Interaction potential energy, hydrogen

The isotopes H, D and T form diatomic molecules. The interaction potential energy of two hydrogen atoms goes through a minimum at a certain interatomic distance when two electrons form a singlet state Tg+, namely, the state with a total electron spin equal to zero (the combination of two electrons with opposite spin). The energy of the triplet state having a total electron spin of unity, increases when... 

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

The interaction of hydrogen (deuterium) molecules with a transition metal surface c an be conveniently described in terms of a Lennard--Jones potential energy diagram (Pig. 1). It cxxislsts of a shallcw molecular precursor well followed by a deep atomic chemisorption potential. Depending on their relative depths and positions the wells m or may not be separated by an activation energy barrier E as schematically Indicated by the dotted cur e in Fig. 1. 

Show explicitly for a hydrogen atom in the Is state that the total energy is equal to one-half the expectation value of the potential energy of interaction between the electron and the nucleus. This result is an example of the quantum-mechanical virial theorem. 

The interaction between an electron and a nucleus in a hydrogen atom gives rise to a potential energy that can be described by the relationship -e2/r. Therefore, using the Hamiltonian operator and postulate IV, the wave equation can be written as... 

As a result of these unfavourable interactions, i.e., opposition to bond strain i.e., between the pair of hydrogens shown at the bottom) and also due to bowsprit interaction, the potential energy of the boat form becomes high and this is why the boat conformation is not the preferred one. Hassel in 1947 established by means of electron diffraction studies that cyclohexane exists predominantly in the chair form. This has also been confirmed by electron diffraction studies and results obtained from Raman and I.R. spectra. Calculations made on the basis of entropy show that only about one molecule in a thousand will be in the boat form. 

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