Wave‐Mechanical Treatment of the LiH Molecule
Variational treatments of the LiH molecule and LiH+ ion have been carried out in which the two electrons of the inner shell of the Li atom are represented by Slater wave functions and the orbitals of the two valence electrons are treated after the method of James and Coolidge (but without the interelectronic distance as one of the coordinates). In this treatment elliptical coordinates are used for the expression of the wave function for the outer electrons, which takes the form of an exponential times a power series. The energy matrix for the LiH molecule contain the matrix terms for the LiH+ ion, for which calculations were also made. The lowest state of the LiH+ ion is a 2Σ state with the dissociation products normal hydrogen and ionized lithium and is the only one‐quantum state. The use of a very flexible eleven‐term function gives at an internuclear distance of three Bohr radii an energy of repulsion of 0.181 ev. The slope of the potential energy curve at this point is found to be —0.791 ev per Bohr radius. The lowest state of the ion is surely stable with an equilibrium distance somewhat greater than three Bohr radii. The energies of the four two‐quantum 2Σ states of LiH+ at the same internuclear distance are obtained from the next four roots of the eleventh‐order determinantal equation used to obtain the energy of the lowest state. These states are found to be quite strongly repulsive at this distance. On applying the variational method to the ground state of the neutral LiH molecule, it is found that the best value for the calculated binding energy that can be expected is smaller than the observed value by over a half volt. The addition of two terms containing the cosine of the difference of the azimuthal angles of the two outer electrons improves the calculated energy by 0.13 ev. An eight‐term wave function has been tried for the 3Σ state of LiH dissociating to the same products as the ground state. The energy found is a repulsion of 1.89 ev at a distance of three Bohr radii, the equilibrium distance of the ground state.
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