Journal of Mathematical Chemistry

, Volume 56, Issue 8, pp 2379–2391 | Cite as

Chemical compound design using nuclear charge distributions

  • B. Christopher RinderspacherEmail author
Original Paper


Finding optimal solutions to design problems in chemistry is hampered by the combinatorially large search space. We develop a general theoretical framework for finding chemical compounds with prescribed properties using nuclear charge distributions. The key is the reformulation of the design problem into an optimization problem on probability density functions in chemical space. In order to achieve tractability, a constrained search formalism on the nuclear charge distributions, which are non-negative, is used to reduce the dimensionality of the problem. Furthermore, we introduce approximations to the exact functional, as derived, for common design properties and constraints.


Chemical design Nuclear charge distribution 

Mathematics Subject Classification

41 46 49 


  1. 1.
    D.N. Bolon, S.L. Mayo, Enzyme-like proteins by computational design. Proc. Nat. Acad. Sci. USA. 98(25), 14274–14279 (2001)CrossRefPubMedGoogle Scholar
  2. 2.
    J.J. Havranek, P.B. Harbury, Automated design of specificity in molecular recognition. Nat. Struct. Biol. 10(1), 45–52 (2003)CrossRefPubMedGoogle Scholar
  3. 3.
    S. Park, Y. Xi, J.G. Saven, Advances in computational protein design. Curr. Opin. Struct. Biol. 14(4), 487–494 (2004)CrossRefPubMedGoogle Scholar
  4. 4.
    N.G. Mang, C. Zeng, Reference energy extremal optimization: a stochastic search algorithm applied to computational protein design. J. Comput. Chem. 29(11), 1762–1771 (2008)CrossRefGoogle Scholar
  5. 5.
    S.V. Dudiy, A. Zunger, Searching for alloy configurations with target physical properties: impurity design via a genetic algorithm inverse band structure approach. Phys. Rev. Lett. 97, 046401 (2006)CrossRefPubMedGoogle Scholar
  6. 6.
    A. Franceschetti, S.V. Dudiy, S.V. Barabash, A. Zunger, J. Xu, M. van Schilfgaarde, First-principles combinatorial design of transition temperatures in multicomponent systems: the case of mn in GaAs. Phys. Rev. Lett. 97(4), 047202 (2006)CrossRefPubMedGoogle Scholar
  7. 7.
    P. Piquini, P.A. Graf, A. Zunger, Band-gap design of quaternary (In, Ga) (As, Sb) semiconductors via the inverse-band-structure approach. Phys. Rev. Lett. 100, 186403 (2008)CrossRefPubMedGoogle Scholar
  8. 8.
    J.-L. Reymond, The chemical space project. Acc. Chem. Res. 48(3), 722–730 (2015)CrossRefPubMedGoogle Scholar
  9. 9.
    S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing. Science 220(4598), 671–680 (1983)CrossRefPubMedGoogle Scholar
  10. 10.
    I.O. Bohachevsky, M.E. Johnson, M.L. Stein, Generalized simulated annealing for function optimization. Technometrics 28(3), 209–217 (1986)CrossRefGoogle Scholar
  11. 11.
    H. Muhlenbein, M. Gorgesschleuter, O. Kramer, Evolution algorithms in combinatorial optimization. Parallel Comput. 7(1), 65–85 (1988)CrossRefGoogle Scholar
  12. 12.
    J. Desmet, M. Demaeyer, B. Hazes, I. Lasters, The dead-end elimination theorem and its use in protein side-chain positioning. Nature 356(6369), 539–542 (1992)CrossRefPubMedGoogle Scholar
  13. 13.
    B.D. Allen, S.L. Mayo, Dramatic performance enhancements for the faster optimization algorithm. J. Comput. Chem. 27(10), 1071–1075 (2006)CrossRefPubMedGoogle Scholar
  14. 14.
    S. Keinan, W.D. Paquette, J.J. Skoko, D.N. Beratan, W.T. Yang, S. Shinde, P.A. Johnston, J.S. Lazo, P. Wipf, Computational design, synthesis and biological evaluation of para-quinone-based inhibitors for redox regulation of the dual-specificity phosphatase Cdc25B. Organ. Biomol. Chem. 6(18), 3256–3263 (2008)CrossRefGoogle Scholar
  15. 15.
    B. Christopher Rinderspacher, J. Andzelm, A. Rawlett, J. Dougherty, D.N. Beratan, W. Yang, Discrete optimization of electronic hyperpolarizabilities in a chemical subspace. J. Chem. Theory Comput. 5(12), 3321–3329 (2009)CrossRefPubMedGoogle Scholar
  16. 16.
    J.M. Elward, B. Christopher Rinderspacher, Smooth heuristic optimization on a complex chemical subspace. Phys. Chem. Chem. Phys. 17(37), 24322–24335 (2015)CrossRefPubMedGoogle Scholar
  17. 17.
    G. Montavon, M. Rupp, V. Gobre, A. Vazquez-Mayagoitia, K. Hansen, A. Tkatchenko, K.-R. Müller, O.A. von Lilienfeld, Machine learning of molecular electronic properties in chemical compound space. New J. Phys. 15(9), 095003 (2013)CrossRefGoogle Scholar
  18. 18.
    A.G. Kusne, T. Gao, A. Mehta, L. Ke, M.C. Nguyen, K.M. Ho, V. Antropov, C.Z. Wang, M.J. Kramer, C. Long et al., On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets. Sci. Rep. 4(1), 6367 (2014)CrossRefPubMedPubMedCentralGoogle Scholar
  19. 19.
    T.C. Le, D.A. Winkler, Discovery and optimization of materials using evolutionary approaches. Chem. Rev. 116(10), 6107–6132 (2016)CrossRefPubMedGoogle Scholar
  20. 20.
    K.W. Moore, A. Pechen, X.-J. Feng, J. Dominy, V. Beltrani, H. Rabitz, Universal characteristics of chemical synthesis and property optimization. Chem. Sci. 2(3), 417–424 (2011)CrossRefGoogle Scholar
  21. 21.
    K.W. Moore, A. Pechen, X.-J. Feng, J. Dominy, V.J. Beltrani, H. Rabitz, Why is chemical synthesis and property optimization easier than expected? Phys. Chem. Chem. Phys. 13, 10048–10070 (2011)CrossRefPubMedGoogle Scholar
  22. 22.
    D.F. Green, A statistical framework for hierarchical methods in molecular simulation and design. J. Chem. Theory Comput. 6(5), 1682–1697 (2010)CrossRefPubMedGoogle Scholar
  23. 23.
    G.A. Arteca, P.G. Mezey, Constant electronic-energy trajectories in abstract nuclear-charge space and level set topology. J. Chem. Phys 87(10), 5882–5891 (1987)CrossRefGoogle Scholar
  24. 24.
    G. Paul, Mezey. A simple relation between nuclear charges and potential surfaces. J. Am. Chem. Soc. 107(11), 3100–3105 (1985)CrossRefGoogle Scholar
  25. 25.
    P.G. Mezey, Classification schemes of nuclear geometries and the concept of chemical structure. metric spaces of chemical structure sets over potential energy hypersurfaces. J. Chem. Phys. 78(10), 6182–6186 (1983)CrossRefGoogle Scholar
  26. 26.
    O.A. von Lilienfeld, R.D. Lins, U. Rothlisberger, Variational particle number approach for rational compound design. Phys. Rev. Lett. 95, 153002 (2005)CrossRefGoogle Scholar
  27. 27.
    O.A. von Lilienfeld, I. Tavernelli, U. Rothlisberger, D. Sebastiani, Variational optimization of effective atom centered potentials for molecular properties. J. Chem. Phys. 122(1), 014113 (2005)CrossRefGoogle Scholar
  28. 28.
    M.L. Wang, X.Q. Hu, D.N. Beratan, W.T. Yang, Designing molecules by optimizing potentials. J. Am. Chem. Soc. 128(10), 3228–3232 (2006)CrossRefPubMedGoogle Scholar
  29. 29.
    O.A. von Lilienfeld, M.E. Tuckerman, Molecular grand-canonical ensemble density functional theory and exploration of chemical space. J. Chem. Phys. 125(15), 154104 (2006)CrossRefGoogle Scholar
  30. 30.
    P.G. Mezey, Cluster topology and bounds for the electronic energy. Surf. Sci. 156, 597–604 (1985)CrossRefGoogle Scholar
  31. 31.
    P.G. Mezey, Simple lower and upper bounds for isomerization energies. Can. J. Chem. 62(7), 1356–1357 (1984)CrossRefGoogle Scholar
  32. 32.
    P.G. Mezey, Constraints on electronic energy hypersurfaces of higher multiplicities. J. Chem. Phys. 80(10), 5055–5057 (1984)CrossRefGoogle Scholar
  33. 33.
    S. Keinan, X.Q. Hu, D.N. Beratan, W.T. Yang, Designing molecules with optimal properties using the linear combination of atomic potentials approach in an AM1 semiempirical framework. J. Phys. Chem. A 111(1), 176–181 (2007)CrossRefPubMedGoogle Scholar
  34. 34.
    P.G. Mezey, Level set topology of the nuclear charge space and the electronic energy functional. Int. J. Quantum Chem. 22(1), 101–114 (1982)CrossRefGoogle Scholar
  35. 35.
    P.G. Mezey, Electronic energy inequalities for isoelectronic molecular systems. Theor. Chim. Acta. 59(4), 321–332 (1981)CrossRefGoogle Scholar
  36. 36.
    P.G. Mezey, Level set topologies and convexity relations for hamiltonians with linear parameters. Chem. Phys. Lett. 87(3), 277–279 (1982)CrossRefGoogle Scholar
  37. 37.
    P.G. Mezey, The holographic electron density theorem, de-quantization, re-quantization, and nuclear charge space extrapolations of the universal molecule model, in Proceedings of the International Conference of Computational Methods in Sciences and Engineering 2017 (ICCMSE-2017), vol 1906 AIP Conference Proceedings, 2017. International Conference of Computational Methods in Sciences and Engineering (ICCMSE), ed. by T.E. Simos, Z.K. Monovasilis, T. Thessaloniki, (Greece, 2017)Google Scholar
  38. 38.
    P.G. Mezey, Relations between real molecules through abstract molecules: the reference cluster approach. Theor. Chem. Acc. 134(11), 134 (2015)CrossRefGoogle Scholar
  39. 39.
    P.G. Mezey, Discrete skeletons of continua in the universal molecule model. in International Conference of Computational Methods in Sciences and Engineering 2009 (ICCMSE 2009), vol 1504 AIP Conference Proceedings, AIP, 2012. 7th International Conference on Computational Methods in Science and Engineering (ICCMSE), ed. by T.E. Simos, G. Maroulis, (Rhodes, Greece, 2009) pp. 725–728Google Scholar
  40. 40.
    P.G. Mezey, On discrete to continuum transformations and the universal molecule model—a mathematical chemistry perspective of molecular families. in AIP Conference Proceedings, vol 2 AIP Conference Proceedings, AIP, 2007. International Conference on Computational Methods in Science and Engineering, ed. by T.E. Simos, G. Maroulis (Corfu, Greece, 2007) pp. 513–516Google Scholar
  41. 41.
    G.A. Arteca, P.G. Mezey, Simple analytic bounds for the electronic-energy from level set boundaries of nuclear-charge space. Phys. Rev. A 35(10), 4044–4050 (1987)CrossRefGoogle Scholar
  42. 42.
    R.J. Harrison, G.I. Fann, T. Yanai, Z. Gan, G. Beylkin, Multiresolution quantum chemistry: Basic theory and initial applications. J. Chem. Phys. 121(23), 11587–11598 (2004)CrossRefPubMedGoogle Scholar
  43. 43.
    C.D. Griffin, R. Acevedo, D.W. Massey, J.L. Kinsey, B.R. Johnson, Multimode wavelet basis calculations via the molecular self-consistent-field plus configuration-interaction method. J. Chem. Phys. 124(13), 134105 (2006)CrossRefPubMedGoogle Scholar
  44. 44.
    D.W. Massey, R. Acevedo, B.R. Johnson, Additions to the class of symmetric-antisymmetric multiwavelets: derivation and use as quantum basis functions. J. Chem. Phys. 124(1), 014101 (2006)CrossRefGoogle Scholar
  45. 45.
    J.E. Pask, P.A. Sterne, Finite element methods in ab initio electronic structure calculations. Modell. Simul. Mater. Sci. Eng. 13(3), R71–R96 (2005)CrossRefGoogle Scholar
  46. 46.
    V. Gavini, K. Bhattacharya, M. Ortiz, Quasi-continuum orbital-free density-functional theory:a route to multi-million atom non-periodic DFT calculation. J. Mech. Phys. Solids 55, 697–718 (2007)CrossRefGoogle Scholar
  47. 47.
    P. Suryanarayana, V. Gavini, T. Blesgen, K. Bhattacharya, M. Ortiz, Non-periodic finite-element formulation of kohn–sham density functional theory. J. Mech. Phys. Solids 58(2), 256–280 (2010)CrossRefGoogle Scholar

Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2018

Authors and Affiliations

  1. 1.US Army Research LaboratoryAberdeenUSA

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