Exact non-additive kinetic potentials in realistic chemical systems

Abstract

In methods based on frozen-density embedding theory or subsystem formulation of density functional theory, the non-additive kinetic potential (v nad t (r)) needs to be approximated. Since v nad t (r) is defined as a bifunctional, the common strategies rely on approximating v nad t [ρ A , ρ B ](r). In this work, the exact potentials (not bifunctionals) are constructed for chemically relevant pairs of electron densities (ρ A and ρ B ) representing: dissociating molecules, two parts of a molecule linked by a covalent bond, or valence and core electrons. The method used is applicable only for particular case, where ρ A is a one-electron or spin-compensated two-electron density, for which the analytic relation between the density and potential exists. The sum ρ A + ρ B is, however, not limited to such restrictions. Kohn-Sham molecular densities are used for this purpose. The constructed potentials are analyzed to identify the properties which must be taken into account when constructing approximations to the corresponding bifunctional. It is comprehensively shown that the full von Weizsäcker component is indispensable in order to approximate adequately the non-additive kinetic potential for such pairs of densities.

Accurate Reference Data for the Nonadditive, Noninteracting Kinetic Energy in Covalent Bonds

“…Also, as compared to analytical studies of non-additive kinetic potentials for four electron systems [9] our paper addresses significantly larger systems, while retaining high accuracy.…”

“…The second goal has been to gain accurate reference data in order to improve density functional approximations for the NAKE and NAKP functionals [9][10][11]. However, one issue that arises with these calculations within standard subsystem-DFT is that the fragment densities are not uniquely determined when the exact NAKE functional is used.…”

Orthogonality of embedded wave functions for different states in frozen-density embedding theory

“…38, and numerical examples in Ref. 39, for instance). This leads to non-unique definition of polarization of the environment.…”

Subsystem density-functional theory as an effective tool for modeling ground and excited states, their dynamics and many-body interactions

“…However, when ground states are considered, there are no doubts that in order to improve the applicability of FDE, new and more accurate nonadditive Kinetic Energy functionals need to be formulated -a strong overlap between subsystems leads to failure of FDE when semilocal NAKE functionals are employed. Efforts in this direction began with the introduction of nonlocal KE functionals [33] and are still ongoing by several groups [39,99,100,[206][207][208][209]. Despite this, a true breakthrough has still to come for the noninteracting KE functionals.…”