Correlation effects in the spectra of polyenes

Classification and quantitative characterisation of the excited states of π-conjugated diradicals

Diradicals are of high current interest as emerging materials for next generation optoelectronic applications. To tune their excited-state properties it would be greatly beneficial to have a detailed understanding of the wave functions of the different states involved but this endeavour is hampered by formal and practical barriers. To tackle these challenges, we present a formal analysis as well as concrete results on diradical excited states. We start with a detailed investigation of the available states of a two-orbital two-electron model viewed from both the valence-bond and molecular orbital perspectives. We highlight the presence of diradical and zwitterionic states and illustrate their connections to the states found in closed-shell molecules. Subsequently, we introduce practical protocols for analysing states from realistic multireference computations applying these to the para-quinodimethane (pQDM) molecule. The analysis reveals four different categories of states - diradical, zwitterionic, HOMO-SOMO as well as biexciton - while also providing insight into their energetics and optical properties. Twisting the CH2 groups allows us to interconvert between the closed- and open-shell forms of pQDM illustrating the connection between the states in both forms. More generally, we hope that this work will lay the foundations for a more powerful rational design approach to diradicals for photophysical applications.

Understanding the Photoprocesses in Biological Systems: Need for Accurate Multireference Treatment

Light-matter interaction is crucial to life itself and revolves around many of the central processes in biology. The need for understanding these photochemical and photophysical processes cannot be overemphasized. Interaction of light with biological systems starts with the absorption of light and subsequent phenomena that occur in the excited states of the system. However, excited states are typically difficult to understand within the mean field approximation of quantum chemical methods. Therefore, suitable multireference methods and methodologies have been developed to understand these phenomena. In this Perspective, we will describe a few methods and methodologies suitable for these descriptions and discuss some persisting difficulties.

Quantification of the Ionic Character of Multiconfigurational Wave Functions: The Qat Diagnostic

The complete active space self-consistent field (CASSCF) method is a cornerstone in modern excited-state quantum chemistry providing the starting point for most common multireference computations. However, CASSCF, when used with a minimal active space, can produce significant errors (>2 eV) even for the excitation energies of simple hydrocarbons if the states of interest possess ionic character. After illustrating this problem in some detail, we present a diagnostic for ionic character, denoted as Q at, that is readily computed from the transition density. A set of 11 molecules is considered to study errors in vertical excitation energies. State-averaged CASSCF obtains a mean absolute error (MAE) of 0.87 eV for the 34 singlet states considered. We highlight a strong correlation between the obtained errors and the Q at diagnostic, illustrating its power to predict problematic cases. Conversely, using multireference configuration interaction with single and double excitations and Pople's size extensivity correction (MR-CISD+P), excellent results are obtained with an MAE of 0.11 eV. Furthermore, correlations with the Q at diagnostic disappear. In summary, we hope that the presented diagnostic will facilitate reliable and user-friendly multireference computations on conjugated organic molecules.

Dynamical Simulations of Carotenoid Photoexcited States Using Density Matrix Renormalization Group Techniques

We present a dynamical simulation scheme to model the highly correlated excited state dynamics of linear polyenes. We apply it to investigate the internal conversion processes of carotenoids following their photoexcitation. We use the extended Hubbard-Peierls model, H^UVP, to describe the π-electronic system coupled to nuclear degrees of freedom. This is supplemented by a Hamiltonian, H^ϵ, that explicitly breaks both the particle-hole and two-fold rotation symmetries of idealized carotenoid structures. The electronic degrees of freedom are treated quantum mechanically by solving the time-dependent Schrödinger equation using the adaptive time-dependent DMRG (tDMRG) method, while nuclear dynamics are treated via the Ehrenfest equations of motion. By defining adiabatic excited states as the eigenstates of the full Hamiltonian, H^=H^UVP+H^ϵ, and diabatic excited states as eigenstates of H^UVP, we present a computational framework to monitor the internal conversion process from the initial photoexcited 1¹B_u⁺ state to the singlet triplet-pair states of carotenoids. We further incorporate Lanczos-DMRG to the tDMRG-Ehrenfest method to calculate transient absorption spectra from the evolving photoexcited state. We describe in detail the accuracy and convergence criteria for DMRG, and show that this method accurately describes the dynamical processes of carotenoid excited states. We also discuss the effect of the symmetry-breaking term, H^ϵ, on the internal conversion process, and show that its effect on the extent of internal conversion can be described by a Landau-Zener-type transition. This methodological paper is a companion to our more explanatory discussion of carotenoid excited state dynamics in Manawadu, D.; Georges, T. N.; Barford, W. Photoexcited State Dynamics and Singlet Fission in Carotenoids. J. Phys. Chem. A 2023, 127, 1342.

Classification of doubly excited molecular electronic states

Electronic states with partial or complete doubly excited character play a crucial role in many areas, such as singlet fission and non-linear optical spectroscopy. Although doubly excited states have been studied in polyenes and related systems for many years, the assignment as singly vs. doubly excited, even in the simplest case of butadiene, has sparked controversies. So far, no well-defined framework for classifying doubly excited states has been developed, and even more, there is not even a well-accepted definition of doubly excited character as such. Here, we present a solution: a physically motivated definition of doubly excited character based on operator expectation values and density matrices, which works independently of the underlying orbital representation, avoiding ambiguities that have plagued earlier studies. Furthermore, we propose a classification scheme to differentiate three cases: (i) two single excitations occurring within two independent pairs of orbitals leaving four open shells (DOS), (ii) the promotion of both electrons to the same orbital, producing a closed-shell determinant (DCS), and (iii) a mixture of singly and doubly excited configurations not aligning with either one of the previous cases (Dmix). We highlight their differences in underlying energy terms and explain their signatures in practical computations. The three cases are illustrated through various high-level computational methods using dimers for DOS, polyenes for Dmix, and cyclobutane and tetrazine for DCS. The conversion between DOS and DCS is investigated using a well-known photochemical reaction, the photodimerization of ethylene. This work provides a deeper understanding of doubly excited states and may guide more rigorous discussions toward improving their computational description while also giving insight into their fundamental photophysics.

Excited states of ortho-nitrobenzaldehyde as a challenging case for single- and multi-reference electronic structure theory

We present a large set of vertical excitation calculations for the ortho-nitrobenzaldehyde (oNBA) molecule, which exhibits a very challenging excited-state electronic structure like other nitroaromatic compounds. The single-reference methods produce mostly consistent results up to about 5.5 eV. By contrast, the CAS second-order perturbation theory (CASPT2) results depend sensitively on the employed parameters. At the CAS self-consistent field level, the energies of the bright ππ * $$ {\pi \pi}^{\ast } $$ states are strongly overestimated while doubly excited states appear too low and mix with these ππ * $$ {\pi \pi}^{\ast } $$ states. This mixing hampers the CASPT2 step, leading to inconsistent results. Only by increasing the number of states in the state-averaging step to about 40-to cover all bright ππ * $$ {\pi \pi}^{\ast } $$ states embedded in the double excitations-and employing extended multistate CASPT2 could CASPT2 results consistent with experiment be obtained. We assign the four bands in the molecule's spectrum: The weakest band at 3.7 eV arises from the n NO 2 π * $$ {n}_{\mathrm{NO}2}{\pi}^{\ast } $$ states, the second one at 4.4 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( L b $$ {L}_b $$ ) state, the shoulder at 5.2 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( L a $$ {L}_a $$ ) state, and the maximum at 5.7 eV from the ππ * $$ {\pi \pi}^{\ast } $$ ( B a / B b $$ {B}_a/{B}_b $$ ) states. We also highlight the importance of modern wave function analysis techniques in elucidating the absorption spectrum of challenging molecules.

Accurate Calculation of Excited-State Absorption for Small-to-Medium-Sized Conjugated Oligomers: Multiconfigurational Treatment vs Quadratic Response TD-DFT

Excited-state absorption (ESA) spectra of π-conjugated compounds are frequently calculated by (quadratic response) time-dependent density functional theory, (QR) TD-DFT, often giving a reasonable representation of the experimental results despite the (known) incomplete electronic description. To investigate whether this is inherent to the method, we calculate here the ESA spectra of small-to-medium-sized oligophenylenevinylenes (nPV) and oligothiophenes (nT) using QR TD-DFT as well as CASPT2 based on CASSCF geometries. CASPT2 gives indeed a reliable, theoretically correct description of the ESA features for all compounds; the computational effort can be reduced without significant loss of accuracy using TD-DFT geometries. QR TD-DFT, based on BHandHLYP and CAM-/B3LYP functionals, fails on short nTs but provides a reasonable description for spectral positions of nPVs and long nTs. The failure on short nTs is, however, only partly due to the incomplete configuration description but, in particular, related to an improper MO description, resulting in an asymmetric energy spacing of the occupied vs unoccupied MOs in the DFT scheme. Longer nTs, on the other side, adapt approximately the MO scheme for alternant hydrocarbons just like in nPVs, while contributions by two triplet excitations combined to a singlet (which inhibits an accurate treatment of polyenes with standard TD-DFT) do not play a relevant role in the current case. For such "well-behaved" systems, a reasonable representation of ESA spectra is found at the QR TD-DFT level due to the rather small energy shifts when including higher-order excitations.

Overlap-Driven Splitting of Triplet Pairs in Singlet Fission

We analyze correlated-triplet-pair (TT) singlet-fission intermediates toward two-triplet separation (T...T) using spin-state-averaged density matrix renormalization group electronic-structure calculations. Specifically, we compare the triplet-triplet exchange (J) for tetracene dimers, bipentacene, a subunit of the benzodithiophene-thiophene dioxide polymer, and a carotenoid (neurosporene). Exchange-split energy gaps of J and 3J separate a singlet from a triplet and a singlet from a quintet, respectively. We draw two new insights: (a) the canonical tetracene singlet-fission unit cell supports precisely three low-lying TT intermediates with order-of-magnitude differences in J, and (b) the separable TT intermediate in carotenoids emanates from a pair of excitations to the second triplet state. Therefore, unlike with tetracenes, carotenoid fission requires above-gap excitations. In all cases, the distinguishability of the molecular triplets-that is, the extent of orbital overlap-determines the splitting within the spin manifold of TT states. Consequently, J represents a spectroscopic observable that distnguishes the resemblance between TT intermediates and the T...T product.

Local Enhancement of Dynamic Correlation in Excited States: Fresh Perspective on Ionicity and Development of Correlation Density Functional Approximation Based on the On-Top Pair Density

We discuss the interplay between the nondynamic and dynamic electron correlation in excited states from the perspective of the suppression of dynamic correlation (SDC) and enhancement of dynamic correlation (EDC) effects. We reveal that there exists a connection between the ionic character of a wave function and EDC. Following this finding we introduce a quantitative measure of ionicity based solely on local functions without referring to valence bond models. The ability to recognize both the SDC and EDC regions underlies the presented method, named CASΠDFT, combining complete active space (CAS) wave function and density functional theory (DFT) via the on-top pair density (Π) function. We extend this approach to excited states by devising an improved representation of the EDC effect in the correlation functional. The generalized CASΠDFT uses different DFT functionals for ground and excited states. Numerical demonstration for singlet π → π* excitations shows that CASΠDFT offers satisfactory accuracy at a fraction of the cost of the ab initio approaches.

Ab Initio Study of Low-Lying Excited States of Carotenoid-Derived Polyenes

Knowledge about excited states of carotenoids is essential for understanding photophysical processes underlying photosynthesis. However, due to the presence of a large number of optically dark states, experimental study of the excited-state manifold is limited to a significant extent. In this paper, we apply high-level ab initio quantum chemical methods to study the low-lying excited states of polyenes containing from 8 to 13 conjugated double bonds, which serve as a model for natural carotenoids. Vertical and adiabatic excitation energies from the ground 1A_g^- state to the excited 2A_g^-, 1B_u⁺, and 1B_u^- states were evaluated by means of density matrix renormalization group (DMRG) with NEVPT2 perturbative correction. The energies of all excited states are highly sensitive to nuclear geometry, especially the 2A_g^- state. Thus, the 2A_g^- and 1B_u⁺ states interchange their relative positions upon geometry relaxation, while the vertical excitation energy to the 2A_g^- state is rather high. At the same time, the 1B_u^- state energy is shown to be higher than other studied excited states at any geometry. With relaxed geometries of the excited states, absorption and transient absorption spectra were calculated within the Franck-Condon approximation bridging the gap between experimental spectroscopic data and computational results.

Toward an understanding of electronic excitation energies beyond the molecular orbital picture

Can we gain an intuitive understanding of excitation energies beyond the molecular picture?

Polyacetylene: Myth and Reality

Polyacetylene, the simplest and oldest of potentially conducting polymers, has never been made in a form that permits rigorous determination of its structure. Trans polyacetylene in its fully extended form will have a potential energy surface with two equivalent minima. It has been assumed that this results in bond length alternation. It is, rather, very likely that the zero-point energy is above the Peierls barrier. The experimental studies that purport to show bond alternation are reviewed and shown to be compromised by serious experimental inconsistencies or by the presence, for which there is considerable evidence, of finite chain polyenes. In this view, addition of dopants results in conductivity by facilitation of charge transport between finite polyenes. The double minimum potential that necessarily occurs for polyacetylene, if viewed as the result of elongation of finite chains, originates from admixture of the 1¹A_g ground electronic state with the 2¹A_g excited electronic singlet state. This excitation is diradical (two electron) in character. The polyacetylene limit is an equal admixture of these two ¹A_g states making theory intractable for long chains. A method is outlined for preparation of high molecular weight polyacetylene with fully extended chains that are prevented from reacting with neighboring chains.

The carotenoid pathway: what is important for excitation quenching in plant antenna complexes?

Plant light-harvesting is regulated by the Non-Photochemical Quenching (NPQ) mechanism involving the slow trapping of excitation energy by carotenoids in the Photosystem II (PSII) antenna in response to high light.

Energy dissipative photoprotective mechanism of carotenoid spheroidene from the photoreaction center of purple bacteria Rhodobacter sphaeroides

Carotenoid spheroidene (SPO) functions for photoprotection in the photosynthetic reaction centers (RCs) and effectively dissipates its triplet excitation energy. Sensitized cis-to-trans isomerization was proposed as a possible mechanism for a singlet-triplet energy crossing for the 15,15'-cis-SPO; however, it has been questioned recently. To understand the dissipative photoprotective mechanism of this important SPO and to overcome the existing controversies on this issue, we carried out a theoretical investigation using density functional theory on the possible triplet energy relaxation mechanism through the cis-to-trans isomerization. Together with the earlier experimental observations, the possible mechanism was discussed for the triplet energy relaxation of the 15,15'-cis-SPO. The result shows that complete cis-to-trans isomerization is not necessary. Twisting the C15-C15' bond leads to singlet-triplet energy crossing at ϕ(14,15,15',14') = 77° with an energy 32.5 kJ mol(-1) (7.7 kcal mol(-1)) higher than that of the T1 15,15'-cis minimum. Further exploration of the minimum-energy intersystem crossing (MEISC) point shows that triplet relaxation could occur at a less distorted structure (ϕ = 58.4°) with the energy height of 26.5 KJ mol(-1) (6.3 kcal mol(-1)). Another important reaction coordinate to reach the MEISC point is the bond-length alternation. The model truncation effect, solvent effect, and spin-orbit coupling were also investigated. The singlet-triplet crossing was also investigated for the 13,14-cis stereoisomer and locked-13,14-cis-SPO. We also discussed the origin of the natural selection of the cis over trans isomer in the RC.

Hybrid-state emission in a polythienylenevinylene derivative with an electron deficient moiety

The photoluminescence (PL) of a novel imide-substituted poly(3-thienylenevinylene) derivative (imidePTV) was studied in film and solution. PL quantum efficiency was measured to be more than two orders of magnitude larger than its nonluminescent counterpart, namely, alkyl-substituted PTV and was interpreted as evidence for a near degeneracy of optically allowed 1(1)Bu and optically forbidden 2(1)Ag excitonic states. As a result, coexistence of 2(1)Ag and 1(1)Bu emissions was observed, and the predominance was found to be sensitive to temperature and morphological environment. PL of solutions in solvents of higher polarity and polarizability and from low-temperature films was dominated by the transition from the dipole allowed 1(1)Bu state. On the other hand, the PL spectra of films at high temperature and solutions in solvents of low polarity and polarizability were primarily from the 2(1)Ag state that obtains a finite transmission moment from an asymmetric perturbation mixing with the 1(1)Bu.

Carotenoids and light-harvesting: from DFT/MRCI to the Tamm-Dancoff approximation

Carotenoids are known to play a fundamental role in photosynthetic light-harvesting (LH) complexes; however, an accurate quantum-mechanical description of that is still missing. This is due to the multideterminant nature of the involved electronic states combined with an extended conjugation which limits the applicability of many of the most advanced approaches. In this study, we apply a multireference configuration interaction extension of density functional theory (DFT/MRCI) to describe transition energies and densities as well as the corresponding excitonic couplings, for the three lowest singlet excited states of nine carotenoids present in three different LH complexes of algae and plants. These benchmark results are used to find an approximated computational approach, which could be used to quantitatively reproduce the key quantities at a reduced computational cost. To this end, we tested the Tamm-Dancoff approximation (TDA) to time-dependent density functional theory in combination with different functionals. By analyzing the errors with respect to DFT/MRCI-TDA results for the full set of electronic properties, we conclude that TDA-TPSS with small basis sets indeed represents an effective approach to investigate LH processes that involve carotenoids.

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.

Electronic excitations in long polyenes revisited

We apply the valence shell model OM2 [W. Weber and W. Thiel, Theor. Chem. Acc. 103, 495, (2000)] combined with multireference configuration interaction (MRCI) to compute the vertical excitation energies and transition dipole moments of the low-energy singlet excitations in the polyenes with 4 ≤ N ≤ 22π-electrons. We find that the OM2/MRCI descriptions closely resemble those of Pariser-Parr-Pople (PPP) π-electron models [P. Tavan and K. Schulten, Phys. Rev. B 36, 4337, (1987)], if equivalent MRCI procedures and regularly alternating model geometries are used. OM2/MRCI optimized geometries are shown to entail improved descriptions particularly for smaller polyenes (N ≤ 12), for which sizeable deviations from the regular model geometries are found. With configuration interaction active spaces covering also the σ- in addition to the π-electrons, OM2/MRCI excitation energies turn out to become smaller by at most 0.35 eV for the ionic and 0.15 eV for the covalent excitations. The particle-hole (ph) symmetry, which in Pariser-Parr-Pople models arises from the zero-differential overlap approximation, is demonstrated to be only weakly broken in OM2 such that the oscillator strengths of the covalent 1B(u)(-) states, which artificially vanish in ph-symmetric models, are predicted to be very small. According to OM2/MRCI and experimental data the 1B(u)(-) state is the third excited singlet state for N < 12 and becomes the second for N ≥ 14. By comparisons with results of other theoretical approaches and experimental evidence we argue that deficiencies of the particular MRCI method employed by us, which show up in a poor size consistency of the covalent excitations for N > 12, are caused by its restriction to at most doubly excited references.

Quantum chemical description of absorption properties and excited-state processes in photosynthetic systems

The theoretical description of the initial steps in photosynthesis has gained increasing importance over the past few years. This is caused by more and more structural data becoming available for light-harvesting complexes and reaction centers which form the basis for atomistic calculations and by the progress made in the development of first-principles methods for excited electronic states of large molecules. In this Review, we discuss the advantages and pitfalls of theoretical methods applicable to photosynthetic pigments. Besides methodological aspects of excited-state electronic-structure methods, studies on chlorophyll-type and carotenoid-like molecules are discussed. We also address the concepts of exciton coupling and excitation-energy transfer (EET) and compare the different theoretical methods for the calculation of EET coupling constants. Applications to photosynthetic light-harvesting complexes and reaction centers based on such models are also analyzed.

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.

Theoretical predictions of red and near-infrared strongly emitting X-annulated rylenes

The optical properties of rylenes are extremely interesting because their emission colors can be tuned from blue to near-infrared by simply elongating the chain length. However, for conjugated chains, the dipole-allowed odd-parity 1B(u) excited state often lies above the dipole-forbidden even-parity 2A(g) state as the chain length increases, thus preventing any significant luminescence according to Kasha's rule. We systemically investigated the 1B(u)∕2A(g) crossover behaviors with respect to the elongating rylene chain length with various quantum chemistry approaches, such as time-depended density functional theory (TDDFT), complete active space self-consistent field theory (CASSCF∕CASPT2), multireference configuration interaction (MRCI)∕Zerner's intermediate neglect of diatomic overlap (ZINDO), and MRCI∕modified neglect of differential overlap. The calculated results by CASSCF∕CASPT2 and MRCI∕ZINDO are completely coherent: the optical active 1B(u) state lies below the dark B(3g) or 2A(g) state for perylene and terrylene, which results in strong fluorescence; while a crossover to S(1) = 2A(g) occurs and leads to much weaker fluorescence for quaterrylene. Then we put forward a molecular design rule on how to recover fluorescence for the longer rylenes by introducing heteroatom bridges. Several heteroatom-annulated rylenes are designed theoretically, which are predicted to be strongly emissive in the red and near-infrared ranges. These are further confirmed by theoretical emission spectra as well as radiative and nonradiative decay rate calculations by using the vibration correlation function formalisms we developed earlier coupled with TDDFT.

Excitation energy transfer in the LHC-II trimer: from carotenoids to chlorophylls in space and time

Exciton model for description of experimentally determined excitation energy transfer from carotenoids to chlorophylls in the LHC-II trimer of spinach is presented. Such an approach allows connecting the excitonic states to the spatial structure of the complex and hence descriptions of advancements of the initially created excitations in space and time. Carotenoids were excited at 490 nm and at 500 nm and induced absorbance changes probed in the Chl Q(y) region to provide kinetic data that were interpreted by using the results from exciton calculations. Calculations included the 42 chlorophylls and the 12 carotenoids of the complex, Soret, Q(x) and Q(y) states of the chlorophylls, and the main absorbing S(2) state of the carotenoids. According to the calculations excitation at 500 nm populates mostly a mixed Lut S(2) Chl a Soret state, from where excitation is transferred to the Q(x) and Q(y) states of the Chl a's on the stromal side. Internal conversion of the mixed state to a mixed Lut S(1) and Chl a Q(y) state provides a channel for Lut S(1) to Chl a Q(y) energy transfer. The results from the calculations support a picture where excitation at 490 nm populates primarily a mixed neoxanthin S(2) Chl b Soret state. From this state excitation from neoxanthin is transferred to iso-energetic Chl b Soret states or via internal conversion to S(1) Chl b Q(y) states. From the Soret states excitation proceeds via internal conversion to Q(y) states of Chl b's mostly on the lumenal side. A rapid Chl b to Chl a transfer and subsequent transfer to the stromal side Chl a's and to the final state completes the process after 490 nm excitation. The interpretation is further supported by the fact that excitation energy transfer kinetics after excitation of neoxanthin at 490 nm and the Chl b Q(y) band at 647 nm (Linnanto et al., Photosynth Res 87:267-279, 2006) are very similar.

Excitation energy calculation of conjugated hydrocarbons: a new Pariser-Parr-Pople model parameterization approaching CASPT2 accuracy

A new parameterization for the Pariser-Parr-Pople (PPP) model for conjugated hydrocarbons is proposed in this work. The distance-dependence of PPP parameters are obtained from CASPT2 ground state and low-lying excited state energies of ethylene and its cation at various C-C single bond lengths and are fitted to a set of carefully chosen mathematical functions. Our new PPP model is applied to the calculation of vertical singlet-triplet energy gaps and the excitation energies for low-lying π→π(*) valence excitations in various π-conjugated molecules. Results with the new PPP model are consistently better than the standard PPP model in use. It often surpasses density functional theory and single-reference excited state methods such as configuration interaction singles or time-dependent density functional theory in terms of its accuracy and agrees reasonably well with high-level theories or experiments.

The intramolecular charge transfer state in carbonyl-containing polyenes and carotenoids

Numerous femtosecond time-resolved optical spectroscopic experiments have reported that the lifetime of the low-lying S(1) state of carbonyl-containing polyenes and carotenoids decreases with increasing solvent polarity. The effect becomes even more pronounced as the number of double bonds in the conjugated π-electron system decreases. The effect has been attributed to an intramolecular charge transfer (ICT) state coupled to S(1), but it is still not clear what the precise molecular nature of this state is, and how it is able to modulate the spectral and dynamic properties of polyenes and carotenoids. In this work, we examine the nature of the ICT state in three substituted polyenes: crocetindial, which contains two terminal, symmetrically substituted carbonyl groups in conjugation with the π-electron system, 8,8'-diapocarotene-8'-ol-8-al, which has one terminal conjugated carbonyl group and one hydroxyl group, and 8,8'-diapocarotene-8,8'-diol, which has two terminal, symmetrically positioned, hydroxyl groups but no carbonyls. Femtosecond time-resolved optical spectroscopic experiments on these molecules reveal that only the asymmetrically substituted 8,8'-diapocarotene-8'-ol-8-al exhibits any substantial effect of solvent on the excited state spectra and dynamics. The data are interpreted using molecular orbital theory which shows that the ICT state develops via mixing of the low-lying S(1) (2(1)A(g)-like) and S(2) (1(1)B(u)-like) excited singlet states to form a resultant state that preferentially evolves in polar solvent and exhibits a very large (∼25 D) dipole moment. Molecular dynamics calculations demonstrate that the features of the ICT state are present in ∼20 fs.