Exchange-correlation kernel

Here, is the unperturbed density, vxc the exchange-correlation potential and vion represents the atomic potential. K r,f) is the Hartree-exchange-correlation kernel, defined by ... 

Analytic or semi-analytic many-body methods provide an independent estimate of ec( .>0- Before the Diffusion Monte Carlo work, the best calculation was probably that of Singwi, Sjblander, Tosi and Land (SSTL) [38] which was parametrized by Hedin and Lundqvist (HL) [39] and chosen as the = 0 limit of Moruzzi, Janak and Williams (MJW) [40]. Table I shows that HL agrees within 4 millihartrees with PW92. A more recent calculation along the same lines, but with a more sophisticated exchange-correlation kernel [42], agrees with PW92 to better than 1 millihartree. 

Gritsenko, O. and Baerends E.Jan., Asymptotic correction of the exchange - correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations. J.Chem.Phys. (2004) 121 655-660. 

This apparent contradiction arises from the adiabatic approximation of exchange-correlation kernels, i.e., their absence of frequency dependence [106], As Eqs. (2-44)... 

TDDFT with an OEP (TDOEP) for excitation energies [109, 110] and frequency-dependent polarizabilities [111] has the same working equations (2-17), (2-21), or (2-22) with (2-60) and (2-61). The corresponding exchange-correlation kernel derived by Gorling [112, 113] is frequency dependent ... 

We finally mention that an extension of the parametrization (206) to nonvanishing q was given by Dabrowski [102], The spin-dependent case was treated by Liu [103]. A similar interpolation for the exchange-correlation kernel of the 2-dimensional electron gas has been derived by Holas and Singwi [95]. 

Here the spin-dependent exchange-correlation kernel is given by the Fourier... 

In Ref. [193] various non-hybrid and hybrid exchange-correlation potentials and suitable adiabatic local density approximations for the exchange-correlation kernel were... 

Earlier we also discussed the uncoupled HF approach to dispersion, where the sum over states is performed at the orbital level. Of course, this approach can also be applied with KS orbitals. However, HeBehnann and Jansen [193] found that the uncoupled sum-over-states approximation yields unacceptable errors. These are mainly due to neglect of the Coulomb and exchange-correlation kernels and are not substantially improved through an asymptotic correction of the exchange-correlation potential. 

The exchange-correlation kernel is thus the functional derivative of the exchange-correlation potential which in turn can be expressed in terms of the functional derivative of the exchange-correlation energy density All these... 

They were interested in the performance of different density-functional approaches. In all cases they used the ALDA for the exchange-correlation kernel, but for the response function Xs of Eq. (96) they used different density functionals. Since most of the current density functionals give a wrong ionization threshold (cf. the discussion of the preceding section), they rigidly shifted the single-particle energies so that the experimental ionization potential was obtained. 

A HYBRID FUNCTIONAL FOR THE EXCHANGE-CORRELATION KERNEL IN TIME-DEPENDENT DENSITY FUNCTIONAL THEORY... 

A review of the approximations in any time-depedendent density functional calculation of excitation energies is given. The single-pole approximation for the susceptibility is used to understand errors in popular approximations for the exchange-correlation kernel. A new hybrid of exact exchange and adiabatic local density approximation is proposed and tested on the He and Be atoms. 

We have shown how the results of TDDFT with approximate exchange-correlation kernel functionals may be understood in terms the well-known... 

It is useful to introduce the exchange-correlation kernel, /xc, defined by... 

In reciprocal space, Ghosez et al. [67] showed that the xc field corresponds to a 1/q divergence in the exchange-correlation kernel for small wavevectors q. This ultra-non-local density dependence is certainly missing from all density based approximations to the exact xc functional, potential or kernel. One possibility for approximating it within Kohn-Sham DFT has been explored recently by de Boeij et al. [68] by using a functional of the current rather than the density, in the low-frequency limit of time-dependent DFT. 

In the so-called adiabatic approximation, the time-dependent exchange-correlation kernel is derived from the time-independent ground-state functional. 

Here ( > p) he accurately known exchange-correlation energy density of the uniform electron gas of spin densities , p- For the time-dependent exchange-correlation kernel of Eq. [40], Eq. [53] leads to... 

Del Sole, and R. W. Godby, Phys. Rev. B, 69,155112 (2004). Long-Range Contribution to the Exchange-Correlation Kernel of Time-Dependent Density Functional Theory. 

Correlation Energies from Scaled Exchange-Correlation Kernels Importance of Spatial vs. Temporal Nonlocality. 

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