
experimental determination 212
ideal gas 193
relevance 156
W
Waldman-Hagler combination rule → combination rules
Wannier function analysis 540
warm-electron convention
definition 209
electrode potentials 268
electron and proton 194
electron convention 194
introduction 167
standard state convention 209
work functions 261
water
as conductor 228
autoprotolysis 437
models → solvent models
permittivity 12
properties (table) 5
Wolf damping 79
work function
and sample shape 395
and SBS 193
Boltzmann vs. Fermi-Dirac statistics 397
cold- vs. warm-electron convention 261, 397
contact work function 401
determination 395
experimental data 395, 396, 470
external vs. internal convention 288
introduction 193, 261
mono- vs. polycrystalline surfaces 263, 395, 397
properties 263
semi-adiabatic 193, 395
spectroscopic 194, 261, 395
wet work function 400
X
x-ray view
electron diffraction 288
electron holography 288
electron work functions 288
intranuclear contribution 539
introduction 286
QM estimates for air-liquid interfacial potential 288
QM estimates for exclusion potential 288
x-ray crystallography 288
Z
zero-charge
potential of → potential of zero charge
zero-current situation
Galvanic cell measurement → Galvanic cell/zero-current condition
introduction → coupled/system at electrochemical equilibrium
Voltaic cell measurement → Voltaic cell/zero-current condition