Transport Properties and Potential Energy Models for Monatomic Gases

The first two chapters of this book are an update and outgrowth of the monograph Nonequilibrium Phenomena in Polyatomic Gases published by OUP in 1990, and a response to considerable improvements in the experimental determination of the transport properties of dilute gases that have taken place during the past 30 years. The experimental determination has improved sufficiently that it has become necessary to carry out calculations at the level of the second Chapman-Cowling approximation in order to give computed results that lie within the current experimental uncertainties now being reported. Chapter 3 is devoted to realistic interatomic potential energy functions, and begins with a discussion of the need for more accurate representations of these functions. Direct inversion of both microscopic data (spectroscopic transition frequencies and atomic beam scattering) and bulk property data (pressure and acoustic second virial coefficients, transport properties) are discussed in detail. The quantum chemical ab initio determination of binary atomic interaction energies and their analytical representation are discussed, followed by a detailed considerations of the interaction energies between pairs of noble gas atoms. Chapter 4 is concerned with connections between theory and experiment, including a detailed discussion of pure noble gases and their binary mixtures. Chapter 5 focuses on how to obtain the spectroscopic and thermophysical properties of a specific molecular system theoretically step by step, and provides a reference for the specific theoretical calculation work.

1 - THE MONATOMIC BOLTZMANN EQUATION
1.1 - The Boltzmann equation for dilute monatomic gases
1.2 - Equations of change and collisional invariants
1.3 - Entropy production
1.4 - The equilibrium state
1.5 - Linearization of the Boltzmann equation
1.6 - The Boltzmann equations for mixtures
2 - SOLUTIONS OF THE BOLTZMANN EQUATION
2.1 - Chapman-Enskog solution for pure monatomic gases
2.2 - Chapman-Enskog solution for binary mixtures
2.3 - Matrix approximations for the inverse collision operator
2.4 - The transport coefficients
2.5 - Effective cross sections
2.6 - Dynamical models for binary atomic interactions
2.7 - The moment method
2.8 - Kinetic models
3 - REALISTIC INTERATOMIC POTENTIAL ENERGY FUNCTIONS
3.1 - The need for realistic potential energy functions
3.2 - The Mie/Lennard-Jones potential energy functions
3.3 - Hartree-Fock plus damped dispersion semi-empirical models
3.4 - Exchange-coulomb semi-empirical models
3.5 - Modern empirical multiproperty-fit potential energy functions
3.6 - Direct inversions of experimental data
3.7 - Ab initio calculation of potential energy functions
3.8 - Interactions between pairs of ground-term noble gas atoms
3.9 - Interactions involving open-shell atoms
4 - COMPARISON BETWEEN THEORY AND EXPERIMENT
4.1 - Comparison between theory and experiment
4.2 - Correlation concept
4.3 - Binary mixtures of noble gases
5 - FROM AB INITIO CALCULATIONS TO SPECTROSCOPIC AND THERMOPHYSICAL PROPERTIES
5.1 - Ab initio calculations
5.2 - Fitting of analytic potential energy functions
5.3 - Spectroscopic properties
5.4 - Thermophysical properties
Appendix A - MATHEMATICAL APPENDICES
A.1 - Maxwellian averages
A.2 - Special functions
A.3 - Vectors and tensors
A.4 - Spherical harmonics and spherical tensors

Hui Li obtained his PhD from the Nanjing University, China in 2005. He was a postdoctoral fellow, research associate, and senior research associate from 2005-2010 at the University of Waterloo, Canada. In 2010, he joined the faculty at the Jilin University, China. He is now a Tang Au-Chin Scholar at the College of Chemistry, Jilin University and an adjunct professor of the University of Waterloo. He was awarded the Tang Au-Chin Young Investigator Award in Theoretical Chemistry (Chinese Chemical Society). His research interests lie in potential energy surfaces, ro-vibrational spectroscopy and dynamics of small molecules, clusters and solutions. Frederick R. W. McCourt achieved his PhD from the University of British Columbia, Canada. He was a postdoctoral fellow at the University of Leiden, The Netherlands. He was an assistant, associate, and full professor of Chemistry at the University of Waterloo, Canada, and is now a Distinguished Professor Emeritus of Chemistry. He was awarded an Alfred P. Sloan Fellowship in 1973. His research interests include the transport properties, interaction potential energy functions, and potential energy surfaces of gases. He has more than 150 book and journal publications in this field.