L. Pueyo

Effects of a quantum‐mechanical lattice on the electronic structure and d–d spectrum of the (MnF6)4− cluster in Mn2+ :KZnF3

The electronic structure of the Mn2+ :KZnF3 impurity system has been computed by means of a Hartree–Fock–Roothaan cluster model. First, the Mn2+ center has been simulated by the (MnF6 )4− unit in vacuo. Then, the effects of the KZnF3 lattice have been included in the cluster calculation using three different lattice models. The well‐known point–charge approximation has been compared with two rigorous quantum–lattice models derived from the ideas of the theory of electronic separability. In these two models the lattice ions are represented by an effective lattice potential and a lattice projection operator that enforces the cluster–lattice orthogonality. In the Coulomb or Hartree model the cluster–lattice exchange interactions are neglected. The ab initio model potential (MP) lattice model makes use of model potentials for representing the lattice ions and includes an accurate nonlocal exchange operator. According to the present results, the point–charge lattice model destroys the acceptable picture of the...

Hirshfeld surfaces as approximations to interatomic surfaces

A simple algebraic model is used to show that Hirshfeld surfaces in condensed phases may be understood as approximations to the interatomic surfaces of the theory of atoms in molecules. The conditions under which this similarity is valid are explored, and both kinds of surfaces are calculated in the LiF and CS2 crystals to illustrate the main results. The link between Hirshfeld and interatomic surfaces provides a physical ground to understand the usage of the former to visualize intermolecular interactions.

The cluster–lattice interaction in the calculation of the electronic structure of CrF3−6 in K2NaCrF6

The cluster–lattice interaction involving the CrF3−6 in K2NaCrF6 has been analyzed, in the way proposed by Pueyo and Richardson [J. Chem. Phys. 67, 3583 (1977)] by computing the lattice potential with the Ewald method and introducing an analytical representation of it in the cluster Fock matrix before self‐consistency. Many different expressions have been tested in order to obtain the best representation of the Ewald results. All of them have been centered in the metal site. The partition of this interaction in core‐lattice and valence‐lattice portions reveals that the earlier procedure of centering the lattice potential function on the ligand site is inappropriate for improving the cluster in‐vacuo calculation of the equilibrium metal–ligand distance. The new results go in the required direction, but the effects of the interaction are now uniformly small. These effects have been examined in several properties, including the 10Dq, the ground state vibrational frequency ν(a1g), the horizontal displacement...

Core-projection effects in near ab initio valence calculations of the electronic ground state of the octahedral CrF4−6

Abstract Core-projection operators have been included in the one-electron effective Hamiltonian of the frozencore formalism developed by Richardson et al. (J. W. Richardson, T. F. Soules, D. M. Vaught, and R. R. Powell, Phys. Rev. B 4, 1721 (1971)) for transition-metal clusters. Projected and unprojected valence-only calculations have been carried out in CrF 4− 6 to evaluate the projection effects of the cluster a 1 g nuclear potential in the neighborhood of the equilibrium geometry. These calculations show that the dependence of the predicted geometry on the type of core-valence partition adopted in the unprojected description is due to insufficient core-valence orthogonality. Such dependence is practically removed by the action of the core-projection operators. The cluster geometry can be accurately computed with a metallic valence set formed by the 3 d orbitals and the empty 4 s and 4 p AOs.

The maximum overlap method: A general and efficient scheme for reducing basis sets. Application to the generation of approximate AO's for the 3d transition metal atoms and ions

Abstract The method of maximum overlap, often applied to the problem of basis set reduction, is formulated in terms of weighted least squares with orthogonality restrictions. An analytical solution for the linear parameters of the reduced set is given. In this form, the method is a general and efficient scheme for reducing basis sets. As an application, orthogonal radial wavefunctions of the STO type have been obtained for the 3d transition metal atoms and ions by simulation of the high-quality sets of Clementi and Roetti. The performance of the reduction has been evaluated by examining several one- and two-electron interactions. Results of these tests reveal that the new functions are highly accurate simulations of the reference AOs. They appear to be appropriate for molecular and solid state calculations.

Local geometry and resonant vibrations of Cu+:NaF. Results of abinitio perturbed ion, cluster‐in‐the‐lattice calculations involving clusters of 179 ions

The ground state electronic structure and energy of a CuF92Na5−86 cluster (Cu+ plus 12 shells of neighbors) embedded into a quantum lattice representing the NaF crystal are determined by using the ab initio perturbed ion (aiPI) method, with unrelaxed Coulomb–Hartree–Fock (uCHF) correlation energy corrections. Parallel calculations are performed on the NaF92Na5−86 cluster of the pure crystal in order to identify the changes induced by the impurity and to estimate the systematic errors in our calculations. The geometry of the first four shells (32 ions) is allowed to relax by following symmetric breathing modes. An inwards relaxation of −0.12 A is predicted for the nearest neighbors (nn) shell, but negligible relaxations are found for the outer shells. The substitution of the Na+ ion by the Cu+ impurity is favored by −1.03 eV. The Cu+ ion is found to occupy an on‐center octahedral position. The 138 independent Oh force constants corresponding to the vibration of the Cu+ and its first four shells of neighbor...

Theoretical calculation of the electronic structure and the optical spectrum of CrF2−6

Abstract The electronic structure of the CrF2−6 cluster has been analyzed by solving the Hartree-Fock equations on several electronic states, at five values of R, the metal-ligand distance in the a1g vibration. The methodology of J. W. Richardson, T. F. Soules, D. M. Vaugth, and R. R. Powell (Phys. Rev. B 4, 1721 (1971)) has been used. The computed Re is in close agreement with the observed value in alkali hexafluorochromates(IV). The nuclear potentials of the d2 triplets are almost parallel to the ground state potential, giving rise to a weak R-dependence of the spin-allowed transitions and a negligible contribution of the a1g progression to the vibrational structure of the broad bands. The absorption spectrum has been discussed in terms of the results of different SCF calculations. A new assignment is proposed that avoids most of the earlier difficulties of the spectral interpretation. The best calculated spectrum agrees with the one observed in Rb2CrF6 within 1.5 kK.

Lattice effects on bonding, covalency, and transferred hyperfine interaction in K2NaCrF6 and CrF3

The effects of the crystal lattice potential on bonding and covalency parameters of K2NaCrF6 and CrF3 have been investigated in terms of a partially relaxed lattice model described earlier. The theoretical values of different quantities in these two crystals are compared with the Hartree–Fock predictions on the CrF3−6 cluster in vacuo. In K2NaCrF6, the lattice potential reduces the orbital energies of the metal and ligand valence MO’s by 16.8 and 15.7 eV, respectively. In CrF3 these figures are 0.5 eV smaller. The 3d states, which have positive orbital energies in the cluster‐in vacuo calculation, become bound states by the action of the lattice potential. The overlap populations suffer different changes in MO’s of different symmetries. The bonding MO’s turn out to be less bonding and the antibonding MO’s still less antibonding, the net effect being an increase in the total overlap population. The covalency parameters λπ and γπ are proportional to the square root of the ligand–metal π overlap and change w...

Quintet-triplet electronic transitions and nephelauxetic effects in CrF4−6. Results of an SCF MO calculation

Abstract The 18 triplets of the octahedral cluster CrF4−6 are computed by using the solutions of SCF MO calculations on thet22ge2g−5T2g state at five metal-ligand distances. The diagonal (first order) calculation is compared with the results of a CI description limited to thed4 configuration. A third representation which includes CI and a correlation energy correction, CEC, locates the five lower triplets within 0.25 eV of their observed values. The last calculation locates the lower3A2g below the3A1g, in contrast with a previous assignment. It is shown that the crystal-field matrices can be better fitted to the published spectrum of CrF4−6 in KCrF3 if the positions of the triplets predicted by our calculation are adopted. Electron delocalization calculated from our MO wavefunction is larger in theeg(σ) block than in thet2g(π) block. A reasonably good estimate of the delocalization effect can be made from appropriate relations among repulsion integrals. However, the trend followed by these relations whenRML changes is opposite to that shown by the delocalization. Furthermore, the trend of the estimates which neglect the metal-ligand overlap integrals is incorrect. Finally, the covalency of this cluster is explored from a purely empirical point of view. The significance of the spin-orbit and Racah-Trees interactions in the empirical generation of a best set of Racah parameters for Cr2+ is examined. Our optimum sets of cluster and free-ion empirical parameters do not show the usually observed covalent reduction.

Determination of the equilibrium Cr+F− distance in Cr+:NaF and Cr+:KMgF3

Abstract The variation of the isotropic superhyperfine constant of the octahedral CrF 5− 6 cluster with the Cr + F − distance has been obtained from the results of Hartree-Fock-Roothaan calculations on the t 3 2 g e 2 g - 6 A 1 g ground state. The effects of the quality of the 3d basis set, type of core-valence partition, core-projection operators, and cluster-lattice interaction on the A s ( R ) curve has been analyzed. From this calculation and the observed values of A s , it is found that R e (Cr + :NaF)=2.47 ± 0.03 A and R e (Cr + :KMgF 3 ) = 2.35 ± 0.03 A. These are the first Cr + F − distances reported to date.