Systematic High‐Accuracy Prediction of Electron Affinities for Biological Quinones

Quinones play vital roles as electron carriers in fundamental biological processes; therefore, the ability to accurately predict their electron affinities is crucial for understanding their properties and function. The increasing availability of cost‐effective implementations of correlated wave function methods for both closed‐shell and open‐shell systems offers an alternative to density functional theory approaches that have traditionally dominated the field despite their shortcomings. Here, we define a benchmark set of quinones with experimentally available electron affinities and evaluate a range of electronic structure methods, setting a target accuracy of 0.1 eV. Among wave function methods, we test various implementations of coupled cluster (CC) theory, including local pair natural orbital (LPNO) approaches to canonical and parameterized CCSD, the domain‐based DLPNO approximation, and the equations‐of‐motion approach for electron affinities, EA‐EOM‐CCSD. In addition, several variants of canonical, spin‐component‐scaled, orbital‐optimized, and explicitly correlated (F12) Møller–Plesset perturbation theory are benchmarked. Achieving systematically the target level of accuracy is challenging and a composite scheme that combines canonical CCSD(T) with large basis set LPNO‐based extrapolation of correlation energy proves to be the most accurate approach. Methods that offer comparable performance are the parameterized LPNO‐pCCSD, the DLPNO‐CCSD(T0), and the orbital optimized OO‐SCS‐MP2. Among DFT methods, viable practical alternatives are only the M06 and the double hybrids, but the latter should be employed with caution because of significant basis set sensitivity. A highly accurate yet cost‐effective DLPNO‐based coupled cluster approach is used to investigate the methoxy conformation effect on the electron affinities of ubiquinones found in photosynthetic bacterial reaction centers. © 2018 Wiley Periodicals, Inc.

[1]  A. Rutherford,et al.  Mechanism of proton-coupled quinone reduction in Photosystem II , 2012, Proceedings of the National Academy of Sciences.

[2]  Jeng-Da Chai,et al.  Long-Range Corrected Hybrid Density Functionals with Improved Dispersion Corrections. , 2012, Journal of chemical theory and computation.

[3]  Notker Rösch,et al.  Comment on “Concerning the applicability of density functional methods to atomic and molecular negative ions” [J. Chem. Phys. 105, 862 (1996)] , 1997 .

[4]  K. Hasegawa,et al.  How does the QB site influence propagate to the QA site in photosystem II? , 2011, Biochemistry.

[5]  A. Krylov,et al.  The effect of pi-stacking and H-bonding on ionization energies of a nucleobase: uracil dimer cation. , 2009, Physical chemistry chemical physics : PCCP.

[6]  R. T. McIver,et al.  Relative electron affinities of substituted benzophenones, nitrobenzenes, and quinones , 1985 .

[7]  The effect of methoxy group rotation and hydrogen bonding on the redox properties of ubiquinone , 2015 .

[8]  A. Rutherford,et al.  Bicarbonate-induced redox tuning in Photosystem II for regulation and protection , 2016, Proceedings of the National Academy of Sciences.

[9]  F. Weigend,et al.  Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations , 2002 .

[10]  Marcel Nooijen,et al.  pCCSD: parameterized coupled-cluster theory with single and double excitations. , 2010, The Journal of chemical physics.

[11]  K. Hasegawa,et al.  Molecular interactions of the quinone electron acceptors QA, QB, and QC in photosystem II as studied by the fragment molecular orbital method , 2014, Photosynthesis Research.

[12]  W Leibl,et al.  Electron transfer in photosystem I. , 2001, Biochimica et biophysica acta.

[13]  Katarzyna Pernal,et al.  Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT). , 2015, Topics in current chemistry.

[14]  F. Neese,et al.  Efficient and accurate local approximations to coupled-electron pair approaches: An attempt to revive the pair natural orbital method. , 2009, The Journal of chemical physics.

[15]  Dimitrios G Liakos,et al.  Is It Possible To Obtain Coupled Cluster Quality Energies at near Density Functional Theory Cost? Domain-Based Local Pair Natural Orbital Coupled Cluster vs Modern Density Functional Theory. , 2015, Journal of chemical theory and computation.

[16]  K. Schwarz.  Instability of stable negative ions in the Xα method or other local density functional schemes , 1978 .

[17]  P. Kebarle,et al.  Electron affinities and electron-transfer reactions , 1987 .

[18]  B. Rabenstein,et al.  Electron transfer between the quinones in the photosynthetic reaction center and its coupling to conformational changes. , 2000, Biochemistry.

[19]  J. Simons.  Theoretical study of negative molecular ions. , 1977, Annual review of physical chemistry.

[20]  Shiang-Tai Lin,et al.  Assessing the role of Hartree‐Fock exchange, correlation energy and long range corrections in evaluating ionization potential, and electron affinity in density functional theory , 2017, J. Comput. Chem..

[21]  Patrick Rinke,et al.  Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules II: Non-Empirically Tuned Long-Range Corrected Hybrid Functionals. , 2016, Journal of chemical theory and computation.

[22]  C. Wraight,et al.  Conformational differences between the methoxy groups of QA and QB site ubisemiquinones in bacterial reaction centers: a key role for methoxy group orientation in modulating ubiquinone redox potential. , 2013, Biochemistry.

[23]  Xiao He,et al.  Correction: MN15: A Kohn–Sham global-hybrid exchange–correlation density functional with broad accuracy for multi-reference and single-reference systems and noncovalent interactions , 2016, Chemical science.

[24]  Bun Chan,et al.  On the inclusion of post‐MP2 contributions to double‐Hybrid density functionals , 2016, J. Comput. Chem..

[25]  G. Scuseria,et al.  Climbing the density functional ladder: nonempirical meta-generalized gradient approximation designed for molecules and solids. , 2003, Physical review letters.

[26]  Dimitrios G Liakos,et al.  Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis. , 2009, The Journal of chemical physics.

[27]  Walter Thiel,et al.  Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3. , 2008, The Journal of chemical physics.

[28]  D. Bruce,et al.  Diverse mechanisms for photoprotection in photosynthesis. Dynamic regulation of photosystem II excitation in response to rapid environmental change. , 2015, Biochimica et biophysica acta.

[29]  Athina Zouni,et al.  The nonheme iron in photosystem II , 2013, Photosynthesis Research.

[30]  Daniel Kats,et al.  Communication: The distinguishable cluster approximation. , 2013, The Journal of chemical physics.

[31]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[32]  Frank Neese,et al.  An overlap fitted chain of spheres exchange method. , 2011, The Journal of chemical physics.

[33]  Michael P. Marshak,et al.  Computational design of molecules for an all-quinone redox flow battery , 2014, Chemical science.

[34]  J. H. Rose,et al.  Failure of the local exchange approximation in the evaluation of the H/sup -/ ground state , 1977 .

[35]  R. Bartlett,et al.  Multireference Double Electron Attached Coupled Cluster Method with Full Inclusion of the Connected Triple Excitations: MR-DA-CCSDT. , 2011, Journal of chemical theory and computation.

[36]  Edward F. Valeev,et al.  Explicitly correlated R12/F12 methods for electronic structure. , 2012, Chemical reviews.

[37]  Anthony K. Grafton,et al.  A COMPARISON OF THE PROPERTIES OF VARIOUS FUSED-RING QUINONES AND THEIR RADICAL ANIONS USING HARTREE-FOCK AND HYBRID HARTREE-FOCK/DENSITY FUNCTIONAL M ETHODS , 1997 .

[38]  S. Grimme,et al.  Theoretical thermodynamics for large molecules: walking the thin line between accuracy and computational cost. , 2008, Accounts of chemical research.

[39]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[40]  F. Neese,et al.  Speeding up equation of motion coupled cluster theory with the chain of spheres approximation. , 2016, The Journal of chemical physics.

[41]  Frank Neese,et al.  The ORCA program system , 2012 .

[42]  Andrew C. Cavell,et al.  Quinone 1 e- and 2 e-/2 H+ Reduction Potentials: Identification and Analysis of Deviations from Systematic Scaling Relationships. , 2016, Journal of the American Chemical Society.

[43]  P. Hamm,et al.  Quinones as Reversible Electron Relays in Artificial Photosynthesis. , 2016, Chemphyschem : a European journal of chemical physics and physical chemistry.

[44]  A. Rutherford,et al.  On the determination of redox midpoint potential of the primary quinone electron acceptor, QA, in Photosystem II , 1995 .

[45]  Daniel Kats,et al.  Communication: The distinguishable cluster approximation. II. The role of orbital relaxation. , 2014, The Journal of chemical physics.

[46]  P. J. O'malley,et al.  An ONIOM study of the spin density distribution of the QA site plastosemiquinone in the photosystem II reaction center. , 2011, The journal of physical chemistry. B.

[47]  H. Bao,et al.  Low-temperature electron transfer suggests two types of Q(A) in intact photosystem II. , 2010, Biochimica et biophysica acta.

[48]  Frank Neese,et al.  Revisiting the Atomic Natural Orbital Approach for Basis Sets: Robust Systematic Basis Sets for Explicitly Correlated and Conventional Correlated ab initio Methods? , 2011, Journal of chemical theory and computation.

[49]  P. Piecuch,et al.  Active-space equation-of-motion coupled-cluster methods for excited states of radicals and other open-shell systems: EA-EOMCCSDt and IP-EOMCCSDt. , 2005, The Journal of chemical physics.

[50]  C. Wraight,et al.  Tuning cofactor redox potentials: the 2-methoxy dihedral angle generates a redox potential difference of >160 mV between the primary (Q(A)) and secondary (Q(B)) quinones of the bacterial photosynthetic reaction center. , 2013, Biochemistry.

[51]  E. Takahashi,et al.  Protein control of the redox potential of the primary quinone acceptor in reactioncCenters from Rhodobacter sphaeroides. , 2001, Biochemistry.

[52]  E. Gross,et al.  Ionization potentials and electron affinities from reduced-density-matrix functional theory , 2012, 1201.6237.

[53]  A. Krylov,et al.  Electronic structure and spectroscopy of nucleic acid bases: ionization energies, ionization-induced structural changes, and photoelectron spectra. , 2010, The journal of physical chemistry. A.

[54]  F. Weigend,et al.  Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy. , 2005, Physical chemistry chemical physics : PCCP.

[55]  Hans-Joachim Werner,et al.  Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar. , 2008, The Journal of chemical physics.

[56]  Daniel Kats,et al.  Accurate thermochemistry from explicitly correlated distinguishable cluster approximation. , 2015, The Journal of chemical physics.

[57]  Rodney J. Bartlett,et al.  Equation of motion coupled cluster method for electron attachment , 1995 .

[58]  Rajeev S. Assary,et al.  Investigation of the redox chemistry of anthraquinone derivatives using density functional theory. , 2014, The journal of physical chemistry. A.

[59]  Jae Hong Kim,et al.  Quinone and its derivatives for energy harvesting and storage materials , 2016 .

[60]  F. Weigend.  Accurate Coulomb-fitting basis sets for H to Rn. , 2006, Physical chemistry chemical physics : PCCP.

[61]  S. Grimme,et al.  Efficient and Accurate Double-Hybrid-Meta-GGA Density Functionals-Evaluation with the Extended GMTKN30 Database for General Main Group Thermochemistry, Kinetics, and Noncovalent Interactions. , 2011, Journal of chemical theory and computation.

[62]  T. Tomo,et al.  Species‐dependence of the redox potential of the primary quinone electron acceptor QA in photosystem II verified by spectroelectrochemistry , 2010, FEBS letters.

[63]  T. Noguchi,et al.  Effects of hydrogen bonding interactions on the redox potential and molecular vibrations of plastoquinone as studied using density functional theory calculations. , 2014, Physical chemistry chemical physics : PCCP.

[64]  X. López,et al.  The extended Koopmans' theorem: vertical ionization potentials from natural orbital functional theory. , 2012, The Journal of chemical physics.

[65]  C. Wraight,et al.  The 2-methoxy group of ubiquinone is essential for function of the acceptor quinones in reaction centers from Rba. sphaeroides. , 2008, Biochimica et Biophysica Acta.

[66]  A. Krieger-Liszkay,et al.  High and low potential forms of the QA quinone electron acceptor in Photosystem II of Thermosynechococcus elongatus and spinach. , 2011, Journal of photochemistry and photobiology. B, Biology.

[67]  M. Head‐Gordon,et al.  Orbital optimized double-hybrid density functionals. , 2013, The Journal of chemical physics.

[68]  M. Gunner,et al.  The Acceptor Quinones of Purple Photosynthetic Bacteria— Structure and Spectroscopy , 2009 .

[69]  Scott E. Boesch,et al.  ELECTRON AFFINITIES OF SUBSTITUTED P-BENZOQUINONES FROM HYBRID HARTREE-FOCK/DENSITY-FUNCTIONAL CALCULATIONS , 1996 .

[70]  Robert Eugene Blankenship,et al.  Kinetics and thermodynamics of the P870+Q−A → P870+Q−B reaction in isolated reaction centers from the photosynthetic bacterium Rhodopseudomonas sphaeroides , 1984 .

[71]  Dimitrios G Liakos,et al.  Improved correlation energy extrapolation schemes based on local pair natural orbital methods. , 2012, The journal of physical chemistry. A.

[72]  W. Lubitz,et al.  3-mm High-field EPR on semiquinone radical anions Q.cntdot.- related to photosynthesis and on the primary donor P.cntdot.+ and acceptor QA.cntdot.- in reaction centers of Rhodobacter sphaeroides R-26 , 1993 .

[73]  K. Schwarz.  First ionisation potentials of atoms obtained with local-density schemes , 1978 .

[74]  S. Grimme.  Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies , 2003 .

[75]  E. Knapp,et al.  Control of quinone redox potentials in photosystem II: Electron transfer and photoprotection. , 2005, Journal of the American Chemical Society.

[76]  M. Koblížek.  The Purple Phototrophic Bacteria , 2009, Photosynthetica.

[77]  K. Burke,et al.  Accuracy of Electron Affinities of Atoms in Approximate Density Functional Theory , 2010 .

[78]  A. Rutherford,et al.  Charge separation in photosystem II: a comparative and evolutionary overview. , 2012, Biochimica et biophysica acta.

[79]  Susannah L. Scott,et al.  Electron affinities of benzo-, naphtho-, and anthraquinones determined from gas-phase equilibria measurements , 1988 .

[80]  J. Burie,et al.  IMPORTANCE OF THE CONFORMATION OF METHOXY GROUPS ON THE VIBRATIONAL AND ELECTROCHEMICAL PROPERTIES OF UBIQUINONES , 1997 .

[81]  F. Neese,et al.  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange , 2009 .

[82]  A. Mohajeri,et al.  Application of Density Functional Theory for evaluation of standard two-electron reduction potentials in some quinone derivatives , 2008 .

[83]  Samira Siahrostami,et al.  Calculation of two-electron reduction potentials for some quinone derivatives in aqueous solution using Møller–Plesset perturbation theory , 2006 .

[84]  A. Zouni,et al.  Light-induced quinone reduction in photosystem II. , 2012, Biochimica et biophysica acta.

[85]  M. Coote,et al.  Electron affinity and redox potential of tetrafluoro-p-benzoquinone: A theoretical study , 2008 .

[86]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[87]  K. Gerwert,et al.  Does different orientation of the methoxy groups of ubiquinone-10 in the reaction centre of Rhodobacter sphaeroides cause different binding at QA and QB? , 2003, European journal of biochemistry.

[88]  D. Truhlar,et al.  Minimally augmented Karlsruhe basis sets , 2011 .

[89]  J Deisenhofer,et al.  Nobel lecture. The photosynthetic reaction centre from the purple bacterium Rhodopseudomonas viridis. , 1989, The EMBO journal.

[90]  Jan M. L. Martin,et al.  DSD-PBEP86: in search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections. , 2011, Physical chemistry chemical physics : PCCP.

[91]  D. Pantazis,et al.  Principles of Natural Photosynthesis. , 2016, Topics in current chemistry.

[92]  Frank Neese,et al.  Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics. , 2009, Journal of chemical theory and computation.

[93]  F. Neese,et al.  Communication: An improved linear scaling perturbative triples correction for the domain based local pair-natural orbital based singles and doubles coupled cluster method [DLPNO-CCSD(T)]. , 2018, The Journal of chemical physics.

[94]  J. Gauss,et al.  Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method , 1994 .

[95]  C. Cramer,et al.  Computational electrochemistry: prediction of liquid-phase reduction potentials. , 2014, Physical chemistry chemical physics : PCCP.

[96]  G. Feher,et al.  Primary acceptor in bacterial photosynthesis: obligatory role of ubiquinone in photoactive reaction centers of Rhodopseudomonas spheroides. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[97]  M. Mimuro,et al.  Redox potentials of primary electron acceptor quinone molecule (QA)− and conserved energetics of photosystem II in cyanobacteria with chlorophyll a and chlorophyll d , 2011, Proceedings of the National Academy of Sciences.

[98]  Ernest R. Davidson,et al.  Density functional theory calculations for F , 1999 .

[99]  D. Z. Goodson.  Extrapolating the coupled-cluster sequence toward the full configuration-interaction limit , 2002 .

[100]  F. Rappaport,et al.  Back‐reactions, short‐circuits, leaks and other energy wasteful reactions in biological electron transfer: Redox tuning to survive life in O2 , 2012, FEBS letters.

[101]  D. Pantazis,et al.  A Hierarchy of Methods for the Energetically Accurate Modeling of Isomerism in Monosaccharides. , 2012, Journal of chemical theory and computation.

[102]  F. Neese,et al.  Accurate thermochemistry from a parameterized coupled-cluster singles and doubles model and a local pair natural orbital based implementation for applications to larger systems. , 2012, The Journal of chemical physics.

[103]  S. Grimme.  Semiempirical hybrid density functional with perturbative second-order correlation. , 2006, The Journal of chemical physics.

[104]  Kirk A Peterson,et al.  Optimized auxiliary basis sets for explicitly correlated methods. , 2008, The Journal of chemical physics.

[105]  Edward F. Valeev,et al.  A new near-linear scaling, efficient and accurate, open-shell domain-based local pair natural orbital coupled cluster singles and doubles theory. , 2017, The Journal of chemical physics.

[106]  D. Kleinfeld,et al.  Electron transfer in reaction centers of Rhodopseudomonas sphaeroides. I. Determination of the charge recombination pathway of D+QAQ(-)B and free energy and kinetic relations between Q(-)AQB and QAQ(-)B. , 1984, Biochimica et biophysica acta.

[107]  Yao-Yuan Chuang,et al.  Infinite basis set extrapolation for double hybrid density functional theory 1: Effect of applying various extrapolation functions , 2011, J. Comput. Chem..

[108]  M. Nonella.  A quantum chemical investigation of structures, vibrational spectra and electron affinities of the radicals of quinone model compounds , 1998, Photosynthesis Research.

[109]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[110]  Donald G Truhlar,et al.  Density functionals with broad applicability in chemistry. , 2008, Accounts of chemical research.

[111]  M. Piris.  A new approach for the two-electron cumulant in natural orbital functional theory , 2006 .

[112]  Electron attachment to DNA and RNA nucleobases: An EOMCC investigation , 2014, 1409.7266.

[113]  John F. Stanton,et al.  The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties , 1993 .

[114]  Petra Fromme,et al.  Three-dimensional structure of cyanobacterial photosystem I at 2.5 Å resolution , 2001, Nature.

[115]  Gregory S. Tschumper,et al.  Atomic and molecular electron affinities: photoelectron experiments and theoretical computations. , 2002, Chemical reviews.

[116]  X. López,et al.  A natural orbital functional for multiconfigurational states. , 2011, The Journal of chemical physics.

[117]  Ajith Perera,et al.  Excited states from modified coupled cluster methods: Are they any better than EOM CCSD? , 2017, The Journal of chemical physics.

[118]  Krishnan Raghavachari,et al.  Assessment of Gaussian-2 and density functional theories for the computation of ionization potentials and electron affinities , 1998 .

[119]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[120]  F. Jensen.  Describing Anions by Density Functional Theory: Fractional Electron Affinity. , 2010, Journal of chemical theory and computation.

[121]  Parr,et al.  Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. , 1988, Physical review. B, Condensed matter.

[122]  S. Flores,et al.  Bio-Inspired Electroactive Organic Molecules for Aqueous Redox Flow Batteries. 1. Thiophenoquinones , 2015 .

[123]  Jan M. L. Martin,et al.  Basis set convergence of explicitly correlated double-hybrid density functional theory calculations. , 2011, The Journal of chemical physics.

[124]  Michelle L Coote,et al.  Accurate calculation of absolute one-electron redox potentials of some para-quinone derivatives in acetonitrile. , 2007, The journal of physical chemistry. A.

[125]  Frank Neese,et al.  Towards a pair natural orbital coupled cluster method for excited states. , 2016, The Journal of chemical physics.

[126]  Yuki Kato,et al.  Redox potentials of ubiquinone, menaquinone, phylloquinone, and plastoquinone in aqueous solution , 2017, Photosynthesis Research.

[127]  A. Rutherford,et al.  Influence of the Redox Potential of the Primary Quinone Electron Acceptor on Photoinhibition in Photosystem II* , 2007, Journal of Biological Chemistry.

[128]  T. Noguchi,et al.  Redox potential of the terminal quinone electron acceptor QB in photosystem II reveals the mechanism of electron transfer regulation , 2015, Proceedings of the National Academy of Sciences.

[129]  Frank Neese,et al.  An efficient and near linear scaling pair natural orbital based local coupled cluster method. , 2013, The Journal of chemical physics.

[130]  Evgeny Epifanovsky,et al.  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. , 2012, The journal of physical chemistry letters.

[131]  Jan M. L. Martin,et al.  Spin‐component‐scaled double hybrids: An extensive search for the best fifth‐rung functionals blending DFT and perturbation theory , 2013, J. Comput. Chem..

[132]  D. Pantazis,et al.  Ionization Energies and Aqueous Redox Potentials of Organic Molecules: Comparison of DFT, Correlated ab Initio Theory and Pair Natural Orbital Approaches. , 2016, Journal of chemical theory and computation.

[133]  G. Feher,et al.  Structure and function of bacterial photosynthetic reaction centres , 1989, Nature.

[134]  T. Heinis,et al.  Entropy changes and electron affinities from gas-phase electron-transfer equilibria: A- + B = A + B- , 1986 .

[135]  C. Adamo,et al.  Importance of Orbital Optimization for Double-Hybrid Density Functionals: Application of the OO-PBE-QIDH Model for Closed- and Open-Shell Systems. , 2016, The journal of physical chemistry. A.

[136]  C. Wraight.  Proton and electron transfer in the acceptor quinone complex of photosynthetic reaction centers from Rhodobacter sphaeroides. , 2004, Frontiers in bioscience : a journal and virtual library.

[137]  C. Wraight,et al.  The 2-Methoxy Group Orientation Regulates the Redox Potential Difference between the Primary (QA) and Secondary (QB) Quinones of Type II Bacterial Photosynthetic Reaction Centers , 2014, The journal of physical chemistry letters.

[138]  Bernard Lévy,et al.  Theoretical estimation of redox potential of biological quinone cofactors , 2017, J. Comput. Chem..

[139]  R. Prince,et al.  Electrochemistry of ubiquinones , 1983 .

[140]  Chun-Hua Wang,et al.  Accurate estimation of the one-electron reduction potentials of various substituted quinones in DMSO and CH3CN. , 2010, The Journal of organic chemistry.

[141]  H. Schaefer,et al.  COMMUNICATIONS Concerning the applicability of density functional methods to atomic and molecular negative ions , 1996 .

[142]  Á. Vázquez-Mayagoitia,et al.  Substituent effect on a family of quinones in aprotic solvents: an experimental and theoretical approach. , 2006, The journal of physical chemistry. A.

[143]  M. Nonella.  A Density Functional Investigation of Model Molecules for Ubisemiquinone Radical Anions , 1998 .

[144]  E. Alexov,et al.  Calculated protein and proton motions coupled to electron transfer: electron transfer from QA- to QB in bacterial photosynthetic reaction centers. , 1999, Biochemistry.