Peridinin Torsional Distortion and Bond-Length Alternation Introduce

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B: Biophysics; Physical Chemistry of Biological Systems and Biomolecules

Peridinin Torsional Distortion and Bond-Length Alternation Introduce Intramolecular-Charge-Transfer and Correlated-Triplet-Pair Intermediate Excited States Elliot J. Taffet, and Gregory D. Scholes J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b02504 • Publication Date (Web): 14 May 2018 Downloaded from http://pubs.acs.org on May 15, 2018

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The Journal of Physical Chemistry

Peridinin Torsional Distortion and Bond-Length Alternation Introduce Intramolecular-ChargeTransfer and Correlated-Triplet-Pair Intermediate Excited States Elliot J. Taffet1 and Gregory D. Scholes*1 1. Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States

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ABSTRACT: The nature of intramolecular charge transfer (ICT) and the mechanism of intramolecular singlet fission (SF) in peridinin remain open research questions. Obtaining an understanding of the population evolution from the bright state to dark states following a photoinduced electronic transition is critical.

Unambiguously describing this evolution in

peridinin, and light-harvesting carotenoids in general, has proven elusive experimentally and computationally. To offer a balanced description of bright- and dark-state electronic structure, we here apply ab initio multireference perturbation theory quantum chemistry—the density matrix renormalization group self-consistent-field (DMRG-SCF) and complete-active-space selfconsistent field (CASSCF) with second-order N-electron valence perturbation theory (NEVPT2). At traditional bright- (S2) and dark-state (S1) optimized geometries, we find that an additional correlated triplet pair (CTP) state and ICT state are derived from the canonical polyene Bu (S3) and 3Ag (S4) dark singlet excited states, respectively. While the S3 state’s physical properties are insensitive to peridinin’s allene-tail donor and lactone-ring acceptor functionalization, the S4 state exhibits a markedly enhanced oscillator strength and HOMO-LUMO transition density. These changes suggest that ICT character stems from mixing between the bright S2 and putatively dark S4.


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1. INTRODUCTION The

carotenoids—substituted

polyene-like

chromophores—play

important

roles

in

photosynthetic transduction and photoprotection. In light-harvesting complexes, they efficiently harvest blue-green light and transfer that energy to chlorophylls (Chl) by electronic energy transfer (EET). The full low-lying spectrum of carotenoids such as peridinin is notoriously difficult to model accurately and can involve multiply excited wavefunctions as compared to the simple single π-π* photoexcitations found in many other conjugated chromophores. In particular, there is substantial evidence for low-lying dark states of multiply-excited character. For example, the inconsistency between EET efficiency from the canonical carotenoid S1 and S2 states predicted by standard resonance energy transfer theory in the light-harvesting LH2 complex and that measured from experiment suggests the involvement of intermediate dark excited states.1-2 Such dark excited states have long been proposed in the context of polyene studies. Schulten and Karplus3 pointed out the existence of a dark S1 state in butadiene, and other dark intermediate states were identified by Tavan and Schulten in the context of longer polyenes.4 Since these theoretical studies, the notion of dark intermediates has been much debated in the experimental and theoretical literature—especially in the context of radiationless relaxation.5-6 These debates take on heightened complexity for carbonyl carotenoids, such as peridinin, that may exhibit photophysics indicative of intramolecular charge transfer (ICT).7-66 Peridinin ICT is believed to stem from electron-rich allene and electron-withdrawing lactone functionalization. ICT character in peridinin has been invoked to explain its unique photophysics distinguished by emission solvatochromism61 and Stark spectroscopy.22 Nonetheless, it is unclear from what state this ICT character is derived.61, 67-70 Unmasking the ICT state, if it exists, is



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paramount to explaining the influence of the lactone-ring electron-withdrawing effect in peridinin7, 63 and its role in photosynthetic energy transfer. Light harvesting by the Peridinin-Chlorophyll-Protein (PCP) complex in photosynthetic dinoflagellates depends heavily on carotenoids.8, 21, 49, 71-72 The peridinins, unlike Chl-a or Chl-b, absorb light in the blue-green (470 nm) region of the solar spectrum, which penetrates deepest into the ocean.29, 73 Peridinin EET to Chl is 90% efficient in PCP.40, 74-75 Questions remain about the mechanism of EET in PCP light-harvesting as well as the mechanism of competing internal conversion.13,

15, 18

Specifically, researchers speculate that a charge-transfer state may be

involved as the energy donor Coulombically coupled to Chl. For example, the decrease in the peridinin S1 state lifetime when isolated in polar solvent14 and when bound to the protein matrix21 suggests a role for an ICT state, or a state with enhanced dipole moment.8 Intuitively, an ICT state can be stabilized in peridinin as opposed to a simple polyene due to the stabilizing effect of its allene electron donor and lactone electron acceptor.76 No consensus, however, exists regarding peridinin ICT characterization within the manifold of excited states. Various works have proposed varying definitions of the ICT state. These include an ICT state derived purely from S1,13 a hybrid S1/ICT state resulting from strong electronic coupling between two independent states below S2,17, 61, 69 and a separate decoupled ICT state.18 In our attempt to resolve the proper definition, we apply ab initio multireference calculations with second-order perturbation theory to distinguish ICT character within a manifold of bright and dark states with an accessible computational cost. This manifold also includes 2 and states predominantly comprised of doubly-excited configurations that are correlated triplet pair (CTP) intermediates as described in the literature regarding singlet fission (SF).77-84 These states are involved in nonphotochemical quenching of excess excitation into low-lying triplet states—a means of thermally 4 ACS Paragon Plus Environment

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dissipating this energy without damaging the photosynthetic reaction center.85 Singlet-fission thermodynamics from these dark intermediate states also are discerned through our calculations. 2. COMPUTATIONAL DETAILS In order to shed light on the relevant low-lying states of carotenoids and their possible adoption of ICT character, we use ab initio multireference perturbation theory (MRPT), and in particular the density matrix renormalization group with second order N-electron valence perturbation theory (first order interacting space86), or NEVPT2,87-89 to calculate the manifold of low-lying excited states of peridinin. From an electronic structure standpoint, the primary challenge is to employ computational methodologies that balance static and dynamic electron correlation.90 One such methodology that has been widely applied in the context of conjugated chromophore excited states is the complete-active-space self-consistent field that provides a full description of the static correlation, coupled to a perturbative treatment of the dynamic correlation (CASPT2).91-93 In this work, for the perturbation theory we use the NEVPT2 formulation, which has the advantage of being intruder-state free.94 In addition, to more efficiently treat larger active spaces, we also use the density matrix renormalization group (DMRG) method,94-129 which provides a compact description of static correlation, particularly in one-dimensional conjugated topologies, as found in the carotenoids. In particular, we use DMRG with the compressed perturber approximation of NEVPT2,94, 118, 130-132 which bypasses the need to compute 4-particle reduced density matrices—the bottleneck in conventional CASSCFNEVPT2 calculations with more than 14 active orbitals.51, 69 In our calculations, we compare the manifold of excited states in peridinin to that of its parent polyene (C16H18) to distinguish CTP and ICT intermediate states. This ICT intermediate state,



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unlike the CTP B state,133-134 has no analog in polyenes but may be involved in peridinin nonradiative decay processes accompanying bond-length alternation and torsional distortion along the S2 and S1 potential energy surfaces. These processes may contribute to the exceptional EET efficiency observed in antenna complexes native to peridinin. We carried out ground and excited state calculations for a truncated peridinin molecule with the bulky non-conjugated side groups removed (Figure 1).

Figure 1. Model peridinin structure applied to our multireference quantum chemical calculations (adapted from Ref. 51). The low-lying electronic eigenstates of interest have unique character in peridinin and other carotenoids: while the S0 and S2 states are single-reference in nature (S0 is defined by the Hartree-Fock electronic configuration and S2 by HOMO-LUMO excitation from S0), the S1 state is multireference in nature because of its predominant doubly-excited HOMO2/LUMO2 configuration. This configuration becomes even more prominent over the course of relaxation in the S1 excited state as the bond-length alternation is diminished by the redistribution of electron


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density.69 As such, we used single-reference DFT(cc-pVDZ/B3LYP) and TDHF135(cc-pVDZ) for the S0 and S2 states, respectively, while employing multireference CASSCF(12,12)/STO-3G with a polarizable-continuum-model (PCM)136 acetonitrile solution for the S1 state. The S1 state was optimized with acetonitrile PCM solvation to interrogate potential intramolecular charge transfer character induced by polar solvent. The PySCF137 program was invoked for orbital optimizations and single-point calculations following the completion of these geometry optimizations with Gaussian 16.138 The DMRG-SCF and CASSCF calculations in this study start from an initial set of mean-field Hartree-Fock molecular orbitals from which we identify an active space139-140 for the multiconfigurational (MC) calculation.

Once the active space was selected, the MC orbital

optimization calculation was carried out with either CASSCF141-143 (for up to 14 electrons in 14 active orbitals107) or for larger active spaces (up to 16 electrons in 20 active orbitals in this study) with DMRG-SCF (with standard bond dimension M=1000) using Pipek-Mezey localization144 and Fiedler vector automation of orbital ordering.145-148 Here we report state-averaged MCSCF calculations encompassing at least four excited states so as to include 1 , 2 , 3 , and . When running calculations on torsionally-distorted C1 peridinin geometries, the DMRG bond dimension for the orbital optimization was decreased to M=500 to lower CPU cost. A state-specific, strongly contracted NEVPT2 calculation94,

131, 149

was carried out on the

converged CASSCF/DMRGSCF states to account for the dynamic correlation stabilization energy. We used the standard strongly-contracted NEVPT2 formulation in conjunction with the CASSCF wavefunctions, while for the DMRG wavefunctions we used the compressed-perturber strongly-contracted NEVPT2 approximation, using a standard bond dimension of 1000.



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3. RESULTS Our work is intended to extend previous state-averaged DMRGSCF calculations on polyenes135 by examining the role of dynamic correlation and considering the effect of bondlength alternation (BLA) on the low-lying electronic states. The calculations we report here (Table 1) include state-specific NEVPT2 energy corrections and consider various peridinin geometries that represent points on the S0/S1/S2 potential energy surfaces, with varying BLA. We find that the S1 state is stabilized through a dynamically-relaxed BLA, predicted by Tavan,4 in the comparison of excitation energies between different optimized state geometries of peridinin (Tables 1 and 2). This stabilization is anticipated, since bond-length rearrangement between double and single bonds configurationally enhances the mixing between the identicallysymmetric 1 (S0) and 2 (S1) states—the S0 state adopts greater HOMO2/LUMO2 character while the S1 state adopts greater ground-state Hartree-Fock character in the multireference description of their wavefunctions. Furthermore, the resulting adiabatic S0-S1 and vertical S0-S2 excitation energies agree with the theoretical51, 53, 69 and experimental7, 150 reports in the peridinin literature—justifying the optimized geometries that were used.

Evolving along the BLA

coordinate from the S0 to S2 to S1, a lowering of the S1 state energy relative to S2 is observed. The strong BLA dependence of the S1 state has been well-documented in polyenes and clearly is manifested in peridinin. In general, when analyzing the first four singlet excited states, characteristics of the canonical 2 , 3 , and states known in polyenes are observed.

Namely, the one-particle

transition density matrix elements for these states are largest for HOMO-1/LUMO, HOMO3/LUMO, HOMO-2/LUMO and HOMO/LUMO excitations, respectively. These transition


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densities and excitation energies (in eV), along with those of triplet states at the S1 optimized geometry, are reported in Table 1 and compared to literature. Comparing these properties with the corresponding excited states of the parent C2h-symmetric polyene C16H18, irreducible representations (irrep.) can be mapped onto the peridinin state manifold.

Moreover, by

comparing these results on the model peridinin structure to those computed using state-averaged DMRG-NEVPT2(8,8)/cc-pVDZ on the full peridinin crystal structure72 in the gas phase, we can map the polyene state manifold to that of the naturally-abundant carotenoid. Using this active space—sufficiently large to capture the HOMO-3/LUMO nature of the highest-lying state of interest (S4)—we identify the same HOMO/LUMO and HOMO-3/LUMO character of the S2 and S4 states, respectively. Moreover, the calculated S0-S2 and S0-S4 vertical transition energies of 2.73 and 4.60 eV, respectively, agree with those acquired from the model structure. Thus, it appears that the truncation of peridinin (perid.) β-rings51 does not affect the ordering or composition of the low-lying excited states, yet lactone-ring and allene-tail functionalization appear to enhance the transition dipole moment (TDM) of 3 relative to that of polyenes (poly., Table 1). state

geom.

method (e, orb.)

∆EPerid.

∆EPoly.

S4

S0

DMRG (16,16)

4.43

4.61

irrep.

3

TDM (D)

transition (magnitude)

calc.a ∆E

expt.b ∆E

4.02

HOMO-3

3.49

N/A

3.1

N/A

LUMO (0.406)

S3

S0

DMRG

3.84

4.03

1

0.603

HOMO-2 LUMO (0.467)



S2

S0

DMRG

2.73

2.84

1

11.9

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HOMO

2.54

2.73c

2.26

2.07d

LUMO (1.09) S1

S1

CAS

1.88

1.99

2

0.716

(14,14)

HOMO-1 LUMO (0.412)

T2

S1

CAS

1.88

1.86

N/A

N/A

N/A

N/A

T1

S1

CAS

0.705

0.89

N/A

N/A

N/A

N/A

Table 1. Calculated Peridinin Excitation Energies (in eV) and Transition Densities as Determined by State-Averaged MRPT, Along with Prior Theoretical and Experimental Results a

Reference 69

b

Reference 7

c

Absorption maximum in n-hexane

d

Two-photon absorption maximum in n-hexane

The computed peridinin S1 state, as anticipated, is assigned the 2 label by analyzing its transition energy, TDM (in Debye), and the largest off-diagonal matrix element (magnitude) of its one-particle transition density matrix with respect to the ground state (transition from a valence occupied orbital to a valence virtual orbital), which reflects the largest excitation contribution.

The DMRG-NEVPT2 gas-phase adiabatic S0-S1 transition energy is in good

agreement with the experimentally-determined adiabatic transition energy of 2.07 eV in the nonpolar solvent n-hexane.7,

150

The geometries of the first excited state of polyenes and

carotenoids, and especially the carbonyl carotenoid peridinin, are expected to reorganize after photoexcitation. This is a known consequence of the out-of-plane S1 excited-state vibrational 10 ACS Paragon Plus Environment

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modes driving conjugation breaking and enhanced coupling to the ground state in polyenes and their derivatives.151 Our geometry optimization for S1 assumes an acetonitrile-like continuum solvation environment and employed CASSCF as the electronic structure method. Over the course of the S1 geometry optimization from a planar initial guess, the Cs symmetry of the ground state is broken. Moreover, additional Peierls distortion,152 or bond undimerization,153-154 along the S1 potential energy surface further stabilizes the S1 state relative to S2, making the lowlying dark state more energetically distinguishable from the bright state. The extent of S1 torsional and BLA dynamical relaxation computed here is supported by good agreement between the adiabatic excitation energy and the experimental ∆ of 2.07 eV.7 Moreover, the peridinin S1 0.716 D TDM reported in Table 1 (more than an order of magnitude smaller than that of S2) is supported by recent literature computational results.51, 69 The S1 TDM is increased only slightly by symmetry breaking—the S0-S1 TDM from the planar S0 optimized geometry is 0.488 D (it is important to emphasize the lack of rigorous symmetry selection rules in the symmetry-reduced peridinin chromophore, meaning that one-photon transitions to excited states derived from, yet not equated with, the covalent 2 , 3 and 1 irreducible representations are not expressly forbidden). Thus, the twisted nature of the S1 geometry does little to enhance the brightness of the state and therefore has little effect on the Coulombic electronic coupling for energy transfer. How is the twisting inherent to the S1 potential energy surface manifest when photoexcitation populates S2? Nonadiabatic, or electron-nuclear coupling between S2 and S1—that is, population transfer driven by nuclear distortions away from the equilibrium condition155—can induce the realization of twisted geometries that stabilize S1 in lieu of S2. To model the specific impact of photoinduced twisting on the S1 state, a relaxed torsional coordinate scan of the S2 potential energy surface was computed so as to isolate the nuclear distortion associated with internal 11 ACS Paragon Plus Environment


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conversion to S1. It should be emphasized that these calculations force the intramolecular torsion to occur on the initially-populated S2 state potential, so finite-temperature nonadiabatic effects on S2 prior to population of S1 are being modeled. The resulting optimized geometries obtained from this scan were used for DMRG-NEVPT2 calculations of the excited-state manifold, including the S3 and S4 states, that may also be populated by S2. The S2 geometric effect of changing the torsional angle (thereby controlling the lactone ring orientation relative to the planar polyene backbone) on the S1 state properties is displayed in Figure 2.

Figure 2. Excitation Energy of the S1 state relative to the dihedral angle represented by the highlighted carbons in the peridinin molecular structure shown above, with transition dipole moments (in Debye) relative to the ground state annotated next to each data point. Though intramolecular torsion involving the acceptor lactone ring would be expected to promote localized charge transfer, no appreciable change to the S1 state excitation energy or


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TDM is observed. This result supports the confirmed experimental observation of an indistinct solvent viscosity effect on the S1 state lifetime,8, 29 which suggests that S1 does not evolve into a TICT state. On the other hand, the photoinduced geometric distortion and donor/acceptor functionalization of peridinin significantly influence the S4 state, or 3 state in the conventional polyene representation. While forbidden by symmetry in the native idealized polyene C2h structure, the S4 state transition from the S0 planar minimum-energy geometry is strongly allowed in peridinin at 4.02 D (Table 1)—less than an order of magnitude below the S0-S2 transition and an order of magnitude above the S0-S1 transition. The characteristics of S4 appear to be most reminiscent of an ICT state realized only in carbonyl carotenoids. The peridinin ICT state has been characterized by the following three criteria: a) having a large dipole moment that manifests from allene-to-lactone charge migration coupled to bond-length rearrangement in the excited state; b) featuring an amalgam of bright ionic and dark covalent wavefunction composition; and c) possessing an enlarged oscillator strength stemming from its S2-borrowed bright character.51 The S4 state, albeit derived from the dark 3 all-trans polyene state, satisfies all three criteria. At the S1 geometry, which features fully-relaxed bond-length reversal,51 we compute at the five-state-averaged CASSCF(14,14)NEVPT2/aug-cc-pVDZ level that the S4 state dipole moment is the largest of those belonging to the putatively “dark” excited states (including S1 and S3). In addition, our calculations indicate that the S4 state wavefunction configurationally consists of a less than 1% greater HOMO3/LUMO single-particle excitation relative to its (HOMO, HOMO-2)/LUMO2 two-particle excitation configuration. The S4 state thus can be thought of as a hybrid covalent-ionic excited state. Lastly, the S4 state oscillator strength is larger than those of the one-photon-forbidden S1 and S3 states by a factor of more than 20—suggesting that the S4 state is non-trivially mixed with 13 ACS Paragon Plus Environment


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the bright S2 state. Moreover, unlike S1 and S3, the S4 state exhibits a transition dipole moment pointing in the same direction as that of S2—with a stronger y-component reflective of charge migration to the electron-withdrawing carbonyl moiety of the lactone ring. The implication of these results is that ICT character stems from an intrinsic part of peridinin’s electronic structure—the S4 excited state. This excited state exists for at all peridinin geometries and environments, yet it is twisting that causes this state to drop closer in energy to the bright S2 state. Following a 10° twist along the S2 potential energy surface, the S4 state falls to within 0.3 eV above the bright state according to state-averaged DMRG-NEVPT2(16,16) computation (Figure 3, Table 2).

(a)

(b)

Figure 3. (a) Change in excitation energies of the S1 2 , S2 , S3 and S4 3 states with respect to torsional angle. The dotted lines are meant as guides for the eye. (b) Change in excited-state transition dipole moment, with the ICT (intramolecular charge transfer) label assigned to the S4 3 state due to the marked increase in transition dipole moment with respect to symmetry-breaking torsional distortion. The dark CTP S1 2 and S3 states overlap at the bottom of the figure due to their similarly small transition dipole moments.


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Table 2. Comparison of the Singlet Excited-State Manifold of Peridinin at its Optimized Planar Bright-State Geometry and Optimized 10° Twisted Bright-State Geometry

= 0° (16,20)

= 10° (16,16)

state

excitation energy (eV)

transition density (magnitude)

TDM (D)

state

excitation energy (eV)

transition density (magnitude)

TDM (D)

dipole moment (D)

S1

2.57

HOMO-1

0.250

S1

2.56

HOMO-1

0.307

4.07

9.95

8.92

0.397

4.08

8.37

5.31

0.852

4.11

1.07

4.35

S2

S3

S4

S5

S6

2.49

3.54

4.29

4.83

4.96

LUMO

LUMO

(0.432)

(0.409)

HOMO

12.9

S2

3.20

HOMO

LUMO

LUMO

(1.15)

(0.868)

HOMO-2

0.243

S3

3.53

HOMO-2

LUMO

LUMO

(0.490)

(0.470)

HOMO-3

2.81

S4

3.48

HOMO

LUMO

LUMO

(0.492)

(0.771)

HOMO-4

0.054

S5

4.80

HOMO-1

LUMO

LUMO+6

(0.375)

(0.232)

HOMO-1

0.407

S6

5.03

HOMO-6

LUMO+7

LUMO

(0.226)

(0.427)



S7

5.17

HOMO

0.339

S7

5.64

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HOMO-7

LUMO+6

LUMO

(0.558)

(0.373)

0.761

4.27

4. DISCUSSION 4a. The ICT state. A 0.28 eV energy difference within a minimal active space that may lead to underestimation of bright ionic state excitation energies156 suggests that population can be transferred from S2 to ICT at a 10∘ torsional distortion. This small energy difference stems from concomitant stabilization of ICT and destabilization of S2 induced by conformational disorder. As such, the twisted “S1/ICT” state may well be the S4 state mediating population transfer from S2 to S1. While the properties of the low-lying CTP (S1 and S3) and high-lying Rydberg (S5-S7) dark states are marginally affected by the intramolecular torsion, the S4 state features not only a nearly-doubled TDM and larger dipole moment but also enhanced HOMO-LUMO and suppressed HOMO-3-LUMO transition density matrix elements. That the contribution from HOMO-LUMO excitation to the S4 state is enlarged by torsional distortion suggests that state mixing between the bright state and the ICT state is promoted by conformational disorder along the relaxation pathway to the S1 optimum. This state mixing may manifest itself as a unique signal in absorption spectra. 4b. The correlated triplet pair. In addition to excitation energy transfer to chlorophyll, lightharvesting peridinins are known to trap excess excitation energy in the form of low-lying triplet states.71, 157 Carotenoids fulfill this role synchronously with population of chlorophyll singlet excited states through non-photochemical quenching of these singlets under conditions of inordinately high photon flux.158 High-intensity solar conditions therefore drive an alternative 16 ACS Paragon Plus Environment

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nonradiative relaxation pathway to triplet states, which can be coupled directly to the singlet manifold through correlated triplet pairs (CTP)—singlet states that are products of two triplets, one on each half of the molecule.156 Efficient ultrafast intramolecular generation of carotenoid triplets may occur through CTP intermediate states, which, in turn, lower the efficiency of energy transfer to chlorophyll.159 These CTP states in peridinin are S1 and S3.160 Inspecting the T1 and T2 excitation energies (Table 1) relative to S1 at its geometry reveals that the potential symmetry-allowed singlet fission pathway proposed by Rondonuwu et al.161 of S1 → T1 + T1 is thermodynamically favored by 0.47 eV. Our calculations also indicate that at the S1 geometry, the alternative proposed pathway of S3 → T1 + T2 is exothermic. Therefore, potential population of the S3 state following conformational disorder may explain the effectiveness of peridinin in accomplishing its two preeminent functions within the PCP complex—transferring solar energy to the photosynthetic reaction center and dumping excess energy in the form of lowlying triplet states that cannot participate in the formation of deleterious singlet oxygen.68 Given the thermodynamic feasibility of two-triplet-exciton generation from both S1 and S3, SF may be enhanced in peridinin at twisted geometries associated with the S1 potential energy surface. As such, prevalent SF, rather than energy transfer, may be activated by internal conversion from S2 to S1.162 The CTP nature of both the S1 and S3 states can be gleaned by analyzing the DMRG-optimized molecular orbitals of the occupied-to-virtual-orbital excitations contributing most significantly to each one-particle transition density matrix.

Figure 4 displays side-by-side these relevant

occupied and virtual molecular orbitals for the CTP states.



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Figure 4. The orbitals comprising (top) the largest S0-S1 vertical transition density matrix element (HOMO-1, left and LUMO, right) along with (bottom) the largest S0-S3 vertical transition density matrix element (HOMO-2, left and LUMO, right). In both cases, the occupied-orbital electron density is concentrated on either side of peridinin— close to the allene tail and lactone ring. This partitioned electron density is more apparent in the HOMO-2, which is associated with the one-particle transition to S3. The virtual orbital (LUMO) populated during the transition, however, possesses greater electron density midway between the terminal substituents. This localization of two spatially-sequestered regions of electron density is characteristic of a CTP state, whereby two triplet populations, entangled by their spin eigenfunctions, constitute a single confined particle. Thus, in an electronic sense, the S1 and S3 states are structurally predisposed to support a CTP. On the other hand, analysis of the S0-ICT transition—a superposition of excitations to the LUMO from the HOMO and HOMO-3 molecular orbitals—reveals a stronger contribution from fully delocalized electron density. As illustrated in Figure 5, the HOMO-3 has concentrated 18 ACS Paragon Plus Environment

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patches of electron density that are spread out evenly over the conjugated region of the chromophore.

Figure 5.

The orbitals comprising (top) the largest S0-S4 vertical transition density matrix

element (HOMO-3, left and LUMO, right) along with (bottom) the largest S0-S2 vertical transition density matrix element (HOMO, left and LUMO, right). Likewise, the HOMO has electron density at each conjugated carbon double bond connecting the allene tail and lactone ring, where the BLA is minimal—signifying ideal conjugation.163-165 Thus, rather than adopting CTP character, with two coupled charge carriers, the ICT state is a single electron-hole pair quasiparticle, or exciton, that is delocalized over the chromophore. The electronic structure of the ICT-state transition directly correlates with its presumed function: facilitating inter-chromophore excitation energy transfer from carotenoid to chlorophyll.51 5. CONCLUSIONS



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Computed peridinin intermediate singlet excited states were determined to be too high in energy to appear in steady-state visible absorption spectroscopy, yet they may confer unexpected properties. Unlike in polyenes, the S4 state in peridinin was shown to have similar character to the S2 state. Calculations on twisted geometries produced an S4 state with S2-like excitation energy, HOMO-LUMO one-particle transition density and transition dipole moment. Therefore, the computed S4 state exhibited bright-state properties resulting from state mixing with S2. This state mixing reflected the ICT-like nature of the S4 state caused by the electron-withdrawing lactone ring in peridinin. Nonetheless, this lactone ring had no impact on the nature of the S3 state, defined by excitations involving molecular orbitals with CTP electronic structure. This electronic structure differed from the delocalized molecular orbitals associated with S4-state excitations. Thus, although S4-state transitions were excitons, S3-state transitions were solitons, and the fission of S3 into two triplet states was calculated to be energetically favored. As such, these two “dark” intermediate excited states were revealed to be fundamentally different. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. *Telephone: (609) 258-0729 Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS


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This work was supported by Princeton University through the Innovation Fund for New Ideas in the Natural Sciences. E.J.T. thanks Dr. Qiming Sun and Sheng Guo for their guidance in utilizing PySCF and the Block DMRG code, and Hwon Kim for robust discussions surrounding the utility of various multireference calculation methods. We thank Professor Garnet Chan (Caltech) for generous help with the DMRG package and valuable comments on the manuscript.

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Peridinin Torsional Distortion and Bond-Length Alternation Introduce

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