A comprehensive benchmark of the XMS-CASPT2 method for the photochemistry of a retinal chromophore model

The development of the QM/MM interface and its application for the on-the-fly QM/MM nonadiabatic dynamics in JADE package: Theory, implementation, and applications

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes.

Picosecond quantum-classical dynamics reveals that the coexistence of light-induced microbial and animal chromophore rotary motion modulates the isomerization quantum yield of heliorhodopsin

Rhodopsins are light-responsive proteins forming two vast and evolutionary distinct superfamilies whose functions are invariably triggered by the photoisomerization of a single retinal chromophore. In 2018 a third widespread superfamily of rhodopsins called heliorhodopsins was discovered using functional metagenomics. Heliorhodopsins, with their markedly different structural features with respect to the animal and microbial superfamilies, offer an opportunity to study how evolution has manipulated the chromophore photoisomerization to achieve adaptation. One question is related to the mechanism of such a reaction and how it differs from that of animal and microbial rhodopsins. To address this question, we use hundreds of quantum-classical trajectories to simulate the spectroscopically documented picosecond light-induced dynamics of a heliorhodopsin from the archaea thermoplasmatales archaeon (TaHeR). We show that, consistently with the observations, the trajectories reveal two excited state decay channels. However, inconsistently with previous hypotheses, only one channel is associated with the -C13C14- rotation of microbial rhodopsins while the second channel is characterized by the -C11C12- rotation typical of animal rhodopsins. The fact that such -C11C12- rotation is aborted upon decay and ground state relaxation, explains why illumination of TaHeR only produces the 13-cis isomer with a low quantum efficiency. We argue that the documented lack of regioselectivity in double-bond excited state twisting motion is the result of an "adaptation" that could be completely lost via specific residue substitutions modulating the steric hindrance experienced along the isomerization motion.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2)

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

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.

What Controls the Quality of Photodynamical Simulations? Electronic Structure Versus Nonadiabatic Algorithm

The field of nonadiabatic dynamics has matured over the last decade with a range of algorithms and electronic structure methods available at the moment. While the community currently focuses more on developing and benchmarking new nonadiabatic dynamics algorithms, the underlying electronic structure controls the outcome of nonadiabatic simulations. Yet, the electronic-structure sensitivity analysis is typically neglected. In this work, we present a sensitivity analysis of the nonadiabatic dynamics of cyclopropanone to electronic structure methods and nonadiabatic dynamics algorithms. In particular, we compare wave function-based CASSCF, FOMO-CASCI, MS- and XMS-CASPT2, density-functional REKS, and semiempirical MRCI-OM3 electronic structure methods with the Landau-Zener surface hopping, fewest switches surface hopping, and ab initio multiple spawning with informed stochastic selection algorithms. The results clearly demonstrate that the electronic structure choice significantly influences the accuracy of nonadiabatic dynamics for cyclopropanone even when the potential energy surfaces exhibit qualitative and quantitative similarities. Thus, selecting the electronic structure solely on the basis of the mapping of potential energy surfaces can be misleading. Conversely, we observe no discernible differences in the performance of the nonadiabatic dynamics algorithms across the various methods. Based on the above results, we discuss the present-day practice in computational photodynamics.

The involvement of triplet states in the isomerization of retinaloids

Rhodopsins form a family of photoreceptor proteins which utilize the retinal chromophore for light energy conversion. Upon light absorption the retinal chromophore undergoes a photoisomerization. This reaction involves a non-radiative relaxation through a conical intersection between the singlet excited state and the ground state. In this work we studied the possible involvement of triplet states in the photoisomerization of retinaloids using the extended multistate (XMS) version of CASPT2. To this end, truncated models of three retinaloids were considered: protonated Schiff base, deprotonated Schiff base and the aldehyde form. The optimized geometries of the reactant, the product and the conical intersection were connected by a linear interpolation of internal coordinates to describe the isomerization. The energetic position of the low-lying singlet and triplet states as well as their spin-orbit coupling matrix elements (SOCME) were calculated along the isomerization profile. The SOCME values peaked in vicinity of the conical intersection for all the retinaloids. Furthermore, the magnitude of SOCME is invariant to the number of double bonds in the model. The SOCME for the protonated Schiff base is negligible (1.5 cm^-1) which renders the involvement of the triplet state as improbable. However, the largest SOCME value of 30 cm^-1 was found for the aldehyde form, followed by 15 cm^-1 for the deprotonated Schiff base.

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.

Nonradiative relaxation mechanisms of the elusive silole molecule

Silole derivatives have been extensively employed for developing organic optoelectronics, but few studies focused on the photophysical properties of the silole molecule. In this work, we investigate these properties by computing the absorption spectra and performing nonadiabatic molecular dynamics of silole employing the algebraic diagrammatic construction [ADC(2)] and extended multi-state XMS-CASPT2 ab initio electronic structure methods. For vertical excitations and excited state optimizations, the equation of motion coupled-cluster singles and doubles (EOM-CCSD) was also used. The nuclear ensemble and the fewest-switches surface hopping molecular dynamics methods coupled with the first two high-level electronic structure methods were applied to probe the relaxation mechanisms of silole. We could reproduce the experimental first absorption maximum value and found an ultrafast relaxation process occurring exclusively through ring-puckering distortions without breaking ring bonds or hydrogen elimination. Minimum energy conical intersection optimizations were carried out and potential energy curves, including triplet states, were calculated to further elucidate the relaxation process of silole.

Modelling Photoionisation in Isocytosine: Potential Formation of Longer-Lived Excited State Cations in its Keto Form

Studying the effects of UV and VUV radiation on non-canonical DNA/RNA nucleobases allows us to compare how they release excess energy following absorption with respect to their canonical counterparts. This has attracted much research attention in recent years because of its likely influence on the origin of our genetic lexicon in prebiotic times. Here we present a CASSCF and XMS-CASPT2 theoretical study of the photoionisation of non-canonical pyrimidine nucleobase isocytosine in both its keto and enol tautomeric forms. We analyse their lowest energy cationic excited states including 2 π + , 2 n O + and 2 n N + and compare these to the corresponding electronic states in cytosine. Investigating lower-energy decay pathways we find - unexpectedly - that keto-isocytosine+ presents a sizeable energy barrier potentially inhibiting decay to its cationic ground state, whereas enol-isocytosine+ features a barrierless and consequently ultrafast pathway analogous to the one previously found for the canonical (keto) form of cytosine+ . Dynamic electron correlation reduces the energy barrier in the keto form substantially (by ∼1 eV) but it is nevertheless still present. We additionally compute the UV/Vis absorption signals of the structures encountered along these decay channels to provide spectroscopic fingerprints to assist future experiments in monitoring these intricate photo-processes.

Theoretical Study of the Photoisomerization Mechanism of All-Trans-Retinyl Acetate

The compound 9-cis-retinyl acetate (9-cis-RAc) is a precursor to 9-cis-retinal, which has potential application in the treatment of some hereditary diseases of the retina. An attractive synthetic route to 9-cis-RAc is based on the photoisomerization reaction of the readily available all-trans-RAc. In the present study, we examine the mechanism of the photoisomerization reaction with the use of state-of-the-art electronic structure calculations for two polyenic model compounds: tEtEt-octatetraene and tEtEtEc-2,6-dimethyl-1,3,5,7,9-decapentaene. The occurrence of photoisomerization is attributed to a chain-kinking mechanism, whereby a series of S₁/S₀ conical intersections associated with kinking deformations at different positions along the polyenic chain mediate internal conversion to the S₀ state, and subsequent isomerization around one of the double bonds. Two other possible photoisomerization mechanisms are taken into account, but they are rejected as incompatible with simulation results and/or the available spectroscopic data.

Wavepacket propagations for the early time dynamics of proton-coupled electron transfer in the charge-transfer state of NH3Cl complex

A charge-transfer (CT) excited state of NH₃Cl, generated by photo-detachment of an electron from the anionic NH₃Cl^- precursor, can be represented as H₂N⁺-H-Cl^- and proceeds to two chemical reactions: one reaction generating NH₂ and HCl resulting from a proton transfer (PT) and the other reaction producing NH₃ and a Cl atom resulting from an electron transfer (ET); both are coupled to form a typical proton-coupled electron transfer (PCET) process. The early time dynamics of this CT were studied using time-dependent wavepacket propagation on three nonadiabatically coupled electronic states in a reduced three-dimensional space. The electronic states were treated using the XMS-CASPT2/aug-cc-pVTZ ab initio methodology. The population dynamics of the three coupled electronic states were analyzed in detail to reveal the initial stage of the PCET process up to ∼100 fs, while the branching ratio, χ = PT/(ET+PT), was determined after wavepacket propagations of up to 2000 fs. Another main result is the dependence of χ on the vibration levels of the initial precursor anion and the isotope substitution of the connecting H atom with deuterium and tritium. Our study reveals the detailed microscopic features of the PCET process embedded in the CT state of the NH₃Cl complex and certain systematic dependences of the branching ratio χ on the above factors.

Parameterization of a linear vibronic coupling model with multiconfigurational electronic structure methods to study the quantum dynamics of photoexcited pyrene

With this work, we present a protocol for the parameterization of a Linear Vibronic Coupling (LVC) Hamiltonian for quantum dynamics using highly accurate multiconfigurational electronic structure methods such as RASPT2/RASSCF, combined with a maximum-overlap diabatization technique. Our approach is fully portable and can be applied to many medium-size rigid molecules whose excited state dynamics requires a quantum description. We present our model and discuss the details of the electronic structure calculations needed for the parameterization, analyzing critical situations that could arise in the case of strongly interacting excited states. The protocol was applied to the simulation of the excited state dynamics of the pyrene molecule, starting from either the first or the second bright state (S₂ or S₅). The LVC model was benchmarked against state-of-the-art quantum mechanical calculations with optimizations and energy scans and turned out to be very accurate. The dynamics simulations, performed including all active normal coordinates with the multilayer multiconfigurational time-dependent Hartree method, show good agreement with the available experimental data, endorsing prediction of the excited state mechanism, especially for S₅, whose ultrafast deactivation mechanism was not yet clearly understood.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

Four resonance structures elucidate double-bond isomerisation of a biological chromophore

Four resonance structures determining the electronic structure of the chromophore’s ground and first excited states. Changing the relative energies of the structures by hydrogen-bonding interactions tunes all chromophore’s photochemical properties.

Ultrafast and radiationless electronic excited state decay of uracil and thymine cations: computing the effects of dynamic electron correlation

In this article we characterise the radiationless decay of the first few electronic excited states of the cations of DNA/RNA nucleobases uracil and thymine, including the effects of dynamic electron correlation on energies and geometries (optimised with XMS-CASPT2). In both systems, we find that one state of ²n and another two of ²π⁺ character can be populated following photoionisation, and their different minima and interstate crossings are located. We find strong similarities between uracil and thymine cations: with accessible conical intersections suggesting that depopulation of their electronic excited states takes place on ultrafast timescales in both systems, suggesting that they are photostable in agreement with previous theoretical (uracil⁺) evidence. We find that dynamic electron correlation separates the energy levels of the "3-state" conical intersection (D₂/D₁/D₀)_CI previously located with CASSCF for uracil⁺, which will therefore have a different geometry and higher energy. Simulating the electronic and vibrational absorptions allows us to characterise spectral fingerprints that could be used to monitor these cation photo-processes experimentally.

State-interaction pair density functional theory for locally avoided crossings of potential energy surfaces in methylamine

State-interaction pair-density functional theory agrees well with extended MS-CASPT2 in regions of strong state coupling near conical intersections.