Asymptotically corrected functionals

All of the calculations described here use local functionals that do not include exact exchange. The best choice of functional for calculating MCD spectra is still an open question. In our experience, the MCD parameters produced with different local functionals do not vary much (83). The exception to this rule is functionals that are asymptotically correct. Asymptotically correct functionals tend to give excitation energies that differ from those produced by standard local functionals, particularly for Rydberg and charge-transfer transitions. The MCD parameters produced by asymptotically correct functionals tend to follow a similar pattern when compared with results of other local functionals. A few studies have considered hybrid functionals (42,43). This work found that hybrid functionals were superior in some applications. More work in this area is needed. 

The results show systematic overestimates for the EDA and GGA calculations. For the asymptotic corrected functional of van Leeuwen and Baerends a general trend is less clearly recognized. In total this means that one has to be very cautious when using such calculations in a predictive manner and it emphasizes the need for improved density-functionals to be used in time-dependent density-functional theory. 

LB94 van Leeuwen-Baerends asymptotically corrected functional... 

It has been the author s contention that, at least for small molecules, the breakdown of the adiabatic approximation is rather minor for one-electron excitations compared to errors already present when common popular functionals are used in the adiabatic approximation. This contention has been largely confirmed by the general quality of excitation energies obtained by asymptotically-corrected functionals. Nevertheless it is known that, in con-... 

Allen, M. J., Tozer, D. J., 2000, Kohn-Sham Calculations Using Hybrid Exchange-Correlation Functionals with Asymptotically Corrected Potentials , J. Chem. Phys., 113, 5185. 

II.C.3) are labeled Im[V]-Approx, while parameters obtained from a SOS expansion based on Im[V]-Approx are denoted by Im[V]-SOS. The asymptotically correct SAOP functional (106,107) is used in all cases. 

We will not carry this analysis further, since in writing the correction function on the form e(z,y) we have not explicitly included the dependence on derivatives of f. However, we note that this section provides reason for a classification of defect correction schemes by a new concept, called convergence order. A procedure which guarantees the asymptotic inequalities (within some disk)... 

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. 

Further, there are asymptotically corrected XC kernels available, and other variants (for instance kernels based on current-density functionals, or for range-separated hybrid functionals) with varying degrees of improvements over adiabatic LDA, GGA, or commonly used hybrid DFT XC kernels [45]. The approximations in the XC response kernel, in the XC potential used to determine the unperturbed MOs, and the size of the one-particle basis set, are the main factors that determine the quality of the solutions obtained from (13), and thus the accuracy of the calculated molecular response properties. Beyond these factors, the quality of the... 

The linear photoresponse of metal clusters was successfully calculated for spherical [158-160, 163] as well as for spheroidal clusters [164] within the jellium model [188] using the LDA. The results are improved considerably by the use of self-interaction corrected functionals. In the context of response calculations, self-interaction effects occur at three different levels First of all, the static KS orbitals, which enter the response function, have a self-interaction error if calculated within LDA. This is because the LDA xc potential of finite systems shows an exponential rather than the correct — 1/r behaviour in the asymptotic region. As a consequence, the valence electrons of finite systems are too weakly bound and the effective (ground-state) potential does not support high-lying unoccupied states. Apart from the response function Xs, the xc kernel /xc[ o] no matter which approximation is used for it, also has a self-interaction error. This is because /ic[no] is evaluated at the unperturbed ground-state density no(r), and this density exhibits self-interaction errors if the KS orbitals were calculated in LDA. Finally the ALDA form of /,c itself carries another self-interaction error. 

Misquitta, A.J. and Szalewicz, K. (2002). Intermolecular forces from asymptotically corrected density functional description of monomers. Chem, Phys. Lett., 357, 301-6. 

Those findings can be related to the measurements of the distribution functions presented in Sec. V, since the osmotic coefficient is a measure of the free counterions contributing to the osmotic pressure. The investigation of the distribution functions showed that the amount of condensed ions is always larger than the prediction from the PB theory. This entails a smaller osmotic coefficient. In addition, the stronger deviation at higher density, as well as the asymptotic correctness in the dilute limit, is in accord with the corresponding behavior of p. 

Asymptotic corrections for exchange functionals have attracted attentions especially in time-dependent DFT (TDDFT) studies. In far regions from atomic nuclei, it is proved that exchange potential for c-spin electrons, = E /bp has the asymptotic relation [77]... 

Table 20.7 summarizes mean absolute errors in calculated excitation energies of five typical molecules by TDDFT. The table also displays calculated results of asymptotically corrected AC [79] and LB [78] (AC-BOP and LBOP) and hybrid B3LYP [72] functionals, which are mentioned in the former section. The ab initio SAC-Cl [103] results are also shown to confirm the accuracies. The 6-311G- -- -(2d,2p) basis set was used in TDDFT calculations [104,105]. As the table indicates, the LC scheme clearly improves Rydberg excitation energies that are underestimated for pure BOP functional, at the same (or better) level as the AC scheme does. It should be noted that LC and AC schemes also provide improvements on valence excitation energies for all molecules. LC and AC results are comparable to SAC-CI results. The LB scheme clearly modifies... 

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