Journal of Computer-Aided Molecular Design

, Volume 9, Issue 1, pp 87–110 | Cite as

Class IV charge models: A new semiempirical approach in quantum chemistry

  • Joey W. Storer
  • David J. Giesen
  • Christopher J. Cramer
  • Donald G. Truhlar
Research Papers


We propose a new criterion for defining partial charges on atoms in molecules, namely that physical observables calculated from those partial charges should be as accurate as possible. We also propose a method to obtain such charges based on a mapping from approximate electronic wave functions. The method is illustrated by parameterizing two new charge models called AM1-CM1A and PM3-CM1P, based on experimental dipole moments and, respectively, on AM1 and PM3 semiempirical electronic wave functions. These charge models yield rms errors of 0.30 and 0.26 D, respectively, in the dipole moments of a set of 195 neutral molecules consisting of 103 molecules containing H, C, N and O, covering variations of multiple common organic functional groups, 68 fluorides, chlorides, bromides and iodides, 15 compounds containing H, C, Si or S, and 9 compounds containing C-S-O or C-N-O linkages. In addition, partial charges computed with this method agree extremely well with high-level ab initio calculations for both neutral compounds and ions. The CM1 charge models provide a more accurate point charge representation of the dipole moment than provided by most previously available partial charges, and they are far less expensive to compute.


Atomic charges Dipole moments Electron density Electrostatic potential fitting Population analysis 


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  1. 1.
    Straatsma, T.P. and McCammon, J.A., Annu. Rev. Phys. Chem., 43 (1992) 407.Google Scholar
  2. 2a.
    For recent comparisons of different methods of charge analysis see: Bachrach, S.M., In Lipkowitz, K.B. and Bovd, D.B. (Eds.) Reviews in Computational Chemistry, Vol. 5, VCH Publishers, New York, NY, 1993, pp. 171–227.Google Scholar
  3. 2b.
    Wiberg, K.B. and Rablen, P.R., J. Comput. Chem., 14 (1993) 1504.Google Scholar
  4. 3.
    Coppens, P., Annu. Rev. Phys. Chem., 43 (1992) 663.Google Scholar
  5. 4a.
    Mulliken, R.S., J. Chem. Phys., 3 (1935) 564.Google Scholar
  6. 4b.
    Mulliken, R.S., J. Chem. Phys., 23 (1955) 1833.Google Scholar
  7. 4c.
    Mulliken, R.S., J. Chem. Phys., 36 (1962) 3428.Google Scholar
  8. 5a.
    Bader, R.W.F., Acc. Chem. Res., 18 (1985) 9.Google Scholar
  9. 5b.
    Bader, R.W.F., Atoms in Molecules. A Quantum Theory, Clarendon Press, Oxford, 1990.Google Scholar
  10. 6.
    Warshel, A., Acc. Chem. Res., 14 (1981) 284.Google Scholar
  11. 7.
    Price, S.L. and Stone, A.J., J. Chem. Phys., 86 (1987) 2859.Google Scholar
  12. 8.
    Shi, X. and Bartell, L.S., J. Am. Chem. Soc., 92 (1988) 5667.Google Scholar
  13. 9.
    Hall, D. and Williams, D.E., Acta Crystallogr., A31 (1975) 56.Google Scholar
  14. 10.
    Momany, F.A., J. Phys. Chem., 82 (1978) 592.Google Scholar
  15. 11a.
    Kollman, P.A., J. Am. Chem. Soc., 99 (1977) 4875.Google Scholar
  16. 11b.
    Kollman, P.A., J. Am. Chem. Soc., 100 (1978) 2974.Google Scholar
  17. 12.
    Smit, P.H., Derissen, J.L. and Van Duijneveldt, F.B., Mol. Phys., 37 (1979) 521.Google Scholar
  18. 13.
    Cox, S.R. and Williams, D.E., J. Comput. Chem., 2 (1981) 304.Google Scholar
  19. 14a.
    Williams, D.E. and Yan, M.J., Adv. Atomic Mol. Phys., 23 (1988) 87.Google Scholar
  20. 14b.
    Williams, D.E., J. Comput. Chem., 9 (1988) 745.Google Scholar
  21. 14c.
    Williams, D.E., Biopolymers, 29 (1990) 1367.Google Scholar
  22. 14d.
    Williams, D.E., In Lipkowitz, K.B. and Bovd, D.B. (Eds.) Reviews in Computational Chemistry, Vol. 2, VCH Publishers, New York, NY, 1991, pp. 219–271.Google Scholar
  23. 15a.
    Chirlian, L.E. and Francl, M.M., J. Comput. Chem., 8 (1987) 894.Google Scholar
  24. 15b.
    Breneman, C.M. and Wiberg, K.B., J. Comput. Chem., 11 (1990) 361.Google Scholar
  25. 16a.
    Singh, U.C. and Kollman, P.A., J. Comput. Chem., 5 (1984) 129.Google Scholar
  26. 16b.
    Besler, B.H., Merz Jr., K.M. and Kollman, P.A., J. Comput. Chem., 11 (1990) 431.Google Scholar
  27. 16c.
    Merz, K.M., J. Comput. Chem., 11 (1992) 749.Google Scholar
  28. 17a.
    Reed, A.E., Weinstock, R.B. and Weinhold, F., J. Chem. Phys., 83 (1985) 735.Google Scholar
  29. 17b.
    Reed, A.E., Weinhold, F. and Curtiss, L.A., Chem. Rev., 88 (1988) 899.Google Scholar
  30. 18.
    Montagnini, R. and Tomasi, J., J. Mol. Struct. (THEOCHEM), 279 (1993) 131.Google Scholar
  31. 19.
    Dewar, M.J.S., Zoebisch, E.G., Healy, E.F. and Stewart, J.J.P., J. Am. Chem. Soc., 107 (1985) 3902.Google Scholar
  32. 20a.
    Stewart, J.J.P., J. Comput. Chem., 10 (1989) 209.Google Scholar
  33. 20b.
    Stewart, J.J.P., J. Comput. Chem., 10 (1989) 221.Google Scholar
  34. 21a.
    Møller, C. and Plesset, M.S., Phys. Rev., 46 (1934) 618.Google Scholar
  35. 21b.
    Pople, J.A., Seeger, R. and Krishnan, R., Int. J. Quantum Chem. Symp., 11 (1977) 49.Google Scholar
  36. 21c.
    Krishnan, R. and Pople, J.A., Int. J. Quantum Chem., 14 (1978) 91.Google Scholar
  37. 21d.
    Krishnan, R., J. Chem. Phys., 72 (1980) 4244.Google Scholar
  38. 21e.
    Hehre, W.J., Radom, L., Schleyer, P.v.R. and Pople, J.A., Ab Initio Molecular Orbital Theory, Wiley, New York, NY, 1986.Google Scholar
  39. 22.
    Hehre, W.J., Ditchfield, R. and Pople, J.A., J. Chem. Phys., 56 (1972) 2257.Google Scholar
  40. 23a.
    Dunning Jr., T.H., J. Chem. Phys., 90 (1989) 1007.Google Scholar
  41. 23b.
    Woon, D.E. and Dunning Jr., T.H., J. Chem. Phys., 98 (1993) 1358.Google Scholar
  42. 24a.
    X/Y denotes electronic structure level X with basis set Y. HF denotes Hartree-Fock, MP2 denotes second-order Møller-Plesset perturbation theory (Ref. 21a), and cc-pVDZ (Ref. 23) denotes a basis set.Google Scholar
  43. 24b.
    X/Y//Z/W denotes that the wave function and energy are calculated by method X with basis set Y at a geometry optimized by method Z with basis set W. X/Y denotes X/Y//X/Y.Google Scholar
  44. 25a.
    Pople, J.A. and Segal, G.A., J. Chem. Phys., 43 (1965) S129.Google Scholar
  45. 25b.
    Dewar, M.J.S. and Thiel, W., J. Am. Chem. Soc., 99 (1977) 4899.Google Scholar
  46. 26.
    Armstrong, D.R., Perkins, P.G. and Stewart, J.J.P., J. Chem. Soc., Dalton Trans., (1973) 838.Google Scholar
  47. 27a.
    Stark, B., In Hellwege, K.-H. and Hellwege, A.M. (Eds.) Molecular Constants from Microwave Spectroscopy, Landolt-Börnstein, New Series, Group II, Vol. 4, Springer-Verlag, Berlin, 1967, pp. 136–151.Google Scholar
  48. 27b.
    Demaison, J., Hütner, W., Stark, B., Buck, I., Tischer, R. and Winnewisser, M., In Hellwege, K.-H. (Ed.) Molecular Constants, Landolt-Börnstein, New Series, Group II, Vol. 6, Springer-Verlag, Berlin, 1974, pp. 261–304.Google Scholar
  49. 27c.
    Demaison, J., Hütner, W. and Tiemann, E., In Hellwege, K.-H. and Hellwege, A.M. (Eds.) Molecular Constants, Landolt-Börnstein, New Series, Group II, Vol. 14a, Springer-Verlag, Berlin, 1982, pp. 584–643.Google Scholar
  50. 27d.
    Nelson, R.D., Lide, D.R. and Maryott, A.A., Natl. Stand., Ref. Data Ser., United States National Bureau of Standards, NSRDS-NBS 10, 1967.Google Scholar
  51. 28a.
    Hocking, W.H., Z. Naturforsch., 31A (1976) 1113.Google Scholar
  52. 28b.
    Caminati, W., J. Mol. Spectrosc., 86 (1981) 193.Google Scholar
  53. 28c.
    Caminati, W. and Corbelli, G., J. Mol. Spectrosc., 90 (1981) 572.Google Scholar
  54. 29.
    Frisch, M.J., Trucks, G.W., Head-Gordon, M., Gill, P.M.W., Wong, M.W., Foresman, J.B., Johnson, B.G., Schlegel, H.B., Robb, M.A., Repolgle, E.S., Gomperts, R., Andres, J.L., Raghavachari, K., Binkley, J.S., Stewart, J.J.P. and Pople, J.A., GAUSSIAN92, Gaussian, Inc., Pittsburgh, PA, 1992.Google Scholar
  55. 30.
    Cramer, C.J., Lynch, G.C., Hawkins, G.D. and Truhlar, D.G., QCPE Bull., 13 (1993) 78. This new code will be made available as AMSOL, version 4.5.Google Scholar
  56. 31a.
    Marquardt, D.W., J. Soc. Indian Appl. Math., 11 (1963) 431.Google Scholar
  57. 31b.
    Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T., Numerical Recipes, Cambridge University Press, Cambridge, 1989.Google Scholar
  58. 32a.
    Jorgensen, W.L., Chandresekhar, J., Madura, J.D., Impey, R.W. and Klein, M.L., J. Chem. Phys., 79 (1983) 926.Google Scholar
  59. 32b.
    Weiner, S.J., Kollman, P.A., Case, D.A., Singh, U.C., Ghio, C., Alagona, G., Profeta Jr., S. and Weiner, P., J. Am. Chem. Soc., 106 (1984) 765.Google Scholar
  60. 32c.
    Weiner, S.J., Kollman, P.A., Nguyen, D.T. and Case, D.A., J. Comput. Chem., 7 (1986) 230.Google Scholar
  61. 32d.
    Jorgensen, W.L. and Tirado-Rives, J., J. Am. Chem. Soc., 110 (1988) 1657.Google Scholar
  62. 33a.
    Cramer, C.J. and Truhlar, D.G., J. Comput.-Aided Mol. Design, 6 (1992) 629.Google Scholar
  63. 33b.
    Cramer, C.J. and Truhlar, D.G., In Lipkowitz, K.B. and Boyd, D.B. (Eds.) Reviews in Computational Chemistry, Vol. 6, VCH Publishers, New York, NY, in press.Google Scholar

Copyright information

© ESCOM Science Publishers B.V 1995

Authors and Affiliations

  • Joey W. Storer
    • 1
    • 2
  • David J. Giesen
    • 1
    • 2
  • Christopher J. Cramer
    • 1
    • 2
  • Donald G. Truhlar
    • 1
    • 2
  1. 1.Department of ChemistryUniversity of MinnesotaMinneapolisU.S.A.
  2. 2.Supercomputer InstituteUniversity of MinnesotaMinneapolisU.S.A.

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