This manuscript presents the second, consistent density functional in the QTP (Quantum Theory Project) family, that is, the CAM-QTP(01). It is a new range-separated exchange-correlation functional in which the non-local exchange contribution is 100% at large separation. It follows the same basic principles of this family that the Kohn-Sham eigenvalues of the occupied orbitals approximately equal the vertical ionization energies, which is not fulfilled by most of the traditional density functional methods. This new CAM-QTP(01) functional significantly improves the accuracy of the vertical excitation energies especially for the Rydberg states in the test set. It also reproduces many other properties such as geometries, reaction barrier heights, and atomization energies.

This manuscript presents the first consistent ionization potential (IP) optimized global hybrid functional to accurately estimate the vertical ionization and excitation energies of the inner-shell electrons in molecules. The new method fulfills the IP theorem that the Kohn-Sham eigenvalues of all the occupied orbitals (including the core orbitals) are good approximations to the exact vertical ionization energies. The accuracy of the one-particle spectrum is essential to enabling the one-particle density functional theory (DFT) to provide accurate results. Compared to its precursor, the range-separated hybrid functional CAM-QTP00, the new method is more computationally efficient. The IP theorem enables the new method to provide inner-shell ionization energies measured by X-ray photoelectron spectroscopy, and it can further accurately simulate the X-ray absorption spectrum (XAS, or NEXAFS). The simulated spectra can be compared to the experiment directly without shifting. In addition, the new method reduces the delocalization error (many-electron self-interaction error) which is a severe problem in DFT.

Though contrary to conventional wisdom, the interpretation of all occupied Kohn-Sham eigenvalues as vertical ionization potentials is justified by several formal and numerical arguments. Similarly, the performance of density functional approximations (DFAs) for fractionally charged systems has been extensively studied as a measure of one- and many-electron self-interaction errors (MSIEs). These complementary perspectives (initially recognized in ab initio dft) are shown to lead to the unifying concept that satisfying Bartlett’s IP theorem in DFA’s mitigates self-interaction errors. In this contribution, we show that the IP-optimized QTP functionals (reparameterization of CAM-B3LYP where all eigenvalues are approximately equal to vertical IPs) display reduced self-interaction errors in a variety of tests including the He₂⁺ potential curve. Conversely, the MSIE-optimized rCAM-B3LYP functional also displays accurate orbital eigenvalues. It is shown that the CAM-QTP and rCAM-B3LYP functionals show improved dissociation limits, fundamental gaps and thermochemical accuracy compared to their parent functional CAM-B3LYP.