Challenging Problems in Charge Density Determination: Polar Bonds and Influence of the Environment

  • Bernd EngelsEmail author
  • Thomas C. Schmidt
  • Carlo Gatti
  • Tanja Schirmeister
  • Reinhold F. Fink
Part of the Structure and Bonding book series (STRUCTURE, volume 147)


The review focuses on the influence of environments on electron densities (ED) and their Laplacians. This is of interest for many applications which uses EDs measured at hand of crystals of a given ligand to predict its pharmaceutical properties. This comprises for example the questions if the ligand fits into the active center of an enzyme and how strong it binds to this active side. This widely used approximation strongly rely on the assumption that the active side of the enzyme influences the ED of the ligand the same way the crystal environment does. This is not obvious since enzymes represent systems made to catalyze reactions. So one could assume that the active sides influence the EDs of ligands in a special way to prepare them for a given reaction. The review shows that this is indeed the case for E64c. Its inhibition properties result since it reacts with cathepsin B and forms a covalently bonded cathepsin B–E64c complex. It clearly comes out that the reaction only takes place since the ED of the ligand is influenced in a way which is not found in the respective crystals. Nevertheless, the review also shows that the above mentioned approximation holds for AMCHA which serves as a model compound for reversible inhibitors. In the last part the review shows in detail that the source function can be used to study the influence of the environment in more detail. In the first part the review summarizes investigations on the reliability of pure theoretical approaches to ED and its Laplacians.


Electron density Ab initio QM/MM Environmental effects Source function E64c Cathepsin B AMCHA Basis set effects 


  1. 1.
    Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136(3B):B864–B871Google Scholar
  2. 2.
    Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140(4A):1133–1138Google Scholar
  3. 3.
    Coppens P (1997) X-ray charge densities and chemical bonding. Oxford University Press, OxfordGoogle Scholar
  4. 4.
    Tsirelson VG, Ozerov RP (1996) Electron density and bonding in crystals. IOP Publishing, BristolGoogle Scholar
  5. 5.
    Parr RG, Yang W (1989) Density functional theory of atoms and molecules. Clarendon, New YorkGoogle Scholar
  6. 6.
    Koritsanszky TS, Coppens P (2001) Chemical applications of X-ray charge-density analysis. Chem Rev 101(6):1583–1627. doi: 10.1021/Cr990112c Google Scholar
  7. 7.
    Koch W, Holthausen MC (1999) A chemist’s guide to density functional theory. Wiley-VCH, WeinheimGoogle Scholar
  8. 8.
    Ernzerhof M, Perdew JP, Burke K (1996) Density functionals: where do they come from, why do they work? In: Density functional theory I, vol 180. Topics in current chemistry. Springer, Berlin 33, pp 1–30Google Scholar
  9. 9.
    Bader RWF (1990) Atoms in molecules: a quantum theory. Oxford University Press, OxfordGoogle Scholar
  10. 10.
    Matta CF, Boyd RJ (2007) The quantum theory of atoms in molecules. Wiley-VCH, WeinheimGoogle Scholar
  11. 11.
    Shaik SS, Hilberty PC (2007) The chemist’s guide to valence bond theory. Wiley, Hoboken, NJGoogle Scholar
  12. 12.
    Bagus PS, Hermann K, Bauschlicher CW (1984) A new analysis of charge-transfer and polarization for ligand-metal bonding – model studies of Al4co and Al4nh3. J Chem Phys 80(9):4378–4386Google Scholar
  13. 13.
    Mulliken RS (1955) Electronic population analysis on Lcao-Mo molecular wave functions. 1. J Chem Phys 23(10):1833–1840Google Scholar
  14. 14.
    Reed AE, Curtiss LA, Weinhold F (1988) Intermolecular interactions from a natural bond orbital, donor–acceptor viewpoint. Chem Rev 88(6):899–926Google Scholar
  15. 15.
    Debye P (1915) Zerstreuung von Röntgenstrahlen. Annalen der Physik 351(6):809–823. doi: 10.1002/andp.19153510606 Google Scholar
  16. 16.
    Coppens P (2005) Charge densities come of age. Angew Chem Int Ed 44(42):6810–6811. doi: 10.1002/anie.200501734 Google Scholar
  17. 17.
    Leusser D, Henn J, Kocher N, Engels B, Stalke D (2004) S=N versus S+-N-: an experimental and theoretical charge density study. J Am Chem Soc 126(6):1781–1793. doi: 10.1021/Ja038941+ Google Scholar
  18. 18.
    Kocher N, Henn J, Gostevskii B, Kost D, Kalikhman I, Engels B, Stalke D (2004) Si–E (E = N, O, F) bonding in a hexacoordinated silicon complex: new facts from experimental and theoretical charge density studies. J Am Chem Soc 126(17):5563–5568. doi: 10.1021/Ja038459r Google Scholar
  19. 19.
    Hibbs DE, Austin-Woods CJ, Platts JA, Overgaard J, Turner P (2003) Experimental and theoretical charge density study of the neurotransmitter thurine. Chem Eur J 9(5):1075–1084Google Scholar
  20. 20.
    Spackman MA, Munshi P, Dittrich B (2007) Dipole moment enhancement in molecular crystals from X-ray diffraction data. Chemphyschem 8(14):2051–2063. doi: 10.1002/cphc.200700339 Google Scholar
  21. 21.
    Lecomte C, Souhassou M, Pillet S (2003) Topology of experimental charge density: a tool for understanding atomic interactions. J Mol Struct 647(1–3):53–64. doi: 10.1016/s0022-2860(02)00524-0 Google Scholar
  22. 22.
    Jelsch C, Guillot B, Lagoutte A, Lecomte C (2005) Advances in protein and small-molecule charge-density refinement methods using MoPro. J Appl Crystallogr 38:38–54. doi: 10.1107/S0021889804025518 Google Scholar
  23. 23.
    Jelsch C, Teeter MM, Lamzin V, Pichon-Pesme V, Blessing RH, Lecomte C (2000) Accurate protein crystallography at ultra-high resolution: valence electron distribution in crambin. Proc Natl Acad Sci USA 97(7):3171–3176Google Scholar
  24. 24.
    Luger P (2007) Fast electron density methods in the life sciences – a routine application in the future? Org Biomol Chem 5(16):2529–2540. doi: 10.1039/B706235d Google Scholar
  25. 25.
    Cachau R, Howard E, Barth P, Mitschler A, Chevrier B, Lamour V, Joachimiak A, Sanishvili R, Van Zandt M, Sibley E, Moras D, Podjarny A (2000) Model of the catalytic mechanism of human aldose reductase based on quantum chemical calculations. J Phys IV 10(P10):3–13Google Scholar
  26. 26.
    Flaig R, Koritsanszky T, Janczak J, Krane HG, Morgenroth W, Luger P (1999) Fast experiments for charge-density determination: topological analysis and electrostatic potential of the amino acids L-Asn, DL-Glu, DL-Ser, and L-Thr. Angew Chem Int Ed 38(10):1397–1400Google Scholar
  27. 27.
    Li X, Wu G, Abramov YA, Volkov AV, Coppens P (2002) Application of charge density methods to a protein model compound: calculation of Coulombic intermolecular interaction energies from the experimental charge density. Proc Natl Acad Sci USA 99(19):12132–12137. doi: 10.1073/pnas.192438999 Google Scholar
  28. 28.
    Flaig R, Koritsanszky T, Zobel D, Luger P (1998) Topological analysis of the experimental electron densities of amino acids. 1. d, l-aspartic acid at 20 K. J Am Chem Soc 120(10):2227–2238Google Scholar
  29. 29.
    Zhurova EA, Zhurov VV, Chopra D, Stash AI, Pinkerton AA (2009) 17 Alpha-estradiol center dot 1/2 H2O: super-structural ordering, electronic properties, chemical bonding, and biological activity in comparison with other estrogens. J Am Chem Soc 131(47):17260–17269. doi: 10.1021/Ja906057z Google Scholar
  30. 30.
    Hansen NK, Coppens P (1978) Electron population analysis of accurate diffraction data. 6. Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr A 34(Nov):909–921Google Scholar
  31. 31.
    Volkov A, Abramov Y, Coppens P, Gatti C (2000) On the origin of topological differences between experimental and theoretical crystal charge densities. Acta Crystallogr A 56:332–339Google Scholar
  32. 32.
    Volkov A, Coppens P (2001) Critical examination of the radial functions in the Hansen–Coppens multipole model through topological analysis of primary and refined theoretical densities. Acta Crystallogr A 57:395–405Google Scholar
  33. 33.
    Koritsanszky T, Volkov A, Coppens P (2002) Aspherical-atom scattering factors from molecular wave functions. 1. Transferability and conformation dependence of atomic electron densities of peptides within the multipole formalism. Acta Crystallogr A 58:464–472. doi: 10.1107/s0108767302010991 Google Scholar
  34. 34.
    Zuo JM, Kim M, O’Keeffe M, Spence JCH (1999) Direct observation of d-orbital holes and Cu–Cu bonding in Cu2O. Nature 401(6748):49–52Google Scholar
  35. 35.
    Wang SG, Schwarz WHE (2000) Final comment on the discussions of “The case of cuprite”. Angew Chem Int Ed 39(21):3794–3796Google Scholar
  36. 36.
    Schwarz WHE (2006) Measuring orbitals: provocation or reality? Angew Chem Int Ed 45(10):1508–1517. doi: 10.1002/anie.200501333 Google Scholar
  37. 37.
    Hibbs DE, Overgaard J, Platts JA, Waller MP, Hursthouse MB (2004) Experimental and theoretical charge density studies of tetrafluorophthalonitrile and tetrafluoroisophthalonitrile. J Phys Chem B 108(11):3663–3672. doi: 10.1021/Jp0377001 Google Scholar
  38. 38.
    Flaig R, Koritsanszky T, Dittrich B, Wagner A, Luger P (2002) Intra- and intermolecular topological properties of amino acids: a comparative study of experimental and theoretical results. J Am Chem Soc 124(13):3407–3417. doi: 10.1021/Ja011492y Google Scholar
  39. 39.
    Overgaard J, Waller MP, Platts JA, Hibbs DE (2003) Influence of crystal effects on molecular charge densities in a study of 9-ethynyl-9-fluorenol. J Phys Chem A 107(50):11201–11208. doi: 10.1021/jp036269x Google Scholar
  40. 40.
    Arnold WD, Sanders LK, McMahon MT, Volkov RV, Wu G, Coppens P, Wilson SR, Godbout N, Oldfield E (2000) Experimental, Hartree–Fock, and density functional theory investigations of the charge density, dipole moment, electrostatic potential, and electric field gradients in l-asparagine monohydrate. J Am Chem Soc 122(19):4708–4717Google Scholar
  41. 41.
    Wagner A, Flaig R, Zobel D, Dittrich B, Bombicz P, Strumpel M, Luger P, Koritsanszky T, Krane HG (2002) Structure and charge density of a C-60-fullerene derivative based on a high resolution synchrotron diffraction experiment at 100 K. J Phys Chem A 106(28):6581–6590. doi: 10.1021/jp0145199 Google Scholar
  42. 42.
    Tafipolsky M, Scherer W, Ofele K, Artus G, Pedersen B, Herrmann WA, McGrady GS (2002) Electron delocalization in acyclic and N-heterocyclic carbenes and their complexes: a combined experimental and theoretical charge-density study. J Am Chem Soc 124(20):5865–5880. doi: 10.1021/Ja011761k Google Scholar
  43. 43.
    Ponec R, Gatti C (2009) Do the structural changes defined by the electron density topology necessarily affect the picture of the bonding? Inorg Chem 48(23):11024–11031. doi:10.1021/Ic901197b and references hereinGoogle Scholar
  44. 44.
    Gatti C (2010) The source function descriptor as a tool to extract chemical information from theoretical and experimental electron densities. Structure and bonding. SpringerGoogle Scholar
  45. 45.
    Peres N, Boukhris A, Souhassou M, Gavoille G, Lecomte C (1999) Electron density in ammonium dihydrogen phosphate: non-uniqueness of the multipolar model in simple inorganic structures. Acta Crystallogr A 55:1038–1048Google Scholar
  46. 46.
    Gatti C (2005) Chemical bonding in crystals: new directions. Z Kristallogr 220(5–6):399–457Google Scholar
  47. 47.
    Bertini L, Cargnoni F, Gatti C (2007) Chemical insight into electron density and wave functions: software developments and applications to crystals, molecular complexes and materials science. Theor Chem Acc 117(5–6):847–884. doi: 10.1007/s00214-006-0208-z Google Scholar
  48. 48.
    Podjarny A, Howard E, Mitschler A, Chevrier B, Lecomte C, Guillot B, Pichon-Pesme V, Jelsch C (2002) X-ray crystallography at subatomic resolution. Europhys News 33(4):113–117Google Scholar
  49. 49.
    Schmidt A, Lamzin VS (2002) Veni, vidi, vici – atomic resolution unravelling the mysteries of protein function. Curr Opin Struct Biol 12(6):698–703Google Scholar
  50. 50.
    Henn J, Ilge D, Leusser D, Stalke D, Engels B (2004) On the accuracy of theoretically and experimentally determined electron densities of polar bonds. J Phys Chem A 108(43):9442–9452. doi: 10.1021/Jp047840a Google Scholar
  51. 51.
    Gatti C, MacDougall PJ, Bader RFW (1988) Effect of electron correlation on the topological properties of molecular charge-distributions. J Chem Phys 88(6):3792–3804Google Scholar
  52. 52.
    Boyd RJ, Ugalde JM (1992) Computational chemistry: structure, interactions and reactivity. Elsevier, AmsterdamGoogle Scholar
  53. 53.
    Wang J, Shi Z, Boyd RJ, Gonzalez CA (1994) A comparative-study of electron-densities in carbon-monoxide calculated from conventional ab-initio and density-functional methods. J Phys Chem 98(28):6988–6994Google Scholar
  54. 54.
    Boyd RJ, Wang J, Eriksson LA (1995) Recent advances in density functional methods. World Scientific, SingaporeGoogle Scholar
  55. 55.
    Jayatilaka D, Dittrich B (2008) X-ray structure refinement using aspherical atomic density functions obtained from quantum-mechanical calculations. Acta Crystallogr A 64(3):383–393. doi: 10.1107/s0108767308005709 Google Scholar
  56. 56.
    Cheeseman JR, Carroll MT, Bader RFW (1988) The mechanics of hydrogen-bond formation in conjugated systems. Chem Phys Lett 143(5):450–458Google Scholar
  57. 57.
    Cremer D, Kraka E (1984) A description of the chemical bond in terms of local properties of electron-density and energy. Croat Chem Acta 57(6):1259–1281Google Scholar
  58. 58.
    Ehrlich P (1913) Chemotherapeutics: scientific principles, methods and results. Lancet 182:445–451Google Scholar
  59. 59.
    Koshland DE (1958) Application of a theory of enzyme specificity to protein synthesis. Proc Natl Acad Sci USA 44(2):98–104Google Scholar
  60. 60.
    Koshland DE (1994) The key-lock theory and the induced fit theory. Angew Chem Int Ed 33(23–24):2375–2378Google Scholar
  61. 61.
    Schmuck C, Engels B, Schirmeister T, Fink R (2008) Chemie fuer Mediziner. Pearson, MuenchenGoogle Scholar
  62. 62.
    Berg JM, Tymoczko JL, Stryer L (2007) Biochemistry. WH Freeman, New YorkGoogle Scholar
  63. 63.
    Schmidt A, Lamzin VS (2007) From atoms to proteins. Cell Mol Life Sci 64(15):1959–1969. doi: 10.1007/s00018-007-7195-7 Google Scholar
  64. 64.
    Cachau RE, Podjarny AD (2005) High-resolution crystallography and drug design. J Mol Recognit 18(3):196–202. doi: Doi 10.1002/Jmr.738 Google Scholar
  65. 65.
    Howard EI, Sanishvili R, Cachau RE, Mitschler A, Chevrier B, Barth P, Lamour V, Van Zandt M, Sibley E, Bon C, Moras D, Schneider TR, Joachimiak A, Podjarny A (2004) Ultrahigh resolution drug design I: details of interactions in human aldose reductase-inhibitor complex at 0.66 angstrom. Proteins 55(4):792–804Google Scholar
  66. 66.
    Muzet N, Guillot B, Jelsch C, Howard E, Lecomte C (2003) Electrostatic complementarity in an aldose reductase complex from ultra-high-resolution crystallography and first-principles calculations. Proc Natl Acad Sci USA 100(15):8742–8747. doi: 10.1073/pnas.1432955100 Google Scholar
  67. 67.
    Lamour V, Barth P, Rogniaux H, Poterszman A, Howard E, Mitschler A, Van Dorsselaer A, Podjarny A, Motas D (1999) Production of crystals of human aldose reductase with very high resolution diffraction. Acta Crystallogr D 55:721–723Google Scholar
  68. 68.
    Grabowsky S, Pfeuffer T, Morgenroth W, Paulmann C, Schirmeister T, Luger P (2008) A comparative study on the experimentally derived electron densities of three protease inhibitor model compounds. Org Biomol Chem 6(13):2295–2307. doi: 10.1039/B802831a Google Scholar
  69. 69.
    Grabowsky S, Pfeuffer T, Checinska L, Weber M, Morgenroth W, Luger P, Schirmeister T (2007) Electron-density determination of electrophilic building blocks as model compounds for protease inhibitors. Eur J Org Chem (17):2759–2768. doi:10.1002/ejoc.200601074Google Scholar
  70. 70.
    Ghermani NE, Spasojevic-de Bire A, Bouhmaida N, Ouharzoune S, Bouligand J, Layre A, Gref R, Couvreur P (2004) Molecular reactivity of busulfan through its experimental electrostatic properties in the solid state. Pharm Res 21(4):598–607Google Scholar
  71. 71.
    Wagner A, Flaig R, Dittrich B, Schmidt H, Koritsanszky T, Luger P (2004) Charge density and experimental electrostatic potentials of two penicillin derivatives. Chem Eur J 10(12):2977–2982. doi: 10.1002/chem.200305627 Google Scholar
  72. 72.
    Flaig R, Koritsanszky T, Soyka R, Haming L, Luger P (2001) Electronic insight into an antithrombotic agent by high-resolution X-ray crystallography. Angew Chem Int Ed 40(2):355–359Google Scholar
  73. 73.
    Klebe G (1994) The use of composite crystal-field environments in molecular recognition and the de-novo design of protein ligands. J Mol Biol 237(2):212–235Google Scholar
  74. 74.
    Klebe G (2008) Structure correlation and ligand/receptor interactions. Structure correlation. Wiley-VCH Verlag GmbH, WeinheimGoogle Scholar
  75. 75.
    Velec HFG, Gohlke H, Klebe G (2005) DrugScore(CSD)-knowledge-based scoring function derived from small molecule crystal data with superior recognition rate of near-native ligand poses and better affinity prediction. J Med Chem 48(20):6296–6303. doi: 10.1021/Jm050436v Google Scholar
  76. 76.
    Boer DR, Kroon J, Cole JC, Smith B, Verdonk ML (2001) SuperStar: comparison of CSD and PDB-based interaction fields as a basis for the prediction of protein–ligand interactions. J Mol Biol 312(1):275–287Google Scholar
  77. 77.
    Bruno IJ, Cole JC, Lommerse JPM, Rowland RS, Taylor R, Verdonk ML (1997) IsoStar: a library of information about nonbonded interactions. J Comput Aided Mol Des 11(6):525–537Google Scholar
  78. 78.
    Dittrich B, Koritsanszky T, Luger P (2004) A simple approach to nonspherical electron densities by using invarioms. Angew Chem Int Ed 43(20):2718–2721. doi: 10.1002/anie.200353596 Google Scholar
  79. 79.
    Hubschle CB, Dittrich B, Grabowsky S, Messerschmidt M, Luger P (2008) Comparative experimental electron density and electron localization function study of thymidine based on 20 K X-ray diffraction data. Acta Crystallogr B 64:363–374. doi: 10.1107/s0108768108005776 Google Scholar
  80. 80.
    Volkov A, Koritsanszky T, Li X, Coppens P (2004) Response to the paper. A comparison between experimental and theoretical aspherical-atom scattering factors for charge-density refinement of large molecules, by Pichon-Pesme, Jelsch, Guillot & Lecomte (2004). Acta Crystallogr A 60:638–639. doi: 10.1107/S0108767304016496 Google Scholar
  81. 81.
    Dittrich B, Weber M, Kalinowski R, Grabowsky S, Hubschle CB, Luger P (2009) How to easily replace the independent atom model – the example of bergenin, a potential anti-HIV agent of traditional Asian medicine. Acta Crystallogr B 65:749–756. doi: 10.1107/S0108768109046060 Google Scholar
  82. 82.
    Dittrich B, Hubschle CB, Holstein JJ, Fabbiani FPA (2009) Towards extracting the charge density from normal-resolution data. J Appl Crystallogr 42:1110–1121. doi: 10.1107/S0021889809034621 Google Scholar
  83. 83.
    Mladenovic M, Arnone M, Fink RF, Engels B (2009) Environmental effects on charge densities of biologically active molecules: do molecule crystal environments indeed approximate protein surroundings? J Phys Chem B 113(15):5072–5082. doi: 10.1021/Jp809537v Google Scholar
  84. 84.
    Bader RFW, Gatti C (1998) A Green’s function for the density. Chem Phys Lett 287(3–4):233–238Google Scholar
  85. 85.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Zakrzewski VG, Montgomery JA Jr, Stratmann RE, Burant JC, Dapprich S, Millam JM, Daniels AD, Kudin KN, Strain MC, Farkas O, Tomasi J, Barone V, Cossi M, Cammi R, Mennucci B, Pomelli C, Adamo C, Clifford S, Ochterski J, Petersson GA, Ayala PY, Cui Q, Morokuma K, Salvador P, Dannenberg JJ, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Cioslowski J, Ortiz JV, Baboul AG, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Gomperts R, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Andres JL, Gonzalez C, Head-Gordon M, Replogle ES, Pople JA (1998) Gaussian98. Gaussian, Inc., Pittsburgh, PAGoogle Scholar
  86. 86.
    Gatti C, Bianchi R, Destro R, Merati F (1992) Experimental vs theoretical topological properties of charge-density distributions – an application to the l-alanine molecule studied by X-ray-diffraction at 23-K. J Mol Struct Theochem 87:409–433Google Scholar
  87. 87.
    Senn HM, Thiel W (2007) QM/MM methods for biological systems. In: Atomistic approaches in modern biology: from quantum chemistry to molecular simulations, vol 268, pp 173–290. doi:10.1007/128_2006_084Google Scholar
  88. 88.
    Monard G, Merz KM (1999) Combined quantum mechanical/molecular mechanical methodologies applied to biomolecular systems. Acc Chem Res 32(10):904–911Google Scholar
  89. 89.
    Gao JL, Truhlar DG (2002) Quantum mechanical methods for enzyme kinetics. Annu Rev Phys Chem 53:467–505. doi: 10.1146/annurev.physchem.53.091301.150114 Google Scholar
  90. 90.
    Field MJ (2002) Simulating enzyme reactions: challenges and perspectives. J Comput Chem 23(1):48–58Google Scholar
  91. 91.
    Monard G, Prat-Resina X, Gonzalez-Lafont A, Lluch JM (2003) Determination of enzymatic reaction pathways using QM/MM methods. Int J Quantum Chem 93(3):229–244. doi: 10.1002/Qua.10555 Google Scholar
  92. 92.
    Ridder L, Mulholland AJ (2003) Modeling biotransformation reactions by combined quantum mechanical/molecular mechanical approaches: from structure to activity. Curr Top Med Chem 3(11):1241–1256Google Scholar
  93. 93.
    Bakowies D, Thiel W (1996) Hybrid models for combined quantum mechanical and molecular mechanical approaches. J Phys Chem 100(25):10580–10594Google Scholar
  94. 94.
    Field MJ, Bash PA, Karplus M (1990) A combined quantum-mechanical and molecular mechanical potential for molecular dynamics simulations. J Comput Chem 11(6):700–733Google Scholar
  95. 95.
    Amara P, Field MJ (2003) Evaluation of an ab initio quantum mechanical/molecular mechanical hybrid-potential link-atom method. Theor Chem Acc 109(1):43–52. doi: 10.1007/s00214-002-0413-3 Google Scholar
  96. 96.
    Reuter N, Dejaegere A, Maigret B, Karplus M (2000) Frontier bonds in QM/MM methods: a comparison of different approaches. J Phys Chem A 104(8):1720–1735Google Scholar
  97. 97.
    Singh UC, Kollman PA (1986) A combined abinitio quantum-mechanical and molecular mechanical method for carrying out simulations on complex molecular systems – applications to the CH3Cl + Cl – exchange reaction and gas-phase protonation of polyethers. J Comput Chem 7(6):718–730Google Scholar
  98. 98.
    Derat E, Bouquant J, Humbel S (2003) On the link atom distance in the ONIOM scheme. An harmonic approximation analysis. J Mol Struct Theochem 632:61–69. doi: 10.1016/s0166-1280(03)00288-4 Google Scholar
  99. 99.
    Klamt A, Schuurmann G (1993) Cosmo – a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient. J Chem Soc Perkin Trans 2(5):799–805Google Scholar
  100. 100.
    Schafer A, Klamt A, Sattel D, Lohrenz JCW, Eckert F (2000) COSMO implementation in TURBOMOLE: extension of an efficient quantum chemical code towards liquid systems. Phys Chem Chem Phys 2(10):2187–2193Google Scholar
  101. 101.
    Mathews II, VanderhoffHanaver P, Castellino FJ, Tulinsky A (1996) Crystal structures of the recombinant kringle 1 domain of human plasminogen in complexes with the ligands epsilon-aminocaproic acid and trans-4-(aminomethyl)cyclohexane-1-carboxylic acid. Biochemistry 35(8):2567–2576Google Scholar
  102. 102.
    Brooks BR, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) Charmm – a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 4(2):187–217Google Scholar
  103. 103.
    MacKerell ADJ, Brooks BR, Brooks CL III, Nilsson L, Roux B, Won Y, Karplus M (1998) The encyclopedia of computational chemistry, vol 1. Wiley, ChichesterGoogle Scholar
  104. 104.
    Huet G, Flipo RM, Richet C, Thiebaut C, Demeyer D, Balduyck M, Duquesnoy B, Degand P (1992) Measurement of elastase and cysteine proteinases in synovial-fluid of patients with rheumatoid-arthritis, seronegative spondylarthropathies, and osteoarthritis. Clin Chem 38(9):1694–1697Google Scholar
  105. 105.
    Sherwood P, de Vries AH, Guest MF, Schreckenbach G, Catlow CRA, French SA, Sokol AA, Bromley ST, Thiel W, Turner AJ, Billeter S, Terstegen F, Thiel S, Kendrick J, Rogers SC, Casci J, Watson M, King F, Karlsen E, Sjovoll M, Fahmi A, Schafer A, Lennartz C (2003) QUASI: a general purpose implementation of the QM/MM approach and its application to problems in catalysis. J Mol Struct Theochem 632:1–28. doi: 10.1016/s0166-1280(03)00285-9 Google Scholar
  106. 106.
    Smith W, Forester TR (1996) DL_POLY_2.0: a general-purpose parallel molecular dynamics simulation package. J Mol Graph 14(3):136–141Google Scholar
  107. 107.
    TURBOMOLE V5.6 2005, a development of University of Karlsruhe and Forschungszentrum Karlsruhe GmbH, 1989–2007, TURBOMOLE GmbH, since 2005. Available from
  108. 108.
    Becke AD (1993) Density-functional thermochemistry. 3. The role of exact exchange. J Chem Phys 98(7):5648–5652Google Scholar
  109. 109.
    Becke AD (1988) Density-functional exchange-energy approximation with corrected asymptotic behaviour. Phys Rev A 38(6):3098–3100Google Scholar
  110. 110.
    Lee CT, Yang WT, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density. Phys Rev B 37(2):785–789Google Scholar
  111. 111.
    Schafer A, Huber C, Ahlrichs R (1994) Fully optimized contracted Gaussian-basis sets of triple zeta valence quality for atoms Li to Kr. J Chem Phys 100(8):5829–5835Google Scholar
  112. 112.
    Schlund S, Muller R, Grassmann C, Engels B (2008) Conformational analysis of arginine in gas phase – a strategy for scanning the potential energy surface effectively. J Comput Chem 29(3):407–415. doi: 10.1002/Jcc.20798 Google Scholar
  113. 113.
    Schlund S, Mladenovic M, Janke EMB, Engels B, Weisz K (2005) Geometry and cooperativity effects in adenosine–carboxylic acid complexes. J Am Chem Soc 127(46):16151–16158. doi: 10.1021/Ja0531430 Google Scholar
  114. 114.
    Schlund S, Schmuck C, Engels B (2007) How important is molecular rigidity for the complex stability of artificial host–guest systems? A theoretical study on self-assembly of gas-phase arginine. Chem Eur J 13(23):6644–6653. doi: 10.1002/chem.200601741 Google Scholar
  115. 115.
    Hupp T, Sturm C, Janke EMB, Cabre MP, Weisz K, Engels B (2005) A combined computational and experimental study of the hydrogen-bonded dimers of xanthine and hypoxanthine. J Phys Chem A 109(8):1703–1712. doi: 10.1021/Jp0460588 Google Scholar
  116. 116.
    Schlund S, Schmuck C, Engels B (2005) “Knock-out” analogues as a tool to quantify supramolecular processes: a theoretical study of molecular interactions in guanidiniocarbonyl pyrrole carboxylate dimers. J Am Chem Soc 127(31):11115–11124. doi: 10.1021/Ja052536w Google Scholar
  117. 117.
    Zhao HM, Pfister J, Settels V, Renz M, Kaupp M, Dehm VC, Wurthner F, Fink RF, Engels B (2009) Understanding ground- and excited-state properties of perylene tetracarboxylic acid bisimide crystals by means of quantum chemical computations. J Am Chem Soc 131(43):15660–15668. doi: 10.1021/Ja902512e Google Scholar
  118. 118.
    Schlund S, Janke EMB, Weisz K, Engels B (2010) Predicting the tautomeric equilibrium of acetylacetone in solution. I. The right answer for the wrong reason? J Comput Chem 31(4):665–670. doi: 10.1002/Jcc.21354 Google Scholar
  119. 119.
    Musch PW, Engels B (2001) The importance of the Ene reaction for the C-2-C-6 cyclization of enyne-allenes. J Am Chem Soc 123(23):5557–5562. doi: 10.1021/Ja010346p Google Scholar
  120. 120.
    Suter HU, Pless V, Ernzerhof M, Engels B (1994) Difficulties in the calculation of electron-spin-resonance parameters using density-functional methods. Chem Phys Lett 230(4–5):398–404Google Scholar
  121. 121.
    Groth P (1968) Crystal structure of trans form of 1,4-aminomethylcyclohexanecarboxylic acid. Acta Chem Scand 22(1):143–158Google Scholar
  122. 122.
    Gatti C, Saunders VR, Roetti C (1994) Crystal-field effects on the topological properties of the electron-density in molecular-crystals – the case of urea. J Chem Phys 101(12):10686–10696Google Scholar
  123. 123.
    Roby KR (1974) Quantum-theory of chemical valence concepts. 1. Definition of charge on an atom in a molecule and of occupation numbers for electron-density shared between atoms. Mol Phys 27(1):81–104Google Scholar
  124. 124.
    Heinzmann R, Ahlrichs R (1976) Population analysis based on occupation numbers of modified atomic orbitals (maos). Theor Chim Acta 42(1):33–45Google Scholar
  125. 125.
    Lecaille F, Kaleta J, Bromme D (2002) Human and parasitic papain-like cysteine proteases: their role in physiology and pathology and recent developments in inhibitor design. Chem Rev 102(12):4459–4488. doi: 10.1021/cr0101656 Google Scholar
  126. 126.
    Sloane BF, Moin K, Krepela E, Rozhin J (1990) Cathepsin-B and its endogenous inhibitors – the role in tumor malignancy. Cancer Metastasis Rev 9(4):333–352Google Scholar
  127. 127.
    Otto HH, Schirmeister T (1997) Cysteine proteases and their inhibitors. Chem Rev 97(1):133–171Google Scholar
  128. 128.
    Powers JC, Asgian JL, Ekici OD, James KE (2002) Irreversible inhibitors of serine, cysteine, and threonine proteases. Chem Rev 102(12):4639–4750. doi: 10.1021/cr010182v Google Scholar
  129. 129.
    Yamamoto A, Tomoo K, Matsugi K, Hara T, In Y, Murata M, Kitamura K, Ishida T (2002) Structural basis for development of cathepsin B-specific noncovalent-type inhibitor: crystal structure of cathepsin B-E64c complex. Biochim Biophys Acta 1597(2):244–251Google Scholar
  130. 130.
    Vahtras O, Almlof J, Feyereisen MW (1993) Integral approximations for LCAO-SCF calculations. Chem Phys Lett 213(5–6):514–518Google Scholar
  131. 131.
    Mladenovic M, Junold K, Fink RF, Thiel W, Schirmeister T, Engels B (2008) Atomistic insights into the inhibition of cysteine proteases: first QM/MM calculations clarifying the regiospecificity and the inhibition potency of epoxide- and aziridine-based inhibitors. J Phys Chem B 112(17):5458–5469. doi: 10.1021/Jp711287c Google Scholar
  132. 132.
    Mladenovic M, Ansorg K, Fink RF, Thiel W, Schirmeister T, Engels B (2008) Atomistic insights into the inhibition of cysteine proteases: first QM/MM calculations clarifying the stereoselectivity of epoxide-based inhibitors. J Phys Chem B 112(37):11798–11808. doi: 10.1021/Jp803895f Google Scholar
  133. 133.
    Mladenovic M, Schirmeister T, Thiel S, Thiel W, Engels B (2007) The importance of the active site histidine for the activity of epoxide- or aziridine-based inhibitors of cysteine proteases. Chemmedchem 2(1):120–128. doi: 10.1002/cmdc.200600159 Google Scholar
  134. 134.
    Mladenovic M, Fink RF, Thiel W, Schirmeister T, Engels B (2008) On the origin of the stabilization of the zwitterionic resting state of cysteine proteases: a theoretical study. J Am Chem Soc 130(27):8696–8705. doi: 10.1021/ja711043x Google Scholar
  135. 135.
    Ishida T, Sakaguchi M, Yamamoto D, Inoue M, Kitamura K, Hanada K, Sadatome T (1988) Conformation of Ethyl (+)-(2S, 3S)-3-(1-N-(3-methylbutyl)amino leucyl-carbonyl)oxirane-2-carboxylate (Loxistatin), a cysteine protease inhibitor – X-ray crystallographic and H-1 nuclear magnetic resonance studies. J Chem Soc Perkin Trans 2(6):851–857Google Scholar
  136. 136.
    Helten H, Schirmeister T, Engels B (2005) Theoretical studies about the influence of different ring substituents on the nucleophilic ring opening of three-membered heterocycles and possible implications for the mechanisms of cysteine protease inhibitors. J Org Chem 70(1):233–237. doi: 10.1021/Jo048373w Google Scholar
  137. 137.
    Helten H, Schirmeister T, Engels B (2004) Model calculations about the influence of protic environments on the alkylation step of epoxide, aziridine, and thiirane based cysteine protease inhibitors. J Phys Chem A 108(38):7691–7701. doi: 10.1021/Jp048784g Google Scholar
  138. 138.
    de Vries AH, Sherwood P, Collins SJ, Rigby AM, Rigutto M, Kramer GJ (1999) Zeolite structure and reactivity by combined quantum-chemical-classical calculations. J Phys Chem B 103(29):6133–6141Google Scholar
  139. 139.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Rob MA, Cheeseman JR, Montgomery JA Jr, Vreven T, Kudin KN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg JJ, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2003) Gaussian 03. Gaussian, Inc., Wallingford, CTGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bernd Engels
    • 1
    Email author
  • Thomas C. Schmidt
    • 1
  • Carlo Gatti
    • 2
    • 3
  • Tanja Schirmeister
    • 4
  • Reinhold F. Fink
    • 1
  1. 1.Institut für Physikalische und Theoretische Chemie, Universität WürzburgWürzburgGermany
  2. 2.Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM)MilanoItaly
  3. 3.Dipartimento di Chimica Fisica ed Elettrochimica, Università di MilanoMilanoItaly
  4. 4.Institut für Pharmazie und Lebensmittelchemie, Universität WürzburgWürzburgGermany

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