The United Atom-Separated Atom Treatment of H2+

A trial wave function consisting of a linear combination of 1S orbitals centered on the nuclei and on a point half-way between them was used in a variational treatment of H2+. A one-electron three-center integral with nonequal charges which arises in the course of this treatment was evaluated. The effective nuclear charges for minimum energy were found approximately by calculating energies for a range of values of the separated atom charge and of the united atom charge. The lowest energy calculated, —0.5969 au, occurred where both effective nuclear charges are equal at 1.25. The energy value should be compared with —0.6031 au, the exact value, and with —0.6001 au obtained by hybridizing 1S and 2Pz orbitals on the separated nuclei. The ratio of the united atom coefficient to separated atom coefficient was found to be 0.3501 for the energy value mentioned.