DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB).

The self-consistent-charge density-functional tight-binding method (SCC-DFTB) is an approximate quantum chemical method derived from density functional theory (DFT) based on a second-order expansion of the DFT total energy around a reference density. In the present study we combine earlier extensions and improve them consistently with, first, an improved Coulomb interaction between atomic partial charges, and second, the complete third-order expansion of the DFT total energy. These modifications lead us to the next generation of the DFTB methodology called DFTB3, which substantially improves the description of charged systems containing elements C, H, N, O, and P, especially regarding hydrogen binding energies and proton affinities. As a result, DFTB3 is particularly applicable to biomolecular systems. Remaining challenges and possible solutions are also briefly discussed.

[1]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

[2]  Julian Tirado-Rives,et al.  Comparison of SCC-DFTB and NDDO-based semiempirical molecular orbital methods for organic molecules. , 2006, The journal of physical chemistry. A.

[3]  Yang Yang,et al.  Extensive conformational transitions are required to turn on ATP hydrolysis in myosin. , 2008, Journal of molecular biology.

[4]  Sándor Suhai,et al.  DFT studies on helix formation in N-acetyl-(L-alanyl)n-N′-methylamide for n=1–20 , 2000 .

[5]  Miquel Duran,et al.  How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers? , 1996 .

[6]  Matthias Scheffler,et al.  On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit. , 2007, The Journal of chemical physics.

[7]  Q. Cui,et al.  Proton transfer function of carbonic anhydrase: Insights from QM/MM simulations. , 2010, Biochimica et biophysica acta.

[8]  G. Seifert,et al.  Tight-binding density functional theory: an approximate Kohn-Sham DFT scheme. , 2007, The journal of physical chemistry. A.

[9]  Thomas Frauenheim,et al.  Atomistic simulations of complex materials: ground-state and excited-state properties , 2002 .

[10]  J. Janak,et al.  Proof that ? E /? n i =e in density-functional theory , 1978 .

[11]  M. Elstner SCC-DFTB: what is the proper degree of self-consistency? , 2007, The journal of physical chemistry. A.

[12]  G. Seifert,et al.  LCAO-Xα Calculations of Transition Metal Clusters , 1985 .

[13]  Timothy Clark,et al.  Towards a ‘‘next generation’’ neglect of diatomic differential overlap based semiempirical molecular orbital technique , 2003 .

[14]  S. F. Boys,et al.  The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors , 1970 .

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

[16]  M. Frisch,et al.  Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields , 1994 .

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

[18]  Krishnan Raghavachari,et al.  GAUSSIAN-3 THEORY USING DENSITY FUNCTIONAL GEOMETRIES AND ZERO-POINT ENERGIES , 1999 .

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

[20]  M. Scheffler,et al.  On the Accuracy of DFT for Describing Hydrogen Bonds: Dependence on the Bond Directionality , 2004 .

[21]  C. Adamo,et al.  Density-functional-based molecular-dynamics simulations of molten salts. , 2005, The Journal of chemical physics.

[22]  Keiji Morokuma,et al.  Systematic study of vibrational frequencies calculated with the self‐consistent charge density functional tight‐binding method , 2004, J. Comput. Chem..

[23]  Keiji Morokuma,et al.  Modeling vibrational spectra using the self-consistent charge density-functional tight-binding method. I. Raman spectra. , 2004, The Journal of chemical physics.

[24]  Walter Thiel,et al.  Beyond the MNDO model: Methodical considerations and numerical results , 1993, J. Comput. Chem..

[25]  Yijing Yan,et al.  Performance of Several Density Functional Theory Methods on Describing Hydrogen-Bond Interactions. , 2009, Journal of chemical theory and computation.

[26]  William A. Goddard,et al.  Bonding Properties of the Water Dimer: A Comparative Study of Density Functional Theories , 2004 .

[27]  Yang Yang,et al.  The hydrolysis activity of adenosine triphosphate in myosin: a theoretical analysis of anomeric effects and the nature of the transition state. , 2009, The journal of physical chemistry. A.

[28]  M. Elstner The SCC-DFTB method and its application to biological systems , 2006 .

[29]  Jeremy C. Smith,et al.  Key role of electrostatic interactions in bacteriorhodopsin proton transfer. , 2004, Journal of the American Chemical Society.

[30]  Walter Thiel,et al.  Looking at self-consistent-charge density functional tight binding from a semiempirical perspective. , 2007, The journal of physical chemistry. A.

[31]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[32]  Alfredo Mayall Simas,et al.  RM1: A reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I , 2006, J. Comput. Chem..

[33]  Donald G Truhlar,et al.  Benchmark Databases for Nonbonded Interactions and Their Use To Test Density Functional Theory. , 2005, Journal of chemical theory and computation.

[34]  G. Seifert,et al.  Calculations of molecules, clusters, and solids with a simplified LCAO-DFT-LDA scheme , 1996 .

[35]  M. Dewar,et al.  Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters , 1977 .

[36]  M. Elstner,et al.  Validation of the density-functional based tight-binding approximation method for the calculation of reaction energies and other data. , 2005, The Journal of chemical physics.

[37]  Wim Klopper,et al.  Computational determination of equilibrium geometry and dissociation energy of the water dimer , 2000 .

[38]  E. Tajkhorshid,et al.  Performance of the AM1, PM3, and SCC-DFTB methods in the study of conjugated Schiff base molecules , 2002 .

[39]  Thomas Frauenheim,et al.  Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment , 2001 .

[40]  Thomas Frauenheim,et al.  An approximate DFT method for QM/MM simulations of biological structures and processes , 2003 .

[41]  Walter Thiel,et al.  Orthogonalization corrections for semiempirical methods , 2000 .

[42]  S. Suhai,et al.  Application of an approximate density-functional method to sulfur containing compounds , 2001 .

[43]  Q. Cui,et al.  Does water relay play an important role in phosphoryl transfer reactions? Insights from theoretical study of a model reaction in water and tert-butanol. , 2009, The journal of physical chemistry. B.

[44]  Q. Cui,et al.  Microscopic pKa analysis of Glu286 in cytochrome c oxidase (Rhodobacter sphaeroides): toward a calibrated molecular model. , 2009, Biochemistry.

[45]  Eamonn F. Healy,et al.  Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model , 1985 .

[46]  Qiang Cui,et al.  Functional specificities of methylglyoxal synthase and triosephosphate isomerase: a combined QM/MM analysis. , 2002, Journal of the American Chemical Society.

[47]  Hua Guo,et al.  Proton transfer in carbonic anhydrase is controlled by electrostatics rather than the orientation of the acceptor. , 2008, Biochemistry.

[48]  D. Levandier,et al.  H2+(X,v+=0~15,N+=1)+Heプロトン移動反応のパルス電界イオン化光電子二次イオンコインシデンス研究 , 2005 .

[49]  Thomas Frauenheim,et al.  Energetics and structure of glycine and alanine based model peptides: Approximate SCC-DFTB, AM1 and PM3 methods in comparison with DFT, HF and MP2 calculations , 2001 .

[50]  Laquai Frederic,et al.  低濃度のPt(II)オクタエチルポルフィリンをドープした青色発光スピロビフルオレン‐アントラセン共重合体における効率的なアップコンバージョン蛍光 , 2005 .

[51]  Peter Politzer,et al.  Electrostatic potentials and covalent radii , 2003, J. Comput. Chem..

[52]  William L. Jorgensen,et al.  PDDG/PM3 and PDDG/MNDO: Improved semiempirical methods , 2002, J. Comput. Chem..

[53]  Harris Simplified method for calculating the energy of weakly interacting fragments. , 1985, Physical review. B, Condensed matter.

[54]  K. Morokuma,et al.  Relativistic parametrization of the self-consistent-charge density-functional tight-binding method. 1. Atomic wave functions and energies. , 2007, The journal of physical chemistry. A.

[55]  M. Elstner,et al.  Automatized parametrization of SCC-DFTB repulsive potentials: application to hydrocarbons. , 2009, The journal of physical chemistry. A.

[56]  D. York,et al.  Benchmark calculations of proton affinities and gas-phase basicities of molecules important in the study of biological phosphoryl transfer. , 2005, Physical chemistry chemical physics : PCCP.

[57]  Sándor Suhai,et al.  A Self‐Consistent Charge Density‐Functional Based Tight‐Binding Method for Predictive Materials Simulations in Physics, Chemistry and Biology , 2000 .

[58]  Jeremy C. Smith,et al.  Long-distance proton transfer with a break in the bacteriorhodopsin active site. , 2009, Journal of the American Chemical Society.

[59]  Thomas Frauenheim,et al.  Modeling zinc in biomolecules with the self consistent charge‐density functional tight binding (SCC‐DFTB) method: Applications to structural and energetic analysis , 2003, J. Comput. Chem..

[60]  Q. Cui,et al.  Amino acids with an intermolecular proton bond as proton storage site in bacteriorhodopsin , 2008, Proceedings of the National Academy of Sciences.

[61]  L. Curtiss,et al.  Gaussian-3 (G3) theory for molecules containing first and second-row atoms , 1998 .

[62]  D. Tobias,et al.  Spectral signatures of the pentagonal water cluster in bacteriorhodopsin. , 2008, Chemphyschem : a European journal of chemical physics and physical chemistry.

[63]  T. H. Dunning Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[64]  G. Seifert,et al.  Density functional tight binding : Contributions from the American chemical society symposium , 2007 .

[65]  M. Krauss,et al.  Dynamics of proton transfer in bacteriorhodopsin. , 2004, Journal of the American Chemical Society.

[66]  T. Frauenheim,et al.  Initial steps toward automating the fitting of DFTB Erep(r). , 2007, The journal of physical chemistry. A.

[67]  Henryk A. Witek,et al.  Modeling vibrational spectra using the self-consistent charge density-functional tight-binding method. I. Raman spectra , 2004 .

[68]  Efthimios Kaxiras,et al.  A Self-Consistent Charge Density-Functional Based Tight-Binding Scheme for Large Biomolecules , 2000 .

[69]  Yang Yang,et al.  Interactions between phosphate and water in solution: a natural bond orbital based analysis in a QM/MM framework. , 2007, The journal of physical chemistry. B.

[70]  J. Stewart Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements , 2007, Journal of molecular modeling.

[71]  K. Morokuma,et al.  Modeling carbon nanostructures with the self-consistent charge density-functional tight-binding method: vibrational spectra and electronic structure of C(28), C(60), and C(70). , 2006, The Journal of chemical physics.

[72]  Seifert,et al.  Construction of tight-binding-like potentials on the basis of density-functional theory: Application to carbon. , 1995, Physical review. B, Condensed matter.

[73]  D. York,et al.  Extension of the self-consistent-charge density-functional tight-binding method: third-order expansion of the density functional theory total energy and introduction of a modified effective coulomb interaction. , 2007, The journal of physical chemistry. A.

[74]  Ross C Walker,et al.  Are current semiempirical methods better than force fields? A study from the thermodynamics perspective. , 2009, The journal of physical chemistry. A.

[75]  Foulkes,et al.  Tight-binding models and density-functional theory. , 1989, Physical review. B, Condensed matter.

[76]  L. Curtiss,et al.  Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation , 1997 .

[77]  D. York,et al.  Description of phosphate hydrolysis reactions with the Self-Consistent-Charge Density-Functional-Tight-Binding (SCC-DFTB) theory. 1. Parameterization. , 2008, Journal of chemical theory and computation.

[78]  J. Stewart Optimization of parameters for semiempirical methods I. Method , 1989 .

[79]  M Elstner,et al.  Quantum mechanics simulation of protein dynamics on long timescale , 2001, Proteins.

[80]  Guohui Li,et al.  Development of effective quantum mechanical/molecular mechanical (QM/MM) methods for complex biological processes. , 2006, The journal of physical chemistry. B.

[81]  Stephan Irle,et al.  Analytical second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding method. , 2004, The Journal of chemical physics.