Hydrogen chain, ground-state energy

Here v and m denote the volume and mass of the molecule or atom, respectively. The r.h.s of Equation 32 denotes the ground-state energy of a quantum mechanical particle enclosed in a potential well (particle in a box problem [Martin and Leonard, 1970]). This condition is not satisfied for liquid helium and liquid hydrogen, while liquid neon is a borderline case. For the theoretical description of their thermophysical properties, application of the Maxwell-Boltzmann statistics sometimes does not suffice. Another assumption states that the internal degrees of freedom of the molecules or atoms are the same in the gas phase and in the liquid phase. In other words, it is assumed that the molecules can rotate and vibrate freely in the liquid phase, too. Molecular rotation may be hindered in the case of long-chain hydrocarbons or silicone fluids with side groups but also for small, nonspherical molecules such as N2,02, CS2, and others, rotation around two axes is restricted due to steric hindrance. Polar molecules exhibit restricted rotation due to the effect of dipolar orientation. 

Ground-State Energy of an Infinite Metailic Hydrogen Chain... 

Fig. 9.14. The infinite chain td" ground-state hydrogen atoms and the influence of bonding and antibonding effects, (a) All interactions are bonding (b) introductim of a single node results in an energy increase (c) two nodes increase the eneigy even more (d) with the maximum number nodes, the eneigy is at its maximum.

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