Density functional theory constrained

However, one feature of the HF potential is that it is not a local potential. In the case of perfect data (i.e. zero experimental error), the fitted orbitals obtained are no longer Kohn-Sham orbitals, as they would have been if a local potential (for example, the local exchange approximation [27]) had been used. Since the fitted orbitals can be described as orbitals which minimise the HF energy and are constrained produce the real density , they are obviously quite closely related to the Kohn-Sham orbitals, which are orbitals which minimise the kinetic energy and produce the real density . In fact, Levy [16] has already considered these kind of orbitals within the context of hybrid density functional theories. 

A new and accurate quantum mechanical model for charge densities obtained from X-ray experiments has been proposed. This model yields an approximate experimental single determinant wave function. The orbitals for this wave function are best described as HF orbitals constrained to give the experimental density to a prescribed accuracy, and they are closely related to the Kohn-Sham orbitals of density functional theory. The model has been demonstrated with calculations on the beryllium crystal. 

In the context of density functional theory (DFT), the shape function can be considered to be the fundamental variable in the Levy-constrained search [5],... 

The basic quantity in density functional theory is the energy functional which within constrained search [24, 25] is defined as... 

In the second place, a quite useful characteristic of LS-DFT is that it renders possible to transform an arbitrary wavefunction, say, the Hartree-Fock single Slater determinant into a locally-scaled one associated with a given one-particle density such as the exact one. Thus, one can easily generate a locally-scaled Hartree-Fock wavefunction that yields the exact p. In this sense, one finds much common ground between LS-DFT and those constructive realizations of the constrained-search approach which reformulate the Hartree-Fock method as well as with those developments which pose the optimized potential method as a particular instance of density functional theory [42,43,57-61]. 

Kaduk B, Van Voorhis T (2010) Communication conical intersections using constrained density functional theory-configuration interaction. J Chem Phys 133 061102... 

M. Levy and J. P. Perdew, The constrained search formulation of density functional theory, in Density Functional Methods in Physics (Dreizler, R. M. and Providencia, J. da, eds) New York Plenum, pp. 11-30 (1985). 

DENSITY-CONSTRAINED VARIATION OF THE KINETIC ENERGY IN THE CONTEXT OF THE LOCAL-SCALING VERSION OF DENSITY FUNCTIONAL THEORY... 

In the spirit of the local-scaling version of density functional theory, we deal below with the calculation of the Hartree-Fock wavefunction and energy by means of a constrained variation at fixed density p(r) = phf( ) as well as by intra-orbit and inter-orbit optimizations. 

Wu, Q., and Van Voorhis, T. Direct optimization method to study constrained systems within density-functional theory. Phys. Rev. A, 72, doi 10.1103/PhysRevA.72.024502 (2005). 

Kaduk B, Kowalczyk T, Van Voorhis T (2012) Constrained density functional theory. Chem... 

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