Vibronic bands in the HOMO-LUMO excitation of linear polyyne molecules

Hydrogen-capped linear carbon chain molecules, namely polyynes H(C=C)(n)H (n >= 2), give rise to three excited states in the HOMO-LUMO excitation. Electric dipole transition from the ground state is fully allowed to one of the three excited states, while forbidden for the other two low-lying excited states. In addition to the strong absorption bands in the UV for the allowed transition, the molecules exhibit weak absorption and emission bands in the near UV and visible wavelength regions. The weak features are the vibronic bands in the forbidden transition. In this article, symmetry considerations are presented for the optical transitions in the centrosymmetric linear polyyne molecule. The argument includes Herzberg-Teller expansion for the state mixing induced by nuclear displacements along the normal coordinate of the molecule, intensity borrowing from fully allowed transitions, and inducing vibrational modes excited in the vibronic transition. The vibronic coupling considered here includes off-diagonal matrix elements for second derivatives along the normal coordinate. The vibronic selection rule for the forbidden transition is derived and associated with the transition moment with respect to the molecular axis. Experimental approaches are proposed for the assignment of the observed vibronic bands.