By Xin Xu
Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Laboratory for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai, 200433, China
An integration approach is developed to calculate ionization potentials (IPs), and electron affinities (EAs), which is an extension of the D-∆MBPT(2) method . The latter is an extension of the single-point method of Cohen et al.  from the perspective of fractional charges. While relaxation effects were included only at the Hartree-Fock (HF) level in the previous methods, such effects are fully taken into account in the present method up to the second-order Møller-Plesset (MP2) level. This is made possible by deriving the full MP2 energy gradient with respect to the orbital occupation numbers, which is solved through the coupled-perturbed HF (CP-HF) equations.
Figure 1. Comparison of the MP2 correlation energy derivatives with respect to the orbital occupation number at different levels of approximations for L = I (as in Ref. 2), II (as in Ref. 1), and III(i.e., the present work). (a) The initial derivatives corresponding to HOMO of the N0-electron system, (b) the final derivatives corresponding to LUMO of the (N0‒1)-electron system, (c) the initial derivatives corresponding to LUMO of the N0-electron system; (d) The final derivatives corresponding to HOMO of the (N0+1)-electron system.
This research was sponsored by the Ministry of Science and Technology of China (2013CB834606, 2011CB808505), and National Natural Science Foundation of China (21133004, 91427301).
 A. Beste, A. Vazquez-Mayagoitia, and J. V. Ortiz, J. Chem. Phys. 138, 074101(2013).
 A. J. Cohen, P. Mori-Sánchez, and W. Yang, J. Chem. Theory Comput. 5, 786 (2009). N. Q. Su and Xin Xu, J. Chem. Theory Comput., in revision.