Derivation of interpretative models for long range electron transfer from constrained density functional theory

Abstract The constrained DFT approach of Wu and Van Voorhis is a promising tool for the study of long range biological electron transfers within Marcus theory. This approach allows one to define chemically relevant non-adiabatic states and to compute the three key parameters entering the rate constant expression; the driving force (Δ G °), the reorganization energy ( λ ) and the electronic coupling H DA . Here we present the implementation of the method in deMon2k and we then successively use it to derive new parameters for the pathway model which is one of the most common interpretative models used in biochemistry to relate the H DA amplitude to the composition of proteins. This original application of CDFT also opens the door towards more elaborate models.

[1]  R. Marcus,et al.  Electron transfers in chemistry and biology , 1985 .

[2]  David N Beratan,et al.  Coupling Coherence Distinguishes Structure Sensitivity in Protein Electron Transfer , 2007, Science.

[3]  Jochen Blumberger,et al.  Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions. , 2009, The Journal of chemical physics.

[4]  V. R. Saunders,et al.  A “Level–Shifting” method for converging closed shell Hartree–Fock wave functions , 1973 .

[5]  T. Voorhis,et al.  Direct optimization method to study constrained systems within density-functional theory , 2005 .

[6]  David N. Beratan,et al.  The Nature of Aqueous Tunneling Pathways Between Electron-Transfer Proteins , 2005, Science.

[7]  E. Molinari,et al.  First-principles density-functional theory calculations of electron-transfer rates in azurin dimers. , 2006, The Journal of chemical physics.

[8]  S. Morris,et al.  Lower Cambrian vertebrates from south China , 1999, Nature.

[9]  J. Onuchic,et al.  Theoretical understanding of the interprotein electron transfer between cytochrome c2 and the photosynthetic reaction center , 2003 .

[10]  Jochen Blumberger,et al.  Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment. , 2008, Physical chemistry chemical physics : PCCP.

[11]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[12]  R. Marcus,et al.  Dynamical effects in electron transfer reactions , 1986 .

[13]  Mikael P. Johansson,et al.  Nanosecond electron tunneling between the hemes in cytochrome bo3 , 2007, Proceedings of the National Academy of Sciences.

[14]  R. Felice,et al.  Water-mediated electron transfer between protein redox centers. , 2007, The journal of physical chemistry. B.

[15]  Dennis R. Salahub,et al.  Defining the Domain of Density Functionals: Charge-Transfer Complexes , 1995 .

[16]  C. Zener Non-Adiabatic Crossing of Energy Levels , 1932 .

[17]  P. Pulay Convergence acceleration of iterative sequences. the case of scf iteration , 1980 .

[18]  David N Beratan,et al.  Persistence of structure over fluctuations in biological electron-transfer reactions. , 2008, Physical review letters.

[19]  J. Pople,et al.  Self‐consistent molecular orbital methods. XX. A basis set for correlated wave functions , 1980 .

[20]  F. Gadéa,et al.  Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H2 and LiH , 2000 .

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

[22]  Andreas M Köster,et al.  Calculation of exchange-correlation potentials with auxiliary function densities. , 2004, The Journal of chemical physics.

[23]  J. Onuchic,et al.  Electron tunneling pathways in proteins. , 1992, Current opinion in chemical biology.

[24]  A. Köster Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods , 2003 .

[25]  M. Newton,et al.  Quantum chemical probes of electron-transfer kinetics: the nature of donor-acceptor interactions , 1991 .

[26]  Troy Van Voorhis,et al.  Constrained Density Functional Theory and Its Application in Long-Range Electron Transfer. , 2006 .

[27]  T. Van Voorhis,et al.  Extracting electron transfer coupling elements from constrained density functional theory. , 2006, The Journal of chemical physics.

[28]  Florian Janetzko,et al.  A MinMax self-consistent-field approach for auxiliary density functional theory. , 2009, The Journal of chemical physics.

[29]  A. Becke A multicenter numerical integration scheme for polyatomic molecules , 1988 .

[30]  D. Beratan,et al.  Ab initio based calculations of electron-transfer rates in metalloproteins. , 2005, The journal of physical chemistry. B.

[31]  Ilya A. Balabin,et al.  Heme–copper oxidases use tunneling pathways , 2008, Proceedings of the National Academy of Sciences.

[32]  S. Larsson Electron transfer in chemical and biological systems. Orbital rules for nonadiabatic transfer , 1981 .

[33]  Harry B Gray,et al.  Electron tunneling through proteins , 2003, Quarterly Reviews of Biophysics.

[34]  A. Stuchebrukhov Long-distance electron tunneling in proteins , 2003 .

[35]  Olivier Parisel,et al.  Long distance electron-transfer mechanism in peptidylglycine alpha-hydroxylating monooxygenase: a perfect fitting for a water bridge. , 2007, Journal of the American Chemical Society.