Electron Pair Correlation: Products of N(N − 1) / 2 Geminals for N Electrons

The use of an antisymmetrized product of an N‐electron spin eigenfunction and $\text{N(N\hspace{0.17em}−\hspace{0.17em}1)\hspace{0.17em}/\hspace{0.17em}2}$ geminals to form an N‐electron, correlated wavefunction is proposed for atoms and molecules. This approach is more general than previous geminal‐product schemes in that the wavefunction explicitly contains a different geminal for each of the pair interactions present in the system. By describing the geminals in terms of bilinear orbital expansions, the formalism remains quite tractable. The example of three pairs of electrons is used to exhibit explicit expressions for density matrices, energy and variational equations which hold for any desired choice of spin and orbital angular momentum state.