Electronic excitations in long polyenes revisited

Characterization of the Ultraviolet-B Absorption Band of Carotenoids Using Solvent-dependent Shifts in Steady-State and Transient Absorption Spectra

The versatile functions of carotenoids in biological systems are associated with the extended π-electron conjugation system. Strong visible absorption resulting from the optically allowed S2 (1Bu+) state and the low-lying optically forbidden S1 (2Ag-) state examined. Carotenoids also exhibit an absorption band in the ultraviolet-B region; however, the origin of this band (hereafter referred to as Suv state) is not well characterized. The Suv state is a candidate for the destination level of the well-known S1 → Sn transient absorption; however, an obvious energy mismatch has been observed. In this study, we examined the steady-state and picosecond transient absorption spectra of lycopene in various solvents. The Suv absorption of carotenoids with diverse conjugation lengths was also examined. The dependence of the energies on solvent polarizability and conjugation length revealed that both Suv and Sn are the "second" Bu+ state. The absorption spectrum for lycopene at 200 K revealed an additional vibrational band, which may be the vibrational origin of the S0 → Suv band. Considering the slow vibrational relaxation of the 2Ag- state, the S1 → Sn transition may represent the 2Ag- (v = 1) → 2Bu+ (v = 0) transition, and the energetic contradiction can be resolved.

Predicting Solvatochromism of Chromophores in Proteins through QM/MM and Machine Learning

Solvatochromism occurs in both homogeneous solvents and more complex biological environments, such as proteins. While in both cases the solvatochromic effects report on the surroundings of the chromophore, their interpretation in proteins becomes more complicated not only because of structural effects induced by the protein pocket but also because the protein environment is highly anisotropic. This is particularly evident for highly conjugated and flexible molecules such as carotenoids, whose excitation energy is strongly dependent on both the geometry and the electrostatics of the environment. Here, we introduce a machine learning (ML) strategy trained on quantum mechanics/molecular mechanics calculations of geometrical and electrochromic contributions to carotenoids' excitation energies. We employ this strategy to compare solvatochromism in protein and solvent environments. Despite the important specifities of the protein, ML models trained on solvents can faithfully predict excitation energies in the protein environment, demonstrating the robustness of the chosen descriptors.

The Solvent-Dependent Photophysics of Diphenyloctatetraene

Despite many decades of study, the excited state photophysics of polyenes remains controversial. In diphenylpolyenes with conjugated backbones that contain between 2 and 4 double carbon-carbon bonds, the first two excited electronic states are nearly degenerate but of entirely different character, and their energy splitting is strongly dependent on solvent polarizability. To examine the interplay between these different states, steady-state and time-resolved fluorescence spectroscopies were used to undertake a comprehensive investigation of diphenylocatetraene's (DPO) excited state dynamics in 10 solvents of different polarizabilities and polarities, ranging from weakly interacting alkanes to polar hydrogen-bonding alcohols. These data revealed that photopreparation of the optically bright 1Bu state resulted in fast (<170 ps) internal conversion to the lower-lying optically dark 2Ag state. The 2Ag state is responsible for almost all the observed DPO fluorescence and gains oscillator strength via vibronic intensity stealing with the near-degenerate 1Bu state. The fluorescence lifetime associated with the 2Ag state decayed monoexponentially (4.2-7.2 ns) in contrast to prior biexponential decay kinetics reported for similar polyenes, diphenylbutadiene and diphenylhexatriene. An analysis combining the measured fluorescence lifetimes and fluorescence quantum yields (the latter varying between 7 and 21%) allowed for a 190 cm-1 Herzberg-Teller vibronic coupling constant between the 1Bu and 2Ag states to be determined. The analysis also revealed that the ordering of electronic states remains constant in all the solvents studied, with the 2Ag state minimum always lower in energy than that of the 1Bu state, thus making it a relatively simple polyene compared to structurally similar diphenylhexatriene.

Twisted Carotenoids Do Not Support Efficient Intramolecular Singlet Fission in the Orange Carotenoid Protein

Singlet exciton fission is the spin-allowed generation of two triplet electronic excited states from a singlet state. Intramolecular singlet fission has been suggested to occur on individual carotenoid molecules within protein complexes provided that the conjugated backbone is twisted out of plane. However, this hypothesis has been forwarded only in protein complexes containing multiple carotenoids and bacteriochlorophylls in close contact. To test the hypothesis on twisted carotenoids in a "minimal" one-carotenoid system, we study the orange carotenoid protein (OCP). OCP exists in two forms: in its orange form (OCPo), the single bound carotenoid is twisted, whereas in its red form (OCPr), the carotenoid is planar. To enable room-temperature spectroscopy on canthaxanthin-binding OCPo and OCPr without laser-induced photoconversion, we trap them in a trehalose glass. Using transient absorption spectroscopy, we show that there is no evidence of long-lived triplet generation through intramolecular singlet fission despite the canthaxanthin twist in OCPo.

Transient "cis-Peak" Is Present in Excited-State Absorption of Central-cis Isomers of Carotenoids

Application of femtosecond time-resolved transient absorption spectroscopy on all-trans and central-cis isomers of two exemplary carotenoids, lutein and spirilloxanthin, performed at room and cryogenic temperatures in the spectral range expanded toward UV revealed new spectroscopic transient features for the cis isomers. Notably, particularly for the central-cis spirilloxanthin, a very distinct additional transient absorption band is observed on the short wavelength side of the main excited-state absorption band of the S₁ state, having the same temporal characteristics as the latter one. This band is absent in transient absorption spectra of all-trans isomers, suggesting it could be assigned to "transient cis-peak." Overall, the results show that the "transient" counterpart of the spectral marker of cis-isomers of carotenoids, or the so-called cis-peak, is detectable in the excited-state absorption spectrum and could be attributed to electronic transition from the S₁ state. This new transient spectral band could be very useful for spectroscopic experiments targeting the dynamics of carotenoid isomers and their severely distorted forms.

Theory, implementation, and disappointing results for two-photon absorption cross sections within the doubly electron-attached equation-of-motion coupled-cluster framework

The equation-of-motion coupled-cluster singles and doubles method with double electron attachment (EOM-DEA-CCSD) is capable of computing reliable energies, wave functions, and first-order properties of excited states in diradicals and polyenes that have a significant doubly excited character with respect to the ground state, without the need for including the computationally expensive triple excitations. Here, we extend the capabilities of the EOM-DEA-CCSD method to the calculations of a multiphoton property, two-photon absorption (2PA) cross sections. Closed-form expressions for the 2PA cross sections are derived within the expectation-value approach using response wave functions. We analyze the performance of this new implementation by comparing the EOM-DEA-CCSD energies and 2PA cross sections with those computed using the CC3 quadratic response theory approach. As benchmark systems, we consider transitions to the states with doubly excited character in twisted ethene and in polyenes, for which EOM-EE-CCSD (EOM-CCSD for excitation energies) performs poorly. The EOM-DEA-CCSD 2PA cross sections are comparable with the CC3 results for twisted ethene; however, the discrepancies between the two methods are large for hexatriene. The observed trends are explained by configurational analysis of the 2PA channels.

Ultrafast Excited-State Dynamics of Carotenoids and the Role of the SX State

Carotenoids are natural pigments with multiple roles in photosynthesis. They act as accessory pigments by absorbing light where chlorophyll absorption is low, and they quench the excitation energy of neighboring chlorophylls under high-light conditions. The function of carotenoids depends on their polyene-like structure, which controls their excited-state properties. After light absorption to their bright S2 state, carotenoids rapidly decay to the optically dark S1 state. However, ultrafast spectroscopy experiments have shown the signatures of another dark state, termed SX. Here we shed light on the ultrafast photophysics of lutein, a xanthophyll carotenoid, by explicitly simulating its nonadiabatic excited-state dynamics in solution. Our simulations confirm the involvement of SX in the relaxation toward S1 and reveal that it is formed through a change in the nature of the S2 state driven by the decrease in the bond length alternation coordinate of the carotenoid conjugated chain.

Excited States of Xanthophylls Revisited: Toward the Simulation of Biologically Relevant Systems

Xanthophylls are a class of oxygen-containing carotenoids, which play a fundamental role in light-harvesting pigment-protein complexes and in many photoresponsive proteins. The complexity of the manifold of the electronic states and the large sensitivity to the environment still prevent a clear and coherent interpretation of their photophysics and photochemistry. In this Letter, we compare cutting-edge ab initio methods (CC3 and DMRG/NEVPT2) with time-dependent DFT and semiempirical CI (SECI) on model keto-carotenoids and show that SECI represents the right compromise between accuracy and computational cost to be applied to real xanthophylls in their biological environment. As an example, we investigate canthaxanthin in the orange carotenoid protein and show that the conical intersections between excited states and excited-ground states are mostly determined by the effective bond length alternation coordinate, which is significantly tuned by the protein through geometrical constraints and electrostatic effects.

Carotenoid-to-(bacterio)chlorophyll energy transfer in LH2 antenna complexes from Rba. sphaeroides reconstituted with non-native (bacterio)chlorophylls

Six variants of the LH2 antenna complex from Rba. sphaeroides, comprising the native B800-B850, B800-free LH2 (B850) and four LH2s with various (bacterio)chlorophylls reconstituted into the B800 site, have been investigated with static and time-resolved optical spectroscopies at room temperature and at 77 K. The study particularly focused on how reconstitution of a non-native (bacterio)chlorophylls affects excitation energy transfer between the naturally bound carotenoid spheroidene and artificially substituted pigments in the B800 site. Results demonstrate there is no apparent trend in the overall energy transfer rate from spheroidene to B850 bacteriochlorophyll a; however, a trend in energy transfer rate from the spheroidene S₁ state to Q_y of the B800 (bacterio)chlorophylls is noticeable. These outcomes were applied to test the validity of previously proposed energy values of the spheroidene S₁ state, supporting a value in the vicinity of 13,400 cm^-1 (746 nm).

Spectroscopy and excited state dynamics of nearly infinite polyenes

Steady-state and transient absorption spectra with <50 fs time resolution were obtained for two conjugated polymers, both with ≈200 conjugated double bonds (N), constrained in planar, stable, polyene frameworks. Solutions of the polymers exhibit the same S2 → S1 → S* → S0 decay pathway observed for the N = 11-19 polyene oligomers and for zeaxanthin homologues with N = 11-23. Comparisons with the excited state dynamics of polydiactylene and a much longer, more disordered polyene polymer (poly(DEDPM)) show that the S2, S1, and S* lifetimes of the four polymers are almost identical. The S* signals in the polymers are assigned to absorption from vibrationally excited ground states. In spite of significant heterogeneities and variations in conjugation lengths in these long polyenes, their S0 → S2 absorptions are vibronically-resolved in room temperature solutions with electronic origins at ≈600 nm. The limiting wavelength for the S0 → S2 transitions is consistent with the persistence of bond length alternation in the electronic ground states and a HOMO-LUMO band gap in polyenes with N ≈ 200. The coincidence of the well-resolved S0 → S2 electronic origins and the convergence of the excited state lifetimes in the four polymers point to a common, "nearly infinite" polyene limit.

Carotenoid Nuclear Reorganization and Interplay of Bright and Dark Excited States

We report quantum chemical calculations using multireference perturbation theory (MRPT) with the density matrix renormalization group (DMRG) plus photothermal deflection spectroscopy measurements to investigate the manifold of carotenoid excited states and establish their energies relative to the bright state (S₂) as a function of nuclear reorganization. We conclude that the primary photophysics and function of carotenoids are determined by interplay of only the bright (S₂) and lowest-energy dark (S₁) states. The lowest-lying dark state, far from being energetically distinguishable from the lowest-lying bright state along the entire excited-state nuclear reorganization pathway, is instead computed to be either the second or first excited state depending on what equilibrium geometry is considered. This result suggests that, rather than there being a dark intermediate excited state bridging a non-negligible energy gap from the lowest-lying dark state to the lowest-lying bright state, there is in fact no appreciable energy gap to bridge following photoexcitation. Instead, excited-state nuclear reorganization constitutes the bridge from S₂ to S₁, in the sense that these two states attain energetic degeneracy along this pathway.

The origin of the dark S1 state in carotenoids: a comprehensive model

In carotenoids, by analogy to polyenes, the symmetry of the π-electron system is often invoked to explain their peculiar electronic features, in particular the inactivity of the S₀ → S₁ transition in one-photon excitation. In this review, we verify whether the molecular symmetry of carotenoids and symmetry of their π-electron system are supported in experimental and computational studies. We focus on spectroscopic techniques which are sensitive to the electron density distribution, including the X-ray crystallography, electronic absorption, two-photon techniques, circular dichroism, nuclear magnetic resonance, Stark and vibrational spectroscopies, and on this basis we seek for the origin of inactivity of the S₁ state. We come across no experimental and computational evidence for the symmetry effects and the existence of symmetry restrictions on the electronic states of carotenoids. They do not possess an inversion centre and the C_2h symmetry approximation of carotenoid structure is by no means justified. In effect, the application of symmetry rules (and notification) to the electronic states of carotenoids in this symmetry group may lead to a wrong interpretation of experimental data. This conclusion together with the results summarized in the review allows us to advance a consistent model that explains the inactivity of the S₀ → S₁ transition. Within this model, S₁ is never accessible from S₀ due to the negative synergy of (i) the contributions of double excitations of very low probability, which elevate S₁ energy, and (ii) a non-verticality of the S₀ → S₁ transition, due to the breaking of Born-Oppenheimer approximation. Certainly, our simple model requires a further experimental and theoretical verification.

Evaluation of full valence correlation energies and gradients

Complete-active-space self-consistent field (CASSCF) wave functions are central to understanding strongly correlated molecules as they capture the entirety of electronic interactions within a subset of the orbital space. The most interesting case for CASSCF is the full valence limit, where all bonding and an equal number of virtual orbitals are included in the active space, and no approximation is made in selecting the important valence orbitals or electrons. While conventional algorithms require exponential computational time to evaluate full valence CASSCF, this article shows that the method of increments can do the same with polynomial effort, in a new method denoted iCASSCF. The method of increments can also provide density matrices and other necessary ingredients for the construction of the nuclear gradient. These goals are met through a many-body expansion that breaks the problem into smaller pieces that are subsequently reassembled to form close approximations of conventional CAS results. Practical demonstrations on a number of medium-sized molecules, with up to 116 valence electrons correlated in 116 orbitals, show the power of this methodology.

Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems

The 21Ag and 11Bu excited states of two prototypical π-conjugated compounds, polyacetylene and polydiacetylene, are investigated with the recently developed particle-particle random phase approximation (pp-RPA) method combined with the B3LYP functional. The polymer-limit transition energies are estimated as 1.38 and 1.72 eV for the 21Ag and 11Bu states, respectively, from an extrapolation of the computed excitation energies of model oligomers. These values increase to 1.95 and 2.24 eV for the same transitions when ground-state structures with ∼33% larger bond length alternation are adopted. Applying the pp-RPA to the vertical excitation energies in oligodiacetylene, the polymer-limit transition energies of the 21Ag and 11Bu states are computed to be 2.06 and 2.28 eV, respectively. These results are in good agreement with experimental values or theoretical best estimates, indicating that the pp-RPA method shows great promise for understanding many photophysical phenomena involving both single and double excitations.

Side Methyl Groups Control the Conformation and Contribute to Symmetry Breaking of Isoprenoid Chromophores

Ab initio DFT computations reveal that the essential structural and photophysical features of the conjugated π-electron system of retinal and carotenoids are dictated by "innocent" methyl substituents. These methyl groups shape the conformation and symmetry of the isoprenoid chromophores by causing a sigmoidal distortion of the polyene skeleton and increasing its flexibility, which facilitates fitting to their binding pockets in proteins. Comparison of in vacuo conformations of the chromophores with their native (protein-bound) conformations showed, surprisingly, that the peripheral groups and interactions with the protein environment are much less significant than the methyl side groups in tuning their structural features. The methyl side groups also contribute to a loss of symmetry elements specific to linear polyenes. In effect, the symmetry-imposed restrictions on the chromophore electronic properties are disabled, which is of tremendous relevance to their photophysics. This is evidenced by their non-negligible permanent dipole moments and by the simulated and experimentally measured circular dichroism spectra, which necessarily reflect the chirality of the conjugated π-electron system.

Diagrammatic Exciton Basis Theory of the Photophysics of Pentacene Dimers

Covalently linked acene dimers are of interest as candidates for intramolecular singlet fission. We report many-electron calculations of the energies and wave functions of the optical singlets, the lowest triplet exciton, and the triplet-triplet biexciton, as well as the final states of excited state absorptions from these states in a family of phenyl-linked pentacene dimers. While it is difficult to distinguish the triplet and the triplet-triplet from their transient absorptions in the 500-600 nm region, by comparing theoretical transient absorption spectra against earlier and very recent experimental transient absorptions in the near- and mid-infrared, we conclude that the end product of photoexcitation in these particular bipentacenes is the bound triplet-triplet and not free triplets. We predict additional transient absorptions at even longer wavelengths, beyond 1500 nm, to the equivalent of the classic 2¹A_g^- in linear polyenes.

A new energy transfer channel from carotenoids to chlorophylls in purple bacteria

It is unclear whether there is an intermediate dark state between the S₂ and S₁ states of carotenoids. Previous two-dimensional electronic spectroscopy measurements support its existence and its involvement in the energy transfer from carotenoids to chlorophylls, but there is still considerable debate on the origin of this dark state and how it regulates the energy transfer process. Here we use ab initio calculations on excited-state dynamics and simulated two-dimensional electronic spectrum of carotenoids from purple bacteria to provide evidence supporting that the dark state may be assigned to a new A_g⁺ state. Our calculations also indicate that groups on the conjugation backbone of carotenoids may substantially affect the excited-state levels and the energy transfer process. These results contribute to a better understanding of carotenoid excited states.

Carotenoids harvest energy from light and transfer it to chlorophylls during photosynthesis. Here, Feng et al. perform ab initio calculations on excited-state dynamics and simulated 2D electronic spectrum of carotenoids, supporting the existence of a new excited state in carotenoids.

Effects of Molecular Symmetry on the Electronic Transitions in Carotenoids

The aim of this work is the verification of symmetry effects on the electronic absorption spectra of carotenoids. The symmetry breaking in cis-β-carotenes and in carotenoids with nonlinear π-electron system is of virtually no effect on the dark transitions in these pigments, in spite of the loss of the inversion center and evident changes in their electronic structure. In the cis isomers, the S2 state couples with the higher excited states and the extent of this coupling depends on the position of the cis bend. A confrontation of symmetry properties of carotenoids with their electronic absorption and IR and Raman spectra shows that they belong to the C1 or C2 but not the C2h symmetry group, as commonly assumed. In these realistic symmetries all the electronic transitions are symmetry-allowed and the absence of some transitions, such as the dark S0 → S1 transition, must have another physical origin. Most likely it is a severe deformation of the carotenoid molecule in the S1 state, unachievable directly from the ground state, which means that the Franck-Condon factors for a vertical S0 → S1 transition are negligible because the final state is massively displaced along the vibrational coordinates. The implications of our findings have an impact on the understanding of the photophysics and functioning of carotenoids.

Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics

Due to the crucial role played by electron correlation, the accurate determination of ground state geometries of π-conjugated molecules is still a challenge for many quantum chemistry methods. Because of the high parallelism of the algorithms and their explicit treatment of electron correlation effects, Quantum Monte Carlo calculations can offer an accurate and reliable description of the electronic states and of the geometries of such systems, competing with traditional quantum chemistry approaches. Here, we report the structural properties of polyacetylene chains H-(C₂H₂)(N)-H up to N = 12 acetylene units, by means of Variational Monte Carlo (VMC) calculations based on the multi-determinant Jastrow Antisymmetrized Geminal Power (JAGP) wave function. This compact ansatz can provide for such systems an accurate description of the dynamical electronic correlation as recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 2015 11 (2), 508-517]. The calculated Bond Length Alternation (BLA), namely the difference between the single and double carbon bonds, extrapolates, for N → ∞, to a value of 0.0910(7) Å, compatible with the experimental data. An accurate analysis was able to distinguish between the influence of the multi-determinantal AGP expansion and of the Jastrow factor on the geometrical properties of the fragments. Our size-extensive and self-interaction-free results provide new and accurate ab initio references for the structures of the ground state of polyenes.

The nature of singlet exciton fission in carotenoid aggregates

Singlet exciton fission allows the fast and efficient generation of two spin triplet states from one photoexcited singlet. It has the potential to improve organic photovoltaics, enabling efficient coupling to the blue to ultraviolet region of the solar spectrum to capture the energy generally lost as waste heat. However, many questions remain about the underlying fission mechanism. The relation between intermolecular geometry and singlet fission rate and yield is poorly understood and remains one of the most significant barriers to the design of new singlet fission sensitizers. Here we explore the structure-property relationship and examine the mechanism of singlet fission in aggregates of astaxanthin, a small polyene. We isolate five distinct supramolecular structures of astaxanthin generated through self-assembly in solution. Each is capable of undergoing intermolecular singlet fission, with rates of triplet generation and annihilation that can be correlated with intermolecular coupling strength. In contrast with the conventional model of singlet fission in linear molecules, we demonstrate that no intermediate states are involved in the triplet formation: instead, singlet fission occurs directly from the initial 1B(u) photoexcited state on ultrafast time scales. This result demands a re-evaluation of current theories of polyene photophysics and highlights the robustness of carotenoid singlet fission.

Combination of transient 2D-IR experiments and ab initio computations sheds light on the formation of the charge-transfer state in photoexcited carbonyl carotenoids

The excited state dynamics of carbonyl carotenoids is very complex because of the coupling of single- and doubly excited states and the possible involvement of intramolecular charge-transfer (ICT) states. In this contribution we employ ultrafast infrared spectroscopy and theoretical computations to investigate the relaxation dynamics of trans-8'-apo-β-carotenal occurring on the picosecond time scale, after excitation in the S2 state. In a (slightly) polar solvent like chloroform, one-dimensional (T1D-IR) and two-dimensional (T2D-IR) transient infrared spectroscopy reveal spectral components with characteristic frequencies and lifetimes that are not observed in nonpolar solvents (cyclohexane). Combining experimental evidence with an analysis of CASPT2//CASSCF ground and excited state minima and energy profiles, complemented with TDDFT calculations in gas phase and in solvent, we propose a photochemical decay mechanism for this system where only the bright single-excited 1Bu(+) and the dark double-excited 2Ag(-) states are involved. Specifically, the initially populated 1Bu(+) relaxes toward 2Ag(-) in 200 fs. In a nonpolar solvent 2Ag(-) decays to the ground state (GS) in 25 ps. In polar solvents, distortions along twisting modes of the chain promote a repopulation of the 1Bu(+) state which then quickly relaxes to the GS (18 ps in chloroform). The 1Bu(+) state has a high electric dipole and is the main contributor to the charge-transfer state involved in the dynamics in polar solvents. The 2Ag(-) → 1Bu(+) population transfer is evidenced by a cross peak on the T2D-IR map revealing that the motions along the same stretching of the conjugated chain on the 2Ag(-) and 1Bu(+) states are coupled.

Double-core excitations in formamide can be probed by X-ray double-quantum-coherence spectroscopy

The attosecond, time-resolved X-ray double-quantum-coherence four-wave mixing signals of formamide at the nitrogen and oxygen K-edges are simulated using restricted excitation window time-dependent density functional theory and the excited core hole approximation. These signals, induced by core exciton coupling, are particularly sensitive to the level of treatment of electron correlation, thus providing direct experimental signatures of electron and core-hole many-body effects and a test of electronic structure theories.

Energetics and dynamics of the low-lying electronic states of constrained polyenes: implications for infinite polyenes

Steady-state and ultrafast transient absorption spectra were obtained for a series of conformationally constrained, isomerically pure polyenes with 5-23 conjugated double bonds (N). These data and fluorescence spectra of the shorter polyenes reveal the N dependence of the energies of six (1)B(u)(+) and two (1)A(g)(-) excited states. The (1)B(u)(+) states converge to a common infinite polyene limit of 15,900 ± 100 cm(-1). The two excited (1)A(g)(-) states, however, exhibit a large (~9000 cm(-1)) energy difference in the infinite polyene limit, in contrast to the common value previously predicted by theory. EOM-CCSD ab initio and MNDO-PSDCI semiempirical MO theories account for the experimental transition energies and intensities. The complex, multistep dynamics of the 1(1)B(u)(+) → 2(1)A(g)(-) → 1(1)A(g)(-) excited state decay pathways as a function of N are compared with kinetic data from several natural and synthetic carotenoids. Distinctive transient absorption signals in the visible region, previously identified with S* states in carotenoids, also are observed for the longer polyenes. Analysis of the lifetimes of the 2(1)A(g)(-) states, using the energy gap law for nonradiative decay, reveals remarkable similarities in the N dependence of the 2(1)A(g)(-) decay kinetics of the carotenoid and polyene systems. These findings are important for understanding the mechanisms by which carotenoids carry out their roles as light-harvesting molecules and photoprotective agents in biological systems.