Theoretical basis for the stabilization of charges by radicals on electrified polymers

Quantum mechanical calculations at various levels of theory indicate that charges (both “+” and “−”) on organic polymers can be stabilized by radicals on nearby polymer chains. The stabilization mechanism is based on the formation of intermolecular odd-electron, two-center bonds with possible concomitant spin density redistribution (depending on the polymer and the number and type of proximal heteroatoms). This result is in line with our previous experimental demonstrations that on various types of polymers charged by contact electrification, radicals co-localize and help stabilize proximal charges (of either polarity). The principle of intramolecular charge-radical stabilization we now confirm on a fundamental level might have ramifications for the design of other macromolecular systems in which chemical reactivity is controlled by radicals flanking the charged groups or by charged groups flanking the radicals.

shows total energies of the PE and PTFE model molecules in their optimized geometries. Table 2 expands the PE model to include the secondary carbocation units. Table 3 lists DFT energies of the optimized PDMS models.

Data in
For PE and PTFE cases, additional Hartree-Fock (HF) calculations were also performed using the 6-311++G(d,p) basis set. This additional investigation was carried because previous DFT studies reported positive energy of the HOMO orbital for the anionic species (R -) of PE, which is a known issue of the DFT methodology 29 . We additionally calculated by HF methods the HOMO (R -) orbital energies (which had negative values), proving that no unbound electron was present in the model system. The detailed values of orbital energies of relevant orbitals are presented in Table   4 (PE and PTFE) and Table 5 (PDMS), alongside with their energy differences.      Table 6. Stabilization energies (D3 + B3LYP/6-311++G(d,p)) due to van der Waals interactions between two neutral molecules (2 x C3H8 -"C3 model" and 2 x C6H14 -"C6 model") in both parallel and "head-to-head" orientations."  Figure S1 shows examples of energy (D3-UB3LYP/3-21G) contour maps for PE C3 and C7 model systems. The optimal parameters established in these initial calculations are indicated in the insets and are subsequently used for higher-level geometry optimization with D3-UB3LYP/6-311++G(d,p). C3 carbocation interacting with a C3 radical, (c) C7 carboanion interacting with a C7 radical, and (d) C7 carbocation interacting with a C7 radical. Insets have the values of parameters corresponding to energy minima. Calculations were performed using DFT (D3-UB3LYP/6-31G).

Section 3. Effects of PE chain branching.
Calculations on the influence of carbon chain branching (mimicking real-life polymer structure) on system's stability were performed for select/representative systems. Specifically, we chose four molecules for the 2-branched models and three molecules for the 3-branched models (see images in Figures S2a,b  Based on the analysis of the results presented in Figure S2c, cation rearrangement causes the lowering of the molecular energy gap (by around 2eV) between SOMO (R • ) and LUMO (R + ) -at the same time strengthening these orbitals interactions. Additional carbon chain branches influence the relevant SOMO (R • ) and LUMO (R + in optimized geometry) orbital energies such that the energy gap is lowered by approximately 0.4eV (compare results of C2_2_X with C2_3_X in Figure S2c). The elongation of the carbon chain within each branch lowers the energy gap by another 0.9 eV (difference between C2_2_1 and C2_2_4) or 0.4 eV (difference between C2_3_2 and C2_3_4). In the anion-radical case, the energy gap between SOMO (R • ) and HOMO (R -) is almost not influenced by branching or elongation (see Figure S2d).   interaction, alongside with sample EPR spectra.
Section 5. NBO analysis for (1monomer + 1 monomer) model of PDMS. Figure S4. Atom labeling for the PDMS models (1 monomer-based) for the interaction of (a) cation with radical; (b) anion with radical.
In the discussion below, BD denotes a 2-center bonding orbital, BD* -2-center antibonding orbital, LP stands for 1-center orbital (valence lone pair), and X(Z) denotes atom X, labeled by number Z.
For the PDMS [R-R] •+ case, we conducted NBO analysis. In both R + and R • we identified interacting orbitals that are responsible for the resulting spin density. a) R + electronic structure. The LUMO α orbital of the R + species (see Figure S4a  In contrast to the simplified orbital interaction model for anion-radical pairs (cf. Figure 1d in the main text), the SOMO α electron is localized on orbital bound to Si(16), instead of being localized on the antibonding orbital (such as BD* O(15)-Si (16)) -this fact is confirmed by the contour of the spin density for the whole molecule.

Section 6. Benchmarks of energy of stabilization.
Additional stabilization energies at more accurate levels of theory were computed using: altered