Advertisement

Molecular Partition Function: Vibrational, Rotational and Electronic Contributions

  • Mario CapitelliEmail author
  • Gianpiero Colonna
  • Antonio D’Angola
Chapter
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 66)

Abstract

In this chapter, the working equations for the vibrational, rotational and electronic partition functions of the diatomic species and their contribution to the thermodynamic properties will be discussed. First, we present closed forms for the vibrational and rotational partition functions based on the harmonic oscillator and rigid rotor models. These approximations can be used for both diatomic and polyatomic molecules. This model considers the molecular partition function as the product of the contributions of four independent degrees of freedom, nuclear (n), vibration (vib), rotation (rot) and electronic (el):
$${ \mathcal{Q}}^{\mathrm{int}} = {\mathcal{Q}}^{n}{\mathcal{Q}}^{\mathrm{vib}}{\mathcal{Q}}^{\mathrm{rot}}{\mathcal{Q}}^{\mathrm{el}}.$$
(5.1)
The energy is the sum of the three corresponding contributions

Keywords

Partition Function Harmonic Oscillator Diatomic Molecule Potential Energy Curve Polyatomic Molecule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Babou Y, Rivier P, Perrin MY, Souflani A (2007) High temperature nonequilibrium partition function and thermodynamic data of diatomic molecules. International Journal of Thermophysics 30(2):416–438ADSCrossRefGoogle Scholar
  2. Capitelli M, Colonna G, Gorse C, Giordano D (1994) Survey of methods of calculating high–temperature thermodynamic properties of air species. Tech. Rep. STR-236, European Space AgencyGoogle Scholar
  3. Capitelli M, Colonna G, Giordano D, Marraffa L, Casavola A, Minnelli D P ad Pagano, Pietanza LD, Taccogna F (2005a) Tables of internal partition functions and thermodynamic properties of high–temperature Mars–atmosphere species from 50 K to 50000 K. Tech. Rep. STR-246, European Space AgencyGoogle Scholar
  4. Drellishak KS, Aeschliman DP, Cambel AB (1964) Tables of thermodynamic properties of argon, nitrogen and oxygen plasmas. AEDC–TDR–64–12Google Scholar
  5. Esposito F (1999) Dinamica quasiclassica di processi collisionali inelastici e reattivi in sistemi H + H 2 e N + N 2 rotovibrazionalmente risolti. PhD thesis, Dottorato di Ricerca in Scienze Chimiche XI Ciclo, Dipartimento di Chimica, Università di BariGoogle Scholar
  6. Giordano D, Capitelli M, Colonna G, Gorse C (1994) Tables of internal partition functions and thermodynamic properties of high–temperature air species from 50 K to 10000 K. Tech. Rep. STR-237, European Space AgencyGoogle Scholar
  7. Herzberg G (1963) Molecular Spectra and Molecular Structure, I. Spectra of Diatomic Molecules. D. Van Nostrand, Inc., New YorkGoogle Scholar
  8. Herzberg G (1966) Electronic Spectra of Polyatomic Molecules. D. Van Nostrand, Inc., New YorkGoogle Scholar
  9. Leonardi E, Petrongolo C (1997) Ab initio study of NO 2. VI. vibrational and vibronic coupling in the \(\tilde{{X}}^{2}{A}_{1}/\tilde{{A}}^{2}{B}_{2}\) conical intersection up to 16 000 cm − 1. Journal of Chemical Physics 106(24):10,066–10,071Google Scholar
  10. Leonardi E, Petrongolo C, Hirsch G, Buenker RJ (1996) Ab initio study of NO 2. V. nonadiabatic vibronic states and levels of the \(\tilde{{X}}^{2}{A}_{1}/\tilde{{A}}^{2}{B}_{2}\) conical intersection. Journal of Chemical Physics 105(20):9051–9067Google Scholar
  11. Pagano D, Casavola A, Pietanza LD, Colonna G, Giordano D, Capitelli M (2008) Thermodynamic properties of high-temperature jupiter-atmosphere components. Journal of Thermophysics and Heat Transfer 22(3):8CrossRefGoogle Scholar
  12. Pagano D, Casavola A, Pietanza LD, Capitelli M, Colonna G, Giordano D, Marraffa L (2009) Internal partition functions and thermodynamic properties of high-temperature jupiter-atmosphere species from 50 K to 50,000 K. Tech. Rep. STR-257Google Scholar
  13. Patch RW, McBride BJ (1969) Partition functions and thermodynamic properties to high temperatures for H 3  +  and H 2  + . NASA Reference Publication TN–D–4523, NASAGoogle Scholar
  14. Stancil PC (1994) Partition functions and dissociation equilibrium constants for H 2  +  and He 2  + . Journal of Quantitative Spectroscopy and Radiative Transfer 51(4):655–658ADSCrossRefGoogle Scholar
  15. Stupochenko EV, Stakhenov IP, Samuilov EV, Pleshanov AS, Rozhdestvenskii IB (1960) Thermodynamic properties of air in the temperature interval from 1000 K to 12000 K and pressure interval from 10 − 3 to 103 atmospheres. American Rocket Society Journal Supplement 30:98zbMATHGoogle Scholar
  16. Wannier GH (1966) Statistical Physics. John Wiley & Sons, New YorkzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Mario Capitelli
    • 1
    Email author
  • Gianpiero Colonna
    • 2
  • Antonio D’Angola
    • 3
  1. 1.Dipartimento di ChimicaUniversità di BariBariItaly
  2. 2.Istituto di Metodologie Inorganiche e dei Plasmi (IMIP) Consiglio Nazionale delle Ricerche (CNR)BariItaly
  3. 3.Dipartimento di Ingegneria e Fisica dell’Ambiente (DIFA)University of BasilicataPotenzaItaly

Personalised recommendations