Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-23T08:17:36.463Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  30 January 2018

Xu Zhang  and
Gang Lu
Xu Zhang
Affiliation:
Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330-8268, USA
Gang Lu*
Affiliation:
Department of Physics and Astronomy, California State University Northridge, Northridge, California 91330-8268, USA
*
a)Address all correspondence to this author. e-mail: ganglu@csun.edu
Get access

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.

Keywords

metalelectronic structuredefects
Type
REVIEW
Information
Journal of Materials Research , Volume 33 , Issue 7: Focus Issue: Advanced Atomistic Algorithms in Materials Science , 13 April 2018 , pp. 796 - 812
Check for updates
Copyright
Copyright © Materials Research Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Contributing Editor: Steven D. Kenny

This section of Journal of Materials Research is reserved for papers that are reviews of literature in a given area.

References

REFERENCES

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. 1–33.Google Scholar
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).Google Scholar
Bernstein, N., Kermode, J.R., and Csanyi, G.: Hybrid atomistic simulation methods for materials systems. Rep. Prog. Phys. 72, 026501 (2009).Google Scholar
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).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
Kermode, J.W., Csanyi, G., and Payne, M.C.: DFT embedding and coarse graining techniques. NIC Series 42, 215 (2009).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
Wang, C.Y. and Zhang, X.: Multiscale modeling and related hybrid approaches. Curr. Opin. Solid State Mater. Sci. 10, 2 (2006).Google Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
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).Google Scholar
Antes, I. and Thiel, W.: On the treatment of link atoms in hybrid methods. ACS Symp. Ser. 712, 50 (1998).Google Scholar
Gao, J. and Truhlar, D.G.: Quantum mechanical methods for enzyme kinetics. Annu. Rev. Phys. Chem. 53, 467 (2002).CrossRefGoogle ScholarPubMed
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).Google Scholar
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).Google Scholar
Zhang, X., Lu, G., and Curtin, W.A.: Multiscale quantum/atomistic coupling using constrained density functional theory. Phys. Rev. B 87, 054113 (2013).CrossRefGoogle Scholar
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).Google Scholar
Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, 1133 (1965).Google Scholar
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).Google Scholar
Garcia-Gonzalez, P., Alvarellos, J.E., and Chacon, E.: Nonlocal kinetic-energy-density functionals. Phys. Rev. B 53, 9509 (1996).Google Scholar
Wang, L.W. and Teter, M.P.: Kinetic-energy functional of the electron density. Phys. Rev. B 45, 13196 (1992).Google Scholar
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).Google Scholar
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).Google Scholar
Shin, I. and Carter, E.A.: Enhanced von Weizsäcker Wang-Govind-Carter kinetic energy density functional for semiconductors. J. Chem. Phys. 140, 18A531 (2014).Google Scholar
Zhao, Q. and Parr, R.G.: Constrained-search method to determine electronic wave functions from electronic densities. J. Chem. Phys. 98, 543 (1992).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).CrossRefGoogle Scholar
Thomas, L.H.: The calculation of atomic fields. Proc. Camb. Phil. Soc. 23, 542 (1927).Google Scholar
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).Google Scholar
von Weizsacker, C.F.: Zur theorie de Kernmassen. Z. Phys. 96, 431 (1935).Google Scholar
Martin, R.M.: Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, Cambridge, 2004); Sec. 12.Google Scholar
E, W., Lu, J., and Yang, J.Z.: Uniform accuracy of the quasicontinuum method. Phys. Rev. B 74, 214115 (2006).Google Scholar
E, W. and Lu, J.: The continuum limit and QM-continuum approximations of quantum mechanical models of solids. Commun. Math. Sci. 5, 679 (2007).Google Scholar
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).Google Scholar
Tadmor, E.B., Ortiz, M., and Phillips, R.: Quasicontinuum analysis of defects in solids. Philos. Mag. A 73, 1529 (1996).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
Zhang, X. and Lu, G.: Electronic origin of void formation in fcc metals. Phys. Rev. B 77, 174102 (2008).Google Scholar
Katz, J.L. and Wiedersich, H.: Nucleation of voids in materials supersaturated with vacancies and interstitials. J. Chem. Phys. 55, 1414 (1971).Google Scholar
Clement, C.F. and Woods, M.H.: The principles of nucleation theory relevant to the void swelling problem. J. Nucl. Mater. 89, 1 (1980).Google Scholar
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).CrossRefGoogle Scholar
Brechet, Y. and Estrin, Y.: On the influence of precipitation on the Portevin-Le Chatelier effect. Acta Metall. Mater. 43, 955 (1995).Google Scholar
Luo, W., Shen, C., and Wang, Y.: Nucleation of ordered particles at dislocations and formation of split patterns. Acta Mater. 55, 2579 (2007).Google Scholar
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).CrossRefGoogle Scholar
Legros, M., Dehm, G., Arzt, E., and Balk, T.J.: Observation of giant diffusivity along dislocation cores. Science 319, 1646 (2008).Google Scholar
Zhang, X. and Lu, G.: Calculation of fast pipe diffusion along a dislocation stacking fault ribbon. Phys. Rev. B 82, 012101 (2010).Google Scholar
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).Google Scholar
Fischer-Cripps, A.C.: Nanoindentation (Springer, New York, 2004).Google Scholar
Peng, Q., Zhang, X., and Lu, G.: Quantum mechanical simulations of nanoindentation of Al thin film. Comput. Mater. Sci. 47, 769 (2010).Google Scholar
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).Google Scholar
Sun, Y., Peng, Q., and Lu, G.: Quantum mechanical modeling of hydrogen assisted cracking in aluminum. Phys. Rev. B 88, 104109 (2013).Google Scholar
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).Google Scholar
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).Google Scholar
Apostol, F. and Mishin, Y.: Hydrogen effect on shearing and cleavage of Al: A first-principles study. Phys. Rev. B 84, 104103 (2011).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
Gasteiger, H.A. and Markovic, N.M.: Just a dream or future reality? Science 324, 48 (2009).Google Scholar
Debe, M.K.: Electrocatalyst approaches and challenges for automotive fuel cells. Nature 486, 43 (2012).Google Scholar
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).Google Scholar
Guo, S., Zhang, S., and Sun, S.: Tuning nanoparticle catalysis for oxygen reduction reaction. Angew. Chem., Int. Ed. 52, 8526 (2013).Google Scholar
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).Google Scholar
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).Google Scholar
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).CrossRefGoogle ScholarPubMed
Zhang, X. and Lu, G.: Computational design of core/shell nanoparticles for oxygen reduction reactions. J. Phys. Chem. Lett. 5, 292 (2014).Google Scholar
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).Google Scholar
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).Google Scholar
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).CrossRefGoogle ScholarPubMed
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).Google Scholar
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).Google Scholar
Deringer, V.L. and Csanyi, G.: Machine learning based interatomic potential for amorphous carbon. Phys. Rev. B 95, 094203 (2017).Google Scholar
Behler, J. and Parrinello, M.: Generalized neural-network representation of high-dimensional potential-energy surfaces. Phys. Rev. Lett. 98, 146401 (2007).Google Scholar
Seko, A., Takahashi, A., and Tanaka, I.: First-principles interatomic potentials for ten elemental metals via compressed sensing. Phys. Rev. B 92, 054113 (2015).Google Scholar
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).Google Scholar
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).Google Scholar
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, 315–322 (2010).Google Scholar
Pezeshki, S. and Lin, H.: Recent developments in QM/MM methods towards open-boundary multi-scale simulations. Mol. Simul. 41, 168 (2014).Google Scholar
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).Google Scholar