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Coupled quantum mechanics/molecular mechanics modeling of metallic materials: Theory and applications

  • Xu Zhang (a1) and Gang Lu (a1)
Abstract

We review two recent advances in coupled quantum mechanics/molecular mechanics (QM/MM) modeling for metallic materials. The QM/MM methods are formulated based on quantum mechanical charge density embedding. In the first method, QM/MM coupling is accomplished by an embedding potential evaluated via orbital-free density functional theory. The charge density embedding in the second QM/MM method is achieved through constrained density functional theory. The extension of QM/MM coupling to the quasicontinuum method is illustrated, offering a route toward quantum mechanical simulations of materials at micron scales and beyond. The theoretical formulations of the QM/MM methods are discussed in detail. We also provide some examples where the QM/MM methods have been applied to understand fundamental physics in a wide range of material problems, ranging from void formation, pipe diffusion along dislocation core, nanoindentation of thin films, hydrogen-assisted cracking, magnetism-induced plasticity to stress-controlled catalysis in metals. An outlook to future development of QM/MM methods for metals is envisioned.

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a) Address all correspondence to this author. e-mail: ganglu@csun.edu
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Contributing Editor: Steven D. Kenny

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1. Lu G. and Kaxiras E.: In Handbook of Theoretical and Computational Nanotechnology, Rieth M. and Schommers W., eds. (American Scientific, Stevenson Ranch, CA, 2004), pp. 133.
2. Abraham F.F., Bernstein N., Broughton J.Q., and Hess D.: Dynamic fracture of silicon: Concurrent simulation of quantum electrons, classical atoms, and the continuum solid. MRS Bull. 25, 27 (2000).
3. Bernstein N., Kermode J.R., and Csanyi G.: Hybrid atomistic simulation methods for materials systems. Rep. Prog. Phys. 72, 026501 (2009).
4. Broughton J.Q., Abraham F.F., Bernstein N., and Kaxiras E.: Concurrent coupling of length scales: Methodology and application. Phys. Rev. B 60, 2391 (1999).
5. Choly N., Lu G., E W., and Kaxiras E.: Multiscale simulations in simple metals: A density-functional-based methodology. Phys. Rev. B 71, 094101 (2005).
6. Csanyi G., Albaret T., Payne M.C., and De Vita A.: “Learn on the fly”: A hybrid classical and quantum-mechanical molecular dynamics simulation. Phys. Rev. Lett. 93, 175503 (2004).
7. Kermode J.W., Csanyi G., and Payne M.C.: DFT embedding and coarse graining techniques. NIC Series 42, 215 (2009).
8. Lu G., Tadmor E.B., and Kaxiras E.: From electrons to finite elements: A concurrent multiscale approach for metals. Phys. Rev. B 73, 024108 (2006).
9. Ogata S., Lidorikis E., Shimojo F., Nakano A., Vashishta P., and Kalia R.K.: Hybrid finite-element/molecular-dynamics/electronic-density-functional approach to materials simulations on parallel computers. Comput. Phys. Commun. 138, 143 (2001).
10. Ogata S. and Belkada R.: A hybrid electronic-density-functional/molecular-dynamics simulation scheme for multiscale simulation of materials on parallel computers: Applications to silicon and alumina. Comput. Mater. Sci. 30, 189 (2004).
11. Ogata S., Shimojo F., Kalia R.K., Nakano A., and Vashishta P.: Environmental effects of H2O on fracture initiation in silicon: A hybrid electronic-density-functional/molecular-dynamics study. J. Appl. Phys. 95, 5316 (2004).
12. Wang C.Y. and Zhang X.: Multiscale modeling and related hybrid approaches. Curr. Opin. Solid State Mater. Sci. 10, 2 (2006).
13. Suryanarayana P., Gavini V., Blesgen T., Bhattacharya K., and Ortiz M.: Non-periodic finite-element formulation of Kohn–Sham density functional theory. J. Mech. Phys. Solids 58, 256 (2010).
14. Nair A.K., Warner D.H., Hennig R.G., and Curtin W.A.: Coupling quantum and continuum scales to predict crack tip dislocation nucleation. Scr. Mater. 63, 1212 (2010).
15. Woodward C. and Rao S.I.: Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc Mo and Ta. Phys. Rev. Lett. 88, 216402 (2002).
16. Kanungo B. and Gavini V.: Large-scale all-electron density functional theory calculations using an enriched finite-element basis. Phys. Rev. B 95, 035112 (2017).
17. Lin H. and Truhlar D.G.: QM/MM: What have we learned, where are we, and where do we go from here? Theor. Chem. Acc. 117, 185 (2007).
18. Antes I. and Thiel W.: On the treatment of link atoms in hybrid methods. ACS Symp. Ser. 712, 50 (1998).
19. Gao J. and Truhlar D.G.: Quantum mechanical methods for enzyme kinetics. Annu. Rev. Phys. Chem. 53, 467 (2002).
20. Zhang X. and Lu G.: Quantum mechanics/molecular mechanics methodology for metals based on orbital-free density functional theory. Phys. Rev. B 76, 245111 (2007).
21. Zhang X., Wang C.Y., and Lu G.: Electronic structure analysis of self-consistent embedding theory for quantum/molecular mechanics simulations. Phys. Rev. B 78, 235119 (2008).
22. Zhang X., Lu G., and Curtin W.A.: Multiscale quantum/atomistic coupling using constrained density functional theory. Phys. Rev. B 87, 054113 (2013).
23. Peng Q., Zhang X., Huang L., Carter E.A., and Lu G.: Quantum simulation of materials at micron scales and beyond. Phys. Rev. B 78, 054118 (2008).
24. Kohn W. and Sham L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, 1133 (1965).
25. Daw M.S. and Baskes M.I.: Embedded-atom method–derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29, 6443 (1984).
26. Garcia-Gonzalez P., Alvarellos J.E., and Chacon E.: Nonlocal kinetic-energy-density functionals. Phys. Rev. B 53, 9509 (1996).
27. Wang L.W. and Teter M.P.: Kinetic-energy functional of the electron density. Phys. Rev. B 45, 13196 (1992).
28. Wang Y.A., Govind N., and Carter E.A.: Orbital-free kinetic-energy density functionals with a density-dependent kernel. Phys. Rev. B 60, 16350 (1999).
29. Hung L., Huang C., and Carter E.A.: Preconditioners and electron density optimization in orbital-free density functional theory. Comput. Phys. Commun. 12, 135 (2012).
30. Shin I. and Carter E.A.: Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors. J. Chem. Phys. 140, 18A531 (2014).
31. Zhao Q. and Parr R.G.: Constrained-search method to determine electronic wave functions from electronic densities. J. Chem. Phys. 98, 543 (1992).
32. Zhao Q., Morrison R.C., and Parr R.G.: From electron densities to Kohn-Sham kinetic energies, orbital energies, exchange–correlation potentials, and exchange–correlation energies. Phys. Rev. A 50, 2138 (1994).
33. Wu Q. and Yang W.: A direct optimization method for calculating density functionals and exchange–correlation potentials from electron densities. J. Chem. Phys. 118, 2498 (2003).
34. Kresse G. and Furthmuller J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).
35. Kresse G. and Furthmuller J.: Efficiency of ab initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15 (1996).
36. Thomas L.H.: The calculation of atomic fields. Proc. Camb. Phil. Soc. 23, 542 (1927).
37. Fermi E.: Eine statistiche methode zur bestimmung einiger eigenschaften des atoms und ihre anwendung auf die theorie des periodischen systems der elemente. Z. Phys. 48, 73 (1928).
38. von Weizsacker C.F.: Zur theorie de Kernmassen. Z. Phys. 96, 431 (1935).
39. Martin R.M.: Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004); Sec. 12.
40. E W., Lu J., and Yang J.Z.: Uniform accuracy of the quasicontinuum method. Phys. Rev. B 74, 214115 (2006).
41. E W. and Lu J.: The continuum limit and QM-continuum approximations of quantum mechanical models of solids. Commun. Math. Sci. 5, 679 (2007).
42. Liu Y., Lu G., Chen Z.Z., and Kioussis N.: An improved QM/MM approach for metals. Model. Simulat. Mater. Sci. Eng. 15, 275 (2007).
43. Tadmor E.B., Ortiz M., and Phillips R.: Quasicontinuum analysis of defects in solids. Philos. Mag. A 73, 1529 (1996).
44. Shenoy V.B., Miller R., Tadmor E.B., Rodney D., Phillips R., and Ortiz M.: An adaptive finite element approach to atomic-scale mechanics—The quasicontinuum method. J. Mech. Phys. Solid 47, 611 (1999).
45. Peng Q., Zhang X., Huang C., Carter E.A., and Lu G.: Quantum mechanical study of solid solution effects on dislocation nucleation during nanoindentation. Model. Simulat. Mater. Sci. Eng. 18, 075003 (2010).
46. Hassan M.H., Blanchard J.P., and Kulcinski G.L.: Stress-enhanced Swelling: Mechanisms and Implication for Fusion Reactors (University of Wisconsin, Madison, WI, 1992).
47. Gleixner R.J. and Nix W.D.: A physically based model of electromigration and stress-induced void formation in microelectronic interconnects. J. Appl. Phys. 86, 1932 (1999).
48. Seppala E.T., Belak J., and Rudd R.E.: Onset of void coalescence during dynamic fracture of ductile metals. Phys. Rev. Lett. 93, 245503 (2004).
49. Zhang X. and Lu G.: Electronic origin of void formation in fcc metals. Phys. Rev. B 77, 174102 (2008).
50. Katz J.L. and Wiedersich H.: Nucleation of voids in materials supersaturated with vacancies and interstitials. J. Chem. Phys. 55, 1414 (1971).
51. Clement C.F. and Woods M.H.: The principles of nucleation theory relevant to the void swelling problem. J. Nucl. Mater. 89, 1 (1980).
52. Pandey A.B., Mishra R.S., Paradkar A.G., and Mahajan Y.R.: Steady state creep behaviour of an Al–Al2O3 alloy. Acta Mater. 45, 1297 (1997).
53. Brechet Y. and Estrin Y.: On the influence of precipitation on the Portevin-Le Chatelier effect. Acta Metall. Mater. 43, 955 (1995).
54. Luo W., Shen C., and Wang Y.: Nucleation of ordered particles at dislocations and formation of split patterns. Acta Mater. 55, 2579 (2007).
55. Baker S.P., Joo Y.C., Knaub M.P., and Arzt E.: Electromigration damage in mechanically deformed Al conductor lines: Dislocations as fast diffusion paths. Acta Mater. 48, 2199 (2000).
56. Legros M., Dehm G., Arzt E., and Balk T.J.: Observation of giant diffusivity along dislocation cores. Science 319, 1646 (2008).
57. Zhang X. and Lu G.: Calculation of fast pipe diffusion along a dislocation stacking fault ribbon. Phys. Rev. B 82, 012101 (2010).
58. Lu G., Kioussis N., Bulatov V.V., and Kaxiras E.: Generalized-stacking-fault energy surface and dislocation properties of aluminum. Phys. Rev. B 62, 3099 (2000).
59. Fischer-Cripps A.C.: Nanoindentation (Springer, New York, 2004).
60. Peng Q., Zhang X., and Lu G.: Quantum mechanical simulations of nanoindentation of Al thin film. Comput. Mater. Sci. 47, 769 (2010).
61. Lynch S.P.: Metallographic and Fractographic techniques for characterising and understanding hydrogen-assisted cracking of metals. In Gaseous Hydrogen Embrittlement of Materials in Energy Technologies, Gangloff R. and Somerday B., eds. (Woodhead, Cambridge, 2012).
62. Sun Y., Peng Q., and Lu G.: Quantum mechanical modeling of hydrogen assisted cracking in aluminum. Phys. Rev. B 88, 104109 (2013).
63. Lu G., Zhang Q., Kioussis N., and Kaxiras E.: Hydrogen-enhanced local plasticity in aluminum: An ab initio study. Phys. Rev. Lett. 87, 095501 (2001).
64. Lu G., Orlikowski D., Park I., Politano O., and Kaxiras E.: Energetics of hydrogen impurities in aluminum and their effect on mechanical properties. Phys. Rev. B 65, 064102 (2002).
65. Apostol F. and Mishin Y.: Hydrogen effect on shearing and cleavage of Al: A first-principles study. Phys. Rev. B 84, 104103 (2011).
66. van der Schaaf B., Gelles D.S., Jitsukawa S., Kimura A., Klueh R.L., Mosloang A., and Odette G.R.: Progress and critical issues of reduced activation ferritic/martensitic steel development. J. Nucl. Mater. 283–287, 52 (2000).
67. Malerba L., Caro A., and Wallenius J.: Multiscale modelling of radiation damage and phase transformations: The challenge of FeCr alloys. J. Nucl. Mater. 382, 112 (2008).
68. Zhang X. and Lu G.: How Cr changes the dislocation core structure of alpha-Fe: The role of magnetism. J. Phys.: Condens. Matter 25, 085403 (2013).
69. Gasteiger H.A. and Markovic N.M.: Just a dream or future reality? Science 324, 48 (2009).
70. Debe M.K.: Electrocatalyst approaches and challenges for automotive fuel cells. Nature 486, 43 (2012).
71. Wang J.X., Inada H., Wu L., Zhu Y., Choi Y.M., Liu P., Zhou W.P., and Adzic R.R.: Oxygen reduction on well-defined core-shell nanocatalysts: Particle size, facet, and Pt shell thickness effects. J. Am. Chem. Soc. 131, 17298 (2009).
72. Guo S., Zhang S., and Sun S.: Tuning nanoparticle catalysis for oxygen reduction reaction. Angew. Chem., Int. Ed. 52, 8526 (2013).
73. Strasser P., Koh S., Anniyev T., Greeley J., More K., Yu C., Liu Z., Kaya S., Nordlund D., Ogasawara H., Toney M.F., and Nilsson A.: Lattice-strain control of the activity in dealloyed core–shell fuel cell catalysts. Nat. Chem. 2, 454 (2010).
74. Zhang L., Iyyamperumal R., Yancey D.F., Crooks R.M., and Henkelman G.: Design of Pt-shell nanoparticles with alloy cores for the oxygen reduction reaction. ACS Nano 7, 9168 (2013).
75. Stamenkovic V.R., Fowler B., Mun B.S., Wang G., Ross P.N., Lucas C.A., and Markovic N.M.: Improved oxygen reduction activity on Pt3Ni(111) via increased surface site availability. Science 315, 493 (2007).
76. Zhang X. and Lu G.: Computational design of core/shell nanoparticles for oxygen reduction reactions. J. Phys. Chem. Lett. 5, 292 (2014).
77. Stamenkovic V.R., Mun B.S., Mayrhofer K.J.J., Ross P.N., Markovic N.M., Rossmeisl J., Greeley J., and Norskov J.K.: Changing the activity of electrocatalysts for oxygen reduction by tuning the surface electronic structure. Angew. Chem., Int. Ed. 45, 2897 (2006).
78. Norskov J.K., Rossmeisl J., Logadottir A., Lindqvist L., Kitchin J.R., Bligaard T., and Jonsson H.: Origin of the overpotential for oxygen reduction at a fuel-cell cathode. J. Phys. Chem. B 108, 17886 (2004).
79. Zhang S., Zhang X., Jiang G., Zhu H., Guo S., Su D., Lu G., and Sun S.: Tuning nanoparticle structure and surface strain for catalysis optimization. J. Am. Chem. Soc. 136, 7734 (2014).
80. Chen Z., Zhang X., and Lu G.: Multiscale computational design of core/shell nanoparticles for oxygen reduction reaction. J. Phys. Chem. C 121, 1964 (2017).
81. Bartok A.P., Payne M.C., Kondor R., and Csanyi G.: Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons. Phys. Rev. Lett. 104, 136403 (2010).
82. Deringer V.L. and Csanyi G.: Machine learning based interatomic potential for amorphous carbon. Phys. Rev. B 95, 094203 (2017).
83. Behler J. and Parrinello M.: Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).
84. Seko A., Takahashi A., and Tanaka I.: First-principles interatomic potentials for ten elemental metals via compressed sensing. Phys. Rev. B 92, 054113 (2015).
85. Li Z., Kermode J.R., and De Vita A.: Molecular dynamics with on-the-fly machine learning of quantum-mechanical forces. Phys. Rev. Lett. 114, 096405 (2015).
86. Zhang Y. and Lin H.: Flexible-boundary quantum-mechanical/molecular-mechanical calculations: Partial charge transfer between the quantum-mechanical and molecular-mechanical subsystems. J. Chem. Theory Comput. 4, 414 (2008).
87. Zhang Y. and Lin H.: Flexible-boundary QM/MM calculations: II. Partial charge transfer across the QM/MM boundary that passes through a covalent bond. Theor. Chem. Acc. 216, 315322 (2010).
88. Pezeshki S. and Lin H.: Recent developments in QM/MM methods towards open-boundary multi-scale simulations. Mol. Simul. 41, 168 (2014).
89. Duster A., Wang C.H., Garza C., Miller D., and Lin H.: Adaptive QM/MM: Where are we, what have we learned, and where will we go from here? Wiley Interdiscip. Rev.: Comput. Mol. Sci. 7, e1310 (2017).
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Journal of Materials Research
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