Impact of Molecular Distortions on Bistability in Spin Crossover Complexes

We present a simple model of molecular distortions in spin crossover complexes, based on crystal field theory and transition state theory. This allows us to model the effects of molecular distortions on <i>T</i>_1/2, the characteristic temperature of thermal crossover, and <i>T</i>_LIESST, the maximum temperature at which trapped excited high spin (HS) complexes are stable. <i>T</i>_1/2 is a purely thermodynamic quantity, determined by the relative free energies of the HS and low spin (LS) states (Δ<i>G</i> = <i>G</i>_HS - <i>G</i>_LS). The average distortion across HS and LS species <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>[</mml:mo><mml:mover><mml:mi>Σ</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>Σ</mml:mi><mml:mrow><mml:mi>H</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>Σ</mml:mi><mml:mrow><mml:mi>L</mml:mi><mml:mi>S</mml:mi></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>]</mml:mo></mml:math> and the change in distortion between spin states (ΔΣ = Σ_HS - Σ_LS) have a significant impact on Δ<i>G</i>. However, the inner coordination sphere stiffness (<i>k</i>) has little impact on Δ<i>G</i>. Therefore, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>Σ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math> and ΔΣ have large effects on <i>T</i>_1/2 whereas <i>k</i> does not. <i>T</i>_LIESST is largely determined by the height of the barrier (<i>E</i>_b) between the metastable HS state and the LS state. <i>E</i>_b is strongly affected by ΔΣ, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mover><mml:mi>Σ</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>, and <i>k</i>; thus <i>T</i>_LIESST is strongly dependent on all of these quantities. Thus, increasing both the relative and absolute distortion of SCO complexes increases <i>T</i>_LIESST and decreases <i>T</i>_1/2, providing a route to high temperature spin-state switching via molecular distortions.