Mapping the Excited State Potential Energy Surface of a Retinal Chromophore Model with Multireference and Equation-of-Motion Coupled-Cluster Methods

Assessment of the Electron Correlation Treatment on the Quantum-Classical Dynamics of Retinal Protonated Schiff Base Models: XMS-CASPT2, RMS-CASPT2, and REKS Methods

We compare the performance of three different multiconfigurational wave function-based electronic structure methods and two implementations of the spin-restricted ensemble-referenced Kohn-Sham (REKS) method. The study is characterized by three features: (i) it uses a small set of quantum-classical trajectories rather than potential energy surface mapping, (ii) it focuses, exclusively, on the photoisomerization of retinal protonated Schiff base models, and (iii) it probes the effect of both methyl substitution and the increase in length of the conjugate π-system. For each tested method, the corresponding analytical gradients are used to drive the quantum-classical (Tully's FSSH method) trajectory propagation, including the recent multistate XMS-CASPT2 and RMS-CASPT2 gradients. It is shown that while CASSCF, XMS-CASPT2, and RMS-CASPT2 yield consistent photoisomerization dynamics descriptions, REKS produces, in some of these systems, qualitatively different behavior that is attributed to a flatter and topographically different excited state potential energy surface. The origin of this behavior can be traced back to the effect of the employed density functional approximation. The above studies are further expanded by benchmarking, at the CASSCF and REKS levels, the electronic structure methods using a QM/MM model of the visual pigment rhodopsin.

Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics

Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled-trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. A set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Quantum-classical simulations of rhodopsin reveal excited-state population splitting and its effects on quantum efficiency

The activation of rhodopsin, the light-sensitive G-protein coupled receptor responsible for dim-light vision in vertebrates, is driven by an ultrafast excited-state double-bond isomerization with a quantum efficiency of almost 70%. The origin of such light sensitivity is not understood and a key question is whether in-phase nuclear motion controls the quantum efficiency value. Here, we use hundreds of quantum-classical trajectories to show that, 15 femtoseconds after light absorption, a degeneracy between the reactive excited state and a neighboring state causes the splitting of the rhodopsin population into subpopulations. These subpopulations propagate with different velocities and lead to distinct contributions to the quantum efficiency. We also show that such splitting is modulated by protein electrostatics, thus linking amino-acid sequence variations to quantum efficiency modulation. Finally, we discuss how such a linkage that in principle could be exploited to achieve higher quantum efficiencies, would simultaneously increase the receptor thermal noise leading to a trade-off that may have played a role in rhodopsin evolution.

Nonadiabatic dynamics with spin-flip vs linear-response time-dependent density functional theory: A case study for the protonated Schiff base C5H6NH2. J Chem Phys 2021;155:124111. [PMID: 34598550 DOI: 10.1063/5.0062757]

Nonadiabatic trajectory surface hopping simulations are reported for trans-C₅H₆NH₂ ⁺, a model of the rhodopsin chromophore, using the augmented fewest-switches algorithm. Electronic structure calculations were performed using time-dependent density functional theory (TDDFT) in both its conventional linear-response (LR) and its spin-flip (SF) formulations. In the SF-TDDFT case, spin contamination in the low-lying singlet states is removed by projecting out the lowest triplet component during iterative solution of the TDDFT eigenvalue problem. The results show that SF-TDDFT qualitatively describes the photoisomerization of trans-C₅H₆NH₂ ⁺, with favorable comparison to previous studies using multireference electronic structure methods. In contrast, conventional LR-TDDFT affords qualitatively different photodynamics due to an incorrect excited-state potential surface near the Franck-Condon region. In addition, the photochemistry (involving pre-twisting of the central double bond) appears to be different for SF- and LR-TDDFT, which may be a consequence of different conical intersection topographies afforded by these two methods. The present results contrast with previous surface-hopping studies suggesting that the LR-TDDFT method's incorrect topology around S₁/S₀ conical intersections is immaterial to the photodynamics.

Protonation States of Molecular Groups in the Chromophore-Binding Site Modulate Properties of the Reversibly Switchable Fluorescent Protein rsEGFP2

The role of protonation states of the chromophore and its neighboring amino acid side chains of the reversibly switching fluorescent protein rsEGFP2 upon photoswitching is characterized by molecular modeling methods. Numerous conformations of the chromophore-binding site in computationally derived model systems are obtained using the quantum chemistry and QM/MM approaches. Excitation energies are computed using the extended multiconfigurational quasidegenerate perturbation theory (XMCQDPT2). The obtained structures and absorption spectra allow us to provide an interpretation of the observed structural and spectral properties of rsEGFP2 in the active ON and inactive OFF states. The results demonstrate that in addition to the dominating anionic and neutral forms of the chromophore, the cationic and zwitterionic forms may participate in the photoswitching of rsEGFP2. Conformations and protonation forms of the Glu223 and His149 side chains in the chromophore-binding site play an essential role in stabilizing specific protonation forms of the chromophore.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

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.

Equation-of-motion coupled-cluster method with double electron-attaching operators: Theory, implementation, and benchmarks

We report a production-level implementation of the equation-of-motion (EOM) coupled-cluster (CC) method with double electron-attaching (DEA) EOM operators of 2p and 3p1h types, EOM-DEA-CCSD. This ansatz, suitable for treating electronic structure patterns that can be described as two-electrons-in-many orbitals, represents a useful addition to the EOM-CC family of methods. We analyze the performance of EOM-DEA-CCSD for energy differences and molecular properties. By considering reduced quantities, such as state and transition one-particle density matrices, we compare EOM-DEA-CCSD wave functions with wave functions computed by other EOM-CCSD methods. The benchmarks illustrate that EOM-DEA-CCSD is capable of treating diradicals, bond-breaking, and some types of conical intersections.

A Fock-operator complete active space self-consistent field (CAS-SCF) method combined with frozen-density embedding

We report the implementation of a Fock-operator complete-active space self-consistent field (CAS-SCF) method combined with frozen-density embedding (FDE) into the KOALA quantum-chemistry program. The implementation is based on configuration interaction from an unrestricted reference determinant and is able to treat electronic configurations such as singlet, triplet, or quintet states embedded in a molecular environment. In order to account for possible spin polarization effects, the FDE contribution is extended to the unrestricted case. We assess the convergence obtained with the implementation at the example of a stretched lithium dimer with significant multi-reference character. The efficiency of the implementation enables the orbital optimization for 25 states in a state-average SA[S₀-S₁₀,T₁-T₁₂,Q₁-Q₂]-CAS(10,10)-SCF calculation for the retinal molecule using a def2-TZVP basis. The FDE ansatz leads to orbitals localized by definition on the target system, thus facilitating the orbital selection required for CAS methods in complex environments.

QM/MM Investigation of the Spectroscopic Properties of the Fluorophore of Bacterial Luciferase

We employ replica-exchange molecular dynamics (REMD) and a hybrid ab initio multiconfigurational quantum mechanics/molecular mechanics (QM/MM) approach to model the absorption and fluorescence properties of bacterial luciferin-luciferase. Specifically, we employ complete active space perturbation theory (CASPT2) and study the effect of active space, basis set, and IPEA shift on the computed energies. We discuss the effect of the protein environment on the fluorophore's excited-state potential energy surface and the role that the protein plays in enhancing the fluorescence quantum yield in bacterial bioluminescence.

Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach

We present a machine learning-assisted excited state molecular dynamics (ML-ESMD) based on the ensemble density functional theory framework. Since we represent a diabatic Hamiltonian in terms of generalized valence bond ansatz within the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS) method, we can avoid singularities near conical intersections, which are crucial in excited state molecular dynamics simulations. We train the diabatic Hamiltonian elements and their analytical gradients with the SchNet architecture to construct machine learning models, while the phase freedom of off-diagonal elements of the Hamiltonian is cured by introducing the phase-less loss function. Our machine learning models show reasonable accuracy with mean absolute errors of ∼0.1 kcal/mol and ∼0.5 kcal/mol/Å for the diabatic Hamiltonian elements and their gradients, respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting the diabatic representation, our models can predict correct conical intersection structures and their topologies. In addition, our ML-ESMD simulations give almost identical result with a direct dynamics at the same level of theory.

Accurate Molecular Geometries in Complex Excited-State Potential Energy Surfaces from Time-Dependent Density Functional Theory

The interplay of electronic excitations and structural changes in molecules impacts nonradiative decay and charge transfer in the excited state, thus influencing excited-state lifetimes and photocatalytic reaction rates in optoelectronic and energy devices. To capture such effects requires computational methods providing an accurate description of excited-state potential energy surfaces and geometries. We suggest time-dependent density functional theory using optimally tuned range-separated hybrid (OT-RSH) functionals as an accurate approach to obtain excited-state molecular geometries. We show that OT-RSH provides accurate molecular geometries in excited-state potential energy surfaces that are complex and involve an interplay of local and charge-transfer excitations, for which conventional semilocal and hybrid functionals fail. At the same time, the nonempirical OT-RSH approach maintains the high accuracy of parametrized functionals (e.g., B3LYP) for predicting excited-state geometries of small organic molecules showing valence excited states.

Quantum and Quantum-Classical Studies of the Photoisomerization of a Retinal Chromophore Model

We report an in-depth analysis of the photo-induced isomerization of the 2-cis-penta-2,4-dieniminium cation: a minimal model of the 11-cis retinal protonated Schiff base chromophore of the dim-light photoreceptor rhodopsin. Based on recently developed three-dimensional potentials parametrized on ab initio multi-state multi-configurational second-order perturbation theory data, we perform quantum-dynamical studies. In addition, simulations based on various quantum-classical methods, among which Tully surface hopping and the coupled-trajectory approach derived from the exact factorization, allow us to validate their performance against vibronic wavepacket propagation and, therefore, a purely quantum treatment. Quantum-dynamics results uncover qualitative differences with respect to the two-dimensional Hahn-Stock potentials, widely used as model potentials for the isomerization of the same chromophore, due to the increased dimensionality and three-mode correlation. Quantum-classical simulations show, instead, that three-dimensional model potentials are capable of capturing a number of features revealed by atomistic simulations and experimental observations. In particular, a recently reported vibrational phase relationship between double-bond torsion and hydrogen-out-of-plane modes critical for rhodopsin isomerization efficiency is correctly reproduced.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

Spin-flip methods in quantum chemistry

This Perspective discusses salient features of the spin-flip approach to strong correlation and describes different methods that sprung from this idea. The spin-flip treatment exploits the different physics of low-spin and high-spin states and is based on the observation that correlation is small for same-spin electrons. By using a well-behaved high-spin state as a reference, one can access problematic low-spin states by deploying the same formal tools as in the excited-state treatments (i.e., linear response, propagator, or equation-of-motion theories). The Perspective reviews applications of this strategy within wave function and density functional theory frameworks as well as the extensions for molecular properties and spectroscopy. The utility of spin-flip methods is illustrated by examples. Limitations and proposed future directions are also discussed.

Nonadiabatic Photodynamics of Retinal Protonated Schiff Base in Channelrhodopsin 2

Channelrhodopsin 2 (ChR2) is a light-gated ion channel and an important tool in optogenetics. Photoisomerization of retinal protonated Schiff base (RPSB) in ChR2 triggers channel activation. Despite the importance of ChR2 in optogenetics, the detailed mechanism for photoisomerization and channel activation is still not fully understood. Here, we report on computer simulations to investigate the photoisomerization mechanism and its effect on the activation of ChR2. Nonadiabatic dynamics simulation of ChR2 was carried out using the ab initio multiple spawning (AIMS) method and quantum mechanics/molecular mechanics (QM/MM) with a restricted ensemble Kohn-Sham (REKS) treatment of the QM region. Our results agree well with spectroscopic measurements and reveal that the RPSB isomerization is highly specific around the C₁₃=C₁₄ bond and follows the "aborted bicycle-pedal" mechanism. In addition, RPSB photoisomerization facilitates its deprotonation and partially increases the hydration level in the channel, which could trigger subsequent channel opening and ion conduction.

Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model

In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.

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.

Photoprotection: extending lessons learned from studying natural sunscreens to the design of artificial sunscreen constituents

Evolution has ensured that plants and animals have developed effective protection mechanisms against the potentially harmful effects of incident ultraviolet radiation (UVR). Tanning is one such mechanism in humans, but tanning only occurs post-exposure to UVR. Hence, there is ever growing use of commercial sunscreens to pre-empt overexposure to UVR. Key requirements for any chemical filter molecule used in such a photoprotective capacity include a large absorption cross-section in the UV-A and UV-B spectral regions and the availability of one or more mechanisms whereby the absorbed photon energy can be dissipated without loss of the molecular integrity of the chemical filter. Here we summarise recent experimental (mostly ultrafast pump-probe spectroscopy studies) and computational progress towards unravelling various excited state decay mechanisms that afford the necessary photostability in chemical filters found in nature and those used in commercial sunscreens. We also outline ways in which a better understanding of the photophysics and photochemistry of sunscreen molecules selected by nature could aid the design of new and improved commercial sunscreen formulations.

Engineering the vibrational coherence of vision into a synthetic molecular device

The light-induced double-bond isomerization of the visual pigment rhodopsin operates a molecular-level optomechanical energy transduction, which triggers a crucial protein structure change. In fact, rhodopsin isomerization occurs according to a unique, ultrafast mechanism that preserves mode-specific vibrational coherence all the way from the reactant excited state to the primary photoproduct ground state. The engineering of such an energy-funnelling function in synthetic compounds would pave the way towards biomimetic molecular machines capable of achieving optimum light-to-mechanical energy conversion. Here we use resonance and off-resonance vibrational coherence spectroscopy to demonstrate that a rhodopsin-like isomerization operates in a biomimetic molecular switch in solution. Furthermore, by using quantum chemical simulations, we show why the observed coherent nuclear motion critically depends on minor chemical modifications capable to induce specific geometric and electronic effects. This finding provides a strategy for engineering vibrationally coherent motions in other synthetic systems.

The ultrafast, vibrationally coherent photoisomerization of rhodopsin is a model of efficient photomechanical energy conversion at the molecular scale. Here, the authors demonstrate a similar photoreaction in synthetic compounds, unraveling the underlying mechanism and discussing its implications.

Accurate Excited-State Geometries: A CASPT2 and Coupled-Cluster Reference Database for Small Molecules

We present an investigation of the excited-state structural parameters determined for a large set of small compounds with the dual goals of defining reference values for further works and assessing the quality of the geometries obtained with relatively cheap computational approaches. In the first stage, we compare the excited-state geometries obtained with ADC(2), CC2, CCSD, CCSDR(3), CC3, and CASPT2 and large atomic basis sets. It is found that CASPT2 and CC3 results are generally in very good agreement with one another (typical differences of ca. 3 × 10^–3 Å) when all electrons are correlated and when the aug-cc-pVTZ atomic basis set is employed with both methods. In a second stage, a statistical analysis reveals that, on the one hand, the excited-state (ES) bond lengths are much more sensitive to the selected level of theory than their ground-state (GS) counterparts and, on the other hand, that CCSDR(3) is probably the most cost-effective method delivering accurate structures. Indeed, CCSD tends to provide too compact multiple bond lengths on an almost systematic basis, whereas both CC2 and ADC(2) tend to exaggerate these bond distances, with more erratic error patterns, especially for the latter method. The deviations are particularly marked for the polarized CO and CN bonds, as well as for the puckering angle in formaldehyde homologues. In the last part of this contribution, we provide a series of CCSDR(3) GS and ES geometries of medium-sized molecules to be used as references in further investigations.

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.

Assessment of the Potential Energy Hypersurfaces in Thymine within Multiconfigurational Theory: CASSCF vs. CASPT2

The present study provides new insights into the topography of the potential energy hypersurfaces (PEHs) of the thymine nucleobase in order to rationalize its main ultrafast photochemical decay paths by employing two methodologies based on the complete active space self-consistent field (CASSCF) and the complete active space second-order perturbation theory (CASPT2) methods: (i) CASSCF optimized structures and energies corrected with the CASPT2 method at the CASSCF geometries and (ii) CASPT2 optimized geometries and energies. A direct comparison between these strategies is drawn, yielding qualitatively similar results within a static framework. A number of analyses are performed to assess the accuracy of these different computational strategies under study based on a variety of numerical thresholds and optimization methods. Several basis sets and active spaces have also been calibrated to understand to what extent they can influence the resulting geometries and subsequent interpretation of the photochemical decay channels. The study shows small discrepancies between CASSCF and CASPT2 PEHs, displaying a shallow planar or twisted ¹(ππ*) minimum, respectively, and thus featuring a qualitatively similar scenario for supporting the ultrafast bi-exponential deactivation registered in thymine upon UV-light exposure. A deeper knowledge of the PEHs at different levels of theory provides useful insight into its correct characterization and subsequent interpretation of the experimental observations. The discrepancies displayed by the different methods studied here are then discussed and framed within their potential consequences in on-the-fly non-adiabatic molecular dynamics simulations, where qualitatively diverse outcomes are expected.

Study of Model Systems for Bilirubin and Bilin Chromophores: Determination and Modification of Thermal and Photochemical Properties

Bilin chromophores and bilirubin are involved in relevant biological functions such as light perception in plants and as protective agents against Alzheimer and other diseases. Despite their extensive use, a deep rationalization of the main factors controlling the thermal and photochemical properties has not been performed yet, which in turn hampers further applications of these versatile molecules. In an effort to understand those factors and allow control of the relevant properties, a combined experimental and computational study has been carried out for diverse model systems to understand the interconversion between Z and E isomers. In this study, we have demonstrated the crucial role of steric hindrance and hydrogen-bond interactions in thermal stability and the ability to control them by designing novel compounds. We also determined several photochemical properties and studied the photodynamics of two model systems in more detail, observing a fast relaxation of the excited state shorter than 2 ps in both cases. Finally, the computational study allowed us to rationalize the experimental evidence.

Rhodopsins carrying modified chromophores--the 'making of', structural modelling and their light-induced reactivity

A series of vitamin-A aldehydes (retinals) with modified alkyl group substituents (9-demethyl-, 9-ethyl-, 9-isopropyl-, 10-methyl, 10-methyl-13-demethyl-, and 13-demethyl retinal) was synthesized and their 11-cis isomers were used as chromophores to reconstitute the visual pigment rhodopsin. Structural changes were selectively introduced around the photoisomerizing C11=C12 bond. The effect of these structural changes on rhodopsin formation and bleaching was determined. Global fit of assembly kinetics yielded lifetimes and spectral features of the assembly intermediates. Rhodopsin formation proceeds stepwise with prolonged lifetimes especially for 9-demethyl retinal (longest lifetime τ3 = 7500 s, cf., 3500 s for retinal), and for 10-methyl retinal (τ3 = 7850 s). These slowed-down processes are interpreted as either a loss of fixation (9dm) or an increased steric hindrance (10me) during the conformational adjustment within the protein. Combined quantum mechanics and molecular mechanics (QM/MM) simulations provided structural insight into the retinal analogues-assembled, full-length rhodopsins. Extinction coefficients, quantum yields and kinetics of the bleaching process (μs-to-ms time range) were determined. Global fit analysis yielded lifetimes and spectral features of bleaching intermediates, revealing remarkably altered kinetics: whereas the slowest process of wild-type rhodopsin and of bleached and 11-cis retinal assembled rhodopsin takes place with lifetimes of 7 and 3.8 s, respectively, this process for 10-methyl-13-demethyl retinal was nearly 10 h (34670 s), coming to completion only after ca. 50 h. The structural changes in retinal derivatives clearly identify the precise interactions between chromophore and protein during the light-induced changes that yield the outstanding efficiency of rhodopsin.