Quantum Mechanical Cell Model of the Liquid State. I

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Abstract
In this paper the cell model for the liquid state, as proposed by Lennard‐Jones and Devonshire, is recast in terms of quantum statistical mechanics. A method is developed by which the energy levels and wave functions in the liquid cell can be determined to any prescribed accuracy. Thus, in the present work, no additional approximations are introduced which are not inherent in the cell model. When a sufficient number of energy levels is obtained, the partition function and thus the thermodynamic properties are derived. A method is devised by which from a knowledge of the wave function, the derivative of the corresponding energy with respect to the volume may be obtained. This derivative is required for the evaluation of the pressure. The theory is applied to H2 and D2 at a density near that of the crystals at 0°K. The corresponding classical Lennard‐Jones and Devonshire thermodynamic functions are obtained and compared with the results of the present theory. The calculations involved were performed on a Bendix G—15D computer. The quantized cell theory predicts that for hydrogen and deuterium experimentally detectable differences in energy, entropy, and specific heat must persist at temperatures as high as − 150°C.

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