Configuration interaction variational theorem

Wlien first proposed, density llinctional theory was not widely accepted in the chemistry conununity. The theory is not rigorous in the sense that it is not clear how to improve the estimates for the ground-state energies. For wavefiinction-based methods, one can include more Slater detenuinants as in a configuration interaction approach. As the wavellmctions improve via the variational theorem, the energy is lowered. In density fiinctional theory, there is no... 

The first computational Implementations of these theorems were made by Doolen, Hidalgo, Nuttall and Stagat (7-9) for two-electron atoms. These were configuration Interaction (Cl) calculations using real valued radial basis functions and the complex Hamiltonian, Hg. They made use of a complex variational principle of the form... 

However, this approach, which exploits the variation theorem to determine the correlated wavefunction for the non-relativistic problem, was soon thwarted by the slow convergence of the configuration interaction expansion. 

In HF theory, one has the Brillouin theorem (BT) stating that singly excited configurations do not interact with the ground state determinant [130], The proof commonly proceeds by utilizing the properties of the HF wave function. An alternative route was followed by Mayer [131, 132, 133] who derived the BT directly from the variational principle, permitting one to obtain the HF... 

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