Molecular Excitons and Plasmons in Acenes and Their Radical Cations

For existing and potential applications of acenes and acene derivatives, properties of their excited states play a central role. In describing these, the molecular orbital picture can reach its limits, and consideration within the quasi-particle picture can enable further insight. In this work, exciton size ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>e</mml:mi> <mml:mi>x</mml:mi> <mml:mi>c</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {d}_{exc} $$</mml:annotation></mml:semantics> </mml:math> ), hole and electron size ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow> <mml:mrow><mml:mi>h</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\sigma}_h $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow> <mml:mrow><mml:mi>e</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {\sigma}_e $$</mml:annotation></mml:semantics> </mml:math> ) and correlation coefficient ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mi>e</mml:mi> <mml:mi>h</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {R}_{eh} $$</mml:annotation></mml:semantics> </mml:math> ) of excited states of acenes and acene cations are investigated using TD-DFT at the TDA/CAM-B3LYP/6-311G* level, with a focus on their development with increasing acene length. Furthermore, employing a previously established approach, it is shown that the electronic structure of the ¹B_b and ²B_b states of neutral and cationic anthracene can be understood as molecular plasmons.