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A nonempirical scaling correction approach for density functional methods involving substantial amount of Hartree–Fock exchange
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10.1063/1.4801922
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Affiliations:
1 Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
2 Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
a) Electronic mail: xz58@ustc.edu.cn
b) Electronic mail: weitao.yang@duke.edu
J. Chem. Phys. 138, 174105 (2013)
/content/aip/journal/jcp/138/17/10.1063/1.4801922
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/17/10.1063/1.4801922

## Figures

FIG. 1.

Deviation of (a) KS kinetic energy and (b) nuclear-electron attraction energy versus from linearity. Here, is the fractional electron number, and = 0 and = 1 correspond to a carbon cation (C) and a neutral carbon atom (C), respectively.

FIG. 2.

Absolute deviation of ( + ) from linearity for unscaled (original) and scaled HF methods. The = 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. for positive and negative , respectively. The inset of (b) shows the calculated ( + ) of a water molecule in unit of hartree.

FIG. 3.

(a) Calculated ε versus calculated − for 70 molecules, and (b) ε versus − for 47 molecules of the G2–97 set. The green solid line indicates ε = − in (a) and ε = − in (b). ε and ε of the scaled HF method are calculated by using Eqs. , and the vertical and are calculated by the ΔSCF method. The mean absolute deviations (MADs) between calculated ε and − are 0.32 and 1.60 eV for scaled and unscaled HF methods; and the MADs between ε and − are 0.38 and 0.90 eV with and without SC, respectively.

FIG. 4.

HF calculated versus experimentally measured − for 18 atoms (H–Ar). The calculated ε by using the HF method with and without SC are also depicted. The green solid line indicates perfect agreement with experimental data of −. Taking the experimental − as references, the MADs for the calculated −, , and are 0.86, 0.47, and 1.13 eV, respectively. Whereas taking the calculated − as references, the MADs for the calculated , and are 1.09 and 0.27 eV, respectively.

## Tables

Table I.

The vertical ionization potentials and the HOMO energies of M(hpp). The s are calculated with the ΔSCF approach. All energies are in units of eV.

/content/aip/journal/jcp/138/17/10.1063/1.4801922
2013-05-02
2014-04-17

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