Excitonic splittings in molecular dimers: why static ab initio calculations cannot match them

Abstract

After decades of research on molecular excitons, only few molecular dimers are available on which exciton and vibronic coupling theories can be rigorously tested. In centrosymmetric H-bonded dimers consisting of identical (hetero)aromatic chromophores, the monomer electronic transition dipole moment vectors subtract or add, yielding S₀ → S₁ and S₀ → S₂ transitions that are symmetry-forbidden or -allowed, respectively. Symmetry breaking by ¹²C/¹³C or H/D isotopic substitution renders the forbidden transition weakly allowed. The excitonic coupling (Davydov splitting) can then be measured between the S₀ → S₁ and S₀ → S₂ vibrationless bands. We discuss the mass-specific excitonic spectra of five H-bonded dimers that are supersonically cooled to a few K and investigated using two-color resonant two-photon ionization spectroscopy. The excitonic splittings Δ_calc predicted by ab initio methods are 5-25 times larger than the experimental excitonic splittings Δ_exp. The purely electronic ab initio splittings need to be reduced ("quenched"), reflecting the coupling of the electronic transition to the optically active vibrations of the monomers. The so-called quenching factors Γ < 1 can be determined from experiment (Γ_exp) and/or calculation (Γ_calc). The vibronically quenched splittings Γ·Δ_calc are found to nicely reproduce the experimental exciton splittings.

Fig. 1. Ground state geometries of the H-bonded dimers (2-pyridone)₂, (o-cyanophenol)₂, (2-aminopyridine)₂, (benzonitrile)₂ and (benzoic acid)₂ (CC2/aug-cc-pVTZ calculations). The monomer transition-dipole moment vectors are indicated as red double-headed arrows.

Fig. 2. Schematic view of (a) the excitonic splitting in a symmetric dimer consisting of identical chromophores A and B, (b) the S₁/S₂ state splitting in a symmetry-broken dimer that is isotopically substituted in chromophore A.

Fig. 3. Experimentally observed splittings Δ_obs between the S₁ and S₂ electronic origins of the ¹³C-isotopomers of the doubly H-bonded dimers in Fig. 1.

Fig. 4. Two-dimensional potential energy surfaces of the S₁ (red) and S₂ (blue) states of a symmetric self-dimer, plotted as a function of the intramolecular vibrational coordinates Q_A and Q_B. (a) Strong coupling case, (b) weak coupling case. The calculated vibronic band patterns are shown as stickplots in (c and d), with negative band intensities (red) for A_g vibronic transitions and positive (blue) intensities for the B_u vibronic transitions.

Fig. 5. Dependence of the S₁/S₂ intensity ratio on the excitonic splitting in H-bonded symmetric molecular dimers. The excitonic splittings were determined from the directly observable splittings of the ¹³C isotopomers, assuming a ¹²C/¹³C isotopic shift Δ_iso of 3.3 cm^–1 for all dimers. The theoretical dependence of the S₁/S₂ intensity ratio on Δ_exc is indicated in red.

Fig. 6. 1D-cuts of the first two excited adiabatic potential energy surfaces along the effective mode for (2-pyridone)₂, (o-cyanophenol)₂ and (2-aminopyridine)₂. The line type of the vibronic wave functions (schematic drawing) is the same as that of the corresponding potential energy curve, its zero is chosen to match its vibronic energy. The excitation energy splitting at the ground state equilibrium geometry (Qeff– = 0) equals the electronic excitonic splitting Δ_vert.