Nonlocal functionals

Kieninger and Suhai122 applied the DFT(SVWN), DFT(B88/P86), and DFT(PW86/P86) methods to study the NH3. . NH+ complex. The BSSE corrected interaction enthalpies obtained using nonlocal functionals were in a fair agreement with the results deduced from experiment and with the ones derived from the MP4 calculations. The corresponding values amounted to -32.0, -26.0, —27.6, —25.9, and —24.8 kcal/mol for DFT(SVWN), DFT(B88/P86), DFT(PW86/P86), MP4, and experiment, respectively. 

Lee, A. M., Colwell, S. M., 1994, The Determination of Hyperpolarizabilities Using Density Functional Theory With Nonlocal Functionals , J. Chem. Phys., 101, 9704. 

The formalism of nonlocal functional density theory provides an attractive way to describe the physical adsorption process at the fluid - solid interface.65 In particular, the ability to model adsorption in a pore of slit - like or cylindrical geometry has led to useful methods for extracting pore size distribution information from experimental adsorption isotherms. At the moment the model has only been tested for microporous carbons and slit - shaped materials.66,67 It is expected that the model will soon be implemented for silica surfaces. 

AU these efforts point out how the GGA form is severely limited, and in practice some compromise must be done between molecular applications, which require more nonlocal functionals [57], and soUd-state uses, for which local functionals always provide good results [58]. One general way to go beyond the GGA is to construct a fiUly nonlocal density functional. This goal is quite ambitious and trials might lead to functionals useless for practical purpose [59]. A more practical way is to construct a functional casting additional semilocal information. This can be done, for instance, including the kinetic energy density of the occupied KS orbitals ... 

It is interesting to note that early x-fiinctionals preceded most GGA s[60,61]. These x-functionals (sometimes referred to as Meta-GGA s [62]), seem to be quite promising, as demonstrated by recent constructions [63-65] based upon fits to chemical data. They have also some important properties. In particular, the PBE fimctional, as well as other GGAs, is not self-interaction free, that is the correlation energy does not vanish for a one-electron density. In this sense, nonlocal functionals, using the kinetic energy density, are Self Interaction Correlation (SIC) free by construction. 

The main issue involved in using DFT and the KS scheme pertains to construction of expressions for the XC functional, Exc[n], containing the many-body aspects of the problems (1.38). The main approaches to this issue are (a) local functionals the Thomas Fermi (TF) and LDA, (b)semilocal or gradient-dependent functionals the gradient-expansion approximation (GEA) and generalized gradient approximation (GGA), and (c) nonlocal functionals hybrids, orbital functionals, and SIC. For detailed discussions the reader is referred to the reviews [257,260-272]. 

Density functional theory calculations require a density functional. By now, a very large number of functionals have been introduced into the literature. The earliest were so-called local functionals. Subsequently, so-called nonlocal functionals were developed, otherwise known as gradient-corrected functionals. Most recently, a class of functionals referred to as hybrid functionals have been developed [16]. At the present time, hybrid functionals are the most accurate functionals available for a wide range of properties. The earliest hybrid functional is known as B3PW91 [16]. A very popular hybrid functional is B3LYP [17]. 

This chapter is intended to give the reader an idea of what types of functionals exist, and to describe what their main features are, separately for local functionals (TF, LDA and Xa Sec. 5.1), semilocal, or gradient-dependent, functionals (GEA and GGA Sec. 5.2), and nonlocal functionals (hybrids, orbital functionals such as meta-GGAs, EXX and SIC, and integral-dependent functionals such as ADA Sec. 5.3). This chapter does deal only most superficially with the actual construction of these functionals. For more... 

We repeat that the construction of the functional H in [25] involves quantities such as the group orbit 5 (2)u of the unperturbed spiral wave. In particular, H will be a nonlocal functional, in general. Keeping in mind that the experimentalist has only a few control parameters at hand, it remains a challenging task to adjust the light intensity pattern in order to obtain the desired spiral tip motion. For specific results in this direction see [38, 84, 85, 87, 88], and our brief discussion in section 3.4. 

In this respect three problems seem to be worthwhile mentioning. The GGA, which has become the standard xc-functional in the nonrelativistic context by now, can neither describe negative ions nor dispersion forces and also fails to reproduce the ground state of highly correlated systems. The first aspect reflects the fact that the single-particle spectrum produced by the GGA is far from the exact KS spectrum, due to the exponential decay of the GGA potential. The spectrum, however, is not only pertinent for the existence of negative ions, but is also particularly important for the study of excitation or ionization processes. The second problem of the GGA points at its semi-local character Only a fully nonlocal functional, which can build up an attractive force even in regions where the density vanishes, is able to reproduce dispersion forces. 

Rapcewicz K, Ashcroft NW (1991) Fluctuation attraction in condensed matter—a nonlocal functional approach. Phys Rev B 44 4032... 

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