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.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

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.

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.

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.

Electronic structure of the para-benzoquinone radical anion revisited

Photoinduced processes in para-benzoquinone anion are studied with multistate multireference perturbation theory: an interplay between autodetachment and internal conversion.

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.

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.

A Fresh Look at Resonances and Complex Absorbing Potentials: Density Matrix-Based Approach

A new strategy of using complex absorbing potentials (CAPs) within electronic structure calculations of metastable electronic states, which are ubiquitous in chemistry and physics, is presented. The stumbling block in numerical applications of CAPs is the necessity to optimize the CAP strength for each system, state, and one-electron basis set, while there is no clear metric to assess the quality of the results and no simple algorithm of achieving numerical convergence. By analyzing the behavior of resonance wave functions, we found that robust results can be obtained when considering fully stabilized resonance states characterized by constant density at large η (parameter determining the CAP strength). Then the perturbation due to the finite-strength CAP can be removed by a simple energy correction derived from energy decomposition analysis and response theory. The utility of this approach is illustrated by CAP-augmented calculations of several shape resonances using EOM-EA-CCSD with standard Gaussian basis sets.

Four Bases Score a Run: Ab Initio Calculations Quantify a Cooperative Effect of H-Bonding and π-Stacking on the Ionization Energy of Adenine in the AATT Tetramer

Benchmark calculations of the lowest ionized state of the (A:T)2 (mixed adenine-thymine) cluster at the geometry taken from the DNA X-ray structure are presented. Vertical ionization energies (IEs) computed by the equation-of-motion coupled-cluster method with single and double substitutions are reported and analyzed. The shift in IE relative to the monomer (A) is -0.7 eV. The performance of the widely used B3LYP, ωB97X-D, and M06-2X functionals with respect to their ability to describe energetics and the character (localization versus delocalization) of the ionized states is also investigated. The shifts in IEs caused by H-bonding and stacking interactions are analyzed in terms of additive versus cooperative effects. It is found that the cooperative effect accounts for more than 20% of the shift in IE relative to the monomer. The cooperative effect and, consequently, the magnitude of the shift are well reproduced by the hybrid quantum mechanics/molecular mechanics scheme in which neutral thymine bases are represented by point charges.

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.

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.

Gas-Phase Spectroscopy of Protonated 3-OH Kynurenine and Argpyrimidine. Comparison of Experimental Results to Theoretical Modeling

The aging process of the human lens is associated with accumulation of chromophores and fluorophores that impair visual function. In the present study, we examined the photodissociation of 3-OH-kynurenine and argpyrimidine. Furthermore, absorption spectra obtained in gas phase using an electrostatic ion storage ring were studied as gas phase absorption have been shown to be more similar to the in vivo condition than absorption spectra obtained in the liquid phase. Experimental results were compared to theoretical modeling using the multistate, multireference perturbation theory approach combined with advanced molecular modeling tools to account for the solvent effects and to provide direct support for band assignments. Absorption maxima were determined both experimentally and theoretically and significant differences between the two chromophores were found. In particular, 3-OH-kynurenine demonstrated a blue-shift of more than 130 nm in the aqueous phase compared to the gas-phase due to the existence of different 3-OH-kynurenine conformers, which are stable under different conditions and originate from the interplay between intra- and intermolecular interactions. Photodissociation of argpyrimidine and 3-OH-kynurenine was observed in vacuum thus confirming the results previously obtained in liquid phase demonstrating that the photodestruction takes place in both media.