Excited State Potential Energy Surfaces of Polyenes and Protonated Schiff Bases

Trajectory surface hopping molecular dynamics simulations for retinal protonated Schiff-base photoisomerization

Global switching trajectory surface hopping molecular dynamics simulations are performed using accurate on-the-fly (TD)CAM-B3LYP/6-31G potential energy surfaces to study retinal protonated Schiff-base photoisomerization up to S₁ excitation. The simulations detected two-layer conical intersection networks: one is at an energy as high as 8 eV and the other is in the energy range around 3-4 eV. Six conical intersections within the low-layer energy region that correspond to active conical intersections under experimental conditions are found via the use of pairwise isomers, within which nonadiabatic molecular dynamics simulations are performed. Eight isomer products are populated with simulated sampling trajectories from which the simulated quantum yield in the gas phase is estimated to be 0.11 (0.08) moving from the all-trans isomer to the 11-cis (11-cis to all-trans) isomer in comparison with an experimental value of 0.09 (0.2) in the solution phase. Each conical intersection is related to one specific twist angle accompanying a related CC double bond motion during photoisomerization. Nonplanar distortion of the entire dynamic process has a significant role in the formation of the relevant photoisomerization products. The present simulation indicates that all hopping points show well-behaved potential energy surface topology, as calculated via the conventional TDDFT method, at conical intersections between S₁ and S₀ states. Therefore, the present nonadiabatic dynamics simulations with the TDDFT method are very encouraging for simulating various large systems related to retinal Schiff-base photoisomerization in the real world.

Describing ground and excited state potential energy surfaces for molecular photoswitches using coupled cluster models

In this article, we use two extensively studied systems, a retinal model system and azobenzene, to explore the use of coupled cluster models for describing ground and singlet excited state potential energy surfaces of photoswitchable systems. While not being suitable for describing nuclear dynamics of photoisomerization, coupled cluster models have useful attributes, such as the inclusion of dynamical correlation, their black box nature, and the systematic improvement offered by truncation level. Results for the studied systems show that when triple excitations (here through the CC3 model) are included, ground and excited state potential energy surfaces for isomerization paths may reliably be generated, also for states of doubly excited character. For ground state equilibrium cis- and trans-azobenzene, the molecular geometry and basis set is seen to significantly impact the vertical excitation energies for the two lowest excited states. Efficient implementations of coupled cluster models can therefore constitute valuable tools for investigating photoswitchable systems and can be used for preliminary black box studies to gather information before more complicated excited state dynamics approaches are pursued.

Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes

The chromophores of rhodopsins (Rh) and light-harvesting (LH) complexes still represent a major challenge for a quantum chemical description due to their size and complex electronic structure. Since gradient corrected and hybrid density functional approaches have been shown to fail for these systems, only range-separated functionals seem to be a promising alternative to the more time consuming post-Hartree-Fock approaches. For extended sampling of optical properties, however, even more approximate approaches are required. Recently, a long-range corrected (LC) functional has been implemented into the efficient density functional tight binding (DFTB) method, allowing to sample the excited states properties of chromophores embedded into proteins using quantum mechanical/molecular mechanical (QM/MM) with the time-dependent (TD) DFTB approach. In the present study, we assess the accuracy of LC-TD-DFT and LC-TD-DFTB for rhodopsins (bacteriorhodopsin (bR) and pharaonis phoborhodopsin (ppR)) and LH complexes (light-harvesting complex II (LH2) and Fenna-Matthews-Olson (FMO) complex). This benchmark study shows the improved description of the color tuning parameters compared to standard DFT functionals. In general, LC-TD-DFTB can exhibit a similar performance as the corresponding LC functionals, allowing a reliable description of excited states properties at significantly reduced cost. The two chromophores investigated here pose complementary challenges: while huge sensitivity to external field perturbation (color tuning) and charge transfer excitations are characteristic for the retinal chromophore, the multi-chromophoric character of the LH complexes emphasizes a correct description of inter-chromophore couplings, giving less importance to color tuning. None of the investigated functionals masters both systems simultaneously with satisfactory accuracy. LC-TD-DFTB, at the current stage, although showing a systematic improvement compared to TD-DFTB cannot be recommended for studying color tuning in retinal proteins, similar to some of the LC-DFT functionals, because the response to external fields is still too weak. For sampling of LH-spectra, however, LC-TD-DFTB is a viable tool, allowing to efficiently sample absorption energies, as shown for three different LH complexes. As the calculations indicate, geometry optimization may overestimate the importance of local minima, which may be averaged over when using trajectories. Fast quantum chemical approaches therefore may allow for a direct sampling of spectra in the near future.

Initial excited-state relaxation of locked retinal protonated schiff base chromophore. An insight from coupled cluster and multireference perturbation theory calculations

The initial S₁ excited-state relaxation of retinal protonated Schiff base (RPSB) analog with central C11C12 double bond locked by eight-membered ring (locked-11.8) was investigated by means of multireference perturbation theory methods (XMCQDPT2, XMS-CASPT2, MS-CASPT2) as well as single-reference coupled-cluster CC2 method. The analysis of XMCQDPT2-based geometries reveals rather weak coupling between in-plane and out-of-plane structural evolution and minor energetical relaxation of three locked-11.8 conformers. Therefore, a strong coupling between bonds length inversion and backbone out-of-plane deformation resulting in a very steep S₁ energy profile predicted by CASSCF/CASPT2 calculations is in clear contradiction with the reference XMCQDPT2 results. Even though CC2 method predicts good quality ground-state structures, the excited-state structures display more advanced torsional deformation leading to ca. 0.2 eV exaggerated energy relaxation and significantly red shifted (0.4-0.7 eV) emission maxima. According to our findings, the initial photoisomerization process in locked-11.8, and possibly in other RPSB analogs, studied fully (both geometries and energies) by multireference perturbation theory may be somewhat slower than predicted by CASSCF/CASPT2 or CC2 methods. © 2018 Wiley Periodicals, Inc.

Is the choice of a standard zeroth-order hamiltonian in CASPT2 ansatz optimal in calculations of excitation energies in protonated and unprotonated schiff bases of retinal?

To account for systematic error of CASPT2 method empirical modification of the zeroth-order Hamiltonian with Ionization Potential-Electron Affinity (IPEA) shift was introduced. The optimized IPEA value (0.25 a.u.), called standard IPEA (S-IPEA), was recommended but due to its unsatisfactory performance in multiple metallic and organic compounds it has been questioned lately as a general parameter working properly for all molecules under CASPT2 study. As we are interested in Schiff bases of retinal, an important question emerging from this conflict of choice, to use or not to use S-IPEA, is whether the introduction of the modified zeroth-order Hamiltonian into CASPT2 ansatz does really improve their energetics. To achieve this goal, we assessed an impact of the IPEA shift value, in a range of 0-0.35 a.u., on vertical excitation energies to low-lying singlet states of two protonated (RPSBs) and two unprotonated (RSBs) Schiff bases of retinal for which experimental data in gas phase are available. In addition, an effect of geometry, basis set, and active space on computed VEEs is also reported. We find, that for these systems, the choice of S-IPEA significantly overestimates both S₀ →S₁ and S₀ →S₂ energies and the best theoretical estimate, in reference to the experimental data, is provided with either unmodified zeroth-order Hamiltonian or small value of the IPEA shift in a range of 0.05-0.15 a.u., depending on active space and basis set size, equilibrium geometry, and character of the excited state. © 2018 Wiley Periodicals, Inc.

New Perspectives on an Old Issue: A Comparative MS-CASPT2 and OM2-MRCI Study of Polyenes and Protonated Schiff Bases

Polyenic systems are involved in light perception of numerous living organisms. Although a π-conjugated backbone is a common feature of all polyenes, their photophysics may vary. We provide a comparative quantum mechanical study of low-lying S₁ and S₂ excited states in short (3-5 double bonds) symmetric all-trans linear polyenes and corresponding protonated Schiff bases. In our investigation, we use the well-established ab initio multireference CASPT2 approach and benchmark the efficient semiempirical OM2-MRCI approach against it. For all protonated Schiff bases, MS-CASPT2 results in two distinct S₁ minima with inverted and noninverted bond length pattern, respectively. We find that OM2-MRCI is a computationally affordable and reliable alternative to MS-CASPT2 for investigations of polyenic systems, particularly when highly demanding calculations (e.g. excited-state dynamics) need to be performed.

Excited-state minima and emission energies of retinal chromophore analogues: Performance of CASSCF and CC2 methods as compared with CASPT2

This study provides gas-phase S₁ excited-state geometries along with emission and adiabatic energies for methylated/demethylated and ring-locked analogues of protonated Schiff base retinal models comprising system of five conjugated double bonds (PSB5), using second order multiconfiguration perturbation theory (CASPT2). CASPT2 results serve as reference data to assess the performance of CC2 (second-order approximate coupled cluster singles and doubles) and a commonly used CASSCF/CASPT2 protocol, that is, complete active space self-consistent field (CASSCF) geometry optimization followed by CASPT2 energy calculation. We find that the CASSCF methodology fails to locate planar S₁ minimum energy structures for four out of five investigated planar models in contrast to CC2 and CASPT2 methods. However, for those which were found: one planar and two twisted minima, there is an excellent agreement between CASSCF and CASPT2 results in terms of geometrical parameters, one-electron properties, as well as emission and adiabatic energies. CC2 performs well for in-plane S₁ minima and their spectroscopic and electronic properties. However, this picture deteriorates for twisted minima. As expected, the CC2 description of the S₂ electronic state, with strong multireference and significant double excitation character, is very poor, exhibiting errors in transition energies exceeding 1 eV. They may be substantially diminished by recalculating transition energies with CASPT2 method. Our work shows that CASSCF/CASPT2 and CC2 shortcomings may influence gas-phase retinal analogues' excited state description in a dramatic way. © 2017 Wiley Periodicals, Inc.

Theoretical description of protein field effects on electronic excitations of biological chromophores

Photoinitiated phenomena play a crucial role in many living organisms. Plants, algae, and bacteria absorb sunlight to perform photosynthesis, and convert water and carbon dioxide into molecular oxygen and carbohydrates, thus forming the basis for life on Earth. The vision of vertebrates is accomplished in the eye by a protein called rhodopsin, which upon photon absorption performs an ultrafast isomerisation of the retinal chromophore, triggering the signal cascade. Many other biological functions start with the photoexcitation of a protein-embedded pigment, followed by complex processes comprising, for example, electron or excitation energy transfer in photosynthetic complexes. The optical properties of chromophores in living systems are strongly dependent on the interaction with the surrounding environment (nearby protein residues, membrane, water), and the complexity of such interplay is, in most cases, at the origin of the functional diversity of the photoactive proteins. The specific interactions with the environment often lead to a significant shift of the chromophore excitation energies, compared with their absorption in solution or gas phase. The investigation of the optical response of chromophores is generally not straightforward, from both experimental and theoretical standpoints; this is due to the difficulty in understanding diverse behaviours and effects, occurring at different scales, with a single technique. In particular, the role played by ab initio calculations in assisting and guiding experiments, as well as in understanding the physics of photoactive proteins, is fundamental. At the same time, owing to the large size of the systems, more approximate strategies which take into account the environmental effects on the absorption spectra are also of paramount importance. Here we review the recent advances in the first-principle description of electronic and optical properties of biological chromophores embedded in a protein environment. We show their applications on paradigmatic systems, such as the light-harvesting complexes, rhodopsin and green fluorescent protein, emphasising the theoretical frameworks which are of common use in solid state physics, and emerging as promising tools for biomolecular systems.

Charged Particle Imaging of the Deprotonated Octatrienoic Acid Anion: Evidence for a Photoinduced Cyclization Reaction

Photoelectron spectroscopy of the deprotonated octatrienoic acid anion, [C₇H₉-CO₂]^-, shows the formation of [C₇H₉]^- and loss of H^- at hν = 4.13 eV. Using velocity map imaging, the H^- fragment was characterized to have a Boltzmann-like kinetic energy distribution consistent with dissociation on a ground electronic state. Similar dynamics were not observed at hν = 4.66 eV even though there is clear evidence for recovery of the ground electronic state of [C₇H₉-CO₂]^-. In accord with supporting electronic structure calculations, the production of H^- at hν = 4.13 eV is explained by excited-state dissociation of CO₂ to form [C₇H₉]^-, which subsequently undergoes a ring-closure isomerization reaction to yield toluene and H^-. These data represent the first evidence for a photoinduced ring-closing isomerization reaction in an anionic polyene and provides an interesting example of the rich anion dynamics that can occur in the detachment continuum and that can influence photochemistry.

Exciton circular dichroism in channelrhodopsin

Channelrhodopsins (ChRs) are of great interest currently because of their important applications in optogenetics, the photostimulation of neurons. The absorption and circular dichroism (CD) spectra of C1C2, a chimera of ChR1 and ChR2 of Chlamydomonas reinhardtii, have been studied experimentally and theoretically. The visible absorption spectrum of C1C2 shows vibronic fine structure in the 470 nm band, consistent with the relatively nonpolar binding site. The CD spectrum has a negative band at 492 nm (Δε(max) = -6.17 M(-1) cm(-1)) and a positive band at 434 nm (Δε(max) = +6.65 M(-1) cm(-1)), indicating exciton coupling within the C1C2 dimer. Time-dependent density functional theory (TDDFT) calculations are reported for three models of the C1C2 chromophore: (1) the isolated protonated retinal Schiff base (retPSB); (2) an ion pair, including the retPSB chromophore, two carboxylate side chains (Asp 292, Glu 162), modeled by acetate, and a water molecule; and (3) a hybrid quantum mechanical/molecular mechanical (QM/MM) model depicting the binding pocket, in which the QM part consists of the same ion pair as that in (2) and the MM part consists of the protein residues surrounding the ion pair within 10 Å. For each of these models, the CD of both the monomer and the dimer was calculated with TDDFT. For the dimer, DeVoe polarizability theory and exciton calculations were also performed. The exciton calculations were supplemented by calculations of the coupling of the retinal transition with aromatic and peptide group transitions. For the dimer, all three methods and three models give a long-wavelength C2-axis-polarized band, negative in CD, and a short-wavelength band polarized perpendicular to the C2 axis with positive CD, differing in wavelength by 1-5 nm. Only the retPSB model gives an exciton couplet that agrees qualitatively with experiment. The other two models give a predominantly or solely positive band. We further analyze an N-terminal truncated mutant because it was assumed that the N-terminal domain has a crucial role in the dimerization of ChRs. However, the CD spectrum of this mutant has an exciton couplet comparable to that of the wild-type, demonstrating that it is dimeric. Patch-clamp experiments suggest that the N-terminal domain is involved in protein stabilization and channel kinetics rather than dimerization or channel activity.

Assessment of Density Functional Theory for Describing the Correlation Effects on the Ground and Excited State Potential Energy Surfaces of a Retinal Chromophore Model

In the quest for a cost-effective level of theory able to describe a large portion of the ground and excited potential energy surfaces of large chromophores, promising approaches are rooted in various approximations to the exact density functional theory (DFT). In the present work, we investigate how generalized Kohn-Sham DFT (GKS-DFT), time-dependent DFT (TDDFT), and spin-restricted ensemble-DFT (REKS) methods perform along three important paths characterizing a model retinal chromophore (the penta-2,4-dieniminium cation) in a region of near-degeneracy (close to a conical intersection) with respect to reference high-level multiconfigurational wave function methods. If GKS-DFT correctly describes the closed-shell charge transfer state, only TDDFT and REKS approaches give access to the open-shell diradical, one which sometimes corresponds to the electronic ground state. It is demonstrated that the main drawback of the usual DFT-based methods lies in the absence of interactions between the charge transfer and the diradicaloid configurations. Hence, we test a new computational scheme based on the State-averaged REKS (SA-REKS) approach, which explicitly includes these interactions into account. The State-Interaction SA-REKS (SI-SA-REKS) method significantly improves on the REKS and the SA-REKS results for the target system. The similarities and differences between DFT and wave function-based approaches are analyzed according to (1) the active space dimensions of the wave function-based methods and (2) the relative electronegativities of the allyl and protonated Schiff base moieties.

Ab initio, density functional theory, and semi-empirical calculations

This chapter introduces the theory and applications of commonly used methods of electronic structure calculation, with particular emphasis on methods applicable for modelling biomolecular systems. This chapter is sectioned as follows. We start by presenting ab initio methods, followed by a treatment of density functional theory (DFT) and some recent advances in semi-empirical methods. Treatment of excited states as well as basis sets are also presented.

The effect of protein environment on photoexcitation properties of retinal

Retinal is the photon absorbing chromophore of rhodopsin and other visual pigments, enabling the vertebrate vision process. The effects of the protein environment on the primary photoexcitation process of retinal were studied by time-dependent density functional theory (TDDFT) and the algebraic diagrammatic construction through second order (ADC(2)) combined with our recently introduced reduction of virtual space (RVS) approximation method. The calculations were performed on large full quantum chemical cluster models of the bluecone (BC) and rhodopsin (Rh) pigments with 165-171 atoms. Absorption wavelengths of 441 and 491 nm were obtained at the B3LYP level of theory for the respective models, which agree well with the experimental values of 414 and 498 nm. Electrostatic rather than structural strain effects were shown to dominate the spectral tuning properties of the surrounding protein. The Schiff base retinal and a neighboring Glu-113 residue were found to have comparable proton affinities in the ground state of the BC model, whereas in the excited state, the proton affinity of the Schiff base is 5.9 kcal/mol (0.26 eV) higher. For the ground and excited states of the Rh model, the proton affinity of the Schiff base is 3.2 kcal/mol (0.14 eV) and 7.9 kcal/mol (0.34 eV) higher than for Glu-113, respectively. The protein environment was found to enhance the bond length alternation (BLA) of the retinyl chain and blueshift the first absorption maxima of the protonated Schiff base in the BC and Rh models relative to the chromophore in the gas phase. The protein environment was also found to decrease the intensity of the second excited state, thus improving the quantum yield of the photoexcitation process. Relaxation of the BC model on the excited state potential energy surface led to a vanishing BLA around the isomerization center of the conjugated retinyl chain, rendering the retinal accessible for cis-trans isomerization. The energy of the relaxed excited state was found to be 30 kcal/mol (1.3 eV) above the minimum ground state energy, and might be related to the transition state of the thermal activation process.

Reduction of the virtual space for coupled-cluster excitation energies of large molecules and embedded systems

We investigate how the reduction of the virtual space affects coupled-cluster excitation energies at the approximate singles and doubles coupled-cluster level (CC2). In this reduced-virtual-space (RVS) approach, all virtual orbitals above a certain energy threshold are omitted in the correlation calculation. The effects of the RVS approach are assessed by calculations on the two lowest excitation energies of 11 biochromophores using different sizes of the virtual space. Our set of biochromophores consists of common model systems for the chromophores of the photoactive yellow protein, the green fluorescent protein, and rhodopsin. The RVS calculations show that most of the high-lying virtual orbitals can be neglected without significantly affecting the accuracy of the obtained excitation energies. Omitting all virtual orbitals above 50 eV in the correlation calculation introduces errors in the excitation energies that are smaller than 0.1 eV. By using a RVS energy threshold of 50 eV, the CC2 calculations using triple-ζ basis sets (TZVP) on protonated Schiff base retinal are accelerated by a factor of 6. We demonstrate the applicability of the RVS approach by performing CC2/TZVP calculations on the lowest singlet excitation energy of a rhodopsin model consisting of 165 atoms using RVS thresholds between 20 eV and 120 eV. The calculations on the rhodopsin model show that the RVS errors determined in the gas-phase are a very good approximation to the RVS errors in the protein environment. The RVS approach thus renders purely quantum mechanical treatments of chromophores in protein environments feasible and offers an ab initio alternative to quantum mechanics/molecular mechanics separation schemes.

Studies of the ground and excited-state surfaces of the retinal chromophore using CAM-B3LYP

The isomerization of the 11-cis isomer (PSB11) of the retinal chromophore to its all-trans isomer (PSBT) is examined. Optimized structures on both the ground state and the excited state are calculated, and the dependence on torsional angles in the carbon chain is investigated. Time-dependent density functional theory is used to produce excitation energies and the excited-state surface. To avoid problems with the description of excited states that can arise with standard DFT methods, the CAM-B3LYP functional was used. Comparing CAM-B3LYP with B3LYP results indicates that the former is significantly more accurate, as a consequence of which detailed cross sections of the retinal excited-state surface are obtained.