Analytical Wave Functions for Methane and the Ammonium Ion

Analytical antisymmetric wave functions for the ground states of CH 4 and NH 4 +, and the corresponding C - H and N - H bond lengths have been obtained. These were calculated by a method which is essentially an application of the variational principle to the procedure used by Buckingham, Massey and Tibbs in their calculation of a self-consistent field for methane. The calculated C - H bond length is in good agreement with the experimental value. No experimental value for the N - H bond length in the free ammonium ion is available. However, the calculated value differs by only about 5% from the experimental value of the N - D bond length in ND 4 Cl. The wave functions should form useful first approximations in future calculations of the physical and chemical properties of CH 4 and NH 4 +. The NH 4 + function has already been used as a first approximation in a self-consistent field calculation at present in progress.