Multiscale modeling and related hybrid approaches

Abstract The general representation about the multiscale modeling and related approaches is briefly reported. The hybrid schemes for coupling between quantum mechanics and molecular mechanics subsystem are introduced and reviewed focusing on recent progress involving the density functional theory based formalism and the methodology of scaled position method as well as scaled position link atom method. The hybrid approaches have important theoretical sense and application potential, especially, for the fields of materials science. Concurrently the hybrid energy density method – density functional-based is also reported, which is from our recent works. Finally, the look into future is briefly presented.

[1]  J. Q. Broughton,et al.  Concurrent Coupling of Length Scales in Solid State Systems , 2000 .

[2]  Daw Model of metallic cohesion: The embedded-atom method. , 1989, Physical review. B, Condensed matter.

[3]  Chacón,et al.  Nonlocal kinetic-energy-density functionals. , 1996, Physical review. B, Condensed matter.

[4]  Tarazona,et al.  Nonlocal kinetic energy functional for nonhomogeneous electron systems. , 1985, Physical review. B, Condensed matter.

[5]  Emily A. Carter,et al.  Accurate ab initio energetics of extended systems via explicit correlation embedded in a density functional environment , 1998 .

[6]  D. Brenner,et al.  Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. , 1990, Physical review. B, Condensed matter.

[7]  Noam Bernstein,et al.  Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture , 1998 .

[8]  M. Karplus,et al.  A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations , 1990 .

[9]  P. Wesseling An Introduction to Multigrid Methods , 1992 .

[10]  T. Arias Multiresolution analysis of electronic structure: semicardinal and wavelet bases , 1998, cond-mat/9805262.

[11]  N. Xu,et al.  Quantum-mechanical investigation of field-emission mechanism of a micrometer-long single-walled carbon nanotube. , 2004, Physical review letters.

[12]  Wang,et al.  Kinetic-energy functional of the electron density. , 1992, Physical review. B, Condensed matter.

[13]  Rajiv K. Kalia,et al.  Hybrid finite-element/molecular-dynamics/electronic-density-functional approach to materials simulations on parallel computers , 2001 .

[14]  Rajan Gupta,et al.  MONTE CARLO RENORMALIZED HAMILTONIAN , 1984 .

[15]  M C Payne,et al.  "Learn on the fly": a hybrid classical and quantum-mechanical molecular dynamics simulation. , 2004, Physical review letters.

[16]  S. Ta'asan,et al.  Multilevel turbulence simulations , 1993 .

[17]  C. Varma,et al.  Phonon dispersion in transition metals , 1977 .

[18]  Tai-Sung Lee,et al.  A pseudobond approach to combining quantum mechanical and molecular mechanical methods , 1999 .

[19]  Wolfgang Hackbusch,et al.  Multigrid Methods III , 1991 .

[20]  Rajiv K. Kalia,et al.  Environmental effects of H2O on fracture initiation in silicon: A hybrid electronic-density-functional/molecular-dynamics study , 2004 .

[21]  Thomas L. Beck,et al.  Multigrid high‐order mesh refinement techniques for composite grid electrostatics calculations , 1999 .

[22]  Liu Senying,et al.  Electronic structure of impurity (oxygen) – stacking-fault complex in nickel , 1990 .

[23]  J. Q. Broughton,et al.  Concurrent coupling of length scales: Methodology and application , 1999 .

[24]  K. Morokuma,et al.  ONIOM: A Multilayered Integrated MO + MM Method for Geometry Optimizations and Single Point Energy Predictions. A Test for Diels−Alder Reactions and Pt(P(t-Bu)3)2 + H2 Oxidative Addition , 1996 .

[25]  Michael Frenklach,et al.  Molecular dynamics with combined quantum and empirical potentials: C2H2 adsorption on Si(100) , 1993 .

[26]  Paul Tavan,et al.  A hybrid method for solutes in complex solvents: Density functional theory combined with empirical force fields , 1999 .

[27]  Ted Belytschko,et al.  Mechanics of defects in carbon nanotubes: Atomistic and multiscale simulations , 2005 .

[28]  Sullivan,et al.  Real-space multigrid-based approach to large-scale electronic structure calculations. , 1996, Physical review. B, Condensed matter.

[29]  A. Nakano,et al.  Coupling length scales for multiscale atomistics-continuum simulations: atomistically induced stress distributions in Si/Si3N4 nanopixels. , 2001, Physical review letters.

[30]  N. Govind,et al.  Orbital-free kinetic-energy density functionals with a density-dependent kernel , 1999 .

[31]  J. Tersoff,et al.  Empirical interatomic potential for carbon, with application to amorphous carbon. , 1988, Physical review letters.

[32]  Shuji Ogata,et al.  A hybrid electronic-density-functional/molecular-dynamics simulation scheme for multiscale simulation of materials on parallel computers: applications to silicon and alumina , 2004 .

[33]  Kresse,et al.  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. , 1996, Physical review. B, Condensed matter.

[34]  Electrons at the Fermi surface , 2011 .

[35]  U. Rothlisberger,et al.  Nuclear magnetic resonance chemical shifts from hybrid DFT QM/MM calculations , 2004 .

[36]  E Weinan,et al.  Multiscale simulations in simple metals: A density-functional-based methodology , 2004, cond-mat/0404414.

[37]  Rajiv K. Kalia,et al.  Hybrid quantum mechanical/molecular dynamics simulation on parallel computers: density functional theory on real-space multigrids , 2002 .

[38]  First-principles study of the effects of Si doping on geometric and electronic structure of closed carbon nanotube , 2005 .

[39]  A. Brandt Guide to multigrid development , 1982 .

[40]  M. Ortiz,et al.  Quasicontinuum analysis of defects in solids , 1996 .

[41]  C. Kölmel,et al.  Combining ab initio techniques with analytical potential functions for structure predictions of large systems: Method and application to crystalline silica polymorphs , 1997 .

[42]  M. Baskes,et al.  Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals , 1983 .

[43]  R. Swendsen Monte Carlo Calculation of Renormalized Coupling Parameters , 1984 .

[44]  P. Madden,et al.  Structure and dynamics at the aluminum solid–liquid interface: An ab initio simulation , 2000 .

[45]  M. Baskes,et al.  Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals , 1984 .

[46]  Efthimios Kaxiras,et al.  A QM/MM Implementation of the Self-Consistent Charge Density Functional Tight Binding (SCC-DFTB) Method , 2001 .

[47]  W. Thiel,et al.  Hybrid Models for Combined Quantum Mechanical and Molecular Mechanical Approaches , 1996 .

[48]  Electron transport through molecules: Self-consistent and non-self-consistent approaches , 2003, cond-mat/0311545.

[49]  Robert Haimes,et al.  Multiscale and Multiresolution Methods , 2002 .

[50]  Foiles,et al.  Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. , 1986, Physical review. B, Condensed matter.