One of the most challenging problems in electronic structure theory is to calculate the correlation energy. The two-particle ab initio methods such as many-body perturbation theory or coupled-cluster theory are derived rigorously and could calculate the correlation energy very accurately, but their computational cost is too high to be applied to large systems. The one-particle density functional theory (DFT), on the other hand, could significantly reduce the computational cost of such calculation, and the accuracy could be maintained by choosing an appropriate functional. The major problem for the DFT methods is that the exchange-correlation functionals include a lot of approximations, and many of them are designed empirically. Therefore, unlike the wave-function based two-particle methods which could eventually converge to the exact solution of the Schrodinger equation, there is no such systematic route for the traditional DFT methods.

The two-particle coupled-cluster theory, however, could be transformed into the one-particle form, that is, the correlation orbital theory (COT). And the eigenvalues of the one-particle operator in this theory equal to the vertical ionization potentials (IP) and electron affinities (EA) obtained from the original coupled-cluster method. Although this method scales the same as the normal coupled-cluster theory, it implies that if the other one-particle operator, such as the Kohn-Sham operator, could make the eigenvalues approximately equal to the exact ionization potentials or electron affinities, it may potentially converge to the exact solution.

The fundamental aim of this project is to emulate the correlated orbital theory using the standard Kohn-Sham DFT methods, that is, to create the new density functionals of which the orbital energies are good approximations of the ionization potentials or electron affinities. This principle is contrary to the idea in the traditional DFT society that the Kohn-Sham eigenvalues and eigenfunctions have no clear physical meaning. Compared with the electron affinities, there is much more experimental ionization data available. Therefore, the new methods are designed primarily based on the IP theorem with reference values from experiments and high-level coupled-cluster results. Thus they are given the name as ionization potential improved density functionals.

This study will demonstrate that this kind of density functional can be constructed efficiently using the traditional exchange and correlation functionals already developed. And the orbital energies can be fitted using the simple water molecule. Due to this unique feature, the new density functionals could improve the accuracy of many physical properties that are challenging to traditional DFT methods. Also, they could reduce the self-interaction error which is intrinsic in density functional theory.