Molecule Expt. ( a ) PBE-eig PBE0-eig HF-eig GW G$_{0}$W$_{0}$(HF) G$_{0}$W$_{0}$(PBE)-QP MP2 ( a ) PBE-tot LiH 7.90 4.34 5.81 8.14 8.0 ( b ) 8.2 ( b ) 8.0 8.20 8.02 Li$_{2}$ 5.11 2.96 3.62 4.62 4.6 4.7 4.4 4.91 5.09 LiF 11.30 6.00 8.62 13.26 11.7 11.2 12.0 12.64 11.87 Na$_{2}$ 4.89 2.81 3.38 4.16 4.1 4.3 4.7 4.48 4.97 NaCl 9.80 5.24 6.92 9.78 9.0 9.2 8.8 9.63 9.37 CO 14.01 9.05 10.98 14.80 13.4 14.1 13.9 15.08 13.88 CO$_{2}$ 13.78 9.08 11.09 14.50 13.1 13.3 13.6 14.71 13.64 CS 11.33 7.40 9.09 12.31 10.8 11.7 11.0 12.58 11.31 C$_{2}$H$_{2}$ 11.49 7.20 8.64 11.05 10.6 11.1 11.2 11.04 11.39 C$_{2}$H$_{4}$ 10.68 6.79 8.11 10.11 9.8 10.4 9.6 10.18 10.67 CH$_{4}$ 13.60 9.43 11.29 14.77 14.1 14.4 14.4 ( c ) 14.82 14.10 CH$_{3}$Cl 11.29 7.08 8.80 11.68 11.0 11.4 11.1 11.90 11.10 CH$_{3}$OH 10.96 6.31 8.49 12.14 10.7 10.8 10.5 12.16 10.72 CH$_{3}$SH 9.44 5.60 7.09 9.50 8.8 9.0 8.4 9.73 9.29 Cl$_{2}$ 11.49 7.32 9.02 12.03 10.9 11.3 11.5 12.37 11.22 ClF 12.77 7.90 9.88 13.33 12.4 12.4 13.0 13.63 12.48 F$_{2}$ 15.70 9.43 12.42 17.90 15.2 15.2 16.2 18.20 15.39 HOCl 11.12 6.68 8.66 11.93 10.6 10.8 11.0 12.23 10.95 HCl 12.74 8.02 9.78 12.96 12.2 12.5 12.5 13.02 12.71 H$_{2}$O$_{2}$ 11.70 6.38 8.78 13.06 11.0 11.1 11.1 13.00 11.18 H$_{2}$CO 10.88 6.28 8.37 11.93 10.4 10.5 10.6 11.97 10.80 HCN 13.61 9.05 10.67 13.19 12.7 13.2 12.4 13.33 13.67 HF 16.12 9.61 12.47 17.74 16.0 15.6 15.7 17.35 16.27 H$_{2}$O 12.62 7.24 9.59 13.88 12.3 12.1 11.9 ( d ) 13.62 12.88 NH$_{3}$ 10.82 6.16 8.11 11.80 10.8 11.0 10.6 11.57 11.02 N$_{2}$ 15.58 10.28 12.51 16.21 15.1 15.7 15.6 16.41 15.39 N$_{2}$H$_{4}$ 8.98 5.75 7.67 11.06 9.8 10.1 9.5 11.07 9.90 SH$_{2}$ 10.50 6.29 7.79 10.48 9.8 10.1 9.9 10.48 10.38 SO$_{2}$ 12.50 8.08 9.96 13.02 11.3 11.7 11.7 13.46 12.12 PH$_{3}$ 10.95 6.79 8.17 10.38 9.9 10.3 10.0 10.50 10.39 P$_{2}$ 10.62 7.09 8.21 9.65 9.2 9.8 9.0 10.09 10.37 SiH$_{4}$ 12.30 8.50 10.13 12.93 12.3 12.6 12.4 ( e ) 13.25 11.95 Si$_{2}$H$_{6}$ 10.53 7.27 8.54 10.82 10.2 10.6 9.9 11.03 10.36 SiO 11.49 7.46 9.14 11.78 10.9 11.2 11.3 11.82 11.27 MAE - 4.35 2.55 0.81 0.5 0.4 0.5 0.82 0.24 TABLE I: Experimental ionization potential (first column) and HOMO energy calculated using different approximations for exchange and correlation. “X-eig” refers to a single-particle eigenvalue while “X-tot” refers to a total energy difference, E ( N ) − E ( N − 1). The G$_{0}$W$_{0}$(PBE) energies have been obtained from the QP equation while the GW and G$_{0}$W$_{0}$ energies are obtained from the DOS in Eq. (9). Last row shows the mean absolute error (MAE) with respect to experiments. All energies are in eV. ( a $^{)}$From Ref. 59. The MP2 calculations use a Gaussian 6-311G ∗∗ basis set. ( b $^{)}$To be compared with the GW value 7.85 and the G$_{0}$ W$_{0}$(HF) value 8.19 reported in Ref. 24. ( c $^{)}$To be compared with the G$_{0}$ W$_{0}$(LDA) value 14.3 reported in Ref. 21. ( d $^{)}$To be compared with the G$_{0}$ W$_{0}$(LDA) value 11.94 reported in Ref. 22. ( e $^{)}$To be compared with the G$_{0}$ W$_{0}$(LDA) values 12.7 and 12.66 reported in Refs. 21 and 22, respectively. are the same as those listed in the last row of Table II. In Table II we provide an overview of the compara- tive performance of the different methods. Shown is the mean average deviation between the IPs calculated with the different methods as well as the experimental values. Note that the numbers in the experiment row/column 6