Internal conversion rate constant calculations considering Duschinsky, anharmonic and Herzberg-Teller effects

A novel method for calculating rate constants for internal conversion (k_IC) that simultaneously accounts for Duschinsky, anharmonic and Herzberg-Teller effects has been developed and implemented. This method has been applied to robust planar molecules like tetraoxa[8]circulene (4B), free-base porphyrin (H2P) and pyrometene (PM567) with small Duschinsky rotation (i.e. with almost identical normal coordinates in the ground and excited states) and to poly[n]fluorenes (P[n]F) (n = 2-14) with a substantial Duschinsky rotation. The obtained results show that the Duschinsky effect is large in the harmonic approximation, whereas it is in general much smaller in the anharmonic approximation. The Duschinsky effect is found to be large for high frequency vibrational modes with energies of ∼3300 cm^-1 such as the X-H (X = C, N and O) stretching modes that mix in the S₁ → S₀ electronic transition. However, even in this case, the increase in k_IC due to the Duschinsky effect does not exceed one order of magnitude. The calculations show that anharmonic contributions to k_IC are larger than Herzberg-Teller contributions which in turn are larger than contributions from the Duschinsky effect ANH > HT > Du. We also show that an approximation, where only X-H bonds are considered in the k_IC calculation, is accurate even for P[n]F (n = 2-14).