On the calculation of quantum partition functions and virial coefficients by path integration

Abstract A new method for calculation of the quantum second virial coefficient directly from the potential by a path integration technique is suggested. The separation of the so-called “bound part” of the second virial coefficient, which is of specific interest to chemical thermodynamics, is discussed. Three-dimensional Morse oscillator calculations are demonstrated. A comparison is made of the results obtained by path integration and by direct summation over vibration—rotation levels.

[1]  J. A. Barker,et al.  Interatomic potentials for krypton and xenon , 1974 .

[2]  A. Mellor,et al.  Further Calculations of Equilibrium Dimer Properties , 1970 .

[3]  M. Miller,et al.  Pair Correlation Function for Gaseous H2 at Low Density and Temperature , 1971 .

[4]  R. Storer.  PATH-INTEGRAL CALCULATION OF THE QUANTUM-STATISTICAL DENSITY MATRIX FOR ATTRACTIVE COULOMB FORCES. , 1968 .

[5]  Classical Path Approximation for the Boltzmann Density Matrix , 1971 .

[6]  A. Douglas,et al.  Absorption spectrum of the Mg2 molecule , 1970 .

[7]  K. Pitzer,et al.  Equation of State and Thermodynamic Properties of Gases at High Temperatures. I. Diatomic Molecules , 1959 .

[8]  Joseph O. Hirschfelder,et al.  Contribution of Bound, Metastable, and Free Molecules to the Second Virial Coefficient and Some Properties of Double Molecules , 1959 .

[9]  A. Gupta,et al.  Formation of dimers in quadrupolar gases , 1968 .

[10]  G. Norman,et al.  The Monte-Carlo method in Feynman's formulation of quantum statistics☆ , 1973 .

[11]  Y. R. Mayhew,et al.  Thermodynamic and transport properties of fluids , 1967 .

[12]  T. L. Hill,et al.  Molecular Clusters in Imperfect Gases , 1955 .

[13]  S. Y. Larsen,et al.  Quantum Mechanical Second Virial Coefficient of a Lennard-Jones Gas. Helium , 1969 .

[14]  W. C. Johnson,et al.  EQUILIBRIUM PROPERTIES OF HYDROGEN GAS FROM 5000 TO 20,000 K , 1962 .

[15]  G. Uhlenbeck,et al.  The quantum theory of the non-ideal gas. II. Behaviour at low temperatures , 1937 .

[16]  V. S. Jorish,et al.  On the calculation of the partition function of an anharmonic oscillator , 1975 .