A strategy to construct approximants to the kinetic-energy-functional dependent component (v[�_A,�_B](→r)) of the effective potential in one-electron equations for orbitals embedded in a frozen-density environment [Eqs. (20) and (21) in Wesolowski and Warshel, J. Phys. Chem. 97, (1993) 8050 ] is proposed. In order to improve the local behavior of the orbital-free effective embedding potential near nuclei in the environment, the exact behavior of v_t[�_A,�_B](→r) at �_A→0 and ∫�_Bd→r = 2 is taken into account. As a result, the properties depending on the quality of this potential are invariably improved compared to the ones obtained using conventional approximants which violated the considered exact condition. The approximants obtained following the proposed strategy and especially the simplest one constructed in this work are nondecomposable, i.e., cannot be used to obtain the analytic expression for the functional of the total kinetic energy.

The fluorine superhyperfine (shf) tensor measured in aFCl:La²⁺has been found to be practically isotropic, a result which is certainly anomalous when compared to that for em>d⁹centers with one unpaired electron in a em>x²âˆ’y²orbital. This puzzling fact has been explored by means of density functional calculations. Obtained results confirm that in the em>C_4vequilibrium geometry the unpaired electron lies in a em>b₁(∼x²âˆ’y²)orbital which overlaps with the sorbitals of four ^−ligands. For explaining the origin of the near isotropy, which is well reproduced by the present calculations, the simple em>D_4hand i>C_4vaF₄^2− F₄^2− and gF₄^2−centers have also been investigated. Although the obtained results stress the high dependence of the isotropic shf constant i>A_son the metal-ligand distance i>R a near isotropy of the shf tensor is only reached for aF₄^2−(but not for F₄^2− under i>C_4vsymmetry which corresponds to the actual symmetry of the a²⁺center in the BaFCl lattice. The origin of this peculiar situation is shown to come from the mixing between dand forbitals of a²⁺allowed in i>C_4vsymmetry thus stressing the role played by forbitals in bonding properties. Writing i>A_s=CR^−n_sit is shown that for the i>D_4haF₄^2−and F₄^2−complexes the exponent i>n_sis around 20, while it is only equal to 4 for gF₄^2− This huge difference is shown to stem from the quite distinct slope of the radial i>dwave function at the equilibrium distance for the two i>d¹centers and the i>d⁹gF₄^2−unit. Finally, the present calculations strongly support that the intense band peaked at 7  890  cm^−1recorded in the optical absorption spectrum of aFCl:La²⁺is indeed a d→4ftransition.

The local structure and optical and vibrational properties associated with Mn²⁺-doped cubic AMF₃ (A = K, Rb; M = Mg, Zn, Cd) fluoroperovskites are studied by means of embedding calculations using Kohn–Sham equations with constrained electron density. It is shown that while an electronic parameter like 10Dq essentially depends on the Mn²⁺–F^− distance, the local vibration frequencies ω_i (i = a_1g, e_g modes) are dominated by the interaction between F^− ligands and nearest M²⁺ ions lying along bonding directions. The high ω_a values observed for KMgF₃:Mn²⁺ and KZnF₃:Mn²⁺, the huge variations of ω_e and ω_a frequencies when the host lattice is changed, as well as the increase of Huang–Rhys factors and the Stokes shift following the host lattice parameter, are shown to be related to this elastic coupling of the MnF₆^4− complex to the rest of the host lattice. The present results support the conclusion that the Stokes shift is determined by the interaction of the excited ⁴T_1g state with a_1g and e_g local modes while the coupling with the t_2g shear mode is not relevant. The variations of local vibrational frequencies and the Stokes shift induced by a hydrostatic pressure on a given system are shown to be rather different to those produced by the chemical pressure associated with distinct host lattices.

Ligand field splitting energies of lanthanides Ln³⁺ (Ln = from Ce to Yb) in octahedral environment are calculated using the Hohenberg–Kohn theorems based orbital-free embedding formalism. The lanthanide cation is described at orbital level whereas its environment is represented by means of an additional term in the Kohn–Sham-like one-electron equations expressed as an explicit functional of two electron densities: that of the cation and that of the ligands. The calculated splitting energies, which are in good agreement with the ones derived from experiment, are attributed to two main factors: (i) polarization of the electron density of the ligands, and; (ii) ion–ligand Pauli repulsion.