Complex potential energy surfaces with projected CAP technique: Vibrational excitation of N2.

The projected complex absorbing potential (CAP) technique is one of the methods that allow one to extend the bound state methods for computing resonances' energies and widths. Here, we explore the accuracy of the potential energy curves generated with different electronic structure theory methods in combination with the projected CAP technique by considering resonant vibrational excitation (RVE) of N2 by electron impact as a model process. We report RVE cross sections computed using the boomerang model with potential energy curves obtained with CAP-based extended multistate complete active space perturbation theory (XMS-CASPT2) and equation of motion coupled-cluster method for electron attachment with single and double substitution (EOM-EA-CCSD) methods. We also compare potential energy curves computed with several electronic structure methods, including XMS-CASPT2, EOM-EA-CCSD, multireference configuration interaction with singles (MR-CIS) and singles and doubles (MR-CISD). A good agreement is observed between the experiment and simulated RVE cross sections obtained with the potential energy curves generated with XMS-CASPT2 and EOM-EA-CCSD methods, thus highlighting the potential of the projected CAP technique combined with accurate electronic structure methods for dynamical simulations of the processes that proceed through metastable electronic states.

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.

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.

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.

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).

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.

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.

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.

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.

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.

Quantum chemistry behind bioimaging: insights from ab initio studies of fluorescent proteins and their chromophores.

The unique properties of green fluorescent protein (GFP) have been harnessed in a variety of bioimaging techniques, revolutionizing many areas of the life sciences. Molecular-level understanding of the underlying photophysics provides an advantage in the design of new fluorescent proteins (FPs) with improved properties; however, because of its complexity, many aspects of the GFP photocycle remain unknown. In this Account, we discuss computational studies of FPs and their chromophores that provide qualitative insights into mechanistic details of their photocycle and the structural basis for their optical properties. In a reductionist framework, studies of well-defined model systems (such as isolated chromophores) help to understand their intrinsic properties, while calculations including protein matrix and/or solvent demonstrate, on the atomic level, how these properties are modulated by the environment. An interesting feature of several anionic FP chromophores in the gas phase is their low electron detachment energy. For example, the bright excited ππ* state of the model GFP chromophore (2.6 eV) lies above the electron detachment continuum (2.5 eV). Thus, the excited state is metastable with respect to electron detachment. This autoionizing character needs to be taken into account in interpreting gas-phase measurements and is very difficult to describe computationally. Solvation (and even microsolvation by a single water molecule) stabilizes the anionic states enough such that the resonance excited state becomes bound. However, even in stabilizing environments (such as protein or solution), the anionic chromophores have relatively low oxidation potentials and can act as light-induced electron donors. Protein appears to affect excitation energies very little (<0.1 eV), but alters ionization or electron detachment energies by several electron volts. Solvents (especially polar ones) have a pronounced effect on the chromophore's electronic states; for example, the absorption wavelength changes considerably, the ground-state barrier for cis-trans isomerization is reduced, and fluorescence quantum yield drops dramatically. Calculations reveal that these effects can be explained in terms of electrostatic interactions and polarization, as well as specific interactions such as hydrogen bonding. The availability of efficient computer implementations of predictive electronic structure methods is essential. Important challenges include developing faster codes (to enable better equilibrium sampling and excited-state dynamics modeling), creating algorithms for properties calculations (such as nonlinear optical properties), extending standard excited-state methods to autoionizing (resonance) states, and developing accurate QM/MM schemes. The results of sophisticated first-principle calculations can be interpreted in terms of simpler, qualitative molecular orbital models to explain general trends. In particular, an essential feature of the anionic GFP chromophore is an almost perfect resonance (mesomeric) interaction between two Lewis structures, giving rise to charge delocalization, bond-order scrambling, and, most importantly, allylic frontier molecular orbitals spanning the methine bridge. We demonstrate that a three-center Hückel-like model provides a useful framework for understanding properties of FPs. It can explain changes in absorption wavelength upon protonation or other structural modifications of the chromophore, the magnitude of transition dipole moment, barriers to isomerization, and even non-Condon effects in one- and two-photon absorption.

On the photodetachment from the green fluorescent protein chromophore.

Motivated by the discrepancies in recent experimental and theoretical studies of photodetachment from isolated model chromophores of the green fluorescent protein (GFP), this study reports calculations of the electron detachment energies and photoelectron spectra of the phenolate and deprotonated p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) anions. The spectra were computed using double-harmonic parallel normal mode approximation. High-level coupled-cluster methods as well as density functional theory were used to compute vertical and adiabatic detachment energies of the phenolate anion serving as a model system representing anionic GFP-like chromophores (HBDI). The benchmark calculations reveal that the basis set has significant effect on the computed detachment energies, whereas the results are less sensitive to the level of electron correlation treatment. At least aug-cc-pVTZ basis set is required. The best ωB97X-D and CCSD(T) estimates of phenolate's adiabatic detachment energy are 2.12 and 2.19 eV; these values are very close to the experimental value, 2.253 eV [Gunion et al. Int. J. Mass Spectrom. Ion Proc. 1992, 117, 601]. The best estimate of the vertical detachment energy of deprotonated HBDI is 2.76 eV, which supports bound character of the bright excited state in the Franck-Condon region. The most intense transition in the computed photoelectron spectra of both phenolate and deprotonated HBDI is the 0-0 S0-D0 transition, which is 0.11 eV below vertical detachment energy. Therefore, the position of the maximum of the photoelectron spectrum does not represent vertical detachment energy, and the direct comparison between theory and experiment must involve spectrum modeling.

Proton transfer in nucleobases is mediated by water.

Water plays a central role in chemistry and biology by mediating the interactions between molecules, altering energy levels of solvated species, modifying potential energy profiles along reaction coordinates, and facilitating efficient proton transport through ion channels and interfaces. This study investigates proton transfer in a model system comprising dry and microhydrated clusters of nucleobases. With mass spectrometry and tunable vacuum ultraviolet synchrotron radiation, we show that water shuts down ionization-induced proton transfer between nucleobases, which is very efficient in dry clusters. Instead, a new pathway opens up in which protonated nucleobases are generated by proton transfer from the ionized water molecule and elimination of a hydroxyl radical. Electronic structure calculations reveal that the shape of the potential energy profile along the proton transfer coordinate depends strongly on the character of the molecular orbital from which the electron is removed; i.e., the proton transfer from water to nucleobases is barrierless when an ionized state localized on water is accessed. The computed energetics of proton transfer is in excellent agreement with the experimental appearance energies. Possible adiabatic passage on the ground electronic state of the ionized system, though energetically accessible at lower energies, is not efficient. Thus, proton transfer is controlled electronically, by the character of the ionized state, rather than statistically, by simple energy considerations.

Complex-scaled equation-of-motion coupled-cluster method with single and double substitutions for autoionizing excited states: theory, implementation, and examples.

Theory and implementation of complex-scaled variant of equation-of-motion coupled-cluster method for excitation energies with single and double substitutions (EOM-EE-CCSD) is presented. The complex-scaling formalism extends the EOM-EE-CCSD model to resonance states, i.e., excited states that are metastable with respect to electron ejection. The method is applied to Feshbach resonances in atomic systems (He, H(-), and Be). The dependence of the results on one-electron basis set is quantified and analyzed. Energy decomposition and wave function analysis reveal that the origin of the dependence is in electron correlation, which is essential for the lifetime of Feshbach resonances. It is found that one-electron basis should be sufficiently flexible to describe radial and angular electron correlation in a balanced fashion and at different values of the scaling parameter, θ. Standard basis sets that are optimized for not-complex-scaled calculations (θ = 0) are not sufficiently flexible to describe the θ-dependence of the wave functions even when heavily augmented by additional sets.

Insight into the common mechanism of the chromophore formation in the red fluorescent proteins: the elusive blue intermediate revealed.

Understanding the chromophore maturation process in fluorescent proteins is important for the design of proteins with improved properties. Here, we present the results of electronic structure calculations identifying the nature of a blue intermediate, a key species in the process of the red chromophore formation in DsRed, TagRFP, fluorescent timers, and PAmCherry. The chromophore of the blue intermediate has a structure in which the π-system of the imidazole ring is extended by the acylimine bond, which can be represented by the model N-[(5-hydroxy-1H-imidazole-2yl)methylidene]acetamide (HIMA) compound. Ab initio and QM/MM calculations of the isolated model and protein-bound (mTagBFP) chromophores identify the anionic form of HIMA as the only structure that has absorption that is consistent with the experiment and is stable in the protein binding pocket. The anion and zwitterion are the only protonation forms of HIMA whose absorption (421 and 414 nm, or 2.95 and 3.00 eV) matches the experimental spectrum of the blue form in DsRed (the absorption maximum is 408 nm or 3.04 eV) and mTagBFP (400 nm or 3.10 eV). The QM/MM optimization of the protein-bound anionic form results in a structure that is close to the X-ray one, whereas the zwitterionic chromophore is unstable in the protein binding pocket and undergoes prompt proton transfer. The computed excitation energy of the protein-bound anionic form of the mTagBFP-like chromophore (3.04 eV) agrees with the experimental absorption spectrum of the protein. The DsRed-like chromophore formation in red fluorescent proteins is revisited on the basis of ab initio results and verified by directed mutagenesis revealing a key role of the amino acid residue 70, which is the second after the chromophore tripeptide, in the formation process.

Effect of microhydration on the electronic structure of the chromophores of the photoactive yellow and green fluorescent proteins.

Electronic structure calculations of microhydrated model chromophores (in their deprotonated anionic forms) of the photoactive yellow and green fluorescent proteins (PYP and GFP) are reported. Electron-detachment and excitation energies as well as binding energies of mono- and dihydrated isomers are computed and analyzed. Microhydration has different effects on the excited and ionized states. In lower-energy planar isomers, the interaction with one water molecule blueshifts the excitation energies by 0.1-0.2 eV, whereas the detachment energies increase by 0.4-0.8 eV. The important consequence is that microhydration by just one water molecule converts the resonance (autoionizing) excited states of the bare chromophores into bound states. In the lower-energy microhydrated clusters, interactions with water have negligible effect on the chromophore geometry; however, we also identified higher-energy dihydrated clusters of PYP in which two water molecules form hydrogen-bonding network connecting the carboxylate and phenolate moieties and the chromophore is strongly distorted resulting in a significant shift of excitation energies (up to 0.6 eV).

Electronic structure of the two isomers of the anionic form of p-coumaric acid chromophore.

A theoretical study of the electronic structure of the photoactive yellow protein (PYP) model chromophore, para-coumaric acid (p-CA), is presented. Electronically excited states of the phenolate and carboxylate isomers of the deprotonated p-CA are characterized by high-level ab initio methods including state-specific and multistate multireference pertrubation theory (SS-CASPT2, and MS-CASPT2), equation-of-motion coupled-cluster methods with single and double substitutions (EOM-CCSD) and with an approximate account of triple excitations (CC3). We found that the two isomers have distinctly different patterns of ionization and excitation energies. Their excitation energies differ by more than 1 eV, in contradiction to the experimental report [Rocha-Rinza et al., J. Phys. Chem. A 113, 9442 (2009)]. The calculations confirm metastable (autoionizing) character of the valence excited states of both phenolate and carboxylate isomers of p-CA(-) in the gas phase. The type of resonance is different in the two forms. In the phenolate, the excited state lies above the detachment continuum (a shape resonance), whereas in the carboxylate the excited π→π(*) state lies below the π-orbital ionization continuum, but is above the states derived from ionization from three other orbitals (Feshbach resonance). The computed oscillator strength of the bright electronic state in the phenolate is higher than in the carboxylate, in agreement with Hückel's model predictions. The analysis of photofragmentation channels shows that the most probable products for the methylated derivatives of the phenolate and carboxylate forms of p-CA(-) are CH(3), CH(2)O and CH(3), CH(2)O, CO(2), respectively, thus suggesting an experimental probe that may discriminate between the two isomers.