Potentials optimized effective

Petersilka, M., Gossmann, U. J., Gross, E. K. U., 1998, Time Dependent Optimized Effective Potential in the Linear Response Regime in Electronic Density Functional Theory. Recent Progress and New Directions, Dobson, J. F., Vignale, G., Das, M. P. (eds.), Plenum Press, New York. 

So an optimized effective potential can be found for the given excited state. The Knieger-Li-Iaffate (KLI) approximation to the optimized effective potential can also be derived [37]. 

On the other hand, development of the xc kernel beyond ALDA does not necessarily bring better results. To illustrate this point, the singlet-singlet excitation energies 0)ks calculated in [24] for the He atom with the combination (accurate vxc)/ALDA are compared in Table 2 with (Ok calculated in [46] with the accurate vxc and with the spatially non-local kernel /ffI(TD0F P)(ri, r2), which is a part of the exchange-only kernel of the time-de-pendent optimized effective potential method (OEP) [47]. They are also compared with the TDDFRT zero-order estimate 0)kso, the difference (10) of the orbital energies obtained with the accurate vxc. 

The computational effort of solving orbital Euler-Lagrange (OEL) equations is significantly reduced if the generally nonlocal exchange-correlation potential vxc can be replaced or approximated by a local potential vxc(r). A variationally defined optimal local potential is determined using the optimized effective potential (OEP) method [380, 398]. This method can be applied to any theory in which the model... 

Colle, R. and Nesbet, R.K. (2001). Optimized effective potential in finite-basis-set treatment, J. Phys. B 34, 2475-2480. 

Norman, M.R. and Koelling, D.D. (1984). Towards a Kohn-Sham potential via the optimized effective potential method, Phys. Rev. B 30, 5530-5540. 

Rigorous properties of the optimized effective potential (OEP) are derived. We present a detailed analysis of the asymptotic form of the OEP, going beyond the leading term. Furthermore, the asymptotic properties of the approximate OEP scheme of Krieger, Li and Iafrate [Phys. Lett. A 146, 256 (1990)] are analysed, showing that the leading asymptotic behavior is preserved by this approximation. 

In this section a number of rigorous statements on the optimized effective potential for finite systems will be derived. For this purpose, the exchange-only potential and the correlation potential have to be treated separately within the OEP scheme. The exact exchange potential of DFT is defined as... 

In the Kohn-Sham equations, the use of such a functional is not straightforward because of the explicite orbital dependency (see the section dealing with optimized effective potential). Strictly speaking, therefore, most of common computer implementations do not solve the associate Kohn-Sham equations. 

Hamel S, Casida ME, Salahub DR (2002b) Exchange-only optimized effective potential for molecules from resolution-of-the-identity techniques Comparison with the local density approximation, with and without asymptotic correction, J Chem Phys, 116 8276-8291... 

Hirata S, Ivanov S, Grabowski I, Bartlet RJ, Burke K, Talman JD (2001) Can optimized effective potentials be determined uniquely , J Chem Phys, 115 1635-1649... 

Krieger JB, Li Y, Iafrate GJ (1992a) Systematic approximations to the optimized effective potential Application to orbital-density-functional theory, Phys Rev A, 46 5453-5458... 

Garza J, Nichols JA, Dixon DA (2000) The optimized effective potential and the self-interaction correction in density functional theory Application to molecules, J Chem Phys, 112 7880-7890... 

The calculation of Table 2 uses the x-only optimized effective potential (OPM) for in the approximation of Krieger, Li and lafrate (KLI) [224] and... 

This should be cured by adding appropriate correlation terms to the xc part of the action functional, which is further backed by the observation that when combining the advantage of approximating by the optimized effective potential, together with a local density prescription of exchange and correlation in the xc kernels/ c and both singlet and the triplet spectrum are reproduced... 

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