Nonadditive kinetic energy functionals

Nalewajski, R. F. 2002b. Studies of the nonadditive kinetic energy functional and the coupling between electronic and geometrical structures. In Recent Advances in Density Functional Methods, Part III., (Eds.) V. Barone, A. Bencini, and P. Fantucci, pp. 257-277. Singapore World Scientific. 

The above choice of GGA approximations for the exchange, correlation, and nonadditive kinetic energy components of Ss will be referred to as the GGA97 set of approximate system-independent functionals hereafter. The interaction energies calculated using the GGA97 set of approximate functionals for the same 22 weak in-... 

The Kohn-Sham (KS) theory for sybsystems (10,11,14, 15), a direct analog of the corresponding Hartree-Fock approach (16,17), which can be used to define the chemical potential, hardness/softness or the Fukui function (FF) characteristics of reactants (10,11), involves the so called nonadditive kinetic energy functional of the noninteracting system (14), the structure of which is still little understood. Similar nonadditive contributions to the exchange-correlation energy may play a vital role in the DFT treatment of the reactive systems, van der Waals... 

Alternatively, the above equation can be interpreted as defining the nonadditive kinetic energy functional itself [see Eq. (15)] ... 

This article extends the Hellmann-Feynman amalysis and the range of application of the related technique of the coupling constant integration, to studying the exchange-correlation density functionals in the subsystem resolution. In particular the nonadditive functionals have been examined in a more detail, with a special emphasis placed upon the density functional for the nonadditive kinetic energy of the noninteracting system, which appeares in the Kohn-Sham theory for subsystems. 

For example, the Gordon-Kim-type division [65] of the kinetic energy functional defines its nonadditive contribution, which constitutes the basis of the DFT-embedding... 

STUDIES OF THE NONADDITIVE KINETIC ENERGY FUNCTIONAL AND THE COUPLING BETWEEN ELECTRONIC AND GEOMETRICAL... 

From Eqs. (13) and (16) one obtains the following exact equation linking the fiinctional derivatives of the density functional for the nonadditive kinetic energy of the non-interacting system with the subsystem densities and the corresponding numbers of electrons ... 

This equation provides an exact integral constraint, which can eventually be used to test (or constrain) the form of approximate, model functionals. It indicates, that the nonadditive kinetic energy functional should be explicitly dependent upon the subsystem numbers of electrons. This depoidence is missing in the case of the nonadditive fimctionals of Eqs. (11, 12). Neitha- of these approximate functionals satisfies Eqs. (17) and (21). 

The kinetic energies defining the nonadditive functional of Eq. (7) are known functionals of the optimum KS orbitals of subsytems, p /%] >... 

It has also been shown that the constrained-search construction of Levy can be used to determine orbitals defining the density functional for the nonadditive kinetic energy. It involves a search over the subsystem wave functions, which integrate to specified, overlapping densities of molecular fiagments. The trial wavefunctions of... 

Studies of the Nonadditive Kinetic Energy Functional and the Coupling between Electronic and Geometrical Structures... 

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