Adsorbate Partition Functions via Phase Space Integration: Quantifying the Effect of Translational Anharmonicity on Thermodynamic Properties

2021 ◽  
Author(s):  
Katrín Blöndal ◽  
Khachik Sargsyan ◽  
David H. Bross ◽  
Branko Ruscic ◽  
C. Franklin Goldsmith
Keyword(s):  
Phase Space ◽  
Thermodynamic Properties ◽  
Partition Functions ◽  
Phase Space Integration

Hamilton-Jacobi Theory

2018 ◽  
Author(s):  
Peter Mann
Keyword(s):  
Phase Space ◽  
Bbgky Hierarchy ◽  
Distribution Functions ◽  
Symplectic Integrators ◽  
Partition Functions ◽  
Von Neumann ◽  
Equipartition Theorem ◽  
Recurrence Theorem ◽  
Phase Amplitude ◽  
Canonical Ensembles

This chapter focuses on Liouville’s theorem and classical statistical mechanics, deriving the classical propagator. The terms ‘phase space volume element’ and ‘Liouville operator’ are defined and an n-particle phase space probability density function is constructed to derive the Liouville equation. This is deconstructed into the BBGKY hierarchy, and radial distribution functions are used to develop n-body correlation functions. Koopman–von Neumann theory is investigated as a classical wavefunction approach. The chapter develops an operatorial mechanics based on classical Hilbert space, and discusses the de Broglie–Bohm formulation of quantum mechanics. Partition functions, ensemble averages and the virial theorem of Clausius are defined and Poincaré’s recurrence theorem, the Gibbs H-theorem and the Gibbs paradox are discussed. The chapter also discusses commuting observables, phase–amplitude decoupling, microcanonical ensembles, canonical ensembles, grand canonical ensembles, the Boltzmann factor, Mayer–Montroll cluster expansion and the equipartition theorem and investigates symplectic integrators, focusing on molecular dynamics.

Erratum: Partition Functions and Thermodynamic Properties of Nitrogen and Oxygen

1965 ◽  
Vol 8 (12) ◽  
pp. 2304 ◽  
Author(s):  
K. S. Drellishak ◽  
D. P. Aeschliman ◽  
Ali Bulent Cambel
Keyword(s):  
Thermodynamic Properties ◽  
Partition Functions

Problems of determination of high temperature thermodynamic properties of rare gases with application to mixtures

1970 ◽  
Vol 4 (2) ◽  
pp. 335-355 ◽  
Author(s):  
M. Capitelli ◽  
E. Molinari
Keyword(s):  
High Temperature ◽  
Thermodynamic Properties ◽  
Thermal Equilibrium ◽  
Partition Functions ◽  
Rare Gases

Thermodynamic properties and compositions of gases in thermal equilibrium at high temperature can in principle be derived quite accurately once the partition functions of the relevant species have been calculated.

scholarly journals Electronic Excitation and Thermodynamic Properties of High Temperature Gases

1971 ◽  
Vol 26 (4) ◽  
pp. 672-682 ◽  
Author(s):  
M. Capitelli ◽  
E. Ficocelli
Keyword(s):  
High Temperature ◽  
Thermodynamic Properties ◽  
Electronic Excitation ◽  
Single Species ◽  
Partition Functions ◽  
Specific Heats

AbstractDifferent cut-off criteria of partition functions have been utilized in order to evaluate the con­tribution of electronic excitation to thermodynamic properties of high temperature gases (5000 °K to 35 000 °K, 10-2-10 atm). It is shown that properties of single species are strongly affected by the cut-off criterion adopted, i. e. the contribution of electronic excitation to these properties is important. It is also shown that the reported absence of this contribution to total enthalpies and specific heats of plasmas is the result of an almost complete compensation between "reactional" and "frozen" terms which are all dependent on electronic excitation.

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