Embracing local suppression and enhancement of dynamic correlation effects in a CAS$\Pi$DFT method for efficient description of excited states
The recently proposed CAS$\Pi$DFT method combines the reliable description of nondynamic electron correlation with complete active space (CAS) wavefunction and the efficient treatment of dynamic correlation by density functional theory (DFT). This marriage is accomplished by adapting the DFT correlation energy functional modified with the local correction function of the on-top pair density ($\Pi$). The role of the correction function is to sensitize the correlation functional to local effects of suppression and enhancement of dynamic correlation and to account for adequate amount of dynamic correlation energy. In this work we show that presence of covalent and ionic configurations in a wavefunction gives rise to spatial regions where effects of either suppression and enhancement of correlation energy, respectively, dominate. Results obtained for potential energy curves of excited states of hydrogen molecule proves that CAS$\Pi$DFT is reliable for states changing their character along the dissociation curve. The method is also applied to the lowest excited states of six-membered heterocyclic nitrogen compounds such as pyridine, pyrazine, pyrimidine, and pyridazine. The obtained excitation energies for the $n \rightarrow\pi^*$ and $\pi \rightarrow\pi^*$ excitations confirm good performance of CAS$\Pi$DFT for excited states. The absolute average error of the method is by $0.1$ eV lower than that of the CCSD method and higher by the same amount than that of the more expansive CC3 variant. Such encouraging performance of CAS$\Pi$DFT is achieved at the negligible computational cost of obtaining the correlation energy comparing with the coupled cluster methods.
- This article is part of the themed collection: New horizons in density functional theory