Longest-Wavelength Electronic Excitations of Linear Cyanines: The Role of Electron Delocalization and of Approximations in Time-Dependent Density Functional Theory

Abstract

The lowest-energy/longest-wavelength electronic singlet excitation energies of linear cyanine dyes are examined, using time-dependent density functional theory (TDDFT) and selected wave function methods in comparison with literature data. Variations of the bond-length alternation obtained with different optimized structures produce small differences of the excitation energy in the limit of an infinite chain. Hybrid functionals with range-separated exchange are optimally 'tuned', which is shown to minimize the delocalization error (DE) in the cyanine π systems. Much unlike the case of charge-transfer excitations, small DEs are not strongly correlated with better performance. A representative cyanine is analyzed in detail. Compared with accurate benchmark data, TDDFT with 'pure' local functionals gives too high singlet excitation energies for all systems, but DFT-based ΔSCF calculations with a local functional severely underestimates the energies. TDDFT strongly overestimates the difference between singlet and triplet excitation energies. An analysis points to systematically much too small magnitudes of integrals from the DFT components of the exchange-correlation response kernel as the likely culprit. The findings support previous suggestions that the differential correlation energy between the ground and excited state is not correctly produced by TDDFT with most functionals.

Inverted Substrate Preferences for Photochemical Heterolysis Arise from Conical Intersection Control

“…For example, the meta-donor-substituted systems have an excited singlet ion diradical form that is electronically analogous to the classic meta xylylene diradical, 49 with a radical at the "carbenium center" and a cation radical donor substituent. There are numerous examples of cations that fall within this type (9,12,13,17,18,19,22,23,24,25,26,27,31). Thus, while the donor group does not act to stabilize the ground-state cation via resonance, it leads to stabilized singlet diradical excited states.…”

Vertical excitation energies of linear cyanine dyes by spin-flip time-dependent density functional theory

“…Geometries at the MP2/cc-pVQZ level were taken from Ref. [4]. The linear cyanine molecules have C 2v symmetry, and the excitation from the ground (A 1 ) to the lowest (B 2 ) singlet state was considered.…”

“…The observation is surprising because the lowest excited-state is described as the excitation from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). Several benchmark studies have been reported using various methodologies including multi-reference perturbation theory, many-body perturbation theory, coupled cluster, diffusion Monte Carlo (DMC), and density functional theory [1][2][3][4][5][6].…”

“…A large number of benchmark studies have been reported to investigate the performance of LR-TDDFT and to propose new density functionals [8]. The previous studies on linear cyanine dyes show the LR-TDDFT method overestimates the excitation energy [2][3][4]. Grimme and Neese found that the double hybrid functional yields the better result [9].…”

Optical signatures of borico dyes: a TD-DFT analysis

“…Indeed, it is well-known that linear-response TD-DFT tend to overshoot the transition energies of cyanine structures (by ca. 0.20-0.60 eV) compared to accurate reference data [27,28,49,50]. Whilst the use of the most modern exchange-correlation functionals, such as M06-2X [28] or optimally-tuned range separated hybrids [50], alleviate TD-DFT's error for cyanines making the obtained absolute deviation more in the line of other states, all tested TD-DFT protocols tend, to the best of our knowledge, to provide too large transition energies for this family of dyes.…”