Asymptotically Correct

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

R. Although expressions for this parameter exist, they are derived by a hybrid of molecular mechanical and thermodynamic arguments which are not at present known to be consistent as droplet size decreases (8). An analysis of the size limitation of the validity of these arguments has, to our knowledge, never been attempted. Here we evaluate these expressions and others which are thought to be only asymptotically correct. Ve conclude, from the consistency of these apparently independent approaches, that the surface of tension, and, therefore, the surface tension, can be defined with sufficient certainty in the size regime of the critical embryo of classical nucleation theory. 

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. 

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. 

This result has been shown to be asymptotically correct in the limit xN — °° (Matsen and Bates 1996a Matsen and Whitmore 1996). These exponents differ from those obtained by Helfand and Wasserman, who found d aAr0< 43 0143 (with a geometry-dependent prefactor) and F JkT (dlaN a)2S (Helfand and Wasserman 1976). The difference arises because Helfand s calculations were only carried out numerically to d/aNm 3, whereas in the limit d/aNm 1, the scaling (eqn 2.4) is obtained. As in the Helfand-Wasserman theory, phase boundaries can be computed using Semenov s theory, and are also found to be independent of (Semenov 1985). 

A simple and asymptotically correct [26-28] model is the Ruderman-Kittel-Kasuya-Yosida or RKKY exchange between two localized moments in a Pauli-paramagnetic matrix. For a free-electron gas of wave-vector kF,... 

Table 1-3. Summary of the symmetry forcing operators, convergence properties, and asymptotic correctness of various symmetry-adapted perturbation theories...

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... 

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. 

Even this simple hydrostatic formula clarifies the nature of the surface tension. The concentration variation within the interfacial region leads to a nonuniform stress tensor. The neglect of this nonuniformity gives rise to the conventional description of bulk phases. The iterative subtractive procedure demanded by the convergent expression given by Equation 5 corrects for this oversimplification at the boundary of the phases and yields an asymptotic correction (2) to the free energy of the total system in terms of its geometrical properties. 

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... 

Of course, this is only an estimate. Raoult s law is only asymptotically correct as The... 

The asymptotically correct approximation (ACA) was first introduced by Hobson [44] for the description of adsorption equilibrium on heterogeneous surfaces it has however become of wide use in the analysis of adsorption isotherms only after Cerofolini s investigation of the involved errors (which are of the same order as in the CA) and demonstration of its usefulness in determining the maximum adsorption energy [28]. The ACA can be extended to desorption kinetics by replacing the supposedly true desorption isotherm kinetics A (t,E) with their asymptotic limits. Since... 

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