Molecular Mechanics

Part of the Scientific Computation book series (SCIENTCOMP)


Many interesting problems that we would like to treat using computational molecular modeling are unfortunately too large to be considered by quantum mechanics (QM). Quantum mechanics methods consider the electronic structure in a molecular system. Even when some of the electrons are omitted, still a large number of particles must be considered, which makes the calculations time-consuming from computations point of view.


  1. Allinger, N.L.: Conformational analysis 130. MM2. a hydrocarbon force field utilizing V1 and V2 torsional terms. J. Am. Chem. Soc. 99, 8127–8134 (1977)Google Scholar
  2. Allinger, N.L., Li, F., Yan, L., Tai, J.C.: Molecular mechanics. the MM3 force field for alkenes. J. Comput. Chem. 11, 848–867 (1990a)Google Scholar
  3. Allinger, N.L., Li, F., Yan, L., Tai, J.C.: Molecular mechanics (MM3) calculations on conjugated hydrocarbons. J. Comput. Chem. 11, 868–895 (1990b)CrossRefGoogle Scholar
  4. Allinger, N.L., Chen, K., Katzenelenbogen, J.A., Wilson, S.R., Anstead, G. M.: Hyperconjugative effects on carbon-carbon bond lengths in molecular mechanics (MM4). J. Comput. Chem. 17, 747–755 (1996a)CrossRefGoogle Scholar
  5. Allinger, N.L., Chen, K., Lii, J-H.: An improved force field (MM4) for saturated hydrocarbons. J. Comput. Chem. 17, 642–668 (1996b)CrossRefGoogle Scholar
  6. Anderson, J.A.: An Introduction to Neural Networks. MIT Press, Cambridge (1995)CrossRefzbMATHGoogle Scholar
  7. Bereau, T., DiStasio, R.A. Jr., Tkatchenko, A., von Lilienfeld, O.A.: Non-covalent interactions across organic and biological subsets of chemical space: physics-based potentials parametrized from machine learning. J. Chem. Phys. 148, 241706–241714 (2018)CrossRefADSGoogle Scholar
  8. Camsari, K.Y., Faria, R., Sutton, B.M., Datta, S.: Stochastic p-bits for invertible logic. Phys. Rev. X 7, 031014 (2017)Google Scholar
  9. Camsari, K.Y., Sutton, B.M., Datta, S.: P-bits for probabilistic spin logic. Appl. Phys. Rev. 6, 011305 (2019)CrossRefADSGoogle Scholar
  10. Carlsson, G.: Topology and data. Bull. Am. Math. Soc. 46, 255 (2009)CrossRefMathSciNetzbMATHGoogle Scholar
  11. Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M. Jr., Ferguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W., Kollman, P.A.: A second generation force field for the simulation of proteins, nucleic acids and organic molecules. J. Am. Chem. Soc. 117, 5179–5197 (1995)CrossRefGoogle Scholar
  12. Edelsbrunner, H., Harer, J.: Computational Topology: An Introduction. Amer. Math. Soc., (2010)zbMATHGoogle Scholar
  13. Ewald, P.: Die Berechnung optischer und elektrostatischer Gitter potenciale. Annalen der Physik 64, 253–287 (1921)CrossRefADSzbMATHGoogle Scholar
  14. Faber, F.A., Christensen, A.S., Huang, B., von Lilienfeld, O.A.: Alchemical and structural distribution based representation for universal quantum machine learning. J. Chem. Phys. 148, 241717–12 (2018)CrossRefADSGoogle Scholar
  15. Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)CrossRefMathSciNetGoogle Scholar
  16. Foloppe, N., MacKerell, A.: All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J. Comput. Chem. 21, 86–104 (2000)Google Scholar
  17. Grimme, S.: A general quantum mechanically derived force field (QMDFF) for molecules and condensed phase simulations. J. Chem. Theory Comput. 10(10), 4497–4514 (2014)CrossRefGoogle Scholar
  18. Hagler, A.T., Lifson, S.: Energy functions for peptides and proteins. II. Amide hydrogen bond and calculation of amide crystal properties. J. Am. Chem. Soc. 96(17), 5327–5335 (1974)Google Scholar
  19. Hagler, A.T., Huler, E., Lifson, S.: Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals. J. Am. Chem. Soc. 96(17), 5319–5327 (1974)Google Scholar
  20. Hagler, A.T., Lifson, S., Dauber, P.: Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 1. Carboxylic acids, amides, and the C:O⋯H-hydrogen bonds. J. Am. Chem. Soc. 101(18), 5111–5121 (1979a)Google Scholar
  21. Hagler, A.T., Lifson, S., Dauber, P.: Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 2. A benchmark for the objective comparison of alternative force fields. J. Am. Chem. Soc. 101(18), 5122–5130 (1979b)Google Scholar
  22. Hall, L.H., Kier, L.B.: Electrotopological state indices for atom types: a novel combination of electronic, topological, and valence state information. J. Chem. Inf. Comput. Sci. 35, 1039–1045 (1995)CrossRefGoogle Scholar
  23. Hardy, D.J., Stone, J.E., Vandivort, K.L., Gohara, D., Rodrigues, C., Schulten, K.: Fast molecular electrostatics algorithms on GPUs. In: Wen mei Hwu, W. (ed.) GPU Computing Gems, pp. 43–58. Morgan Kaufmann Publishers, San Francisco (2011)Google Scholar
  24. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning, 2 edn. Springer, New York (2009)CrossRefzbMATHGoogle Scholar
  25. Hu, M., Strachan, J.P., Li, Z., Grafals, E.M., Davila, N., Graves, C., Lam, S., Ge, N., Yang, J.J., Williams, R.S.: Dot-product engine for neuromorphic computing: programming 1t1m crossbar to accelerate matrix-vector multiplication. In: Proceedings of the 53rd annual design automation conference, p. 19 (2016)Google Scholar
  26. Hünenberger, P.H., van Gunsteren, W.F.: Computer Simulation of Biomolecular Systems, Theoretical and Experimental Applications. Kluwer, Dordrecht (1997)Google Scholar
  27. Jorgensen, W.L., Tirado-Rives, J.: The OPLS potential functions for proteins – energy minimizations for crystals of cyclic-peptides and crambin. J. Am. Chem. Soc. 110, 1666–1671 (1988)CrossRefGoogle Scholar
  28. Leach, A.R.: Molecular Modelling. Principles and Applications, 2nd edn. Pearson Education Limited, Edingburgh Gate/Prentice Hall (2001)Google Scholar
  29. Lee, J., Bahri, Y., Novak, R., Schoenholz, S.S., Pennington, J., Sohl-Dickstein, J.: Deep neural networks as gaussian processes. In: Conference Proceedings in ICLR, pp. 1–8 (2018)Google Scholar
  30. Lifson, S., Warshel, A.: Consistent force field for calculations of conformations, vibrational spectra, and enthalpies of cycloalkane and n-alkane molecules. J. Chem. Phys. 49, 5116–5129 (1968)CrossRefADSGoogle Scholar
  31. London, F.: Zur Theorie und Systematik der Molekularkrafte. Zeitschrift für Physik 63, 245–279 (1930)CrossRefADSzbMATHGoogle Scholar
  32. Lubbers, N., Smith, J.S., Barros, K.: Hirarchical modeling of molecular energies using a deep neural network. J. Chem. Phys. 148, 241715–8 (2018)CrossRefADSGoogle Scholar
  33. Luty, B.A., David, M.E., Tironi, I.G., van Gunsteren., W.F.: A comparison of particle-particle, particle-mesh and Ewald methods for calculating electrostatic interactions in periodic molecular systems. Mol. Simul. 14, 11–20 (1994)Google Scholar
  34. Luty, B.A., Tironi, I.G., van Gunsteren, W.F.: Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys. 103, 3014–3021 (1995)CrossRefADSGoogle Scholar
  35. MacKerell, A., Banavali, N.: All-atom empirical force field for nucleic acids: II. Parameter optimization based on small molecule and condensed phase macromolecular target data. J. Comput. Chem. 21, 105–120 (2000)Google Scholar
  36. MacKerell, A.D. Jr., Feig, M., Brooks III, C.L.: Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J. Comput. Chem. 25, 1400–1415 (2004)CrossRefGoogle Scholar
  37. Mamuye, A.L., Rucco, M., Tesei, L., Merelli, E.: Persistent homology analysis of RNA. Mol. Based Math. Biol. 4, 14–25 (2016)Google Scholar
  38. Mehler, E.L.: The Lorentz-Debye-Sack theory and dielectric screening of electrostatic effects in proteins and nucleic acids. In: Murray, J.S., Sen, K. (eds.) Molecular Electrostatic Potential: Concepts and Applications, vol. 3, pp. 371–405. Elsevier Science, Amsterdam (1996)CrossRefGoogle Scholar
  39. Mehler, E.L., Guarnieri, F.: A self-consistent, micro-environment modulated screened Coulomb potential approximation to calculate pH-dependent electrostatic effects in proteins. Biophys. J. 77, 3–22 (1999)CrossRefGoogle Scholar
  40. Metz, M.P., Piszczatowski, K., Szalewicz, K.: Automatic generation of intermolecular potential energy surfaces. J. Chem. Theory Comput. 12(12), 5895–5919 (2016)CrossRefGoogle Scholar
  41. Misquitta, A.J., Podeszwa, R., Jeziorski, B., Szalewicz, K.: Intermolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations. J. Chem. Phys. 123(21), 214103 (2005)CrossRefADSGoogle Scholar
  42. Mobley, D.L., Bannan, C.C., Rizzi, A., Bayly, C.I., Chodera, J.D., Lim, V.T., Lim, N.M., Beauchamp, K.A., Shirts, M.R., Gilson, M.K., Eastman, P.K.: Open force field consortium: escaping atom types using direct chemical perception with SMIRNOFF. BioRxiv, Mar 21 (2018)Google Scholar
  43. Rasmussen, C.E., Williams, C.K.: Gaussian Processes for Machine Learning, vol. 1. MIT Press, Cambridge (2006)zbMATHGoogle Scholar
  44. Rogers, D., Hahn, M.: Extended-connectivity fingerprints. J. Chem. Inf. Model. 50, 742–754 (2010)CrossRefGoogle Scholar
  45. Rupp, M., Tkatchenko, A., M’́uller, K.R., von Lilienfeld, O.A.: Fast and accurate modeling of molecular atomization energies with machine learning. Phys. Rev. Lett. 108, 058301 (2012)Google Scholar
  46. Täuber, U.C.: Renormalization group: applications in statistical physics. Nucl. Phys. B Proc. Suppl. 00:1–28, (2011)Google Scholar
  47. Unke, O.T., Meuwly, M.: A reactive, scalable, and transferable model for molecular energies from a neural network approach based on local information. J. Chem. Phys. 148, 241708–15 (2018)CrossRefADSGoogle Scholar
  48. Vandenbrande, S., Waroquier, M., Speybroeck, V.V., Verstraelen, T.: The monomer electron density force field (MEDFF): a physically inspired model for noncovalent interactions. J. Chem. Theory Comput. 13(1), 161–179 (2017)CrossRefGoogle Scholar
  49. van Gunsteren, W.F., Bakowies, D., Baron, R., Chandrasekhar, I., Christen, M., Daura, X., Gee, P., Geerke, D.P., Glättli, A., Hünenberger, P.H., Kastenholz, M.A., Oostenbrink, C., Schenk, M., Trzesniak, D., van der Vegt, N.F.A., Yu, H.B.: Biomolecular modeling: goals, problems, perspectives. Angew. Chem. Int. Ed. 45(25), 4064–4092 (2006)CrossRefGoogle Scholar
  50. Van Vleet, M.J., Misquitta, A.J., Stone, A.J., Schmidt, J.: Beyond Borm-Mayer: improved models for short-range repulsion in ab initio force fields. J. Chem. Theory Comput. 12, 3851–3870 (2016)CrossRefGoogle Scholar
  51. Warshel, A., Lifson, S.: Consistent force field calculations. II. Crystal structures, sublimation energies, molecular and lattice vibrations, molecular conformations, and enthalpies of alkanes. J. Chem. Phys. 53, 582 (1970)Google Scholar
  52. Weininger, D.: SMILES, a chemical language and information system. 1. Introduction to methodology and encoding rules. J. Chem. Inf. Comput. Sci. 28, 31–36 (1988)Google Scholar
  53. Xia, K., Zhao, Z., Wei, G.W.: Multiresolution persistent homology for excessively large biomolecular datasets. J. Chem. Phys. 143, 134103 (2015)CrossRefADSGoogle Scholar
  54. Zeni, C., Rossi, K., Glielmo, A., Fekete, Á., Gaston, N., Baletto, F., De Vita, A.: Building machine learning force fields for nanoclusters. J. Chem. Phys. 148(24), 241739 (2018)CrossRefADSGoogle Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Computer EngineeringInternational Balkan UniversitySkopjeNorth Macedonia
  2. 2.Advanced Computing Research CenterUniversity of New York TiranaTiranaAlbania

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