Deviation of (a) KS kinetic energy T s and (b) nuclear-electron attraction energy E ne versus n from linearity. Here, n is the fractional electron number, and n = 0 and n = 1 correspond to a carbon cation (C+) and a neutral carbon atom (C), respectively.
Absolute deviation of E v (N + n) from linearity for unscaled (original) and scaled HF methods. The n = 0 point represents (a) a carbon atom and (b) a water molecule. The green dashed line marks zero deviation as a reference. The HF curve is obtained through SCF calculation, while the scaled HF curve includes the post-SCF energy corrections of Eqs. (11) and (12) for positive and negative n, respectively. The inset of (b) shows the calculated E v (N + n) of a water molecule in unit of hartree.
(a) Calculated εHOMO versus calculated −I for 70 molecules, and (b) εLUMO versus −A for 47 molecules of the G2–97 set. The green solid line indicates εHOMO = −I in (a) and εLUMO = −A in (b). εHOMO and εLUMO of the scaled HF method are calculated by using Eqs. (11) and (12) , and the vertical I and A are calculated by the ΔSCF method. The mean absolute deviations (MADs) between calculated εHOMO and −I are 0.32 and 1.60 eV for scaled and unscaled HF methods; and the MADs between εLUMO and −A are 0.38 and 0.90 eV with and without SC, respectively.
HF calculated versus experimentally measured −I for 18 atoms (H–Ar). The calculated εHOMO by using the HF method with and without SC are also depicted. The green solid line indicates perfect agreement with experimental data of −I. Taking the experimental −I as references, the MADs for the calculated −I, , and are 0.86, 0.47, and 1.13 eV, respectively. Whereas taking the calculated −I as references, the MADs for the calculated , and are 1.09 and 0.27 eV, respectively.
The vertical ionization potentials and the HOMO energies of M2(hpp)4. The Is are calculated with the ΔSCF approach. All energies are in units of eV.
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