Semiempirical (SE) methods can be derived from either Hartree–Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

In spite of considerable interest, the active site of channelrhodopsin still lacks a detailed atomistic description, the understanding of which could strongly enhance the development of novel optogenetics tools. We present a computational study combining different state-of-the-art techniques, including hybrid quantum mechanics/molecular mechanics schemes and high-level quantum chemical methods, to properly describe the hydrogen-bonding pattern between the retinal chromophore and its counterions in channelrhodopsin-2 Wild-Type and C128T mutant. Especially, we show by extensive ground state dynamics that the active site, containing a glutamic acid (E123) and a water molecule, is highly dynamic, sampling three different hydrogen-bonding patterns. This results in a broad absorption spectrum that is representative of the different structural motifs found. A comparison with bacteriorhodopsin, characterized by a pentagonal hydrogen-bonded active site structure, elucidates their different absorption properties.

Different trends in the temperature dependence of the mobility can be observed in organic semiconductors, which constitutes a serious challenge for theoretical approaches. In this work, we apply an atomistic bottom-up simulation for the calculation of temperature-dependent mobilities of a broad selection of materials, ranging from single crystal to amorphous solid. We evaluate how well the method is able to distinguish temperature dependences of different materials and how the findings relate to experimental observations. The applied method is able to cover the full range of temperature dependencies from activated transport in amorphous materials to band-like transport in crystals. In well-characterized materials, we find good agreement with the experiment and a band-like temperature dependence. In less-ordered materials, we find discrepancies from the experiment that indicated that experimentally studied materials possess a higher degree of disorder than do the simulated defect-free morphologies.

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green’s function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor–acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor–acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

A linear scaling QM/MM model for studying charge transport in high-mobility molecular semiconductors is presented and applied to an anthracene single crystal and a hexabenzocoronene derivative in its liquid crystalline phase. The model includes both intra- and intermolecular electron–phonon couplings, long-range interactions with the environment, and corrections to the self-interaction error of density functional theory. By performing Ehrenfest simulations of the cationic system, hole mobilities are derived and compared to the experiment. A detailed picture of the charge carrier dynamics is given, and the performance of our method is discussed.

We present an extension to the recent 3OB parametrization of the Density Functional Tight Binding Model DFTB31,2 for biological and organic systems. Parameters for the halogens F, Cl, Br, and I have been developed for use in covalently bound systems and benchmarked on a test set of 106 molecules (the ‘OrgX’ set), using bonding distances, bonding angles, atomization energies, and vibrational frequencies to assess the performance of the parameters. Additional testing has been done with the X40 set of 40 supramolecular systems containing halogens,3 adding a simple correction for the halogen bonds that are strongly overbound in DFTB3. Furthermore, parameters for Ca, K, and Na as counterions in biological systems have been created. To benchmark geometries as well as ligand binding energies a test set ‘BioMe’ of 210 molecules has been created that cover coordination to various functional groups frequently occurring in biological systems. The new DFTB3/3OB parameter set outperforms DFT calculations with a double-ζ basis set in terms of energies and can reproduce DFT geometries, with some minor deviations in bond distances and angles due to the use of a minimal basis set.

Relaxation of the twisted-retinal photoproduct state triggers proton-coupled reaction cycle in retinal proteins. Given the crowded protein environments in which the retinal resides, a key open question is whether the retinal relaxation path is governed by the intrinsic torsional properties of the retinal or rather by the interactions of the retinal with protein and water groups. Here we address this question by performing systematic quantum mechanical/molecular mechanical molecular dynamics computations of retinal dynamics in bacteriorhodopsin at different temperatures, reaction path computations, and assessment of the vibrational fingerprints of the retinal molecule. The results demonstrate a complex dependence of the retinal dynamics and preferred geometry on temperature. As the temperature increases, the retinal dihedral angle samples values largely determined by its internal conformational energy. The protein environment shapes the energetics of retinal relaxation and provides hydrogen-bonding partners that stabilize the retinal geometry.

The photoreceptor protein cryptochrome is thought to host, upon light absorption, a radical pair that is sensitive to very weak magnetic fields, endowing migratory birds with a magnetic compass sense. The molecular mechanism that leads to formation of a stabilized, magnetic field sensitive radical pair has despite various theoretical and experimental efforts not been unambiguously identified yet. We challenge this unambiguity through a unique quantum mechanical molecular dynamics approach where we perform electron transfer dynamics simulations taking into account the motion of the protein upon the electron transfer. This approach allows us to follow the time evolution of the electron transfer in an unbiased fashion and to reveal the molecular driving force that ensures fast electron transfer in cryptochrome guaranteeing formation of a persistent radical pair suitable for magnetoreception. We argue that this unraveled molecular mechanism is a general principle inherent to all proteins of the cryptochrome/photolyase family and that cryptochromes are, therefore, tailored to potentially function as efficient chemical magnetoreceptors.

We report the parametrization of the approximate density functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of organic and biologically relevant molecules. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of molecules of biological relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these molecules; vibrational frequencies are also examined, although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, especially for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant reduction of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calculations, DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination number of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary solution; this suggests that the current DFTB3 methodology has limited transferability for complex phosphorus chemistry at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodology are needed for a reliable method that describes phosphorus chemistry without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calculations for studying phosphorus/sulfur chemistry in condensed phase systems, especially as a low-level method that drives the sampling in a dual-level QM/MM framework.

Semi-empirical (SE) methods are derived from Hartree–Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2–3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.

Parametrization of the approximative DFT method SCC-DFTB for halogen elements is presented. The new parameter set is intended to describe halogenated organic as well as inorganic molecules, and it is compatible with the established parametrization of SCC-DFTB for carbon, hydrogen, oxygen, and nitrogen. The performance of the parameter set is tested on a representative set of molecules and discussed.

DFTB3 is a recent extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB) and derived from a third order expansion of the density functional theory (DFT) total energy around a given reference density. Being applied in combination with the parametrization of its predecessor (MIO), DFTB3 improves for hydrogen binding energies, proton affinities, and hydrogen transfer barriers. In the present study, parameters especially designed for DFTB3 are presented, and its performance is evaluated for small organic molecules focusing on thermochemistry, geometries, and vibrational frequencies from our own and several databases from literature. The new parameters remove significant overbinding errors, reduce errors for geometries of noncovalent interactions, and improve the overall performance.

The first proton transfer in the bacteriorhodopsin photocycle takes place during the L → M transition. Structural details of the pre proton transfer L intermediate have been investigated using experiments and computations. Here, we assess L-state structural models by performing hybrid quantum mechanical/molecular mechanical molecular dynamics and excitation energy calculations. The computations suggest that a water-bridged twisted retinal structure gives the closest agreement with the experimental L/bR shift in the excitation energy.

Channelrhodopsin-2 is a light-gated ion channel, which has been studied intensively over the last decade. Vibrational spectroscopic experiments started to shed light on the structural changes, that occur during the photocycle, especially in the hydrogen-bonded network surrounding the protonated D156 and C128 – the DC gate. However, the interpretation of these experiments was only based on homology models. Since then, an X-ray structure and better computational models became available. In this article, we show that in combination with a recent reparametrization, the approximate DFT method, DFTB, is able to describe the effects of hydrogen bonding on the CO stretch vibration in carboxylic acids reliably and agrees well with full DFT results. We apply DFTB in a QM/MM framework to perform vibrational analysis of buried aspartic acids in bacteriorhodopsin and channelrhodopsin-2. Using this approach, we can simulate the FTIR spectral difference between D115 in the dark-adapted and K states of bacteriorhodopsin. The FTIR experiments on the DC gate in channelrhodopsin-2 are well described using an indirect model, where D156 and C128 are bridged via a water molecule.

In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed.

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.

In this work, we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical-potential equalization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for the NDDO type of methods by Giese and York, has been shown to significantly emend minimal basis methods with respect to the response properties and has been applied to SCC-DFTB recently. CPE allows this inherent limitation of minimal basis methods to be overcome by supplying an additional response density. The systematic underestimation is thereby corrected quantitatively without the need to extend the atomic orbital basis (i.e., without increasing the overall computational cost significantly). The dependency of polarizability as a function of the molecular charge state, especially, was significantly improved from the CPE extension of DFTB3. The empirical parameters introduced by the CPE approach were optimized for 172 organic molecules in order to match the results from density functional theory methods using large basis sets. However, the first-order derivatives of molecular polarizabilities (e.g., required to compute Raman activities) are not improved by the current CPE implementation (i.e., Raman spectra are not improved).

The present work outlines the implementation and performance of two cost efficient post-SCF extensions into the third-order SCC-DFTB code. The first one, the charge model 3 (CM3), corrects for errors in bond dipoles for an improved description of molecular charge distribution as compared to the standard Mulliken partitioning scheme. The second one focuses on the response of the charge density, that is, the electronic molecular polarizability, described inaccurately from SCC-DFTB due to the usage of a minimal atomic orbital basis. Here, a variational approach, based on scaled dipole integrals, was implemented, which clearly outperforms standard finite electric field approaches for polarizability calculations by approximately 1 order of magnitude. Both extensions in the present work rely on a set of empirical parameters, which were fitted against 112 organic molecules to match a reference data set from full density functional calculations with a large basis. As an achievement, notably improved electronic properties, that is, molecular dipole moments and polarizabilities, result from SCC-DFTB calculations at negligible additional computational cost. Furthermore, the accuracy of infrared and Raman intensities was tested as first-order derivatives of the new dipoles and polarizabilities as a function of normal mode vibrations. As a result, the current implementations cannot contribute to an improved prediction of relative intensity pattern from SCC-DFTB as compared to ab initio reference data.

Identifying the group that acts as the proton storage/loading site is a challenging but important problem for understanding the mechanism of proton pumping in biomolecular proton pumps, such as bacteriorhodopsin (bR) and cytochrome c oxidase. Recent experimental studies of bR propelled the idea that the proton storage/release group (PRG) in bR is not an amino acid but a water cluster embedded in the protein. We argue that this idea is at odds with our knowledge of protein electrostatics, since invoking the water cluster as the PRG would require the protein to raise the pKa of a hydronium by almost 11 pKa units, which is difficult considering known cases of pKa shifts in proteins. Our recent quantum mechanics/molecular mechanics (QM/MM) simulations suggested an alternative “intermolecular proton bond” model in which the stored proton is shared between two conserved Glu residues (194 and 204). Here we show that this model leads to microscopic pKa values consistent with available experimental data and the functional requirement of a PRG. Extensive QM/MM simulations also show that, independent of a number of technical issues, such as the influence of QM region size, starting X-ray structure, and nuclear quantum effects, the “intermolecular proton bond” model is qualitatively consistent with available spectroscopic data. Potential of mean force calculations show explicitly that the stored proton strongly prefers the pair of Glu residues over the water cluster. The results and analyses help highlight the importance of considering protein electrostatics and provide arguments for why the “intermolecular proton bond” model is likely applicable to the PRG in biomolecular proton pumps in general.

The self-consistent-charge density-functional tight-binding method (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy around a reference density. In the present study, we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between atomic partial charges and, second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodology called DFTB3, which substantially improves the description of charged systems containing elements C, H, N, O, and P, especially regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomolecular systems. Remaining challenges and possible solutions are also briefly discussed.

Experimental Fourier-transform infrared spectra and DFT calculated infrared spectra are compared to investigate the effect of adsorbed nitrogen on the OH-stretch band complex of water clusters. Using a collisional cooling experiment, pure as well as partially and completely N2-covered water clusters consisting of 20−200 water molecules have been generated in thermal equilibrium in the aerosol phase within the temperature range of 5−80 K. Computational IR-spectra simulations have been performed for discrete pure and N2-covered water clusters including 10, 15, 20, and 30 water molecules. The adsorbed N2 molecules especially affect the three-coordinated water molecules at the cluster surface which could be observed as a blue shift of the companion O−H band at 2900 cm−1 and a red shift of the dangling O−H band at 3700 cm−1 by about 20 cm−1 in both cases. The most striking effect of the N2 adsorbate is an intensity increase of the dangling O−H band by a factor of 3−5. Furthermore, the onset temperature of nitrogen adsorption at the water cluster surface was experimentally found to be roughly 30 K for cluster sizes of about 100 water molecules. Experimental and computational results are in good agreement. The presented results are based on and support the work of V. Buch, J. P. Devlin, and co-workers (e.g., J. Phys. Chem. B, 1997; J. Phys. Chem. A, 2003; Int. Rev. Phys. Chem., 2004).

In this report, we study the photoactivation process in Escherichia coli DNA photolyase, involving long-range electron transport along a conserved chain of Trp residues between the protein surface and the flavin adenine dinucleotide (FAD) cofactor. Fully coupled nonadiabatic (Ehrenfest) quantum mechanics/molecular mechanics (QM/MM) simulations allow us to follow the time evolution of charge distributions over the natural time scale of multiple charge transfer events and conduct rigorous statistical analysis. Charge transfer rates in excellent agreement with experimental data are obtained without the need for any system-specific parametrization. The simulations are shown to provide a more detailed picture of electron transfer than a classical analysis of Marcus parameters. The protein and solvent both strongly influence the localization and transport properties of a positive charge, but the directionality of the process is mainly caused by solvent polarization. The time scales of charge movement, delocalization, protein relaxation and solvent reorganization overlap and lead to nonequilibrium reaction conditions. All these contributions are explicitly considered and fully resolved in the model used and provide an intricate picture of multistep biochemical electron transfer in a flexible, heterogeneous environment.

We examined the shift of absorption maxima between the chlamydomonas-type channelrhodopsins (ChRs) and bacteriorhodopsin (BR). Starting from the BR X-ray structure, we modeled the color tuning in the binding pockets of the ChRs by mutating up to 28 amino acids in the vicinity of the chromophore. By applying the efficient self-consistent charge density functional tight binding (SCC-DFTB) method in a quantum mechanical/molecular mechanical (QM/MM) framework, including explicit polarization and calculating excitation energies with the semiempirical OM2/MRCI method and the ab initio SORCI method, we have shown that multiple mutations in the binding pocket of BR causes large hypsochromic shifts that are of the same order as the experimentally observed shifts of the absorption maxima between BR and the ChRs. This study further demonstrates that mutations in the proximity of the Schiff base and complex counterion lead to a stronger but more flexible interaction with the retinal, which could serve as a possible explanation for the spectral patterns found in the ChRs.

Proton-transfer reactions in the bacteriorhodopsin light-driven proton pump are coupled with structural rearrangements of protein amino acids and internal water molecules. It is generally thought that the first proton-transfer step from retinal Schiff base to the nearby Asp85 is coupled with movement of the Arg82 side chain away from Asp85 and toward the extracellular proton release group. This movement of Arg82 likely triggers the release of the proton from the proton release group to the extracellular bulk. The exact timing of the movement of Arg82 and how this movement is coupled with proton transfer are still not understood in molecular detail. Here, we address these questions by computing the free energy for the movement of the Arg82 side chain. The calculations indicate that protonation of Asp85 leads to a fast reorientation of the Arg82 side chain toward the extracellular proton release group.

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.

We present a coarse-grained tight-binding method based on density functional theory (DFT) for the simulation of charge transfer in complex materials. The charge-transfer parameters are computed using a fragment-orbital approach combined with the approximative DFT method self-consistent charge density functional tight binding (SCC-DFTB), which allows to follow the dynamics of excess charge along nanosecond MD trajectories, still accounting for the important impact of structural fluctuations and solvent effects. Since DFT suffers from the self-interaction error, which would lead to a delocalization of the hole charge over the entire system, we study the effect of an empirical self-interaction correction in detail. The wave function of the excess charge is propagated within the framework of time-dependent DFT, where the electron (hole) and the atomic system are propagated simultaneously according to the derived coupled equations of motion. In the case of DNA, the solvent polarization effects are a dominant factor affecting the hole transport. The hole charge polarizes the surrounding water, which in turn supports a localization of the hole charge—a water polaron is formed, extended dynamically over several nucleobases. As this polarization of water accompanies the migrating hole, the motion of hole is significantly slowed down due to the solvent reorganization energy involved. The estimated hopping rate between neighboring adenines in poly(A)-DNA is in the order of 100 ns−1, and our simulations clearly show that the charge transfer occurs in a nonadiabatic fashion, due to the small average electronic coupling of around 0.06 eV.

Channelrhodopsins (ChRs) are light-gated cation channels that mediate ion transport across membranes in microalgae (vectorial catalysis). ChRs gain increasing attention as useful tools for the analysis of neural networks in tissues and living animals (optogenetics). In fact, various mutagenesis approaches have realized practical applications with high reliability by enhancement of the expression level, channel kinetics control, and color tuning. Furthermore, the recently published x-ray structure has provided valuable information for further atomistic studies and engineering ChRs for a wider application. The present study is a computational attempt to describe the functional mechanism at the atomic level based on the x-ray structure. We present several structural characteristics that are highly involved in ion channel gating and ion transport, including (1) water distribution, (2) cation binding sites, (3) intrahelical hydrogen bond, (4) DC gate, and (5) active site.Download high-res image (200KB)Download full-size imageHighlights► The x-ray structure of ChR, as well as its application in optogenetics, was recently released. ► Based on the x-ray structure, the structure of ChR2 is modeled and simulated. ► Various structural properties involved in the channel function are revealed. ► The first atomic level understanding promotes the engineering of applications.

The first proton transfer in the bacteriorhodopsin photocycle takes place during the L → M transition. Structural details of the pre proton transfer L intermediate have been investigated using experiments and computations. Here, we assess L-state structural models by performing hybrid quantum mechanical/molecular mechanical molecular dynamics and excitation energy calculations. The computations suggest that a water-bridged twisted retinal structure gives the closest agreement with the experimental L/bR shift in the excitation energy.

Channelrhodopsin-2 is a light-gated ion channel, which has been studied intensively over the last decade. Vibrational spectroscopic experiments started to shed light on the structural changes, that occur during the photocycle, especially in the hydrogen-bonded network surrounding the protonated D156 and C128 – the DC gate. However, the interpretation of these experiments was only based on homology models. Since then, an X-ray structure and better computational models became available. In this article, we show that in combination with a recent reparametrization, the approximate DFT method, DFTB, is able to describe the effects of hydrogen bonding on the CO stretch vibration in carboxylic acids reliably and agrees well with full DFT results. We apply DFTB in a QM/MM framework to perform vibrational analysis of buried aspartic acids in bacteriorhodopsin and channelrhodopsin-2. Using this approach, we can simulate the FTIR spectral difference between D115 in the dark-adapted and K states of bacteriorhodopsin. The FTIR experiments on the DC gate in channelrhodopsin-2 are well described using an indirect model, where D156 and C128 are bridged via a water molecule.

In this work, a fragment-orbital density functional theory-based method is combined with two different non-adiabatic schemes for the propagation of the electronic degrees of freedom. This allows us to perform unbiased simulations of electron transfer processes in complex media, and the computational scheme is applied to the transfer of a hole in solvated DNA. It turns out that the mean-field approach, where the wave function of the hole is driven into a superposition of adiabatic states, leads to over-delocalization of the hole charge. This problem is avoided using a surface hopping scheme, resulting in a smaller rate of hole transfer. The method is highly efficient due to the on-the-fly computation of the coarse-grained DFT Hamiltonian for the nucleobases, which is coupled to the environment using a QM/MM approach. The computational efficiency and partial parallel character of the methodology make it possible to simulate electron transfer in systems of relevant biochemical size on a nanosecond time scale. Since standard non-polarizable force fields are applied in the molecular-mechanics part of the calculation, a simple scaling scheme was introduced into the electrostatic potential in order to simulate the effect of electronic polarization. It is shown that electronic polarization has an important effect on the features of charge transfer. The methodology is applied to two kinds of DNA sequences, illustrating the features of transfer along a flat energy landscape as well as over an energy barrier. The performance and relative merit of the mean-field scheme and the surface hopping for this application are discussed.

Semi-empirical (SE) methods are derived from Hartree–Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2–3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.