Section S6: Quantum Chemical Calculations S6.1 Excitation Properties of Simple Systems: The Infinite Square Well and Quantum Harmonic Oscillator It can be shown that for one dimensional potential well systems, the majority of oscillator strength lies in the lowest energy excited state. In the case of an infinite square well the oscillator strength for the n to n+1 transition is given by and clearly tends toward n as n increases. For the simple harmonic oscillator (SHO), the result is exact at fn,n+1 = n. The symmetry of eigenstates in the two systems leads to a larger transition dipole matrix element for transitions between consecutive states than between any other pairs of states. S6.2 Number of π-electrons for the polymers studied To normalise transition strengths by the number of electrons available, we assume that transitions in the visible region are due to the π system and therefore count the number of electrons in each unit,. We note that, especially for multi-ring structures with added functionalities, the number of π electrons may not be well-defined, but any such uncertainties affect the normalisation only slightly. Table S6.1 shows the oligomer structure and corresponding polymer name for the materials studied and Table S6.2 shows the number of π-conjugated electrons that we count in each conjugated unit. S6.1 Names and chemical structures of oligomers studied Polymer (Oligomer) Abbreviation Polymer Full Name Oligomer Structure P3HT (T) PFO (F) PCPDTBT Si-PCPDTBT Poly((4,4'-bis(2-
and C-C inter-ring stretch TT and DPP 1335 1376 N-CH3 stretch in DPP, and C-C stretch between TT and DPP on both sides 1373 1371 1405 C-N stretch and C=C s stretch between rings in DPP 1408 1391 1426 C=C stretch in TT and stretch and CH3 umbrella mode in DPP 1426 1414 1463 C=C stretch in TT (between rings) and CH3 umbrella mode in DPP 1456 C=C as stretch (one ring) and C-H bend in TT and DPP CH3 umbrella mode 1477 1523 TT C=C stretch (one C=C on each side of DPP) 1524 TT C=C s stretch (opposite sides opposite rings) 1492 1534 TT C=C s stretch (one C=C on each side of T) 1532 CH2 δ in CH3 DPP 1507 1534 TT C=C s stretch (opposite sides opposite rings) 1513 1560 DPP C=C s stretch (opposite sides opposite rings) 1561 as: symmetric, δ: bend Table S7.2Absolute resonance Raman Cross Sections (σR) for the vibrational modes of included in RRIA analysis. Transition (cm-1) σR(737 nm) (x10-9 Å2) σR(683 nm) σR(637 nm) (x10-9 Å2) σR(737 nm) σR(683 nm) σR(637 nm)
v6 1477 1477 0.25 1477 1477 -0.18 v7 1492 1492 0.35 1492 1300 -0.28 v8 1507 1507 0.18 1507 1507 -0.14 v9 1513 1513 0.245 1513 1513 -0.15 Γ (cm-1) 300 300 Θ (cm-1) 450 450 Ε00(cm1) 12400 13700 Μ1(Å) 2.38 1.75 HMW-CF-1 HMW-CF-2 v1 1327 1327 0.06 1327 1327 0.05 v2 1335 1335 0.165 1335 1335 -0.20 v3 1371 1371 0.255 1371 1371 -0.18 v4 1391 1391 0.23 1391 1391 -0.10 v5 1414 1414 0.27 1414 1414 -0.11 v6 1477 1477 0.25 1477 1477 -0.15 v7 1492 1300 0.42 1492 1300 -0.50 v8 1507 1507 0.07 1507 1507 0.10 v9 1513 1513 0.35 1513 1513 -0.37 Γ (cm-1) 350 350 Θ (cm-1) 350 350 Ε00(cm1) 12300 13600 Μ1(Å) 2.79 1.70 aground state frequency bexcited state frequency cnon-dimensional displacement between the ground and excited potential Figure S7.3 Experimental (solid black line) and calculated (dashed red line) absorption cross sections of C3 LMW and HMW polymers in 1,2-dichlorobenzene (upper plots) and chloroform (lower plots) when one dipole-allowed transition is included in the model. Figure S7.4 Experimental (points) and calculated (solid line) Raman excitation profiles for the 1492 cm-1 mode of LMW and HMW C3 polymer in 1,2-dichlorobenzene (upper plots) and chloroform (lower plots) using a single dipole-allowed transition in the RRIA.