Characteristic Functions and Energy of a Lithium Crystal

An expression for the energy of a lithium crystal is derived which involves an unknown parameter. The best value of the energy is obtained by making the energy of the crystal a minimum with respect to this parameter according to the Ritz approximation method. The characteristic functions involved are similar to those which Bloch derived. They differ from Bloch’s in that a function containing the above mentioned unknown parameter takes the place of the atomic functions which he used. The value of the binding energy which is obtained for the lithium crystal is -.85 elec.-volts. The lattice constant is found to be 3.07 Angstroms, and a calculation of the compressibility gives 10x10-12 ergs/cm3. The energy is 50% too low, the lattice constant 12% too low and the compressibility 13% too high.