By Weitao Yang
Department of Chemistry and Physics, Duke University, Durham, N.C. 27708, U.S.A. 
Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China

Fractional fractional charges and fractional spins provide a clear analysis of the errors of commonly used functionals.  For an effective and universal alleviation of the delocalization error, we develop a local scaling correction scheme by imposing the Perdew-Parr-Levy- Balduz linearity condition to local regions of a system. Our novel scheme is applicable to various mainstream density functional approximations. It substantially reduces the delocalization error, as exemplified by the significantly improved description of dissociating molecules, transition-state species, and charge-transfer systems. The usefulness of our novel scheme affirms that the explicit treatment of fractional electron distributions is essentially important for reducing the intrinsic delocalization error associated with approximate density functionals.

Progress with many-body theory approach will be also be presented. We have formulated the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations, opening new a channel for density functional approximations. This method has many highly desirable properties. It has minimal delocalization error with a nearly linear energy behavior for systems with fractional charges, describes van der Waals interactions similarly and thermodynamic properties significantly better than the conventional RPA, and eliminates static correlation error for single bond systems. It is the first known functional with closed-form dependence on orbitals, which captures the energy derivative discontinuity in strongly correlated systems. We also adopted pp-RPA to approximate the pairing matrix fluctuation and then determine excitation energies by the differences of two-electron addition/removal energies. This approach captures all types of interesting excitations: single and double excitations are described accurately, Rydberg excitations are in good agreement with experimental data and CT excitations display correct 1/R dependence.

References

1.  A.J. Cohen, P. Mori-Sanchez, and W. T. Yang. Challenges for Density Functional Theory.  Chem. Rev.  112:289, 2012
2. X. Zheng, A. J. Cohen, P. Mori-Sanchez, X. Q. Hu, and W. T. Yang. Improving band gap prediction in density functional theory from molecules to solids. Physical Review Letters, 107(2):026403, 2011.
3. Chen Li,1 Xiao Zheng, Aron J. Cohen, Paula Mori-Sánchez, and Weitao Yang, Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations Physical Review Letters  114, 053001.2015
4. H. van Aggelen, Y. Yang, and W. T. Yang. Exchange-correlation energy from pairing matrix fluctuation and the particle-particle random-phase approximation. Physical Review A, 88(3):030501, 2013.
5. Y. Yang, H. van Aggelen, and W. T. Yang. Double, Rydberg and charge transfer excitations from pairing matrix fluctuation and particle-particle random phase approximation. Journal of Chemical Physics, 139:224105, 2013.
6. Y. Yang, D. G. Peng, J. F. Lu, and W. T. Yang. Excitation energies from particle-particle random phase approximation: Davidson algorithm and benchmark studies. Journal of Chemical Physics, 141:124104, 2014.