

We report a detailed DFT study of the energetic and structural properties of the spincrossover Co(II) complex [Co(tpy)_{2}]^{2+}Â (tpy = 2,2â€²:6â€²,2â€²â€²terpyridine) in the lowspin (LS) and the highspin (HS) states, using several generalized gradient approximation and hybrid functionals. In either spinstate, 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 HSâ€“LS zeropoint energy difference Î”E^{0}_{HL} (tpy)Â Â which strongly depend on the functional used. This dependency on the functional was also reported for the DFT estimates of the zeropoint energy differenceÂ Î”E^{0}_{HL}Â (bpy)Â Â in the HS complex [Co(bpy)_{3}]^{2+}Â (bpy = 2,2â€²bipyridine) [A. Vargas, A. Hauser and L. M. Lawson Daku,Â J. Chem. Theory Comput., 2009,Â 5, 97]. The comparison of theÂ Î”E^{0}_{HL}Â (tpy)Â Â andÂ Î”E^{0}_{HL}Â (bpy)Â Â estimates showed that all functionals correctly predict an increase of the zeropoint energy difference upon the bpy â†’ tpy ligand substitution, which furthermore weakly depends on the functionals, amounting to (Î”E^{0}_{HL})_{bpy>tpy}Â â‰ˆ +2670 cm^{1}Â . 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 spinstate energetics of complexes of a transition metal ion, or of these complexes in different environments, provided that the spinstate energetics is accurately known in one case. Thus, making use of the availability of a highly accurateÂ ab initioÂ estimate of the HSâ€“LS energy difference in the complex [Co(NCH)_{6}]^{2+}Â [L. M. Lawson Daku, F. Aquilante, T. W. Robinson and A. Hauser,Â J. Chem. Theory Comput., 2012,Â 8, 4216], we obtain for [Co(tpy)_{2}]^{2+}Â and [Co(bpy)_{3}]^{2+}best estimates ofÂ Î”E^{0}_{HL}Â (bpy)Â â‰ˆ 2800 cm^{1}Â Â andÂ Î”E^{0}_{HL}Â (tpy)Â â‰ˆÂ 0 cm^{1}Â , in good agreement with the known magnetic behaviour of the two complexes. 


Density functional theory is applied within a supramolecular approach to the study of the guestâˆ’host interactions in [Fe(bpy)_{3}]^{2+}@Y and their influence on the structural, energetic, and ^{57}Fe MÃ¶ssbauer spectroscopy properties of the encapsulated [Fe(bpy)_{3}]^{2+} complex in the low and highspin states. The structures of the isolated complex and the supramolecular model used for [Fe(bpy)_{3}]^{2+}@Y were optimized in both spinstates 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 spinstate, the structure of [Fe(bpy)_{3}]^{2+} shrinks and distorts upon encapsulation. Still, the structural changes experienced by the complex in a given spinstate remain limited, especially in that they do not lead to a substantial variation of the ^{57}Fe quadrupole splitting, whose calculated values are in very good agreement with avalaible experimental data. The decomposition of the guestâˆ’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 highspin/lowspin energy difference Î”E_{HL}^{el} in [Fe(bpy)_{3}]^{2+} and [Fe(bpy)_{3}]^{2+}@Y, they consistently predict that the encapsulation entails a destabilization of the highspin state with regard to the lowspin state of Î”(Î”E_{HL}^{el}) = 2500 cm^{âˆ’1}. Using for [Fe(bpy)_{3}]^{2+} the CASPT2 value of Î”E_{HL}^{el} = 3700 cm^{âˆ’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 highspin/lowspin energy difference in [Fe(bpy)_{3}]^{2+}@Y, a best ab initio estimate of Î”E_{HL}^{el} = 6200 cm^{âˆ’1}. 


The trigonal planar geometry of the nitrogen atom in commonly used phosphoramidite ligands is not in line with the traditional valence shell electron pair repulsion (VSEPR) model. In this work, the effects governing nitrogen configuration in several substituted aminophosphines, A_{2}PNB_{2} (A or BÂ =Â H, F, Cl, Br, Me, OMe, BINOP), are examined using modern computational analytic tools. The electron delocalization descriptions provided by both electron localization function (ELF) and block localized wavefunction analysis support the proposed relationships between conformation and negative hyperconjugative interactions. In the parent H_{2}PNH_{2}, the pyramidal nitrogen configuration results from nitrogen lone pair electron donation into the Ïƒ* P â€” H orbital. While enhanced effects are seen for F_{2}PNMe_{2}, placing highly electronegative fluorine substituents on nitrogen (i.e., Me_{2}PNF_{2}) eliminates delocalization of the nitrogen lone pair. Understanding and quantifying these effects can lead to greater flexibility in designing new catalysts. 


Whereas there are hundreds of known iron(II) spincrossover compounds, only a handful of cobalt(II) spincrossover 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 spincrossover 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+} (bpyÂ =Â 2,2â€²bipyridine, terpyÂ =Â 2,2â€²:6â€²,2â€³terpyridine) presenting and discussing results from magnetic susceptibility measurements, Xray crystallography, optical spectroscopy, and EPR spectroscopy. 


Stateoftheart generalized gradient approximation (GGA) (PBE, OPBE, RPBE, OLYP, and HCTH), metaGGA (VSXC and TPSS), and hybrid (B3LYP, B3LYP*, O3LYP, and PBE0) functionals are compared for the determination of the structure and the energetics of the D_{3} [Co(bpy)_{3}]^{2+} complex in the ^{4}A_{2} and ^{4}E trigonal components of the highspin ^{4}T_{1g}( t^{5}_{2g} e^{2}_{g} ) state and in the lowspin ^{2}E state of octahedral ^{2}E_{g}( t^{6}_{2g} e^{1}_{g}) parentage. Their comparison extends also to the investigation of the Jahnâˆ’Teller instability of the ^{2}E state through the characterization of the extrema of C_{2} 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 spinstate energetics because the calculated values of the highspin/lowspin energy difference Î”E^{el}_{HL} vary between âˆ’3212 and 3919 cm^{}^{1}. Semilocal functionals tend to give too large Î”E^{el}_{HL} values and thus fail to correctly predict the highspin state as the ground state of the isolated complex, while hybrid functionals tend to overestimate the stability of the highspin state with respect to the lowspin 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 timedependent density functional response theory. The calculated absorption and circular dichroism spectra agree well with experimental results. 


The highspinÂ â†’Â lowspin relaxation in spincrossover compounds can be described as nonadiabatic multiphonon process in the strong coupling limit, in which the lowtemperature tunnelling rate increases exponentially with the zeropoint energy difference between the two states. Based on the hypothesis that the experimental bond length difference between the highspin and the lowspin state of ~0.2Â Ã… is also valid for lowspin iron(II) complexes, extrapolation of the single configurational coordinate model allows an estimate of the zeropoint energy difference for lowspin complexes from kinetic data. DFT calculations on lowspin [Fe(bpy)_{3}]^{2+} support the structural assumption. However, for lowspin [Fe(terpy)_{2}]^{2+} the relaxation rate constant shows an anomalous behaviour in so far as it is more in line with spincrossover 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. 


In the iron(II) lowspin complex [Fe(bpy)_{3}]^{2+}, the zeropoint energy difference between the ^{5}T_{2g}(t^{4}_{2g}e^{2}_{g}) highspin and the ^{1}A_{1g}(t^{6}_{2g}) lowspin states, Î”E^{0}_{HL}, is estimated to lie in the range of 25005000 cm^{1}. This estimate is based on the lowtemperature dynamics of the highspinâ†’lowspin relaxation following the lightinduced population of the highspin state and on the assumption that the bondlength difference between the two states Î”r_{HL} is equal to the average value of â‰ˆ0.2 Ã…, as found experimentally for the spincrossover system. Calculations based on density functional theory (DFT) validate the structural assumption insofar as the lowspinstate optimised geometries are found to be in very good agreement with the experimental Xray structure of the complex and the predicted highspin 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 Î”E^{0}_{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. 