Molecular tuning of the magnetic response in organic semiconductors

We demonstrate an extreme variability and tunability of the molecular gyromagnetic coupling $g$-tensor with respect to the geometric and electronic structure in a much studied class of organic semiconductors (OSCs). This class of OSCs is composed of a structural theme of phenyl- and chalcogenophene (group XVI element containing, five-membered) rings and alkyl functional groups, and it forms the basis of several intensely studied high-mobility polymers and molecular OSCs. We show how in this class the $g$-tensor shifts, $\mathrm{\Delta }g$, are determined by the effective molecular spin-orbit coupling (SOC), defined by the overlap of the atomic spin density and the heavy atoms in the polymers. We explain the dramatic variations in SOC with molecular geometry, chemical composition, functionalization, and charge dwell time, by using a first-principles theoretical model based on atomic spin populations. Our approach guides the tuning of the magnetic response of these and other OSCs by chemical synthesis.

Figure 1

Structural formulas of all molecules studied in this work. (a) Single chalcogen pair molecules, with the central BXBX (X = “T” and “S” for M = sulfur and selenium, respectively) structure shown in blue. Adding one and two sets of fused phenyl rings gives DNXX (green) and DAXX (red), respectively. Further shown is the bonding site of the C8 alkyl chain functional group (R), and that same group shifted to the adjacent bonding site ($\mathrm{R}s$). (b) Linear (L) and curved (C) dual chalcogen pair molecules DXBYBY, including the mixed pair DSBTBT molecules, where M1 = sulfur and M2 = selenium. Otherwise with nomenclature and functionalization as in (a). (c) The pure hydrocarbons benzene, rubrene, and pentacene included for improved fit quality.

Figure 2

Illustration of the relationship between predicted $g$-tensors and molecular spin density distributions, and the variations of the latter with molecular geometry and functionalization. At left (right), the histogram shows calculated $\mathrm{\Delta }g$ for the linear (curved) DSBSBS molecules without alkyl chains, and C8 / $\mathrm{C}8s$ alkyl chains bonded at spin density maxima and minima. As shown by the blue isocontour in the accompanying spin density plots, the L-DSBSBS molecule has heavy spin density weight at the chalcogen atoms—$\mathrm{\Delta }g$ is large. The spin density structure is not significantly changed when alkylating L-DSBSBS at the two sites. The $opposite$ is true in the C-DSBSBS molecule, despite its identical chemical composition: alkylating C-DSBSBS at a bonding site corresponding to a spin density maximum (C8-C-DSBSBS) pulls spin density away from all chalcogens, whereas alkylating at a spin density minimum ($\mathrm{C}8s$-C-DSBSBS) leaves significant weight on the outer chalcogen pair. Qualitatively similar variations are found in all other molecules studied here.

Figure 3

Correlation plot of $\mathrm{\Delta }{g}^{\mathrm{OZ}/\mathrm{SOC}}$ terms fitted on the form of Eq. (2). The fit was done separately for a single chalcogen pair (solid, magenta triangles) and dual chalcogen pair molecules (empty, inverted triangles). Dual pair molecules with same and mixed chalcogens were fitted together, but are colored differently to show the identical validity of the approximation regardless of chalcogen composition. The $R^2$ for the single- and dual-chalcogen pair statistics are 0.990 and 0.991, respectively.

Figure 4

Correlation plot of a fit of the shift in $\mathrm{\Delta }g$ upon alkylation of molecules against the corresponding change in local chalcogen spin population, analogous to Eq. (2) and Fig. 3. See Fig. 3 for the plot legend. $R^2$ of the entire statistic shown is 0.988.

Figure 5

Illustration of the influence of charge dwell-time effects on the $g$-tensor shift. See Sec. 3d. If a charge—here an electron hole ${\mathrm{h}}^{+}$—dwells for sufficiently long at a molecule, it relaxes to the ionic geometry, causing changes in the bond lengths $R_{AB}$, shifting the push-pull charge balance along the bonds. While $\mathrm{\Delta }{R}_{AB}$ are nearly identical in C8-BTBT and C8-BSBS, the relatively greater polarizability of selenium more strongly pulls electrons toward (pushes holes from) the chalcogen, causing spin density depletion at the same, and a stronger suppression of the $g$-shift in C8-BSBS than in C8-BTBT [see Eq. (4)].