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 to transition is given by and clearly tends toward as n n+1 n n increases. For the simple harmonic oscillator (SHO), the result is exact at fn,n+1 = The n. 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 for the polymers studied π-electrons To normalise transition strengths by the number of electrons available, we assume that transitions in the visible region are due to the system and therefore count the number of π electrons in each unit,. We note that, especially for multi-ring structures with added functionalities, the number of electrons may not be well-defined, but any such π 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 electrons that we count in each conjugated unit. π-conjugated S6.1 Names and chemical structures of oligomers studied Polymer Polymer Full Name Oligomer Structure (Oligomer) Abbreviation P3HT (T) PFO (F) PCPDTBT Si-PCPDTBT Poly((4,4'-bis(2-
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-
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