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Fukui function and response function for nonlocal and fractional systems
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Image of FIG. 1.
FIG. 1.

Numerical calculations of the linear-response functions and the Fukui functions of a fractional system. All calculations are performed in the level B3LYP/6-31G(d) in QM4D package. λ’s in subfigures (a) and (b) indicate the stepsize for the numerical derivatives. The path of the plot is along the -axis for both subfigures. (a) The linear-response function of Li with = 1.8 and = 1.0. A δ potential at = (0.0, 0.0, 1.0) au is set to evaluate the numerical derivative. (b) The α-spin Fukui function () = ∂ρ()/∂ of a special lithium atom with 1.8 α electrons and 1.2 β electrons.

Image of FIG. 2.
FIG. 2.

Numerical and analytical + = 3 derivatives for CO molecule at the level of LDA/6-31G(d). The plot path is along the -axis. The coordinates of the carbon and the oxygen atoms are (0.0, 0.0, 2.0) and (0.0, 0.0, 4.104777) a.u., respectively. λ indicates the stepsize of the numerical derivatives for all cases. When derivative is concerned, only electron removal direction is considered.


Generic image for table
Table I.

δ δ in the Taylor expansion of [, ] up to the order of + = 3. See the text for the meaning of each derivative.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Fukui function and response function for nonlocal and fractional systems