The extended Koopmans’ theorem and its exactness

The extended Koopmans’ theorem (EKT) is shown to give accurate and potentially exact values for the lowest ionization potential (IP). Accurate results are reported for LiH, H+5, He2, and Li2. Results obtained for the lowest IP’s of LiH and He2 are nearly identical with those obtained by taking the difference of the total energies from separate, full configuration interaction calculations on the N-electron and the (N−1)-electron systems. The differences between the two IP calculations for a series of increasingly larger basis sets are 0.0017, 0.0004, and 0.0001 eV for LiH and are 0.0154, 0.0018, and 0.0007 eV for He2. The implication is that the lowest IP can be calculated to arbitrary accuracy. The EKT method is easily implemented as part of a multiconfigurational self-consistent-field calculation by diagonalizing the matrix of Lagrange multipliers with the first-order reduced density matrix as the metric.