We report a detailed DFT study of the energetic and structural properties of the spin-crossover Co(II) complex [Co(tpy)₂]²⁺ (tpy = 2,2′:6′,2′′-terpyridine) in the low-spin (LS) and the high-spin (HS) states, using several generalized gradient approximation and hybrid functionals. In either spin-state, the results obtained with the functionals are consistent with one another and in good agreement with available experimental data. Although the different functionals correctly predict the LS state as the electronic ground state of [Co(tpy)₂]²⁺, they give estimates of the HS–LS zero-point energy difference ΔE⁰_HL (tpy)  which strongly depend on the functional used. This dependency on the functional was also reported for the DFT estimates of the zero-point energy difference ΔE⁰_HL (bpy)  in the HS complex [Co(bpy)₃]²⁺ (bpy = 2,2′-bipyridine) [A. Vargas, A. Hauser and L. M. Lawson Daku, J. Chem. Theory Comput., 2009, 5, 97]. The comparison of the ΔE⁰_HL (tpy)  and ΔE⁰_HL (bpy)  estimates showed that all functionals correctly predict an increase of the zero-point energy difference upon the bpy → tpy ligand substitution, which furthermore weakly depends on the functionals, amounting to (ΔE⁰_HL)_bpy->tpy  ≈ +2670 cm^-1 . From these results and basic thermodynamic considerations, we establish that, despite their limitations, current DFT methods can be applied to the accurate determination of the spin-state energetics of complexes of a transition metal ion, or of these complexes in different environments, provided that the spin-state energetics is accurately known in one case. Thus, making use of the availability of a highly accurate ab initio estimate of the HS–LS energy difference in the complex [Co(NCH)₆]²⁺ [L. M. Lawson Daku, F. Aquilante, T. W. Robinson and A. Hauser, J. Chem. Theory Comput., 2012, 8, 4216], we obtain for [Co(tpy)₂]²⁺ and [Co(bpy)₃]²⁺best estimates of ΔE⁰_HL (bpy) ≈ -2800 cm^-1  and ΔE⁰_HL (tpy) ≈ 0 cm^-1 , in good agreement with the known magnetic behaviour of the two complexes.

Electrochemical and photophysical analysis of new donor–acceptor systems 2 and 3, in which a benzothiadiazole (BTD) unit is covalently linked to a tetrathiafulvalene (TTF) core, have verified that the lowest excited state can be ascribed to an intramolecular-charge-transfer (ICT) π(TTF)→π*(benzothiadiazole) transition. Owing to better overlap of the HOMO and LUMO in the fused scaffold of compound 3, the intensity of the ¹ICT band is substantially higher compared to that in compound 2. The corresponding CT fluorescence is also observed in both cases. The radical cation TTF^+. is easily observed through chemical and electrochemical oxidation by performing steady-state absorption experiments. Interestingly, compound 2 is photo-oxidized under aerobic conditions.

Highly accurate estimates of the high-spin/low-spin energy difference ΔE_HL^el in the high-spin complexes [Fe(NCH)₆]²⁺ and [Co(NCH)₆]²⁺ have been obtained from the results of CCSD(T) calculations extrapolated to the complete basis set limit. These estimates are shown to be strongly influenced by scalar relativistic effects. They have been used to assess the performances of the CASPT2 method and of 30 density functionals of the GGA, meta-GGA, global hybrid, RSH and double-hybrid types. For the CASPT2 method, the results of the assessment support the proposal [Kepenekian, M.; Robert, V.; Le Guennic, B. J. Chem. Phys.2009, 131, 114702] that the ionization potential–electron affinity (IPEA) shift defining the zeroth-order Hamiltonian be raised from its standard value of 0.25 au to 0.50–0.70 au for the determination of ΔE_HL^el in Fe(II) complexes with a [FeN₆] core. At the DFT level, some of the assessed functionals proved to perform within chemical accuracy (±350 cm^-1) for the spin-state energetics of [Fe(NCH)₆]²⁺, others for that of [Co(NCH)₆]²⁺, but none of them simultaneously for both complexes. As demonstrated through a reparametrization of the CAM-PBE0 range-separated hybrid, which led to a functional that performs within chemical accuracy for the spin-state energetics of both complexes, performing density functionals of broad applicability may be devised by including in their training sets highly accurate data like those reported here for [Fe(NCH)₆]²⁺ and [Co(NCH)₆]²⁺.

Four novel bimetallic borohydrides have been discovered, K₂M(BH₄)₄ (M = Mg or Mn), K₃Mg(BH₄)₅, and KMn(BH₄)₃, and are carefully investigated structurally as well as regarding their decomposition reaction mechanism by means of in situ synchrotron radiation powder X-ray diffraction (SR-PXD), vibrational spectroscopies (Raman and IR), thermal analysis (TGA and DTA), and ab initio density functional theory (DFT) calculations. Mechano-chemical synthesis (ball-milling) using the reactants KBH₄, α-Mg(BH₄)₂, and α-Mn(BH₄)₂ ensures chlorine-free reaction products. A detailed structural analysis reveals significant similarities as well as surprising differences among the two isomorphs K₂M(BH₄)₄, most importantly concerning the extent to which the complex anion [M(BH₄)₄]^2– is isolated in the structure. Anisotropic thermal expansion and an increase in symmetry at high temperatures in K₃Mg(BH₄)₅ is ascribed to the motion of BH₄ groups inducing hydrogen repulsive effects, and the dynamics of K₃Mg(BH₄)₅ are investigated. Decomposition in the manganese system proceeds via the formation of KMn(BH₄)₃, the first perovkite type borohydride reported to date.

The crystal chemistry of the barium fluoride chloride system is studied both experimentally and theoretically. Different synthetic approaches yield nanocrystalline materials as well as large single crystals. The crystalline phases identified so far are BaFCl, Ba₁₂F₁₉Cl₅ and Ba₇F₁₂Cl₂ (in two modifications) and compared with analogous compounds. It is demonstrated that the compound Ba₂F₃Cl reported by Fessenden and Lewin 50 years ago corresponds to Ba₇F₁₂Cl₂. The phase diagram of the BaCl₂ – BaF₂ system is reinvestigated for fluoride mole fractions between 0.5 and 1. The peritectic formation of Ba₁₂F₁₉Cl₅ is observed. Periodic DFT calculations are performed for all structures in this system, including a hypothetical structure for Ba₂F₃Cl, based on the experimental structure of Ba₂H₃Cl. The energy of formation of the different barium fluoride chloride compounds from BaCl₂ and BaF₂ (normalized for one barium atom per formula unit), as calculated by DFT at 0K, is within only about ± 15 kJ/mol. Comparison with recent experimental results on calcium and strontium hydride chloride (bromide) compounds, suggest the possibility of a mutual exclusion between the M₂X₃Y and M₇X₁₂Y₂ (M = Ca, Sr, Ba, Pb, X = H, F, Y = Cl,Br) structures. The single crystal structure of PbFBr is also reported.

The photophysical properties of the free neutral radical galvinoxyl were studied by a combination of femtosecond time-resolved spectroscopy and quantum chemical calculations. The electronic absorption spectrum is dominated by an intense band at 430 nm that is ascribed to the D9,10←D0 transitions. Upon photoexcitation at 400 nm, the population of the D9,10 states decays within less than 200 fs to the electronic ground state. This ultrafast internal conversion does not involve intramolecular modes with large amplitude motion as the measured dynamics does not show any significant dependence on the environment, but is most probably facilitated by a high density of electronic states of different character. Depending on the solvent, a weak transient band due to the galvinoxylate anion is also observed. This closed-shell species, which is fluorescent although its deactivation is also dominated by non-radiative decay, is generated upon biphotonic ionization of the solvent and electron capture. The ultrashort excited-state lifetime of the galvinoxyl radical precludes photoinduced disproportionation previously claimed to be at the origin of the formation of both anion and cation.

In this article, the synthesis of a novel high-conjugated ligand and its corresponding Ru(II) complex PTFTF:Ru is reported, along with the linear and nonlinear optical characterizations. Two-photon absorption based optical power limiting properties (OPL), especially in the near infrared, are described and compared to those of the analogous complexes previously published. Combined with a preliminary theoretical approach, this allows us to highlight several key parameters for OPL optimization in such molecular systems and more particularly the spectral overlap between TPA and excited-state absorption.

Even flow: Photoinduced symmetry-breaking charge separation takes place in a few picoseconds in a 1,3-bis(perylene)propane dyad in polar solvents. Polarized transient absorption measurements show that the direction of the charge flow is random and entirely governed by the fluctuations of the solvent orientation around the dyad.

The structural and vibrational properties of the isostructural compounds Ca₂FeH₆ and Sr₂RuH₆ are determined by periodic DFT calculations and compared with their previously published experimental crystal structures as well as new experimental vibrational data. The analysis of the vibrational data is extended to the whole series of alkaline-earth iron and ruthenium hydrides A₂TH₆ (A = Mg,Ca,Sr; T = Fe, Ru) in order to identify correlations between selected frequencies and the T-H bond length. The bulk moduli of Ca₂FeH₆ and Sr₂RuH₆ have also been determined within DFT. Their calculated values prove to compare well with the experimental values reported for Mg₂FeH₆ and several other compounds of this structure.

The photoreactivity of two iron(II)−styrylpyridine frameworks Fe(stpy)₄(NCSe)₂ (stpy = 4-styrylpyridine) has been investigated for the very first time in a crystalline solid. A quantitative cis-to-trans isomerization of stilbenoids is shown to occur in the confined environment of the inorganic solid. The photochromic reaction was driven by a visible excitation into the metal-to-ligand charge transfer absorption of the high-spin all-cis complex. The solid-state transformation is accompanied by a unit-cell volume increase and an amorphization. Interestingly, the photoproduct formed by irradiating the high-spin all-cis reactant undergoes a spin conversion when the temperature is decreased. This observation is related to the “ligand-driven light-induced spin change” effect in a constrained environment.

The effect on crystal structure and vibrational frequencies of physical pressure in BaFCl and chemical pressure in Ba_1−xSr_xFCl solid solutions is studied using periodic density-functional theory (DFT) calculations performed within the local-density approximation (LDA) and the generalized gradient approximation (GGA). These results are compared with previously published experimental data for BaFCl in conjunction with new experimental data for Ba_1−xSr_xFCl and show overall a good agreement with experiment. The GGA method outperforms the LDA method for the description of BaFCl under pressure. However, the two DFT methods perform equally well for the description of the solid solutions, which have been studied within the virtual-crystal approximation. They also give consistent values of the energy of formation of Ba_1−xSr_xFCl, which can be correlated with the experimentally observed melting points. The comparison of the calculated mode Grüneisen parameters shows that, for the investigated systems, the effect of the chemical pressure and that of the physical pressure are not identical.

The new double-cation Al-Li-borohydride is an attractive candidate material for hydrogen storage due to a very low hydrogen desorption temperature (~70 °C) combined with a high hydrogen density (17.2 wt %). It was synthesised by high-energy ball milling of AlCl₃ and LiBH₄. The structure of the compound was determined from image-plate synchrotron powder diffraction supported by DFT calculations. The material shows a unique 3D framework structure within the borohydrides (space group=P-43n, a=11.3640(3) Å). The unexpected composition Al₃Li₄(BH₄)₁₃ can be rationalized on the basis of a complex cation [(BH₄)Li₄]³⁺ and a complex anion [Al(BH₄)₄]^-. The refinements from synchrotron powder diffraction of different samples revealed the presence of limited amounts of chloride ions replacing the borohydride on one site. In situ Raman spectroscopy, differential scanning calorimetry (DSC), thermogravimetry (TG) and thermal desorption measurements were used to study the decomposition pathway of the compound. Al-Li-borohydride decomposes at ~70 °C, forming LiBH₄. The high mass loss of about 20 % during the decomposition indicates the release of not only hydrogen but also diborane.

The mechanism of the photoinduced low-spin → high-spin spin crossover is actively being investigated in Fe(II) complexes in solution using ultrafast spectroscopies. These studies accurately inform on the reaction coordinate of the Fe(II) chromophore upon photoexcitation. However, they leave open questions regarding the role of the solvent. Here, we report the description from a fully ab initio molecular dynamics study of the structure of [Fe(bpy)₃]²⁺ in water and of the organization of its solvation shell in the low-spin and the high-spin states. In particular, the low-spin → high-spin change of states is shown to be accompanied (i) by a 0.191 Å lengthening of the Fe−N bond, in agreement with experiment, and (ii) by an increased thermal fluctuation of the molecular edifice, which both result from the weakening of the Fe−N bond. Furthermore, our results suggest that about two water molecules are expelled from the first solvation shell of [Fe(bpy)₃]²⁺, which consists of water molecules intercalated between the bpy ligands.

We report a thorough investigation of the absorption spectra of the cis and trans isomers of the 4-styrylpyridine photoswitch based on TDDFT calculations. The spectra of both isomers were analysed first from the results of excitation calculations performed on their optimised geometries. The main absorption band of the cis isomer is thus predicted to be due to the S₀ ^→ S₁ and S₀ ^→ S₂ transitions, while the main absorption band of the trans isomer is predicted to originate exclusively from the S₀ ^→ S₁ transition. The convolution of the calculated oscillator strengths with Gaussians helped mimic the broadening of the electronic transitions. However, it proved necessary to use Gaussians with a large full width at half maximum of 5000 cm^-1; and, compared to experiment, the calculated main absorption bands of the two isomers are significantly red-shifted and far too symmetric. Consequently, as required for the detailed analysis of the finite-temperature absorption spectrum of a molecule as flexible as 4-styrylpyridine, the influence of the thermal fluctuations has been taken into account by calculating the spectra as time averages over Car–Parrinello molecular dynamics trajectories. For both isomers, this led to a noticeable improvement in the relative positions of the calculated and experimental main absorption bands, and the asymmetry of the calculated bands brings them in better agreement with the experimental ones. Furthermore, these last results show that, actually, the S₀ ^→ S₁ and S₀ ^→ S₂ transitions both contribute significantly to the finite-temperature main absorption bands of the two isomers. Finally, in order to also take the vibrational broadening into account, the Franck–Condon factors of the relevant vibrations were calculated within the displaced harmonic oscillator approximation. By thus taking both the thermal and the vibrational broadening into account for the calculation of the absorption bands, the agreement between experiment and theory could be further improved.

Transition metal complexes of chiroporphyrins, in which two adjacent meso substituents are linked by a strap of eightmethylene groups, [M(BCP8)], can exist as either an αααα or αβαβ atropisomer depending on the nature of thecoordinated metal cation. This remarkable conformational versatility was investigated by density-functional theorycalculations for the d⁵ chloroiron(III) complex in the low-spin and high-spin states and for the d⁴ high-spinchloromanganese(III) complex. The lowest-lying electronic state of all of the conformers of the chloroiron(III) bridledchiroporphyrin is found to be the high-spin state. For the chloroiron(III) complex in the low-spin or the high-spin stateand for the high-spin chloromanganese(III) complex, the most stable form is predicted to be the αααα conformer inwhich the chloride axial ligand is located within the cavity provided by the bridles. The predicted stereochemistries arecompared with those similarly obtained (i) for the chloroiron(III) and chloromanganese(III) complexes of thetetramethylchiroporphyrin, which is devoid of straps, and (ii) for the d¹⁰ zinc(II) and low-spin d⁸ nickel(II) BCP8complexes, on the basis of the effects tied to the occupancy of the stereochemically active d_x²-y²-type antibondingorbital level, to the restraints imposed by the straps, and to the presence of the axial chloride ligand.

Density functional theory is applied within a supramolecular approach to the study of the guest−host interactions in [Fe(bpy)₃]²⁺@Y and their influence on the structural, energetic, and ⁵⁷Fe Mössbauer spectroscopy properties of the encapsulated [Fe(bpy)₃]²⁺ complex in the low- and high-spin states. The structures of the isolated complex and the supramolecular model used for [Fe(bpy)₃]²⁺@Y were optimized in both spin-states using different generalized gradient approximation (PBE, HCTH, OLYP) and hybrid (B3LYP*, O3LYP) functionals. The results obtained are consistent with one another and show that, in either spin-state, the structure of [Fe(bpy)₃]²⁺ shrinks and distorts upon encapsulation. Still, the structural changes experienced by the complex in a given spin-state remain limited, especially in that they do not lead to a substantial variation of the ⁵⁷Fe quadrupole splitting, whose calculated values are in very good agreement with avalaible experimental data. The decomposition of the guest−host interaction energy into its electrostatic, Pauli and orbital contributions shows that the bonding between the complex and the supercage is more electrostatic than covalent. The ability of modern functionals to accurately describe the interactions explains the remarkable consistency of the results obtained with the various functionals. In particular, although the functionals perform very differently for the determination of the high-spin/low-spin energy difference ΔE_HL^el in [Fe(bpy)₃]²⁺ and [Fe(bpy)₃]²⁺@Y, they consistently predict that the encapsulation entails a destabilization of the high-spin state with regard to the low-spin state of Δ(ΔE_HL^el) = 2500 cm⁻¹. Using for [Fe(bpy)₃]²⁺ the CASPT2 value of ΔE_HL^el = 3700 cm⁻¹ [Pierloot, K.; Vancoillie, S. J. Chem. Phys.2006, 125, 124303; Pierloot, K.; Vancoillie, S. J. Chem. Phys.2008, 128, 034104], we obtain for the high-spin/low-spin energy difference in [Fe(bpy)₃]²⁺@Y, a best ab initio estimate of ΔE_HL^el = 6200 cm⁻¹.

The spin-transition (¹A₁↔⁵T₂) behaviour of a new mononuclear iron(II) compound [Fe^II(L)₃][PF₆]₂[L = 2-[3-(2′-pyridyl)pyrazole-1-ylmethyl]pyridine] has been investigated by ⁵⁷Fe Mössbauer spectroscopy. Analysis of the Mössbauer spectra revealed low value of the quadrupole splitting of the high-spin state which reflects iron(II) to be in nearly cubic lattice site. Mössbauer spectra under light show the light-induced excited spin state trapping effect and the observed quadrupole splitting of the metastable high-spin state is found little sensitive to the high-spin fraction value. DFT calculations are in progress to document the almost cubic nature of the ligand-field acting on the iron atom.

The synthesis and characterization of new 1,10-phenanthroline-based chromophores LT1, LT2 and LD1 featuring fluorene unit(s) are reported. Their absorption and emission as well as their two-photon absorption properties in the 450–650 nm spectral range are discussed in comparison with the parent 1,10-phenanthroline and already described ligands L1 and L2.

The influence of pressure on the structural and vibrational properties of a₂RuH₆has been investigated using periodic density functional theory calculations performed at the local density approximation (LDA) and generalized gradient approximation (GGA) levels. At ambient pressure, the calculated structure and vibrational frequencies are in satisfactory agreement with experimental data. The calculated em>P-Vcurves could be fitted with the Vinet equation of state, yielding em>B₀=67.6and em>B₀=58.5  GPaat the LDA and GGA levels, respectively, and em>B₀^′=4.0at both theoretical levels. The unit cell parameter is found to decrease faster with increasing pressure than the Ru–H bond length. The calculated pressure dependence of the vibrational frequencies agrees well with experiment for em>ν₅(T_2g)but not for em>ν₉(A_1g)

The influence of solute−solvent interactions on the vibrational energy relaxation dynamics of perylene and substituted perylenes in the first singlet excited-state upon excitation with moderate (<0.4 eV) excess energy has been investigated by monitoring the early narrowing of their fluorescence spectrum. This narrowing was found to occur on timescales ranging from a few hundreds of femtoseconds to a few picoseconds. Other processes, such as a partial decay of the fluorescence anisotropy and the damping of a low-frequency oscillation due to the propagation of a vibrational wavepacket, were found to take place on a very similar time scale. No significant relationship between the strength of nonspecific solute−solvent interactions and the vibrational energy relaxation dynamics of the solutes could be evidenced. On the other hand, in alcohols the spectral narrowing is faster with a solute having H-bonding sites, indicating that this specific interaction tends to favor vibrational energy relaxation. No relationship between the dynamics of spectral narrowing and macroscopic solvent properties, such as the thermal diffusivity, could be found. On the other hand, a correlation between this narrowing dynamics and the number of low-frequency modes of the solvent molecules was evidenced. All these observations cannot be discussed with a model where vibrational energy relaxation occurs via two consecutive and dynamically well-separated steps, namely ultrafast intramolecular vibrational redistribution followed by slower vibrational cooling. On the contrary, the results indicate that both intra- and intermolecular vibrational energy redistribution processes are closely entangled and occur, at least partially, on similar timescales.

We report an in-depth theoretical study of 4-styrylpyridine in its singlet S₀ ground state. The geometries and the relative stabilities of the trans and cis isomers were investigated within density functional theory (DFT) as well as within Hartree-Fock (HF), second-order Møller-Plesset (MP2), and coupled cluster (CC) theories. The DFT calculations were performed using the B3LYP and PBE functionals, with basis sets of different qualities, and gave results that are very consistent with each other. The molecular structure is thus predicted to be planar at the energy minimum, which is associated with the trans conformation, and to become markedly twisted at the minimum of higher energy, which is associated with the cis conformation. The results of the calculations performed with the post-HF methods approach those obtained with the DFT methods, provided that the level of treatment of the electronic correlation is high enough and that sufficiently flexible basis sets are used. Calculations carried out within DFT also allowed the determination of the geometry and the energy of the molecule at the biradicaloid transition state associated with the thermal cis ↔trans isomerization and at the transition states associated with the enantiomerization of the cis isomer and with the rotations of the pyridinyl and phenyl groups in the trans and cis isomers. Car-Parrinello molecular dynamics simulations were also performed at 50, 150, and 300 K using the PBE functional. The studies allowed us to evidence the highly flexible nature of the molecule in both conformations. In particular, the trans isomer was found to exist mainly in a nonplanar form at finite temperatures, while the rotation of the pyridinyl ring in the cis isomer was incidentally observed to take place within ≈1 ps during the simulation carried out at 150 K on this isomer.

Whereas there are hundreds of known iron(II) spin-crossover compounds, only a handful of cobalt(II) spin-crossover compounds have been discovered to date, and hardly an in depth study on any of them exists. This review begins with an introduction into the theoretical aspects to be considered when discussing spin-crossover compounds in general and cobalt(II) systems in particular. It is followed by case studies on [Co(bpy)₃]²⁺ and [Co(terpy)₂]²⁺ (bpy = 2,2′-bipyridine, terpy = 2,2′:6′,2″-terpyridine) presenting and discussing results from magnetic susceptibility measurements, X-ray crystallography, optical spectroscopy, and EPR spectroscopy.

Circular dichroism (CD) spectra and density functional theory (DFT) calculations are reported for a series of conformationally bistable chiroporphyrins with 8-methylene bridles MBCP-8, which can display either an αααα or an αβαβ orientation of their meso substituents. From DFT geometry optimizations, the most stable form of ZnBCP-8 is found to be the αααα conformer. By passing to NiBCP-8, there is a strong stabilization of the αβαβ conformation with respect to the αααα conformation, consistent with the X-ray structures of αααα-ZnBCP-8 and αβαβ-NiBCP-8. A correlation between the sign of the CD signal in the Soret region and the conformation of the BCP-8 compounds is reported: the αααα conformers H₂BCP-8 and ZnBCP-8 show a positive CD signal, whereas the αβαβ conformers NiBCP-8 and CuBCP-8 exhibit a negative signal. The possible contributions to the rotational strengths of αβαβ-NiBCP-8 and αααα-ZnBCP-8, calculated on the basis of their crystal structures, have been analyzed. The CD signals are found to result from a combination of both the inherent chirality of the porphyrin and of extrinsic contributions due to the chiral bridles. These results may have a broad significance for understanding the chiroptical properties of chiral porphyrins and hemoproteins and for monitoring stimuli-responsive, conformationally bistable chiroporphyrin compounds.

Photoswitching of the dielectric constant has been observed for the first time in the spin-crossover complex [Fe(L)(CN)₂]·H₂O (L=2,13-dimethyl-6,9-dioxa-3,12,18-triazabicyclo[12.3.1]octadeca-1(18),2,12,14,16-pentaene, see picture). The electrical detection of a photoinduced change in spin state could allow the use of such complexes in optical information-storage devices.

Frequency shifts of the Ag  I  4d¹⁰5s  ²S_1∕2(F=0,M_F=0) to 4d⁹5s^{2  2}D_5∕2(F^′=2,M_F^′=0) electric-quadrupole transition at 330.6  nm due to external fields are calculated using multiconfigurational self-consistent field methods. As this forbidden transition is free from first order Doppler and Zeeman effects, it is under investigation for the realization of an atomic optical clock. The calculated perturbations are the light shift, the blackbody frequency shift, and the quadratic Zeeman shift. Results show that a total uncertainty of 10⁻¹⁸ could be reach without confining the atoms in a Lamb-Dicke regime in an optical lattice.

State-of-the-art generalized gradient approximation (GGA) (PBE, OPBE, RPBE, OLYP, and HCTH), meta-GGA (VSXC and TPSS), and hybrid (B3LYP, B3LYP*, O3LYP, and PBE0) functionals are compared for the determination of the structure and the energetics of the D₃ [Co(bpy)₃]²⁺ complex in the ⁴A₂ and ⁴E trigonal components of the high-spin ⁴T_1g( t⁵_2g e²_g ) state and in the low-spin ²E state of octahedral ²E_g( t⁶_2g e¹_g) parentage. Their comparison extends also to the investigation of the Jahn−Teller instability of the ²E state through the characterization of the extrema of C₂ symmetry of this spin state's potential energy surface. The results obtained for [Co(bpy)₃]²⁺ in either spin manifold are very consistent among the functionals used and are in good agreement with available experimental data. The functionals, however, perform very differently with respect to the spin-state energetics because the calculated values of the high-spin/low-spin energy difference ΔE^el_HL vary between −3212 and 3919 cm^-1. Semilocal functionals tend to give too large ΔE^el_HL values and thus fail to correctly predict the high-spin state as the ground state of the isolated complex, while hybrid functionals tend to overestimate the stability of the high-spin state with respect to the low-spin state. Reliable results are, however, obtained with the OLYP, HCTH, B3LYP*, and O3LYP functionals which perform best for the description of the isolated complex. The optical properties of [Co(bpy)₃]²⁺ in the two spin states are also analyzed on the basis of electronic excitation calculations performed within time-dependent density functional response theory. The calculated absorption and circular dichroism spectra agree well with experimental results.

The high-spin → low-spin relaxation in spin-crossover compounds can be described as non-adiabatic multi-phonon process in the strong coupling limit, in which the low-temperature tunnelling rate increases exponentially with the zero-point energy difference between the two states. Based on the hypothesis that the experimental bond length difference between the high-spin and the low-spin state of ~0.2 Å is also valid for low-spin iron(II) complexes, extrapolation of the single configurational coordinate model allows an estimate of the zero-point energy difference for low-spin complexes from kinetic data. DFT calculations on low-spin [Fe(bpy)₃]²⁺ support the structural assumption. However, for low-spin [Fe(terpy)₂]²⁺ the relaxation rate constant shows an anomalous behaviour in so far as it is more in line with spin-crossover systems. This is attributed to very anisotropic bond length changes associated with the spin state change, and the subsequent breakdown of the single mode model.

The molecular structure of the highly oxygen-sensitive complex [L³Cu^I(NCCH₃)](BF₄) (1) reveals approximately symmetrical coordination by the fac-tridentate (tripodal) ligand L³ = tris(3-isopropyl-4,5-trimethylenepyrazolyl)methane and a rather short Cu^I-N(acetonitrile) distance of 1.865(5) Å. In CH₂Cl₂ at -78 °C the colourless compound reacts with O₂ to yield a labile purple intermediate (λ_max 517 nm) - presumably a peroxodicopper(II) complex - which decomposes at -30 °C. No such intermediate was observed on reaction of the Cu^I complex of bis(2-pyridylmethyl)benzylamine with O₂ at -80 °C. However, an EPR spectrum with g^|| = 2.17 and g^_|_ = 2.03 without ^63,65Cu hyperfine splitting was observed at low temperatures. Exposure of the precursor 1 to air under ambient conditions yields dinuclear [L³Cu^||(μ-OH)₂Cu^IIL³](BF₄)₂ (2) which exhibits an EPR detectable dissociation into monomers in CH₂Cl₂ solution. The structure of the hexakis(dichloromethane) solvate of 2 with Cu-Cu and Cu-O distances of 3.055 and 1.94Å, respectively, is typical for dihydroxo-bridged dicopper compounds with square-pyramidal Cu^|| configuration (τ = 0.03), adopting an anti arrangement. In agreement with the relatively wide Cu-O-Cu angles of 103.5° an analysis of the temperature dependence of the magnetic susceptibility revealed a rather strong (J = -633 cm^-1) antiparallel spin-spin coupling. The effect is ascribed to the steric bulk of the ligand L³.

The ability of different density functionals to describe the structural and energy differences between the high- [⁵T_2g:(t_2g)⁴(e_g)²] and low- [¹A_1g:(t_2g)⁶(e_g)⁰] spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, [Fe(H₂O)₆]²⁺, [J. Chem. Phys. 120, 9473 (2004)] to include a second compound—namely, the hexaminoferrous cation, [Fe(NH₃)₆]²⁺—and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations (GGAs) known as HCTH and the meta-GGA VSXC [which together we refer to as highly parametrized density functionals (HPDFs)], now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field (CASPT2) calculations, with spectroscopy oriented configuration interaction (SORCI) calculations, and with ligand field theory (LFT) estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin–high-spin energy difference, ΔELHadia, of 12 000–13 000 cm⁻¹ for [Fe(H₂O)₆]²⁺ and 9 000–11 000 cm⁻¹ for [Fe(NH₃)₆]²⁺. All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, ΔELHadia, is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This “density functional theory (DFT) spin pairing-energy problem” persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates ΔELHadia by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Nørskov gives good results for ΔELHadia as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0.

In the iron(II) low-spin complex [Fe(bpy)₃]²⁺, the zero-point energy difference between the ⁵T_2g(t⁴_2ge²_g) high-spin and the ¹A_1g(t⁶_2g) low-spin states, ΔE⁰_HL, is estimated to lie in the range of 2500-5000 cm^-1. This estimate is based on the low-temperature dynamics of the high-spin→low-spin relaxation following the light-induced population of the high-spin state and on the assumption that the bond-length difference between the two states Δr_HL is equal to the average value of ≈0.2 Å, as found experimentally for the spin-crossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the low-spin-state optimised geometries are found to be in very good agreement with the experimental X-ray structure of the complex and the predicted high-spin geometries are all very close to one another for a whole series of common GGA (PB86, PW91, PBE, RPBE) and hybrid (B3LYP, B3LYP*, PBE1PBE) functionals. This confirmation of the structural assumption underlying the estimation of ΔE⁰_HL from experimental relaxation rate constants permits us to use this value to assess the ability of the density functionals for the calculation of the energy difference between the HS and LS states. Since the different functionals give values from -1000 to 12000 cm^-1, the comparison of the calculated values with the experimental estimate thus provides a stringent criterion for the performance of a given functional. Based on this comparison the RPBE and B3LYP* functionals give the best agreement with experiment.

A comparison of density functionals is made for the calculation of energy and geometry differences for the high- [⁵T_2g: (t_2g)⁴(e_g)²] and low- [¹A_1g: (t_2g)⁶(e_g)⁰] spin states of the hexaquoferrous cation [Fe(H₂O)₆]²⁺. Since very little experimental results are available (except for crystal structures involving the cation in its high-spin state), the primary comparison is with our own complete active-space self-consistent field (CASSCF), second-order perturbation theory-corrected complete active-space self-consistent field (CASPT2), and spectroscopy-oriented configuration interaction (SORCI) calculations. We find that generalized gradient approximations (GGAs) and the B3LYP hybrid functional provide geometries in good agreement with experiment and with our CASSCF calculations provided sufficiently extended basis sets are used (i.e., polarization functions on the iron and polarization and diffuse functions on the water molecules). In contrast, CASPT2 calculations of the low-spin–high-spin energy difference ΔE_LH = E_LS−E_HS appear to be significantly overestimated due to basis set limitations in the sense that the energy difference of the atomic asymptotes (⁵D→¹I excitation of Fe²⁺) are overestimated by about 3000 cm⁻¹. An empirical shift of the molecular ΔE_LH based upon atomic calculations provides a best estimate of 12 000–13 000 cm⁻¹. Our unshifted SORCI result is 13 300 cm⁻¹, consistent with previous comparisons between SORCI and experimental excitation energies which suggest that no such empirical shift is needed in conjunction with this method. In contrast, after estimation of incomplete basis set effects, GGAs with one exception underestimate this value by 3000–4000 cm⁻¹ while the B3LYP functional underestimates it by only about 1000 cm⁻¹. The exception is the GGA functional RPBE which appears to perform as well as or better than the B3LYP functional for the properties studied here. In order to obtain a best estimate of the molecular ΔE_LH within the context of density functional theory (DFT) calculations we have also performed atomic excitation energy calculations using the multiplet sum method. These atomic DFT calculations suggest that no empirical correction is needed for the DFT calculations.

Magnetization measurements and variable temperature optical spectroscopy have been used to investigate, within the 4−300 K temperature range, the electronic structure of the reduced high-potential iron protein (HiPIP) from Chromatium vinosum and the model compounds (Cat)₂[Fe₄S₄(SR)₄], where RS^- = 2,4,6-triisopropylphenylthiolate (1), 2,6-diphenylphenylthiolate (2), diphenylmethylthiolate (3), 2,4,6-triisopropylbenzylthiolate (4, 4‘), 2,4,6-triphenylbenzylthiolate (5, 5‘), 2,4,6-tri-tert-butylbenzylthiolate (6), and Cat⁺ = ⁺NEt₄ (1, 2, 3, 4‘, 5‘, 6), ⁺PPh₄ (4, 5). The newly synthesized 2^2-, 3^2-, 5^2-, and 6^2- complexes are, as 1^2- and 4^2-, excellent models of the reduced HiPIPs:  they exhibit the [Fe₄S₄]^3+/2+ redox couple, because of the presence of bulky ligands which stabilize the [Fe₄S₄]³⁺ oxidized core. Moreover, the presence of SCH₂ groups in 4^2-, 5^2-, and 6^2-, as in the [Fe₄S₄] protein cores, makes them good biomimetic models of the HiPIPs. The X-ray structure of 2 is reported:  it crystallizes in the orthorhombic space group Pcca with no imposed symmetry and a D_2d-distorted geometry of the [Fe₄S₄]²⁺ core. Fit of the magnetization data of the reduced HiPIP and of the 1, 2, 3, 4, 5, and 6 compounds within the exchange and double exchange theoretical framework leads to exchange coupling parameters J = 261−397 cm^-1. A firm determination of the double exchange parameters B or, equivalently, the transfer integrals β = 5B could not be achieved that way. The obtained |B| values remain however high, attesting thus to the strength of the spin-dependent electronic delocalization which is responsible for lowest lying electronic states being characterized by delocalized mixed-valence pairs of maximum spin ⁹/₂. Electronic properties of these systems are then accounted for by the population of a diamagnetic ground level and excited paramagnetic triplet and quintet levels, which are respectively J and 3J above the ground level. Optical studies of 1, 2, 4‘, 5‘, and 6 but also of (NEt₄)₂[Fe₄S₄(SCH₂C₆H₅)₄] and the isomorph (NEt₄)₂[Fe₄S₄(S-t-Bu)₄] and (NEt₄)₂[Fe₄Se₄(S-t-Bu)₄] compounds reveal two absorption bands in the near infrared region, at 705−760 nm and 1270−1430 nm, which appear to be characteristic of valence-delocalized and ferromagnetically coupled [Fe₂X₂]⁺ (X = S, Se) units. The |B| and |β| values can be directly determined from the location at 10|B| of the low-energy band, and are respectively of 699−787 and 3497−3937 cm^-1. Both absorption bands are also present in the 77 K spectrum of the reduced HiPIP, at 700 and 1040 nm (Cerdonio, M.; Wang, R.-H.; Rawlings, J.; Gray, H. B. J. Am. Chem. Soc. 1974, 96, 6534−6535). The blue shift of the low-energy band is attributed to the inequivalent environments of the Fe sites in the protein, rather than to an increase of |β| when going from the models to the HiPIP. The small differences observed in known geometries of [Fe₄S₄]²⁺ clusters, especially in the Fe−Fe distances, cannot probably lead to drastic changes in the direct Fe−Fe interactions (parameter β) responsible for the delocalization phenomenon. These differences are however magnetostructurally significant as shown by the 261−397 cm^-1 range spanned by J. The cluster's geometry, hence the efficiency of the Fe−μ₃-S−Fe superexchange pathways, is proposed to be controlled by the more or less tight fit of the cluster within the cavity provided by its environment.

We report a theoretical density functional analysis of the exchange interactions in (VO)₂P₂O₇ using molecular fragments. The calculations confirm that the magnetic structure must be decribed on the basis of linear dimer chains. The strongest exchange interaction is found through O-P-O bridges. The magnitude of the exchange parameters is governed not only by V-V distance but also by the whole structure along the superexchange pathway. The two chains present in the structure of (VO)₂P₂O₇ are magnetically inequivalent. For the monoclinic phase of (VO)₂P₂O₇, important variations in the calculated parameters for dimers with identical bridges are observed within one chain. The magnetic structure of this chain should be described not by two but by three or even four coupling constants.

The ¹H and ¹⁵N resonances of the carbon monoxide complex of ferrocytochrome c‘ ofRhodobacter capsulatus, a ferrous diamagnetic heme protein, have been extensively assigned by TOCSY−HSQC, NOESY−HSQC, and HSQC−NOESY−HSQC 3D heteronuclear experiments performed on a 7 mM sample labeled with ¹⁵N. Based on short-range and medium-range NOEs and H^N exchange rates, the secondary structure consists of four helices: helix 1 (3−29), helix 2 (33−48), helix 3 (78−101), and helix 4 (103−125). The ¹⁵N, ¹H^N, and ¹H^αchemical shifts of the CO complex form are compared to those of the previously assigned oxidized (or ferric) state. From the chemical shift differences between these redox states, the orientation and the anisotropy of the paramagnetic susceptibility tensor have been determined using the crystallographic coordinates of the ferric state. The χ-tensor is axial, and the orientation of the z-axis is approximately perpendicular to the heme plane. The paramagnetic chemical shifts of the protons of the heme ligand have been determined and decomposed into the Fermi shift and dipolar shift contributions. Magnetic susceptibility studies in frozen solutions have been performed. Fits of the susceptibility data using the model of Maltempo (Maltempo, M. M. J. Chem. Phys. 1974, 61, 2540−2547) are consistent with a rather low contribution of the S = ³/₂ spin state over the range of temperatures and confirm the value of the axial anisotropy. Values in the range 10.4−12.5 cm^-1 have been inferred for the axial zero-field splitting parameter (D). Analysis of the contact shift and the susceptibility data suggests that cytochrome c‘ of Rb. capsulatus exhibits a predominant high-spin character of the iron in the oxidized state at room temperature.

We present a theoretical analysis of the temperature dependence of the vanadyl pyrophosphate VO₂P₂O₇ ³¹P NMR spectra. Four distinct phosphorus sites responsible for four signals are identified in the crystal structure. The magnetic states of the crystal are described by two alternative models: the spin ladder and the dimer chain. Within both models, finite clusters with and without periodic conditions are considered. The fit of the experimental NMR data allows us to define combinations of hyperfine coupling parameters which are found to be similar in both spin models.

In contrast to high-spin ferrous paramagnetic heme proteins, the chemical shifts of the heme protons are very unusual in the ferrocytochromes c‘. Magnetic susceptibility studies ofRhodobacter capsulatus ferrocytochrome c‘ in frozen solutions have been performed and indicate an S = 2 spin state and a large negative axial (D) zero-field splitting parameter (−18.3 cm^-1) as well as a significant rhombic (E) value (−4.9 cm^-1). The ¹H and ¹⁵N resonances have been extensively assigned by TOCSY−HSQC, NOESY−HSQC, and HSQC−NOESY−HSQC 3-D heteronuclear experiments performed on a 8 mM sample labeled with ¹⁵N. Based on short-range and medium-range NOEs and H^N exchange rates, the secondary structure consists of four helices: helix-1 (3−30), helix-2 (34−49), helix-3 (78−97), and helix-4 (103−117). The ¹⁵N, H^N, and H^α chemical shifts of the reduced (or ferro) state are compared to those previously assigned for the diamagnetic carbon monoxide complex form. From the chemical shift differences between these redox states, the orientation and the anisotropy of the paramagnetic susceptibility tensor have been determined using the crystallographic coordinates of the ferric state. Values of −23 and −3 cm^-1 have been inferred for D and E, and the z-axis of the tensor is tilted approximately 30° from the normal to the heme. The paramagnetic chemical shifts of the heme protons have been determined and split up into Fermi shift and the dipolar shift contributions. The pattern of the contact shifts is very unusual, exhibiting a 2-fold symmetry, and is discussed in terms of molecular orbital interactions between the porphyrin macrocycle and the imidazole ring.

The tetranuclear complexes {(μ₄-TCNX)[Ru(NH₃)₅]₄}(A)₈ and (μ₄-TCNX)[Mn(CO)₂(C₅Me₅)]₄ [A = PF₆ or CF₃SO₃; TCNX = TCNE (tetracyanoethene), TCNQ (7,7,8,8-tetracyano-p-quinodimethane), or TCNB (1,2,4,5-tetracyanobenzene)] were studied by variable-temperature (2−300 K) SQUID susceptometry. Mono- and dinuclear species [(PhCN)Ru(NH₃)₅](PF₆)₂ (PhCN = benzonitrile) and {(μ-L)[Ru(NH₃)₅]₂}(PF₆)₄ (L = 1,4-dicyanobenzene (terephthalodinitrile) or pyrazine) were also investigated for comparison and were found to be essentially diamagnetic. Despite the even electron count, both the ruthenium and manganese tetranuclear complexes are paramagnetic, albeit with different spin−spin exchange coupling patterns. The manganese systems are characterized by exchange-coupled S = 1 states at the individual metal centers, whereas the magnetic behavior of the tetranuclear ruthenium compounds results from an exchange-coupling interaction between two S = ¹/₂ sites, identified as Ru^III/Ru^II mixed-valence pairs.