Lipkowitz Kenny B., Gundari Thomas R. (ed.). Reviews in Computational Chemistry. Volume 24

John Wiley & Sons, Inc., 2007. – 517 p.
This volume of Reviews in Computational Chemistry includes an appendix with a lengthy compilation of books on the various topics in computational chemistry: thermodynamics of confined phases, elements of statistical thermodynamics, a first glimpse (one-dimensional hard-rod fluids), mean-field theory, confined fluids with short-range interactions, confined fluids with long-range interactions, statistical mechanics of disordered confined fluids, mathematical aspects of equilibrium thermodynamics, mathematical aspects of statistical thermodynamics, mathematical aspects of one dimensional hard-rod fluids, mathematical aspects of mean-field theories, mathematical aspects of monte carlo simulations, mathematical aspects of ewald summation, and mathematical aspects of the replica formalism.Thermodynamics of confined phasesIntroductory remarks
Deformation of macroscopic bodies
Strain tensor
Stress tensor
Gibbs fundamental equation
Bulk fluids
Slit-pore with unstructured substrate surfaces
Slit-pore with structured substrate surfaces
Equilibrium states and thermodynamic potentials
Conditions for thermodynamic equilibrium
Thermodynamic potentials
Legendre transformation
Homogeneity of confined phases
Mechanical expressions for the grand putential
Gibbs-Duhem equations and symmetry
Phase transitionsElements of statistical thermodynamicsIntroductory remarks
Concepts of quantum statistical thermodynamics
The most probable distribution
Justification of the most probable distribution
The Shrodinger-Hill approach
Connection with thermodynamics
Determination of Lagrangian multipliers
Statistical expression for the entropy
Statistical physical averages and thermodynamics
Fluctuations
Equivalence of ensembles
The classic limit
Symmetry considerations
Kirkwood-Wigner theory
The canonical partition function in the classic limit
Laplace transformation of probability densitiesA first glimpse: One-dimensional hard-rod fluidsIntroductory remarks
Pure hard-rod bulk fluid
Statistical thermodynamics of hard-rod fluids
Virial equations of state
Bulk isothermal compressibility
Density distribution
Hard rods confined between hard walls
Aspects of statistical thermodynamics
"Stratification" of confined one-dimensional fluidsMean-field theoryIntroductory remarks !J,
Van der Vaals theory of adsorption
Sorption experiments
An equation of state for pure confined fluids
Critical behavior and gas-liquid coexistence
Gas sorption in mesoscopic slit-pores
Lattice model of confined pure fluids
The model system
High-temperature expansion
Thermodynamics of pure confined lattice fluids
The Bogoliubov variational theorem
Mean-field approximation
The limit, of vanishing temperature
Phase behavior of pure lattice fluids
Morphologies in the limit [i]T = 0
Coexisting phases of the lattice fluid
The impact of shear strain
Binary mixtures on a lattice
Model system
Mean-field approximation
Equilibrium states
Phase behavior of binary lattice mixtures
Symmetric binary bulk mixtures
Decomposition of symmetric binary mixtures
Neutron scattering experiments
Experimental details
Lattice model of water iBA mixtures
Phase diagram
Concentration profiles and contrast factorsConfined fluids with short-range interactionsIntroductory remarks
Monte Carlo simulations
Importance sampling
The grand canonical ensemble
Corrections to the configurational energy
A mixed isostress isostrain ensemble
Chemically homogeneous substrates
Experiments with the surface forces apparatus
Derjaguin's approximation
Normal component of the stress tensor
Stratification of confined fluids
Chemically heterogeneous substrates
The model
Structure and phase transitions
Chemical patterns of low symmetry
Nanopatterned model substrate
Thermodynamic perturbation theory
Computation of the grand potential
Rheological properties of confined fluids
The quasistatic approach
Molecular expression for the shear stress
Fluid bridges exposed to a shear strain
Thermodynamic stability
Phase behavior of shear-deformed confined fluids
The Joule-Thomson effect
Experimental background and applications
Model system
Thermodynamic considerations
The limit of low densities
Confined fluids at moderate densities
Exact treatment of the Joule-Thomson coefficient
Isostress isostrain ensemble MC simulations
Inversion temperature at low density
Density dependence of the inversion temperature
Lattice Monte Carlo Calculations
Advantages and disadvantages of lattice models
Grand canonical ensemble Monte Carlo simulations
Thermodynamic integration for lattice fluids
Comparison with mean-field density functional theoryConfined fluids with long-range interactionsIntroductory remarks
Three-dimensional Ewald summation
Ionic systems
From point charges to point dipoles
Ewald summation for confined fluids
The rigorous approach
Slab-adapted Ewald summation
Reliability of the slab-adapted Ewald method
Unsulating solid substrates
Dipolar interactions and normal stress
Orientational order in confined dipolar fluids
Conducting solid substrates
The boundary-value problem in electrostatics
Image charges in metals
Dipolar fluids
Metallic substrates and ferroelectricityStatistical mechanics of disordered confined fluidsIntroductory remarks
Queuched-annealed models
The introduction of replicas
Correlation functions and fluctuations in the disordered fluid
lntegral equations
Replica Ornstein-Zernike equations
Closure relationships
Thermodynamics of the replicated fluid
Applications
Model systems
Dipolar fluids in simple matrices
Dipolar fluids in complex matricesA Mathematical aspects of equilibrium thermodynamics[/i]

The trace of a matrix product
Legendre transformation
Euler's theorem

[b]Mathematical aspects of statistical thermodynamicsStirling's approximation
Elements of function theory
The Cauchy-Riemann differential equations
The method of steepest descent
GauB's integral theorem in two dimensions
Cauchy integrals and the Laurent series
Lagrangian multipliers
Maximum term method
Basis sets and the canonical ensemble partition function[/b]
Parseval's equation
Proof of Eq (2.41)
[i]The classic limit of quantum statistics
The Dirac δ-function
Proof of the completeness relation
Quantum corrections due to wave-function symmetry
Quantum corrections to the Hamiltonian functionMathematical aspects of one-dimensional hard-rod fluidsDistance between mirror images
Integral transformations
Gaussian density distribution
Limiting behavior of the prohaoility density
Moivre-Laplace approximationMathematical aspects of mean-field theoriesVan der Waals model for confined fluidsEvaluation of the double integral in Eq (4.21)
Newton's method
Maxwell's constraint
Lattice models
Numerical solntion of Eq (4.86)
Binary mixturesMathematical aspects of Monte Carlo simulationsStochastic processes
The Chapman-Kolmogoroff equation
The Principle of Detailed Balance
Chemically striped substrates
Molceular expressions for stresses
Normal component of stress tensor
Shear stress
Virial expression for the bulk pressureMathematical aspects of Ewald summationThree-dimensional Coulombic systems
Energy contributions in Ewald formulation
Force and stress tensor components
Three-dimensional dipolar systcm
Self-energy
Force and torque
Stress tensor
Slab geometry
Rigorous expressions
Force, torque, and stress in systems with slab geometry
Metallic substratesMathematical aspects of the replica formalismReplica expressions in the grand canonical ensemble
Derivation of Eq (7.23)
Molecular fluids
Proof of Eq (7.33)
Numerical solution of integral equationBibliography
Index