Application of Box and Voronoi CAPs for Metastable Electronic States in Molecular Clusters.

The complex absorbing potential (CAP) approach offers a practical tool for characterization of energies and lifetimes of metastable electronic states, such as temporary anions and core ionized states. Here, we present an implementation of the smooth Voronoi CAP combined with the equation-of-motion coupled cluster with single and double substitutions method for metastable states. The performances of the smooth Voronoi CAP and box CAP are compared for different classes of systems: resonances in isolated molecules and localized and delocalized resonances in molecular clusters. The benchmark calculations show that the Voronoi CAP is generally more robust when applied to molecular clusters, but box CAPs are equally reliable for localized resonances or in the cases when the resonance does not exhibit significant electron density delocalization into the intramolecular region. As such, the choice of the CAP shape and onset should be guided by the character of the metastable states.

Projected CAP-EOM-CCSD method for electronic resonances.

The complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) method is routinely used to investigate metastable electronic states in small molecules. However, the requirement of evaluating eigenvalue trajectories presents a barrier to larger simulations, as each point corresponding to a different value of the CAP strength parameter requires a unique eigenvalue calculation. Here, we present a new implementation of CAP-EOM-CCSD that uses a subspace projection scheme to evaluate resonance positions and widths at the overall cost of a single electronic structure calculation. We analyze the performance of the projected CAP-EOM-CC scheme against the conventional scheme, where the CAP is incorporated starting from the Hartree-Fock level, for various small and medium sized molecules, and investigate its sensitivity to various parameters. Finally, we report resonance parameters for a set of molecules commonly used for benchmarking CAP-based methods, and we report estimates of resonance energies and widths for 1- and 2-cyanonaphtalene, molecules that were recently detected in the interstellar medium.

The redox potential of a heme cofactor in Nitrosomonas europaea cytochrome c peroxidase: a polarizable QM/MM study.

Redox reactions are crucial to biological processes that protect organisms against oxidative stress. Metalloenzymes, such as peroxidases which reduce excess reactive oxygen species into water, play a key role in detoxification mechanisms. Here we present the results of a polarizable QM/MM study of the reduction potential of the electron transfer heme in the cytochrome c peroxidase of Nitrosomonas europaea. We have found that environment polarization does not substantially affect the computed value of the redox potential. Particular attention has been given to analyzing the role of electrostatic interactions within the protein environment and the solvent on tuning the redox potential of the heme co-factor. We have found that the electrostatic interactions predominantly explain the fluctuations of the vertical ionization/attachment energies of the heme for the sampled configurations, and that the long range electrostatic interactions (up to 40 Å) contribute substantially to the absolute values of the vertical energy gaps.

Effective Fragment Potentials for Flexible Molecules: Transferability of Parameters and Amino Acid Database.

An accurate but efficient description of noncovalent interactions is a key to predictive modeling of biological and materials systems. The effective fragment potential (EFP) is an ab initio-based force field that provides a physically meaningful decomposition of noncovalent interactions of a molecular system into Coulomb, polarization, dispersion, and exchange-repulsion components. An EFP simulation protocol consists of two steps, preparing parameters for molecular fragments by a series of ab initio calculations on each individual fragment, and calculation of interaction energy and properties of a total molecular system based on the prepared parameters. As the fragment parameters (distributed multipoles, polarizabilities, localized wave function, etc.) depend on a fragment geometry, straightforward application of the EFP method requires recomputing parameters of each fragment if its geometry changes, for example, during thermal fluctuations of a molecular system. Thus, recomputing fragment parameters can easily become both computational and human bottlenecks and lead to a loss of efficiency of a simulation protocol. An alternative approach, in which fragment parameters are adjusted to different fragment geometries, referred to as "flexible EFP", is explored here. The parameter adjustment is based on translations and rotations of local coordinate frames associated with fragment atoms. The protocol is validated on extensive benchmark of amino acid dimers extracted from molecular dynamics snapshots of a cryptochrome protein. A parameter database for standard amino acids is developed to automate flexible EFP simulations in proteins. To demonstrate applicability of flexible EFP in large-scale protein simulations, binding energies and vertical electron ionization and electron attachment energies of a lumiflavin chromophore of the cryptochrome protein are computed. The results obtained with flexible EFP are in a close agreement with the standard EFP procedure but provide a significant reduction in computational cost.

eMap: A Web Application for Identifying and Visualizing Electron or Hole Hopping Pathways in Proteins.

eMap is a web-based platform for identifying and visualizing electron or hole transfer pathways in proteins based on their crystal structures. The underlying model can be viewed as a coarse-grained version of the Pathways model, where each tunneling step between hopping sites represented by electron transfer active (ETA) moieties is described with one effective decay parameter that describes protein-mediated tunneling. ETA moieties include aromatic amino acid residue side chains and aromatic fragments of cofactors that are automatically detected, and, in addition, electron/hole residing sites that can be specified by the users. The software searches for the shortest paths connecting the user-specified electron/hole source to either all surface-exposed ETA residues or the user-specified target. The identified pathways are ranked according to their effective length. The pathways are visualized in 2D as a graph, in which each node represents an ETA site, and in 3D using available protein visualization tools. Here, we present the capability and user interface of eMap 1.0, which is available at https://emap.bu.edu .

Polarizable embedding for simulating redox potentials of biomolecules.

Redox reactions play a key role in various biological processes, including photosynthesis and respiration. Quantitative and predictive computational characterization of redox events is therefore highly desirable for enriching our knowledge on mechanistic features of biological redox-active macromolecules. Here, we present a computational protocol exploiting polarizable embedding hybrid quantum-classical approach and resulting in accurate estimates of redox potentials of biological macromolecules. A special attention is paid to fundamental aspects of the theoretical description such as the effects of environment polarization and of the long-range electrostatic interactions on the computed energetic parameters. Environment (protein and the solvent) polarization is shown to be crucial for accurate estimates of the redox potential: hybrid quantum-classical results with and without account for environment polarization differ by 1.4 V. Long-range electrostatic interactions are shown to contribute significantly to the computed redox potential value even at the distances far beyond the protein outer surface. The approach is tested on simulating reduction potential of cryptochrome 1 protein from Arabidopsis thaliana. The theoretical estimate (0.07 V) of the midpoint reduction potential is in good agreement with available experimental data (-0.15 V).

Dipole-Supported Electronic Resonances Mediate Electron-Induced Amide Bond Cleavage.

Dissociative electron attachment (DEA) plays a key role in radiation damage of biomolecules under high-energy radiation conditions. The initial step in DEA is often rationalized in terms of resonant electron capture into one of the metastable valence states of a molecule followed by its fragmentation. Our combined theoretical and experimental investigations indicate that the manifold of states responsible for electron capture in the DEA process can be dominated by core-excited (shake-up) dipole-supported resonances. Specifically, we present the results of experimental and computational studies of the gas-phase DEA to three prototypical peptide molecules, formamide, N-methylformamide (NMF), and N,N-dimethyl-formamide (DMF). In contrast to the case of electron capture by positively charged peptides in which amide bond rupture is rare compared to N─C_{α} bond cleavage, fragmentation of the amide bond was observed in each of these three molecules. The ion yield curves for ions resulting from this amide bond cleavage, such as NH_{2}^{-} for formamide, NHCH_{3}^{-} for NMF, and N(CH_{3})_{2}^{-} for DMF, showed a double-peak structure in the region between 5 and 8 eV. The peaks are assigned to Feshbach resonances including core-excited dipole-supported resonances populated upon electron attachment based on high-level electronic structure calculations. Moreover, the lower energy peak is attributed to formation of the core-excited resonance that correlates with the triplet state of the neutral molecule. The latter process highlights the role of optically spin-forbidden transitions promoted by electron impact in the DEA process.

First-Principles Models for Biological Light-Harvesting: Phycobiliprotein Complexes from Cryptophyte Algae.

There have been numerous efforts, both experimental and theoretical, that have attempted to parametrize model Hamiltonians to describe excited state energy transfer in photosynthetic light harvesting systems. The Frenkel exciton model, with its set of electronically coupled two level chromophores that are each linearly coupled to dissipative baths of harmonic oscillators, has become the workhorse of this field. The challenges to parametrizing such Hamiltonians have been their uniqueness, and physical interpretation. Here we present a computational approach that uses accurate first-principles electronic structure methods to compute unique model parameters for a collection of local minima that are sampled with molecular dynamics and QM geometry optimization enabling the construction of an ensemble of local models that captures fluctuations as these systems move between local basins of inherent structure. The accuracy, robustness, and reliability of the approach is demonstrated in an application to the phycobiliprotein light harvesting complexes from cryptophyte algae. Our computed Hamiltonian ensemble provides a first-principles description of inhomogeneous broadening processes, and a standard approximate non-Markovian reduced density matrix dynamics description is used to estimate lifetime broadening contributions to the spectral line shape arising from electronic-vibrational coupling. Despite the overbroadening arising from this approximate line shape theory, we demonstrate that our model Hamiltonian ensemble approach is able to provide a reliable fully first-principles method for computation of spectra and can distinguish the influence of different chromophore protonation states in experimental results. A key feature in the dynamics of these systems is the excitation of intrachromophore vibrations upon electronic excitation and energy transfer. We demonstrate that the Hamiltonian ensemble approach provides a reliable first-principles description of these contributions that have been detailed in recent broad-band pump-probe and two-dimensional electronic spectroscopy experiments.

Extending Quantum Chemistry of Bound States to Electronic Resonances.

Electronic resonances are metastable states with finite lifetime embedded in the ionization or detachment continuum. They are ubiquitous in chemistry, physics, and biology. Resonances play a central role in processes as diverse as DNA radiolysis, plasmonic catalysis, and attosecond spectroscopy. This review describes novel equation-of-motion coupled-cluster (EOM-CC) methods designed to treat resonances and bound states on an equal footing. Built on complex-variable techniques such as complex scaling and complex absorbing potentials that allow resonances to be associated with a single eigenstate of the molecular Hamiltonian rather than several continuum eigenstates, these methods extend electronic-structure tools developed for bound states to electronic resonances. Selected examples emphasize the formal advantages as well as the numerical accuracy of EOM-CC in the treatment of electronic resonances. Connections to experimental observables such as spectra and cross sections, as well as practical aspects of implementing complex-valued approaches, are also discussed.

Photoinduced Chemistry in Fluorescent Proteins: Curse or Blessing?

Photoinduced reactions play an important role in the photocycle of fluorescent proteins from the green fluorescent protein (GFP) family. Among such processes are photoisomerization, photooxidation/photoreduction, breaking and making of covalent bonds, and excited-state proton transfer (ESPT). Many of these transformations are initiated by electron transfer (ET). The quantum yields of these processes vary significantly, from nearly 1 for ESPT to 10-4-10-6 for ET. Importantly, even when quantum yields are relatively small, at the conditions of repeated illumination the overall effect is significant. Depending on the task at hand, fluorescent protein photochemistry is regarded either as an asset facilitating new applications or as a nuisance leading to the loss of optical output. The phenomena arising due to phototransformations include (i) large Stokes shifts, (ii) photoconversions, photoactivation, and photoswitching, (iii) phototoxicity, (iv) blinking, (v) permanent bleaching, and (vi) formation of long-lived intermediates. The focus of this review is on the most recent experimental and theoretical work on photoinduced transformations in fluorescent proteins. We also provide an overview of the photophysics of fluorescent proteins, highlighting the interplay between photochemistry and other channels (fluorescence, radiationless relaxation, and intersystem crossing). The similarities and differences with photochemical processes in other biological systems and in dyes are also discussed.

Free Energies of Redox Half-Reactions from First-Principles Calculations.

Quantitative prediction of the energetics of redox half-reactions is still a challenge for modern computational chemistry. Here, we propose a simple scheme for reliable calculations of vertical ionization and attachment energies, as well as of redox potentials of solvated molecules. The approach exploits linear response approximation in the context of explicit solvent simulations with spherical boundary conditions. It is shown that both vertical ionization energies and vertical electron affinities, and, consequently redox potentials, exhibit linear dependence on the inverse radius of the solvation sphere. The explanation of the linear dependence is provided, and an extrapolation scheme is suggested. The proposed approach accounts for the specific short-range interactions within hybrid DFT and effective fragment potential approach as well as for the asymptotic system-size effects. The computed vertical ionization energies and redox potentials are in excellent agreement with the experimental values.

Turning On and Off Photoinduced Electron Transfer in Fluorescent Proteins by π-Stacking, Halide Binding, and Tyr145 Mutations.

Photoinduced electron transfer in fluorescent proteins from the GFP family can be regarded either as an asset facilitating new applications or as a nuisance leading to the loss of optical output. Photooxidation commonly results in green-to-red photoconversion called oxidative redding. We discovered that yellow FPs do not undergo redding; however, the redding is restored upon halide binding. Calculations of the energetics of one-electron oxidation and possible electron transfer (ET) pathways suggested that excited-state ET proceeds through a hopping mechanism via Tyr145. In YFPs, the π-stacking of the chromophore with Tyr203 reduces its electron-donating ability, which can be restored by halide binding. Point mutations confirmed that Tyr145 is a key residue controlling ET. Substitution of Tyr145 by less-efficient electron acceptors resulted in highly photostable mutants. This strategy (i.e., calculation and disruption of ET pathways by mutations) may represent a new approach toward enhancing photostability of FPs.

Electronic structure of the para-benzoquinone radical anion revisited.

Photoinduced dynamics of the para-benzoquinone anion features a subtle interplay between autodetachment and non-adiabatic transitions involving a dense manifold of resonances. We report the results of a multistate multireference perturbation theory study of the electronic structure of the para-benzoquinone anion in the ground, several low-lying excited electronic states, and in the lowest electron-detached state (the ground state of the neutral molecule). The electronic structure calculations revealed non-planar equilibrium geometry of the (2)Au excited state of the anion, but the effects of non-planarity on the shape of the absorption spectrum are found to be minor. Despite the large differences in the vertical excitation energies for the two lowest bright excited states, (2)Au (2.55 eV) and (2)B3u (2.93 eV), the simulated absorption spectra significantly overlap for the photon energies below 2.7 eV. Relevant minimum energy crossing points have been located using the CASSCF method. Excited-state deactivation channels are discussed in the context of accurate energetics and recent spectroscopic studies of the para-benzoquinone anion.

First-Principles Calculations of the Energy and Width of the (2)A(u) Shape Resonance in p-Benzoquinone: A Gateway State for Electron Transfer.

Quinones are versatile biological electron acceptors and mobile electron carriers in redox processes. We present the first ab initio calculations of the width of the (2)A(u) shape resonance in the para-benzoquinone anion, the simplest member of the quinone family. This resonance state located at 2.5 eV above the ground state of the anion is believed to be a gateway state for electron attachment in redox processes involving quinones. We employ the equation-of-motion coupled-cluster method for electron affinity augmented by a complex-absorbing potential (CAP-EOM-EA-CCSD) to calculate the resonance position and width. The calculated width, 0.013 eV, is in excellent agreement with the width of the resonant peak in the photodetachment spectrum, thus supporting the assignment of the band to resonance excitation to the autodetaching (2)A(u) state. The methodological aspects of CAP-EOM-EA-CCSD calculations of resonances positions and widths in medium-sized molecules, such as basis set and CAP box size effects, are also discussed.

Barrierless proton transfer across weak CH⋯O hydrogen bonds in dimethyl ether dimer.

We present a combined computational and threshold photoelectron photoion coincidence study of two isotopologues of dimethyl ether, (DME - h6)n and (DME - d6)n n = 1 and 2, in the 9-14 eV photon energy range. Multiple isomers of neutral dimethyl ether dimer were considered, all of which may be present, and exhibited varying C-H⋯O interactions. Results from electronic structure calculations predict that all of them undergo barrierless proton transfer upon photoionization to the ground electronic state of the cation. In fact, all neutral isomers were found to relax to the same radical cation structure. The lowest energy dissociative photoionization channel of the dimer leads to CH3OHCH3 (+) by the loss of CH2OCH3 with a 0 K appearance energy of 9.71 ± 0.03 eV and 9.73 ± 0.03 eV for (DME - h6)2 and deuterated (DME - d6)2, respectively. The ground state threshold photoelectron spectrum band of the dimethyl ether dimer is broad and exhibits no vibrational structure. Dimerization results in a 350 meV decrease of the valence band appearance energy, a 140 meV decrease of the band maximum, thus an almost twofold increase in the ground state band width, compared with DME - d6 monomer.

Role of zwitterions in kindling fluorescent protein photochemistry.

Kindling fluorescent protein (KFP), one of the chronologically first members of photoswitchable colored proteins from the green fluorescent protein (GFP) family, increasingly attracts efforts from experimental and theoretical sides. Ambiguous conclusions in solving puzzles of photochemistry of KFP and of its parent natural protein asFP595 are partially explained by lack of reliable theoretical data on chromophore properties in the electronically excited state. We report the results of state-of-the-art quantum chemistry calculations of the structure and energy of the KFP chromophore, 2-acetyl-,4-(p-hydroxybenzylidene)-1-methyl-5-imidazolone (AHBMI), both in the ground and excited states. Ground state equilibrium structures of anionic and zwitterionic protonation states of AHBMI were computed by the conventional MP2 method while excited state structures were characterized by the extended multireference perturbation theory method XMCQDPT2 including optimization of geometry parameters at this level. In particular, the computational results demonstrate that the basicity of the N2 nitrogen atom of the imidazolinone ring should noticeably increase upon electronic excitation, thus affecting excited state proton transfer events in proteins. The results of these simulations as well as of quantum mechanical-molecular mechanical (QM/MM) calculations for model protein systems evidence that KFP conformations with the zwitterionic chromophore are hardly expected to occur in the ground state, but may be populated upon excitation.

Complex absorbing potentials within EOM-CC family of methods: theory, implementation, and benchmarks.

A production-level implementation of equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) for electron attachment and excitation energies augmented by a complex absorbing potential (CAP) is presented. The new method enables the treatment of metastable states within the EOM-CC formalism in a similar manner as bound states. The numeric performance of the method and the sensitivity of resonance positions and lifetimes to the CAP parameters and the choice of one-electron basis set are investigated. A protocol for studying molecular shape resonances based on the use of standard basis sets and a universal criterion for choosing the CAP parameters are presented. Our results for a variety of π(*) shape resonances of small to medium-size molecules demonstrate that CAP-augmented EOM-CCSD is competitive relative to other theoretical approaches for the treatment of resonances and is often able to reproduce experimental results.

Chromophore photoreduction in red fluorescent proteins is responsible for bleaching and phototoxicity.

Red fluorescent proteins (RFPs) are indispensable tools for deep-tissue imaging, fluorescence resonance energy transfer applications, and super-resolution microscopy. Using time-resolved optical spectroscopy this study investigated photoinduced dynamics of three RFPs, KillerRed, mRFP, and DsRed. In all three RFPs, a new transient absorption intermediate was observed, which decays on a microsecond-millisecond time scale. This intermediate is characterized by red-shifted absorption at 1.68-1.72 eV (λmax = 720-740 nm). On the basis of electronic structure calculations, experimental evidence, and published literature, the chemical nature of the intermediate is assigned to an unusual open-shell dianionic chromophore (dianion-radical) formed via photoreduction. A doubly charged state that is not stable in the isolated (gas phase) chromophore is stabilized by the electrostatic field of the protein. Mechanistic implications for photobleaching, blinking, and phototoxicity are discussed.