Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

On-Top Exchange-Correlation Hole

To see this in more detail, consider the ratio of the system-averaged on-top exchange-correlation hole to the system-average of the density itself, , as defined in Eq. (20). This ratio satisfies the inequalities... [Pg.13]

Fig. 7. Local on-top exchange-correlation hole at full coupling strength divided by density as a function of r in the He atom. The nuclear cusp produces greater LSD error for r-0... Fig. 7. Local on-top exchange-correlation hole at full coupling strength divided by density as a function of r in the He atom. The nuclear cusp produces greater LSD error for r-0...
As mentioned above, LSD yields a reasonable description of the exchange-correlation hole, because it satisfies several exact conditions. However, since the correlation hole satisfies a zero sum rule, the scale of the hole must be set by its value at some value of . The local approximation is most accurate at points near the electron. In fact, while not exact at m = 0, LSD is highly accurate there. Thus the on-top hole provides the missing link between the uniform electron gas and real atoms and molecules [18]. [Pg.13]

By (1.95), the LSD on-top exchange hole rix (r, r) is exact, at least when the Kohn-Sham wavefunction is a single Slater determinant. The LSD on-top correlation hole n (r,r) is nonexact [63] (except in the high-density, low-density, fully spin-polarized, or slowly-varying limit), but it is often quite realistic [64]. By (1.85), its cusp is then also realistic. [Pg.34]

Successful density functional approximations such as the PW91 GGA or the self-interaction correction (SIC) [57] to LSD recover [19] LSD values for the on-top hole density and cusp. The weighted density approximation (WDA) [41,42], which recovers the LSD exchange hole density but not the LSD correlation hole density [19] in the limit u -> 0, needs improvement in this respect. [Pg.15]


See other pages where On-Top Exchange-Correlation Hole is mentioned: [Pg.13]    [Pg.15]    [Pg.13]    [Pg.15]    [Pg.13]    [Pg.15]    [Pg.13]    [Pg.15]    [Pg.87]    [Pg.92]    [Pg.3]    [Pg.5]    [Pg.12]    [Pg.70]    [Pg.75]    [Pg.3]    [Pg.5]    [Pg.12]    [Pg.48]    [Pg.5]    [Pg.6]    [Pg.21]    [Pg.27]    [Pg.5]    [Pg.6]    [Pg.21]    [Pg.27]    [Pg.50]    [Pg.65]   


SEARCH



Correlation holes

Exchange correlation

Exchange holes

On-top hole

© 2024 chempedia.info