Spin state/stereochemistry relationships in metalloporphyrins: The vibromic approach

Abstract

Consider the pseudo Jahn–Teller instability [1] of the planar nuclear configuration of the MeP system with respect to the out-of-porphyrin plane displacement and to the change of hole diameter depending on the electronic state and the nature of the metal. The planar MeP has the D 4h symmetry, the out-of-plane metal displacement is of A 2u symmetry, and the change in hole diameter corresponds to the totally symmetric displacement. It may be concluded from selection rules and 3d MeP electronic structure calculations [2], that in Fe IIP and Mn IIP there are intermediate-spin ground, iψ O, and excited, iψ 1, and electronic states, which are mixed by A 2u displacements. The iψ 1 state can be constructed from the iψ O one by a one-electron a 2u(π) → a 1g(d z 2 ). The lowest high-spin states hψ O can be obtained from the iψ O one by electron e g(dπ) → b 1g(d x 2 − y 2 ) excitations. These states are mixed by A 2u displacements with two near lying excited states. The first, hψ 1, can be obtained from the hψ O by electron a 2u(π) → a 1g(d z 2 ) excitation, the mixing hψ O − hψ 1 being characterized by the same vibronic parameters as the iψ O − iψ 1 mixing. The second state hψ 2 is formed by the b 1g(d x 2 − y 2 ) → b 2u(π*) excitation. We have shown recently [3, 4] that in both cases the ψ O − ψ 1 mixing gives the main contribution to the instability of the planar MeP configuration, whereas the contribution of the ψ O − ψ 2 mixing per se is insufficient for the formation of such an instability (herefrom it may be concluded that in MeP with completely occupied a 1g(d z 2 ) MO, e.g. in Cu IIP, Zn IIP, and diamagnetic Ni IIP, the in-plane position of the metal is stable due to the lack of low lying ψ 1 states). On the other hand the occupation of the antibonding b 1g(d x 2 − y 2 ) MO in the hψ O state results, first, in the increase of the hole diameter due to the stronger interaction with the totally symmetric displacements and, second, in an additional reduction of A 2u force constant. Therefore, under the out-of-plane metal displacement the energy lowering in the hψ O state occurs more readily than in the iψ O one. As a result the intersection of the two terms takes place, provided the ψ O−ψ 1 vibronic mixing is strong enough (for the corresponding quantitative criterion see Ref. [4]). Thus for large enough out-of-plane displacements of the metal atom the hψ O state becomes the ground one, in contrast with the planar configuration case, where iψ O is the ground state and vice versa, if the MeP system is found in the highspin state, it means that the size of the hole is greater and the out-of-plane metal displacement is larger, compared with iψ O. Note, that as far as the out-of-plane displacement of the metal atom is determined by the a 2u(π) − a 1g(d z 2 ) MO mixing, the essential influence of the environment of the MeP (both peripheral and axial) on the magnitude of this displacement and spin equilibrium has to be expected. The results obtained are in qualitative agreement with the experimental data available [5].