The topology of the ground-state potential energy surface of M(CN)₆ with orbitally degenerate ²T_2g (M = Ti^III (t_2g¹), Fe^III and Mn^II (both low-spin t_2g⁵)) and ³T_1g ground states (M = V^III (t_2g²), Mn^III and Cr^II (both low-spin t_2g⁴)) has been studied with linear and quadratic Jahn−Teller coupling models in the five-dimensional space of the ε_g and Ï„_2g octahedral vibrations (T_g⊗(ε_g+Ï„_2g) Jahn−Teller coupling problem (T_g = ²T_2g, ³T_1g)). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t_2g^1,5 or t_2g^2,4 ground-state electronic configurations. The results show that coupling to the Ï„_2g bending mode is dominant and leads to a stabilization of D_3d structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)₆]^3-, where the minimum is of D_4h symmetry. The Jahn−Teller stabilization energies for the D_3d minima are found to increase in the order of increasing CN−M Ï€ back-donation (Ti^III < V^III < Mn^III < Fe^III < Mn^II < Cr^II). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable D_3d minima, the effect of configuration interaction and spin−orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn−Teller distortion parameters with structures from X-ray diffraction data. Jahn−Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)₆]^3-, and the ³T_1g ground-state splitting of [Mn(CN)₆]^3-, deduced from near-IR spectra. The implications of the pseudo Jahn−Teller coupling due to t_2g−e_g orbital mixing via the trigonal modes (Ï„_2g) and the effect of the dynamic Jahn−Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)₆]^3- are also addressed.

A new 1,3-dithiol-2-ylidene substituted naphthopyranone 2 has been synthesized and characterized. UV–vis spectroscopic and cyclic voltammetry results, interpreted on the basis of density functional theory, show that 2 displays an intramolecular charge-transfer transition and acts like a donor–acceptor (D–A) system. Furthermore, a weak fluorescence originating from the excited charge-transfer state is observed.

The ligand-field induced splitting energies of f-levels in lanthanide-containing elpasolites are derived using the first-principles universal orbital-free embedding formalism [Wesolowski and Warshel, J. Phys. Chem. 1993, 97, 8050]. In our previous work concerning chloroelpasolite lattice (Cs₂NaLnCl₆), embedded orbitals and their energies were obtained using an additional assumption concerning the localization of embedded orbitals on preselected atoms leading to rather good ligand-field parameters. In this work, the validity of the localization assumption is examined by lifting it. In variational calculations, each component of the total electron density (this of the cation and that of the ligands) spreads over the whole system. It is found that the corresponding electron densities remain localized around the cation and the ligands, respectively. The calculated splitting energies of f-orbitals in chloroelpasolites are not affected noticeably in the whole lanthanide series. The same computational procedure is used also for other elpasolite lattices (Cs₂NaLnX₆, where X=F, Br, and I)—materials which have not been fabricated or for which the ligand-field splitting parameters are not available.

The cubic Prussian blue analogue Mn₃[Mn(CN)₆]₂ · 15 H₂O, which has the advantage of being transparent and magnetic (T_N = 35 K) at the same time, has been investigated by density functional theory (DFT) calculations. The three-dimensional structure is built of Mn^II ions linked to Mn^III ions by μ-bridging cyanides, to form a crystal structure, which is related to the NaCl type. In a first step, the relative stabilities of the mononuclear complexes [Mn(CN)₆]^z- (z = 2 to 4) have been studied as a function of the oxidation state, spin configuration, and the linkage isomerism of the cyanide ligand. The results we have obtained by this investigation are in good agreement with our chemical expertise. In addition, the calculations have been extended to the dinuclear [Mn₂(CN)₁₁]^z- (z = 5 and 6) clusters. Furthermore, we used DFT to model the magnetic properties as well as the ³T₁ → ¹T₂ transition, which has been observed by single-crystal near-IR spectra of Mn₃[Mn(CN)₆]₂ · 15 H₂O.

Metal (4f)−ligand (Cl 3p) bonding in LnCl₆^3- (Ln = Ce to Yb) complexes has been studied on the basis of 4f→4f and Cl,3p→4f charge-transfer spectra and on the analysis of these spectra within the valence bond configuration interaction model to show that mixing of Cl 3p into the Ln 4f ligand field orbitals does not exceed 1%. Contrary to this, Kohn−Sham formalism of density functional theory using currently available approximations to the exchange-correlation functional tends to strongly overestimate 4f−3p covalency, yielding, for YbCl₆^3-, a much larger mixing of Cl 3p→4f charge transfer into the f¹³ ionic ground-state wave function. Thus, ligand field density functional theory, which was recently developed and applied with success to complexes of 3d metals in our group, yields anomalously large ligand field splittings for Ln, the discrepancy with experiment increasing from left to the right of the Ln 4f series. It is shown that eliminating artificial ligand-to-metal charge transfer in Kohn−Sham calculations by a procedure described in this work leads to energies of 4f−4f transitions in good agreement with experiment. We recall an earlier concept of Ballhausen and Dahl which describes ligand field in terms of a pseudopotential and give a thorough analysis of the contributions to the ligand field from electrostatics (crystal field) and exchange (Pauli) repulsion. The close relation of the present results with those obtained using the first-principles based and electron density dependent effective embedding potential is pointed out along with implications for applications to other systems.

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.

Nitrosyl metal complexes, such as the sodium nitroprusside, have attracted chemists' interest for more than 30 years. The existence of long-lived metastable states easily populated by irradiation are the principal reason for this interest. Those long-lived states are interesting either for technical applications or for fundamental research. In this work, we present a comparative density functional theory (DFT) study of the ground state of two different nitrosyl compounds:  sodium nitroprusside and cyclopentadienylnitrosylnickel(II).

The photochemical reactions of the nitroprusside and the CpNiNO complexes are explained on the basis of ΔSCF and time-dependent density functional theory (TD-DFT) calculations. Both similarities and differences in the photochemical processes are highlighted.

Vertical excitations calculated for the CrO₄^2- , MnO₄^2-  , RuO₄, CrF₆, FeCp₂, RuCp₂ and CpNiNO species are compared to experimental spectra. The results obtained from the time-dependent density-functional theory−response theory (TD-DFRT) method are compared to both previously reported ΔSCF calculations and experiment. The results show that, in general, excited states of metal oxide and metallocene compounds are well described by TD-DFRT. However, serious difficulties are met with the CrF₆ system.

The ground- and excited-state properties of both [Ru(bz)₂]²⁺ and crystalline bis(η⁶-benzene)ruthenium(II) p-toluenesulfonate are investigated using the density functional theory. A symmetry-based technique is employed to calculate the energies of the multiplet structure splitting of the singly excited triplet states. For the crystalline system, a Buckingham potential is introduced to describe the intermolecular interactions between the [Ru(bz)₂]²⁺ system and its first shell of neighbor molecules. The overall agreement between experimental and calculated ground- and excited-state properties is good, as far as the absolute transition energies, the Stokes shift, and the geometry of the excited states are concerned. The calculated d-d excitation energies of the isolated cluster are typically 1000-2000 cm^-1 too low. An energy lowering is obtained in a_1g → e_1g(³E_1g) excited state when the geometry of [Ru(bz)₂]²⁺ is bent along the e_1u Renner-Teller active coordinate. It vanishes as the crystal packing is taken into account.

The ground- and excited-state properties of both gas phase and crystalline ruthenocene, Ru(cp)₂, are investigated using density functional theory. A symmetry-based technique is employed to calculate the energies of the multiplet splittings of the singly excited triplet states. For the crystalline system, a Buckingham potential is introduced to describe the intermolecular interactions between a given Ru(cp)₂ molecule and its first shell of neighbors. The overall agreement between experimental and calculated ground- and excited-state properties is very good as far as absolute transition energies, the Stokes shift and the geometry of the excited states are concerned. An additional energy lowering in the ³B₂ component of the 5a1′→4e1″ excited state is obtained when the pseudolinear geometry of Ru(cp)₂ is relaxed along the low-frequency bending vibration.

The pseudo rotation of PF5 has been investigated using both static and dynamic density functional theory (DFT) methods. The lowest energy path is the Berry pseudorotation, corresponding to the concerted exchange of two apical and two equatorial ligands. The potential energy surface has been derived and the transition state localised. In ab initio molecular dynamics the Berry pseudorotation has been observed and occurs with a typical period of 0.6 ps at 750 K. Analysis of the trajectories and comparison of the spectral density with the vibrational frequencies is presented.

The ground and excited state properties of the Cr³⁺ ion doped into the cubic host lattices Cs₂NaYCl₆ and Cs₂NaYBr₆ have been studied using density functional theory. A new symmetry based technique was employed to calculate the energies of the multiplets ⁴A_2g, ⁴T_2g, ²E_g, and ⁴T_1g. The geometry of the CrX^{3 -Â} ₆ cluster was optimized in the ground and excited states. A Madelung correction was introduced to take account of the electrostatic effects of the lattice. The experimental Cr–X distance in the ground state can be reproduced to within 0.01 Ã… for both chloride and bromide systems. The calculated d–d excitation energies are typically 2000–3000 cm^–1 too low. An energy lowering is obtained in the first ⁴T_2g excited state when the octahedral symmetry of CrX^{3 -Â} ₆ is relaxed along the eg Jahn–Teller coordinate. The geometry corresponding to the energy minimum is in excellent agreement with the ⁴T_2g geometry derived from high-resolution optical spectroscopy of Cs₂NaYCl₆:Cr³⁺. It corresponds to an axially compressed and equatorially elongated CrX^{3 -Â} ₆ octahedron.

The luminescence of [CrX₆]^3– X=Br^–, Cl^– has been studied through density functional theory (DFT) using both deMon and ADF codes. Multiplet energies⁴A₂,²E,⁴T₂, and⁴T₁ have been expressed as energies of non-redundant single determinants and calculated as in Ref. [1]. The influence of the metal ligand distance on the multiplet energies has been investigated. Of particular interest to this work is the Jahn-Teller effect distortion. We found that the system moves to a more stable geometry when the axial bond length is compressed and the equatorial one elongated in agreement with the experimental value.

Quantum chemical calculations based on density functional theory have been performed on ruthenocene. Excellent agreement is obtained with groundâ€� and excitedâ€�state properties derived from optical spectroscopy. In particular, the energies of the first d–d excitations, the unusually large Stokes shift, the structural expansion of Ru(cp)₂ and the substantial reduction of the Ruâ€�cp force constant in the first triplet excited state are almost quantitatively reproduced. The lowestâ€�energy excitation is found to have substantial charge transfer character.