Mapping the cooperativity pathways in spin crossover complexes

Crystal packing energy calculations are applied to the [Fe(PM-L)2(NCS)2] family of spin crossover (SCO) complexes (PM-L = 4-substituted derivatives of the N-(2-pyridylmethylene)-4-aminobiphenyl ligand) with the aim of relating quantitatively the cooperativity of observed SCO transitions to intermolecular interactions in the crystal structures. This approach reveals a linear variation of the transition abruptness with the sum of the magnitudes of the interaction energy changes within the first molecular coordination sphere in the crystal structure. Abrupt transitions are associated with the presence of significant stabilising and destabilising changes in intermolecular interaction energies. While the numerical trend established for the PM-L family does not directly extend to other classes of SCO complex in which the intermolecular interactions may be very different, a plot of transition abruptness against the range of interaction energy changes normalised by the largest change shows a clustering of complexes with similar transition abruptness. The changes in intermolecular interactions are conveniently visualised using energy difference frameworks, which illustrate the cooperativity pathways of an SCO transition.

: Selected data for complexes studied. The refcode refers to the entry in the Cambridge Structural Database. T = temperature of the crystal structure determination; ΔT60 is defined in Fig.  S1. Scheme 1 from the main text is reproduced below for convenience.

Complex
Spin

Section S2: Supplementary details on energy framework generation
The frameworks were generated using the CSD Python API (application programming interface). A vector Ma-Mb defined between the molecular centroids of each interaction identified in a PIXEL calculation (Fig. S2). An atom is placed at the mid-point of the vector, Mp; to enable colour-coding of the framework struts, which are drawn as coordination polyhedra, radium was used for stabilising contacts and meitnerium destabilising contacts. Six deuterium atoms are placed orthogonal to the vector Ma-Mb and at a distance E/n from both Ma and Mb. E is the energy of the interaction in kJ mol −1 and n scales the diameter of the struts of the framework. Direct visual comparisons between frameworks can be made provided the same value of n is used; in this work n was chosen to be 200 for energy frameworks and 25 for energy difference frameworks. The struts are then constructed by representing the atom at Mp as a hexagonal prism with the vertices at the deuterium atoms. The updated structure is saved as a .MOL2 format file, which can then be visualised in Mercury. As has been described by Spackman, frameworks may be generated for each separate component of the interaction energy (electrostatic, polarisation, dispersion, repulsion) or as the total.  Table S1.     Section S4: The relationship of SCO behaviour to structural parameters and PIXEL energies In the following sections we examine the correlations of shortest C…S distance, lattice energy and layer stacking with the SCO transition abruptness in the Fe(PM-L)2(NCS)2 family of complexes.

The shortest C…S Interaction
The suggestion that spin transition abruptness is related to the strength of the intermolecular interactions mediated by the short C…S contacts may be analysed in terms of interaction energies using the PIXEL results for the interaction denoted O (see Fig. 2iii in the main text) and its analogues in other structures (see also Table S4). While there are substantial differences in intermolecular interaction energies in these systems, no simple trend can be identified between the transition abruptness (ΔT60) and either the total dimer energy in the high or low spin forms or the change in dimer energy between spin states (Fig. S5i). We suggest that SCO behaviour cannot be fully described or predicted from the energy of the C…S interaction, and we therefore investigated whether parameters such as lattice energy or inter-layer spacing, which are features of the whole crystal structure, might be more effective.

Lattice Energies
The lattice energies calculated using PIXEL are available for each structure and are listed in Table S5. The lattice energy change between spin-states at 110 and 290 K is in the order of -20 to -50 kJ mol −1 for all complexes, with the two polymorphs of Fe(PM-BiA)2(NCS)2 having very similar lattice energies for both spin states (EL(HS) and EL(LS), respectively). This may explain why both polymorphs are observed under ambient conditions, though the energies are too similar to state with confidence which is the more stable form. From these results there is no clear correlation between transition width and the lattice energies of either the HS or LS structures. Neither is there a correlation with change in lattice energy between spin-states for the HS  LS transition, defined as ΔEL = EL(LS) − EL(HS) (Fig. S5ii).

Layer Spacing
Previous studies find no clear trend relating to the isotropic cell contraction (∆VSC) and the SCO characteristics, but do point towards the anisotropy of the cell contraction as a parameter relating to the abruptness of transition. 2 The change in layer spacing is a component of the anisotropic cell volume contraction and thus provides information on the nature of crystal packing changes in relation to SCO behaviour for Fe(PM-L)2(NCS)2 with this layered packing. Although there is no apparent trend between the level of interpenetration of the layers described above and the abruptness of transition, the change in layer separation between spin-states does suggest that large negative changes in layer separation correlate with sharper SCO (Fig. S5iii), though this correlation does not extend to the broader transitions.     Section S6: Data used for generation of energy difference frameworks.    Table S7: PIXEL-C interaction energy changes (HS>LS) for first intermolecular co-ordination sphere contacts of Fe(PM-L)2(NCS)2 complexes and other structures studied.       Table S8: Correlations for PIXEL energy terms with respect to ΔT60 for PM-L Structures studied. Note that the magnitude of all energies is not equivalent to the magnitude of all total energies because total energies take into account the sign of each energy term, where the magnitude of all energies is from absolute values (see Equation 1).

BiA-I State Interaction Transformation Matrix and Vector Centroid Distances
Feature Symbol