Role of the Molecular Environment in Flavoprotein Color and Redox Tuning: QM Cluster versus QM/MM Modeling

We investigate the origin of the excitation energy shifts induced by the apoprotein in the active site of the bacterial photoreceptor BLUF (Blue Light sensor Using Flavin adenine dinucleotide). In order to compute the vertical excitation energies of three low-lying electronic states, including two π-π* states of flavin (S1 and S2) and a π-π* tyrosine-flavin electron-transfer state (ET), with respect to the energy of the closed-shell ground state (S0), we prepared alternative quantum mechanical (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) models. We found that the excitation energies computed with both types of models correlate with the magnitude of the charge transfer character of the excitation. Accordingly, we conclude that the small charge transfer character of the light absorbing S0-S1 transition and the substantial charge transfer character of the nonabsorbing but redox active S0-ET transition explain the small color changes but substantial redox tuning in BLUF and also in other flavoproteins. Further analysis showed that redox tuning is governed by the electrostatic interaction in the QM/MM model and transfer of charge between the active site and its environment in the QM cluster. Moreover, the wave function polarization of the QM subsystem by the MM subsystem influences the magnitude of the charge transfer, resulting in the QM/MM and QM excitation energies that are not entirely consistent.

Space and Time Evolution of the Electrostatic Potential During the Activation of a Visual Pigment

Animal and microbial retinal proteins employ the Schiff base of retinal as their chromophore. Here, the possible consequences of the charge translocation associated with the light-induced dynamics of the chromophore of a visual opsin are investigated along a representative semiclassical trajectory. We show that the evolution of the electrostatic potential projected by the chromophore onto the surrounding protein displays intense but topographically localized sudden variations in proximity of the decay region. pKa calculations carried out on selected snapshots used as probes, indicate that the only residue which may be sensitive to the electrostatic potential shift is Glu181. Accordingly, our results suggest that the frail Tyr191/268-Glu181-Wat2-Ser186 hydrogen bond network may be perturbed by the transient variations of the electrostatic potential.

Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model

The penta-2,4-dieniminium cation (PSB3) displays similar ground state and first excited state potential energy features as those of the retinal protonated Schiff base (RPSB) chromophore in rhodopsin. Recently, PSB3 has been used to benchmark several electronic structure methods, including highly correlated multireference wave function approaches, highlighting the necessity to accurately describe the electronic correlation in order to obtain reliable properties even along the ground state (thermal) isomerization paths. In this work, we apply two quantum Monte Carlo approaches, the variational Monte Carlo and the lattice regularized diffusion Monte Carlo, to study the energetics and electronic properties of PSB3 along representative minimum energy paths and scans related to its thermal cis–trans isomerization. Quantum Monte Carlo is used in combination with the Jastrow antisymmetrized geminal power ansatz, which guarantees an accurate and balanced description of the static electronic correlation thanks to the multiconfigurational nature of the antisymmetrized geminal power term, and of the dynamical correlation, due to the presence of the Jastrow factor explicitly depending on electron–electron distances. Along the two ground state isomerization minimum energy paths of PSB3, CASSCF calculations yield wave functions having either charge transfer or diradical character in proximity of the two transition state configurations. Here, we observe that at the quantum Monte Carlo level of theory, only the transition state with charge transfer character can be located. The conical intersection, which becomes highly sloped, is observed only if the path connecting the two original CASSCF transition states is extended beyond the diradical one, namely by increasing the bond-length-alternation (BLA). These findings are in good agreement with the results obtained by MRCISD+Q calculations, and they demonstrate the importance of having an accurate description of the static and dynamical correlation when studying isomerization and transition states of conjugated systems.

Probing the Photodynamics of Rhodopsins with Reduced Retinal Chromophores

While the light-induced population dynamics of different photoresponsive proteins has been investigated spectroscopically, systematic computational studies have not yet been possible due to the phenomenally high cost of suitable high level quantum chemical methods and the need of propagating hundreds, if not thousands, of nonadiabatic trajectories. Here we explore the possibility of studying the photodynamics of rhodopsins by constructing and investigating quantum mechanics/molecular mechanics (QM/MM) models featuring reduced retinal chromophores. In order to do so we use the sensory rhodopsin found in the cyanobacterium Anabaena PCC7120 (ASR) as a benchmark system. We find that the basic mechanistic features associated with the excited state dynamics of ASR QM/MM models are reproduced using models incorporating a minimal (i.e., three double-bond) chromophore. Furthermore, we show that ensembles of nonadiabatic ASR trajectories computed using the same abridged models replicate, at both the CASPT2 and CASSCF levels of theory, the trends in spectroscopy and lifetimes estimated using unabridged models and observed experimentally at room temperature. We conclude that a further expansion of these studies may lead to low-cost QM/MM rhodopsin models that may be used as effective tools in high-throughput in silico mutant screening.

Mechanism of excited state deactivation of indan-1-ylidene and fluoren-9-ylidene malononitriles

A joint experimental and computational study on the non-radiative double bond isomerisation decay channel of indan-1-ylidene malononitrile and fluoren-9-ylidene malononitrile is presented in this work.

Protein Influence on Electronic Spectra Modeled by Multipoles and Polarizabilities

We have developed automatic methods to calculate multipoles and anisotropic polarizabilities for all atoms and bond centers in a protein and to include such a model in the calculation of electronic properties at any level of quantum mechanical theory. This approach is applied for the calculation of the electronic spectra of retinal in rhodopsin at the CASPT2//CASSCF level (second-order multiconfigurational perturbation theory) for the wild-type protein, as well as two mutants and isorhodopsin in QM/MM structures based on two crystal structures. We also perform a detailed investigation of the importance and distance dependence of the multipoles and the polarizabilities for both the absolute and the relative absorption energies. It is shown that the model of the surrounding protein strongly influences the spectrum and that different models give widely different results. For example, the Amber 1994 and 2003 force fields give excitation energies that differ by up to 16 kJ/mol. For accurate excitation energies, multipoles up to quadrupoles and anisotropic polarizabilities are needed. However, interactions with residues more than 10 Å from the chromophore can be treated with a standard polarizable force field without any dipoles or quadrupoles.

Assessment of Approximate Coupled-Cluster and Algebraic-Diagrammatic-Construction Methods for Ground- and Excited-State Reaction Paths and the Conical-Intersection Seam of a Retinal-Chromophore Model

As a minimal model of the chromophore of rhodopsin proteins, the penta-2,4-dieniminium cation (PSB3) poses a challenging test system for the assessment of electronic-structure methods for the exploration of ground- and excited-state potential-energy surfaces, the topography of conical intersections, and the dimensionality (topology) of the branching space. Herein, we report on the performance of the approximate linear-response coupled-cluster method of second order (CC2) and the algebraic-diagrammatic-construction scheme of the polarization propagator of second and third orders (ADC(2) and ADC(3)). For the ADC(2) method, we considered both the strict and extended variants (ADC(2)-s and ADC(2)-x). For both CC2 and ADC methods, we also tested the spin-component-scaled (SCS) and spin-opposite-scaled (SOS) variants. We have explored several ground- and excited-state reaction paths, a circular path centered around the S1/S0 surface crossing, and a 2D scan of the potential-energy surfaces along the branching space. We find that the CC2 and ADC methods yield a different dimensionality of the intersection space. While the ADC methods yield a linear intersection topology, we find a conical intersection topology for the CC2 method. We present computational evidence showing that the linear-response CC2 method yields a surface crossing between the reference state and the first response state featuring characteristics that are expected for a true conical intersection. Finally, we test the performance of these methods for the approximate geometry optimization of the S1/S0 minimum-energy conical intersection and compare the geometries with available data from multireference methods. The present study provides new insight into the performance of linear-response CC2 and polarization-propagator ADC methods for molecular electronic spectroscopy and applications in computational photochemistry.

Molcas 8: New capabilities for multiconfigurational quantum chemical calculations across the periodic table

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization.

Directionality of Double-Bond Photoisomerization Dynamics Induced by a Single Stereogenic Center

In light-driven single-molecule rotary motors, the photoisomerization of a double bond converts light energy into the rotation of a moiety (the rotor) with respect to another (the stator). However, at the level of a molecular population, an effective rotary motion can only be achieved if a large majority of the rotors rotate in the same, specific direction. Here we present a quantitative investigation of the directionality (clockwise vs counterclockwise) induced by a single stereogenic center placed in allylic position with respect to the reactive double bond of a model of the biomimetic indanylidene-pyrrolinium framework. By computing ensembles of nonadiabatic trajectories at 300 K, we predict that the photoisomerization is >70% unidirectional for the Z → E and E → Z conversions. Most importantly, we show that such directionality, resulting from the asymmetry of the excited state force field, can still be observed in the presence of a small (ca. 2°) pretwist or helicity of the reactive double bond. This questions the validity of the conjecture that a significant double-bond pretwist (e.g., >10°) in the ground state equilibrium structure of synthetic or natural rotary motors would be required for unidirectional motion.

Shape of Multireference, Equation-of-Motion Coupled-Cluster, and Density Functional Theory Potential Energy Surfaces at a Conical Intersection

We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.

Learning from photobiology how to design molecular devices using a computer

Learning how to model photo-responsive proteins may open the way to the design of lightpowered biomimetic molecular devices.

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.