Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences.  However, there are major failures for many predicted properties. These errors can be characterized and understood through the perspective of fractional charges and fractional spins.  The fractional perspectives offer a possible pathway forward. Based on this, we have developed scaling and local scaling approaches leading to significantly improved density functional approximations.

Following a many-body theoretical approach, we developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix fluctuations.  This formulation of the exchange-correlation energy opens new a channel for density functional approximations based on the many-body perturbation theory. We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation (pp-RPA). This resulting 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. Most significantly, it is the first known functional with an explicit and closed-form dependence on the occupied and unoccupied 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. Furthermore, the pp-RPA has a computational cost similar to TDDFT and consequently are promising for practical calculations.

References:

[1]    J. Cohen, P. Mori-Sanchez, and W. T. Yang. Insights into current limitations of density functional theory. Science, 321:792, 2008.

[2]    P. Mori-Sanchez, A. J. Cohen, and W. T. Yang. Localization and delocalization errors in density functional theory and implications for band-gap prediction. Physical Review Letters, 100:146401, 2008.

[3]    P. Mori-Sanchez, A. J. Cohen, and W. T. Yang. Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems. Physical Review Letters, 102:066403, 2009.

[4]    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, 107:026403, 2011.

[5]    J. Cohen, P. Mori-Sanchez, and W. T. Yang. Challenges for Density Functional Theory.  Chem. Rev.  112:289, 2012.

[6]    Li, X. Zheng, A J. Cohen, P. Mori-Sánchez, and W. T. Yang, Local Scaling Correction for Reducing Delocalization Error in Density Functional Approximations. Physical Review Letters  114, 053001,2015

[7]    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, 030501(R), 2013.

[8]    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.

[9]    D. G. Peng, H. van Aggelen, Y. Yang, and W. T. Yang. Linear-response time-dependent density-functional theory with pairing fields. Journal of Chemical Physics, 140:18A522, 2014.

Weitao Yang was born in Chaozhou, China. He received his B.S. degree from Peking University and Ph.D. degree from the University of North Carolina at Chapel Hill. He is currently the Philip Handler Professor of Chemistry and Physics at Duke University. Yang’s interests are in developing theory and applying it to complex problems in chemistry and biology.

Yang's major contributions have been in the development of theoretical and computational methods in electronic structure theory. His contributions have made electronic structure calculations much more efficient and accurate. Yang pioneered the development of the linear scaling divide-and-conquer method for electronic structure calculations of large systems. Development and application of linear scaling methods have attracted much interest. Yang’s 1991 Physical Review Letters paper marked the beginning of the linear scaling field. Prof. Yang has contributed to the development of density-functionals that go beyond the local density-functional approximation. The Becke-Lee-Yang-Parr (B3LYP) density-functional, the combination of the Lee-Yang-Parr correlation functional with the Becke exchange functional, is the most widely used approximation in practical electronic structure calculations. His recent studies have revealed the origins of failure of common density functional approximations as the delocalization and static correlation error, through the perspectives of fractional charges and fractional spins. This further leads to the development of much improved approximations. Prof. Yang has developed multiscale approaches combining the methods of quantum chemistry and statistical mechanics to address the reaction mechanisms of solution and enzymatic catalysis. Professor Yang has held visiting professorships from many institutions including the Japanese Society for Promotion of Science, Kyoto University, the University of Hong Kong, Tsinghua University and Peking University, and VrijeUniversiteit Brussel. He received the 1997 Annual Medal of the International Academy of Quantum Molecular Science, and the 2006 Humboldt Research Award for Senior U.S. Scientists. He has held Sloan fellowship, and is the co-author (with Robert G. Parr) of one of the leading textbooks on density-functional theory. He is an elected member of the International Academy of Quantum Molecular Science, http://www.IAQMS.org/, an elected fellow of American Association for the Advancement of Science and of the American Physical Society. Yang is recognized by the Institute for Scientific Information as a Highly Cited Researcher. In 2010, Yang was the International Solvay Chair in Chemistry, International Solvay Institutes for Physics and Chemistry, Brussels, Belgium. In 2012, Yang was awarded the 2012 American Chemical Society National Award for Computers in Chemical and Pharmaceutical Research.