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

Correction for 'Benchmark and performance of long-range corrected time-dependent density functional tight binding (LC-TD-DFTB) on rhodopsins and light-harvesting complexes' by Beatrix M. Bold et al., Phys. Chem. Chem. Phys., 2020, 22, 10500-10518, https://doi.org/10.1039/C9CP05753F.

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.

Far Red Fluorescent Proteins: Where Is the Limit of the Acylimine Chromophore?

The search for new near-infrared probes for fluorescence imaging applications is a rapidly growing field of research. Monomeric fluorescent proteins that autocatalyze their chromophore are the most versatile markers for in vivo applications, but the development of bright far-red fluorescent proteins (RFPs) has proven difficult. In this contribution, we search for the theoretical limit of the red shift and how it can be reached without sacrificing the fluorescence quantum yield. Through extensive excited-state pathway calculations, molecular dynamics sampling, and statistical modeling using QM/MM schemes, we provide a new understanding of the chromophore's photophysics including the role of its acylimine extension, which is the main difference from other families of fluorescent proteins. The excited-state dynamics of the mPlum RFP and its mutants provide an ideal basis due to mPlum's flexible binding pocket and extended dynamic Stokes shift. We found a large number of structural species with red-shifted emission that differ in rotamer states and H-bonds between key amino acid residues in the binding pocket. By analyzing their spectral and structural features, we derive guidelines for future rational genetic design strategies.

Confined linear carbon chains as a route to bulk carbyne.

Strong chemical activity and extreme instability in ambient conditions characterize carbyne, an infinite sp(1) hybridized carbon chain. As a result, much less has been explored about carbyne as compared to other carbon allotropes such as fullerenes, nanotubes and graphene. Although end-capping groups can be used to stabilize carbon chains, length limitations are still a barrier for production, and even more so for application. We report a method for the bulk production of long acetylenic linear carbon chains protected by thin double-walled carbon nanotubes. The synthesis of very long arrangements is confirmed by a combination of transmission electron microscopy, X-ray diffraction and (near-field) resonance Raman spectroscopy. Our results establish a route for the bulk production of exceptionally long and stable chains composed of more than 6,000 carbon atoms, representing an elegant forerunner towards the final goal of carbyne's bulk production.

Effect of a Single Water Molecule on the Electronic Absorption by o- and p-Nitrophenolate: A Shift to the Red or to the Blue?

Many photoactive biomolecules are anions and exhibit ππ* optical transitions but with a degree of charge transfer (CT) character determined by the local environment. The phenolate moiety is a common structural motif among biochromophores and luminophores, and nitrophenolates are good model systems because the nitro substituent allows for CT-like transitions. Here we report gas-phase absorption spectra of o- and p-nitrophenolate·H2O complexes to decipher the effect of just one H2O and compare them with ab initio calculations of vertical excitation energies. The experimental band maximum is at 3.01 and 3.00 eV for ortho and para isomers, respectively, and is red-shifted by 0.10 and 0.13 eV relative to the bare ions, respectively. These shifts indicate that the transition has become more CT-like because of localization of negative charge on the phenolate oxygen, i.e., diminished delocalization of the negative excess charge. However, the transition bears less CT than that of m-nitrophenolate·H2O because this complex absorbs further to the red (2.56 eV). Our work emphasizes the importance of local perturbations: one water causes a larger shift than experienced in bulk for para isomer and almost the full shift for ortho isomer. Predicting microenvironmental effects in the boundary between CT and non-CT with high accuracy is nontrivial. However, in agreement with experiment, our calculations show a competition between the effects of electronic delocalization and electrostatic interaction with the solvent molecule. As a result, the excitation energy of ortho and para isomers is less sensitive to hydration than that of the meta isomer because donor and acceptor orbitals are only weakly coupled in the meta isomer.

Solvent-mediated folding of dicarboxylate dianions: aliphatic chain length dependence and origin of the IR intensity quenching.

We combine infrared photodissociation spectroscopy with quantum chemical calculations to characterize the hydration behavior of microsolvated dicarboxylate dianions, (CH2)m(COO(-))2·(H2O)n, as a function of the aliphatic chain length m. We find evidence for solvent-mediated folding transitions, signaled by the intensity quenching of the symmetric carboxylate stretching modes, for all three species studied (m = 2, 4, 8). The number of water molecules required to induce folding increases monotonically with the chain length and is n = 9-12, n = 13, and n = 18-19 for succinate (m = 2), adipate (m = 4), and sebacate (m = 8), respectively. In the special case of succinate, the structural transition is complicated by the possibility of bridging water molecules that bind to both carboxylates with merely minimal chain deformation. On the basis of vibrational calculations on a set of model systems, we identify the factors responsible for intensity quenching. In particular, we find that the effect of hydrogen bonds on the carboxylate stretching mode intensities is strongly orientation dependent.

On the effect of a single solvent molecule on the charge-transfer band of a donor-acceptor anion.

Many biochromophore anions located within protein pockets display charge-transfer (CT) transitions that are perturbed by the nearby environment, such as water or amino acid residues. These anions often contain the phenolate moiety as the electron donor and an acceptor group that couples to the donor via a π-conjugated system. Here we show using action spectroscopy that single molecules of water, methanol, and acetonitrile cause blue shifts in the electronic transition energy of the bare m-nitrophenolate anion by 0.22, 0.22, and 0.12 eV, respectively (uncertainty of 0.05 eV). These shifts are similar to CC2-predicted ones and are in accordance with the weaker binding to the phenolate end of the ion by acetonitrile in comparison with water and methanol. The nitro acceptor group is almost decoupled from the phenolate donor, and this ion therefore represents a good model for CT excitations of an anion. We found that the shift caused by one acetonitrile molecule is almost half of that experienced in bulk acetonitrile solution, clearly emphasizing the important role played by the microenvironment. In protic solvents, the shifts are larger because of hydrogen bonds to the phenolate oxygen. Finally, but not least, we provide experimental data that serve to benchmark calculations of excited states of ion-solvent complexes.

Substitution effects on the absorption spectra of nitrophenolate isomers.

Charge-transfer excitations highly depend on the electronic coupling between the donor and acceptor groups. Nitrophenolates are simple examples of charge-transfer systems where the degree of coupling differs between ortho, meta and para isomers. Here we report the absorption spectra of the isolated anions in vacuo to avoid the complications of solvent effects. Gas-phase action spectroscopy was done with two different setups, an electrostatic ion storage ring and an accelerator mass spectrometer. The results are interpreted on the basis of CC2 quantum chemical calculations. We identified absorption maxima at 393, 532, and 399 nm for the para, meta, and ortho isomer, respectively, with the charge-transfer transition into the lowest excited singlet state. In the meta isomer, this π-π* transition is strongly redshifted and its oscillator strength reduced, which is related to the pronounced charge-transfer character, as a consequence of the topology of the conjugated π-system. Each isomer's different charge distribution in the ground state leads to a very different solvent shift, which in acetonitrile is bathochromic for the para and ortho, but hypsochromic for the meta isomer.

Building a model of the blue cone pigment based on the wild type rhodopsin structure with QM/MM methods.

Understanding the mechanism of color tuning of the retinal chromophore by its host protein became one of the key issues in the research on rhodopsins. While early mutation studies addressed its genetic origin, recent studies advanced to investigate its structural origin, based on X-ray crystallographic structures. For the human cone pigments, no crystal structures have been produced, and homology models were employed to elucidate the origin of its blue-shifted absorption. In this theoretical study, we take a different route to establish a structural model for human blue. Starting from the well-resolved structure of bovine rhodopsin, we derive multiple mutant models by stepwise mutation and equilibration using molecular dynamics simulations in a hybrid quantum mechanics/molecular mechanics framework. Our 30fold mutant reproduces the experimental UV-vis absorption shift of 0.45 eV and provides new insights about both structural and genetic factors that affect the excitation energy. Electrostatic effects of individual amino acids and collaborative structural effects are analyzed using semiempirical (OM2/MRCI) and ab initio (SORCI) multireference approaches.

The protonation state of Glu181 in rhodopsin revisited: interpretation of experimental data on the basis of QM/MM calculations.

The structure and spectroscopy of rhodopsin have been intensely studied in the past decade both experimentally and theoretically; however, important issues still remain unresolved. Of central interest is the protonation state of Glu181, where controversial and contradictory experimental evidence has appeared. While FTIR measurements indicate this residue to be unprotonated, preresonance Raman and UV-vis spectra have been interpreted in favor of a protonated Glu181. Previous computational approaches were not able to resolve this issue, providing contradicting data as well. Here, we perform hybrid QM/MM calculations using DFT methods for the electronic ground state, MRCI methods for the electronically excited states, and a polarization model for the MM part in order to investigate this issue systematically. We constructed various active-site models for protonated as well as unprotonated Glu181, which were evaluated by computing NMR, IR, Raman, and UV-vis spectroscopic data. The resulting differences in the UV-vis and Raman spectra between protonated and unprotonated models are very subtle, which has two major consequences. First, the common interpretation of prior Raman and UV-vis experiments in favor of a neutral Glu181 appears questionable, as it is based on the assumption that a charge at the Glu181 location would have a sizable impact. Second, also theoretical results should be interpreted with care. Spectroscopic differences between the structural models must be related to modeling uncertainties and intrinsic methodological errors. Despite a detailed comparison of various rhodopsins and mutants and consistently favorite results with charged Glu181 models, we find merely weak evidence from UV-vis and Raman calculations. On the contrary, difference FTIR and NMR chemical shift measurements on Rh mutants are indicative of the protonation state of Glu181. Supported by our results, they provide strong and independent evidence for a charged Glu181.

Long-distance proton transfer with a break in the bacteriorhodopsin active site.

Bacteriorhodopsin is a proton-pumping membrane protein found in the plasma membrane of the archaeon Halobacterium salinarium. Light-induced isomerization of the retinal chromophore from all-trans to 13-cis leads to a sequence of five conformation-coupled proton transfer steps and the net transport of one proton from the cytoplasmic to the extracellular side of the membrane. The mechanism of the long-distance proton transfer from the primary acceptor Asp85 to the extracellular proton release group during the O --> bR is poorly understood. Experiments suggest that this long-distance transfer could involve a transient state [O] in which the proton resides on the intermediate carrier Asp212. To assess whether the transient protonation of Asp212 participates in the deprotonation of Asp85, we performed hybrid Quantum Mechanics/Molecular Mechanics proton transfer calculations using different protein structures and with different retinal geometries and active site water molecules. The structural models were assessed by computing UV-vis excitation energies and C=O vibrational frequencies. The results indicate that a transient [O] conformer with protonated Asp212 could indeed be sampled during the long-distance proton transfer to the proton release group. Our calculations suggest that, in the starting proton transfer state O, the retinal is strongly twisted and at least three water molecules are present in the active site.

Absorption spectra of 4-nitrophenolate ions measured in vacuo and in solution.

From blue to red: While four pi-conjugated nitrophenolates absorb within a relatively narrow region in solution, they cover the entire visible spectrum when isolated in vacuo [picture: see text]. The work combines gas- and solution-phase spectroscopy and provides the first benchmark of theoretical excitation energies for nitrophenolates.

Effect of polarization on the opsin shift in rhodopsins. 1. A combined QM/QM/MM model for bacteriorhodopsin and pharaonis sensory rhodopsin II.

The optical and IR-spectroscopic properties of the protonated Schiff base of retinal are highly sensitive to the electrostatic environment. This feature makes retinal a useful probe to study structural differences and changes in rhodopsins. It also raises an interest to theoretically predict the spectroscopic response to mutation and structural evolution. Computational models appropriate for this purpose usually combine sophisticated quantum mechanical (QM) methods with molecular mechanics (MM) force fields. In an effort to test and improve the accuracy of these QM/MM models, we consider in this article the effects of polarization and inter-residual charge transfer within the binding pocket of bacteriorhodopsin (bR) and pharaonis sensory rhodopsin II (psRII, also called pharaonis phoborhodopsin, ppR) on the excitation energy using an ab initio QM/QM/MM approach. The results will serve as reference for assessing empirical polarization models in a consecutive article.

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins.

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.

Computational photochemistry of retinal proteins.

High spectral tunability and quantum yield are the striking features of rhodopsin photochemistry. They rely on a strong and complex interaction of their chromophore, the protonated Schiff base of retinal, with its protein environment. In this article, we review the progress in the computational modeling of these systems, focusing on the optical properties and the excited state dynamics. While the earlier success of atomistic theoretical models was based on the breakthrough in X-ray crystallography and combined quantum mechanical molecular mechanical (QM/MM) methodology, recent advances point out the importance of high-level QM methods and the incorporation of effects that are neglected in conventional QM/MM or ONIOM schemes, like polarization and charge transfer.

Color tuning in rhodopsins: the mechanism for the spectral shift between bacteriorhodopsin and sensory rhodopsin II.

The mechanism of color tuning in the rhodopsin family of proteins has been studied by comparing the optical properties of the light-driven proton pump bacteriorhodopsin (bR) and the light detector sensory rhodopsin II (sRII). Despite a high structural similarity, the maximal absorption is blue-shifted from 568 nm in bR to 497 nm in sRII. The molecular mechanism of this shift is still a matter of debate, and its clarification sheds light onto the general mechanisms of color tuning in retinal proteins. The calculations employ a combined quantum mechanical/molecular mechanical (QM/MM) technique, using a DFT-based method for ground state properties and the semiempirical OM2/MRCI method and ab initio SORCI method for excited state calculations. The high efficiency of the methodology has allowed us to study a wide variety of aspects including dynamical effects. The absorption shift as well as various mutation experiments and vibrational properties have been successfully reproduced. Our results indicate that several sources contribute to the spectral shift between bR and sRII. The main factors are the counterion region at the extracellular side of retinal and the amino acid composition of the binding pocket. Our analysis allows a distinction and identification of the different effects in detail and leads to a clear picture of the mechanism of color tuning, which is in good agreement with available experimental data.