Intermolecular Interaction Energies from Experimental Charge Density Studies



The estimation of intermolecular interaction energies from experimental charge densities, obtained by high resolution X-ray crystallographic measurements, is overviewed. Two main approaches are explored: one based on the conventional theory of intermolecular forces and using the charge density functions directly to deduce electrostatic and possibly other contributions of the total interaction energy, and another involving the characterization of interaction strengths from local properties determined at critical points in the total electron density.


  1. 1.
    Jeziorski B, Moszynski R, Szalewicz K (1994) Perturbation theory approach to intermolecular potential energy surfaces of van der Waals complexes. Chem Rev 94:1887Google Scholar
  2. 2.
    Moszynski R (2007) In: Sokalski WA (ed) Molecular materials with specific interactions. Springer, Dordrecht, pp 1–152Google Scholar
  3. 3.
    Stone AJ (1997) The theory of intermolecular forces. Oxford University Press, OxfordGoogle Scholar
  4. 4.
    Koritsanszky TS, Coppens P (2001) Chemical applications of X-ray charge-density analysis. Chem Rev 101:1583Google Scholar
  5. 5.
    Stewart RF (1976) Electron population analysis with rigid pseudoatoms. Acta Crystallogr A 32:565Google Scholar
  6. 6.
    Hansen N, Coppens P (1978) Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr A 34:909Google Scholar
  7. 7.
    Jayatilaka D (1998) Wave function for beryllium from X-Ray diffraction data. Phys Rev Lett 80:798Google Scholar
  8. 8.
    Jayatilaka D, Grimwood DJ (2001) Wavefunctions derived from experiment. I. Motivation and theory. Acta Crystallogr A 57:76Google Scholar
  9. 9.
    Hibbs DE, Howard ST, Huke JP, Waller MP (2005) A new orbital-based model for the analysis of experimental molecular charge densities: an application to (Z)-N-methyl-C-phenylnitrone. Phys Chem Chem Phys 7:1772Google Scholar
  10. 10.
    Waller MP, Howard ST, Platts JA, Piltz RO, Willock DJ, Hibbs DE (2006) Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine. Chem Eur J 12:7603Google Scholar
  11. 11.
    van Smaalen S, Netzel J (2009) The maximum entropy method in accurate charge-density studies. Phys Scr 79:048304Google Scholar
  12. 12.
    Destro R, Loconte L, Presti LL, Roversi P, Soave R (2004) On the role of data quality in experimental charge-density studies. Acta Crystallogr A 60:365Google Scholar
  13. 13.
    Abramov Y, Volkov A, Coppens P (1999) On the evaluation of molecular dipole moments from multipole refinement of X-ray diffraction data. Chem Phys Lett 311:81Google Scholar
  14. 14.
    Bianchi R, Gatti C, Adovasio V, Nardelli M (1996) Theoretical and experimental (113 K) electron-density study of lithium bis(tetramethylammonium) hexanitrocobaltate(III). Acta Crystallogr B 52:471Google Scholar
  15. 15.
    de Vries RY, Feil D, Tsirelson VG (2000) Extracting charge density distributions from diffraction data: a model study on urea. Acta Crystallogr B 56:118Google Scholar
  16. 16.
    Spackman M, Byrom P (1996) Molecular electric moments and electric field gradients from X-ray diffraction data: model studies. Acta Crystallogr B 52:1023Google Scholar
  17. 17.
    Spackman MA, Byrom PG, Alfredsson M, Hermansson K (1999) Influence of intermolecular interactions on multipole-refined electron densities. Acta Crystallogr A 55:30Google Scholar
  18. 18.
    Volkov A, Abramov YA, Coppens P (2001) Density-optimized radial exponents for X-ray charge-density refinement from ab initio crystal calculations. Acta Crystallogr A 57:272Google Scholar
  19. 19.
    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 57:395Google Scholar
  20. 20.
    Volkov A, Gatti C, Abramov YA, Coppens P (2000) Evaluation of net atomic charges and atomic and molecular electrostatic moments through topological analysis of the experimental charge density. Acta Crystallogr A 56:252Google Scholar
  21. 21.
    Swaminathan S, Craven BM, Spackman MA, Stewart RF (1984) Theoretical and experimental studies of the charge density in urea. Acta Crystallogr B 40:398Google Scholar
  22. 22.
    Stewart RF, Bentley J, Goodman B (1975) Generalized X-ray scattering factors in diatomic molecules. J Chem Phys 63:3786Google Scholar
  23. 23.
    Spackman MA (1992) Molecular electric moments from X-ray diffraction data. Chem Rev 92:1769Google Scholar
  24. 24.
    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 120:2227Google Scholar
  25. 25.
    Sorensen H, Stewart R, McIntyre G, Larsen S (2003) Simultaneous variation of multipole parameters and Gram-Charlier coefficients in a charge-density study of tetrafluoroterephthalonitrile based on X-ray and neutron data. Acta Crystallogr A 59:540Google Scholar
  26. 26.
    Roversi P, Destro R (2004) Approximate anisotropic displacement parameters for H atoms in molecular crystals. Chem Phys Lett 386:472Google Scholar
  27. 27.
    Madsen AØ, Sørensen HO, Flensburg C, Stewart RF, Larsen S (2004) Modeling of the nuclear parameters for H atoms in X-ray charge-density studies. Acta Crystallogr A 60:550Google Scholar
  28. 28.
    Whitten AE, Spackman MA (2006) Anisotropic displacement parameters for H atoms using an ONIOM approach. Acta Crystallogr B 62:875Google Scholar
  29. 29.
    Jayatilaka D, Dittrich B (2008) X-ray structure refinement using aspherical atomic density functions obtained from quantum-mechanical calculations. Acta Crystallogr A 64:383Google Scholar
  30. 30.
    Hoser AA, Dominiak PM, Wozniak K (2009) Towards the best model for H atoms in experimental charge-density refinement. Acta Crystallogr A 65:300Google Scholar
  31. 31.
    Dittrich B, Spackman MA (2007) Can the interaction density be measured? The example of the non-standard amino acid sarcosine. Acta Crystallogr A 63:426Google Scholar
  32. 32.
    Ma Y, Politzer P (2004) Determination of noncovalent interaction energies from electronic densities. J Chem Phys 121:8955Google Scholar
  33. 33.
    Welch GWA, Karamertzanis PG, Misquitta AJ, Stone AJ, Price SL (2008) Is the induction energy important for modeling organic crystals? J Chem Theory Comput 4:522Google Scholar
  34. 34.
    Spackman MA, Munshi P, Dittrich B (2007) Dipole moment enhancement in molecular crystals from X-ray diffraction data. Chemphyschem 8:2051Google Scholar
  35. 35.
    Whitten AE, Turner P, Klooster WT, Piltz RO, Spackman MA (2006) Reassessment of large dipole moment enhancements in crystals: a detailed experimental and theoretical charge density analysis of 2-methyl-4-nitroaniline. J Phys Chem A 110:8763Google Scholar
  36. 36.
    Suponitsky KY, Tsirelson VG, Feil D (1999) Electron-density-based calculations of intermolecular energy: case of urea. Acta Crystallogr A 55:821Google Scholar
  37. 37.
    Ma Y, Politzer P (2004) Electronic density approaches to the energetics of noncovalent interactions. Int J Mol Sci 05:130Google Scholar
  38. 38.
    Volkov A, Coppens P (2004) Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning. J Comput Chem 25:921Google Scholar
  39. 39.
    Buckingham AD (1967) Advances in chemical physics. In: Hirschfelder J (ed) Intermolecular forces. Wiley, Madison, pp 107–142Google Scholar
  40. 40.
    Stone AJ, Price SL (1988) Some new ideas in the theory of intermolecular forces: anisotropic atom-atom potentials. J Phys Chem 92:3325Google Scholar
  41. 41.
    Stone AJ (1985) Distributed polarizabilities. Mol Phys 56:1065Google Scholar
  42. 42.
    Spackman MA (1986) A simple qualitative model of hydrogen bonding. J Chem Phys 85:6587Google Scholar
  43. 43.
    Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theor Chim Acta 44:129Google Scholar
  44. 44.
    Hirshfeld FL (1971) Difference densities by least-squares refinement: fumaramic acid. Acta Crystallogr B 27:769Google Scholar
  45. 45.
    Bader RWF (1990) Atoms in molecules – a quantum theory. University of Oxford Press, OxfordGoogle Scholar
  46. 46.
    Ángyán JG, Jansen G, Loos M, Hättig C, Hess BA (1994) Distributed polarizabilities using the topological theory of atoms in molecules. Chem Phys Lett 219:267Google Scholar
  47. 47.
    Jansen G, Hättig C, Hess BA, Ángyán JG (1996) Intermolecular interaction energies by topologically partitioned electric properties. 1. Electrostatic and induction energies in one-centre and multicentre multipole expansions. Mol Phys 88:69Google Scholar
  48. 48.
    Hättig C, Jansen G, Hess BA, Ángyán JG (1997) Intermolecular interaction energies by topologically partitioned electric properties. II. Dispersion energies in one-centre and multicentre expansions. Mol Phys 91:145Google Scholar
  49. 49.
    Bouhmaida N, Ghermani N, Lecomte C, Thalal A (1997) Modelling electrostatic potential from experimentally determined charge densities. 2. Total potential. Acta Crystallogr A 53:556Google Scholar
  50. 50.
    Ángyán JG, Chipot C (1994) A comprehensive approach to molecular charge density models: from distributed multipoles to fitted atomic charges. Int J Quantum Chem 52:17Google Scholar
  51. 51.
    Jansen G (2000) Convergence of multipole expanded intermolecular interaction energies for Gaussian-type-function and Slater-type-function basis sets. Theor Chem Acc 104(6):499Google Scholar
  52. 52.
    Popelier PLA, Rafat M (2003) The electrostatic potential generated by topological atoms: a continuous multipole method leading to larger convergence regions. Chem Phys Lett 376:148Google Scholar
  53. 53.
    Volkov A, King HF, Coppens P (2006) Dependence of the intermolecular electrostatic interaction energy on the level of theory and the basis set. J Chem Theory Comput 2:81Google Scholar
  54. 54.
    Volkov A, Koritsanszky T, Coppens P (2004) Combination of the exact potential and multipole methods (EP/MM) for evaluation of intermolecular electrostatic interaction energies with pseudoatom representation of molecular electron densities. Chem Phys Lett 391:170–175Google Scholar
  55. 55.
    Spackman M (2006) The use of the promolecular charge density to approximate the penetration contribution to intermolecular electrostatic energies. Chem Phys Lett 418:158Google Scholar
  56. 56.
    Volkov A, King HF, Coppens P, Farrugia LJ (2006) On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. Acta Crystallogr A 62:400Google Scholar
  57. 57.
    Piquemal JP, Chevreau H, Gresh N (2007) Toward a separate reproduction of the contributions to the Hartree-Fock and DFT intermolecular interaction energies by polarizable molecular mechanics with the SIBFA potential. J Chem Theory Comput 3:824Google Scholar
  58. 58.
    Slipchenko LV, Gordon MS (2007) Electrostatic energy in the effective fragment potential method: theory and application to benzene dimer. J Comput Chem 28:276Google Scholar
  59. 59.
    Kairys V, Jensen J (1999) Evaluation of the charge penetration energy between non-orthogonal molecular orbitals using the Spherical Gaussian Overlap approximation. Chem Phys Lett 315:140Google Scholar
  60. 60.
    Qian W, Krimm S (2006) Charge density treatment of the molecule-charge interaction and its relation to the electrical component of hydrogen bonding: accuracy and distance dependence. J Mol Struct Theochem 766:93Google Scholar
  61. 61.
    Aubert E, Porcher F, Souhassou M, Lecomte C (2004) Electrostatic potential and interaction energies of molecular entities occluded in the AlPO4-15 molecular sieve: determination from X-ray charge density analysis. J Phys Chem Solids 65:1943Google Scholar
  62. 62.
    Bouhmaida N, Bonhomme F, Guillot B, Jelsch C, Ghermani NE (2009) Charge density and electrostatic potential analyses in paracetamol. Acta Crystallogr B 65:363Google Scholar
  63. 63.
    Spackman MA (2007) Comment on On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model by Volkov, King, Coppens & Farrugia (2006). Acta Crystallogr A 63:198Google Scholar
  64. 64.
    Volkov A, Coppens P (2007) Response to Spackman’s comment on On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. Acta Crystallogr A 63:201Google Scholar
  65. 65.
    Su Z, Coppens P (1992) On the mapping of electrostatic properties from the multipole description of the charge-density. Acta Crystallogr A 48:188Google Scholar
  66. 66.
    Stewart R, Craven B (1993) Molecular electrostatic potentials from crystal diffraction: the neurotransmitter γ-aminobutyric acid. Biophys J 65:998Google Scholar
  67. 67.
    Ghermani N, Bouhmaida N, Lecomte C (1993) Modeling electrostatic potential from experimentally determined charge-densities. 1. Spherical-atom approximation. Acta Crystallogr A 49:781Google Scholar
  68. 68.
    Koritsanszky T, Volkov A (2004) Atomic density radial functions from molecular densities. Chem Phys Lett 385:431Google Scholar
  69. 69.
    Spackman M, Maslen E (1986) Chemical-properties from the promolecule. J Phys Chem 90:2020Google Scholar
  70. 70.
    Destro R, Soave R, Barzaghi M (2008) Physicochemical properties of zwitterionic L- and DL-alanine crystals from their experimental and theoretical charge densities. J Phys Chem B 112:5163Google Scholar
  71. 71.
    Brock C, Dunitz J, Hirshfeld F (1991) Transferability of deformation densities among related molecules - atomic multipole parameters from perylene for improved estimation of molecular vibrations in naphthalene and anthracene. Acta Crystallogr B 47:789Google Scholar
  72. 72.
    Pichon-Pesme V, Lecomte C, Lachekar H (1995) On building a data bank of transferable experimental electron density parameters: application to polypeptides. J Phys Chem 99:6242Google Scholar
  73. 73.
    Zarychta B, Pichon-Pesme V, Guillot B, Lecomte C, Jelsch C (2007) On the application of an experimental multipolar pseudo-atom library for accurate refinement of small-molecule and protein crystal structures. Acta Crystallogr A 63:108Google Scholar
  74. 74.
    Dittrich B, Koritsanszky T, Luger P (2004) A simple approach to nonspherical electron densities by using invarioms. Angew Chem Int Ed 43(20):2718Google Scholar
  75. 75.
    Dittrich B, Hübschle CB, Luger P, Spackman MA (2006) Introduction and validation of an invariom database for amino-acid, peptide and protein molecules. Acta Crystallogr D 62:1325Google Scholar
  76. 76.
    Hübschle CB, Luger P, Dittrich B (2007) Automation of invariom and of experimental charge density modelling of organic molecules with the preprocessor program InvariomTool. J Appl Crystallogr 40:623Google Scholar
  77. 77.
    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 58:464Google Scholar
  78. 78.
    Volkov A, Li X, Koritsanszky T, Coppens P (2004) Ab initio quality electrostatic atomic and molecular properties including intermolecular energies from a transferable theoretical pseudoatom databank. J Phys Chem A 108:4283Google Scholar
  79. 79.
    Dominiak PM, Volkov A, Li X, Messerschmidt M, Coppens P (2007) A theoretical databank of transferable aspherical atoms and its application to electrostatic interaction energy calculations of macromolecules. J Chem Theory Comput 3:232Google Scholar
  80. 80.
    Domagala S, Jelsch C (2008) Optimal local axes and symmetry assignment for charge-density refinement. J Appl Crystallogr 41:1140Google Scholar
  81. 81.
    Allen F (2002) The Cambridge Structural Database: a quarter of a million crystal structures and rising. Acta Crystallogr B 58:407Google Scholar
  82. 82.
    Volkov A, Messerschmidt M, Coppens P (2007) Improving the scattering-factor formalism in protein refinement: application of the University at Buffalo Aspherical-Atom Databank to polypeptide structures. Acta Crystallogr D 63:160Google Scholar
  83. 83.
    Li X, Volkov A, Szalewicz K, Coppens P (2006) Interaction energies between glycopeptide antibiotics and substrates in complexes determined by X-ray crystallography: application of a theoretical databank of aspherical atoms and a symmetry-adapted perturbation theory-based set of interatomic potentials. Acta Crystallogr D 62:639Google Scholar
  84. 84.
    Dominiak PM, Volkov A, Dominiak AP, Jarzembska KN, Coppens P (2009) Combining crystallographic information and an aspherical-atom data bank in the evaluation of the electrostatic interaction energy in an enzyme-substrate complex: influenza neuraminidase inhibition. Acta Crystallogr D 65:485Google Scholar
  85. 85.
    Pichon-Pesme V, Jelsch C, Guillot B, Lecomte C (2004) A comparison between experimental and theoretical aspherical-atom scattering factors for charge-density refinement of large molecules. Acta Crystallogr A 60:204Google Scholar
  86. 86.
    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 60:638Google Scholar
  87. 87.
    Bak J, Dominiak PM, Wilson CC, Wozniak K (2009) Experimental charge density study of paracetamol – multipole refinement in the presence of a disordered methyl group. Acta Crystallogr A 65:490Google Scholar
  88. 88.
    Gavezzotti A (2002) Calculation of intermolecular interaction energies by direct numerical integration over electron densities. I. Electrostatic and polarization energies in molecular crystals. J Phys Chem B 106:4145Google Scholar
  89. 89.
    Gavezzotti A (2003) Towards a realistic model for the quantitative evaluation of inter-molecular potentials and for the rationalization of organic crystal structures. Part II. Crystal energy landscapes. CrystEngComm 5:439Google Scholar
  90. 90.
    Gavezzotti A (2003) Calculation of intermolecular interaction energies by direct numerical integration over electron densities. 2. An improved polarization model and the evaluation of dispersion and repulsion energies. J Phys Chem B 107:2344Google Scholar
  91. 91.
    Gavezzotti A (2005) Quantitative ranking of crystal packing modes by systematic calculations on potential energies and vibrational amplitudes of molecular dimers. J Chem Theory Comp 1:834Google Scholar
  92. 92.
    Dunitz JD, Gavezzotti A (2009) How molecules stick together in organic crystals: weak intermolecular interactions. Chem Soc Rev 38:2622Google Scholar
  93. 93.
    Spackman MA (1986) Atom-atom potentials via electron gas theory. J Chem Phys 85:6579Google Scholar
  94. 94.
    Coppens P, Abramov Y, Carducci M, Korjov B, Novozhilova I, Alhambra C, Pressprich M (1999) Experimental charge densities and intermolecular interactions: electrostatic and topological analysis of DL-histidine. J Am Chem Soc 121:2585Google Scholar
  95. 95.
    Abramov Y, Volkov A, Wu G, Coppens P (2000) The experimental charge-density approach in the evaluation of intermolecular interactions. application of a new module of the XD programming package to several solids including a pentapeptide. Acta Crystallogr A 56:585Google Scholar
  96. 96.
    Cox S, Hsu L, Williams D (1981) Nonbonded potential function models for crystalline oxohydrocarbons. Acta Crystallogr A 37:293Google Scholar
  97. 97.
    Williams D, Cox S (1984) Nonbonded potentials for azahydrocarbons: the importance of the coulombic interaction. Acta Crystallogr B 40:404Google Scholar
  98. 98.
    Spackman M (1987) A simple quantitative model of hydrogen-bonding - application to more complex-systems. J Phys Chem 91:3179Google Scholar
  99. 99.
    Mitchell J, Price S (1990) The nature of the N-H… O = C hydrogen bond: an intermolecular perturbation theory study of the formamide/formaldehyde complex. J Comput Chem 11:1217Google Scholar
  100. 100.
    Coombes DS, Price SL, Willock DJ, Leslie M (1996) Role of electrostatic interactions in determining the crystal structures of polar organic molecules. A distributed multipole study. J Phys Chem 100:7352Google Scholar
  101. 101.
    Price SL (2008) Computational prediction of organic crystal structures and polymorphism. Int Rev Phys Chem 27:541Google Scholar
  102. 102.
    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 6:2295Google Scholar
  103. 103.
    Kim YS, Gordon RG (1974) Study of the electron gas approximation. J Chem Phys 60:1842Google Scholar
  104. 104.
    Clementi E, Roetti C (1974) Roothaan-Hartree-Fock atomic wavefunctions: basis functions and their coefficients for ground and certain excited states of neutral and ionized atoms, Z ≤ 54. Data Nucl Data Tables 14:177Google Scholar
  105. 105.
    Destro R, Roversi P, Barzaghi M, Marsh RE (2000) Experimental charge density of α-glycine at 23 K. J Phys Chem A 104:1047Google Scholar
  106. 106.
    Abramov YA, Volkov A, Wu G, Coppens P (2000) Use of X-ray charge densities in the calculation of intermolecular interactions and lattice energies: application to glycylglycine, DL-histidine, and DL-proline and comparison with theory. J Phys Chem B 104:2183Google Scholar
  107. 107.
    Abramov Y, Volkov A, Coppens P (2000) Anisotropic atom-atom potentials from X-ray charge densities: application to intermolecular interactions and lattice energies in some biological and nonlinear optical materials. J Mol Struct Theochem 529:27Google Scholar
  108. 108.
    Li X, Wu G, Abramov Y, Volkov A, 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 99:12132Google Scholar
  109. 109.
    Munshi P, Guru Row TN (2006) Topological analysis of charge density distribution in concomitant polymorphs of 3-acetylcoumarin, a case of packing polymorphism. Cryst Growth Design 6:708Google Scholar
  110. 110.
    Lo Presti L, Soave R, Destro R (2006) On the interplay between CH⋯O and OH⋯O interactions in determining crystal packing and molecular conformation: an experimental and theoretical charge density study of the fungal secondary metabolite austdiol (C12H12O5). J Phys Chem B 110:6405Google Scholar
  111. 111.
    Soave R, Barzaghi M, Destro R (2007) Progress in the understanding of drug-receptor interactions, Part 2: experimental and theoretical electrostatic moments and interaction energies of an angiotensin II receptor antagonist (C30H30N6O3S). Chem Eur J 13:6942Google Scholar
  112. 112.
    Szalewicz K, Jeziorski B (1979) Symmetry-adapted double-perturbation analysis of intramolecular correlation effects in weak intermolecular interactions: the He-He interaction. Mol Phys 38:191Google Scholar
  113. 113.
    Williams HL, Mas EM, Szalewicz K, Jeziorski B (1995) On the effectiveness of monomer-, dimer-, and bond-centered basis functions in calculations of intermolecular interaction energies. J Chem Phys 103:7374Google Scholar
  114. 114.
    Bukowski R, Cencek W, Jankowski P, Jeziorski B, Jeziorska M, Kucharski SA, Misquitta AJ, Moszynski R, Patkowski K, Rybak S, Szalewicz K, Williams HL, Wormer PES, (2003) SAPT2002: an ab initio program for Many-Body Symmetry-Adapted Perturbation Theory calculations of intermolecular interaction energies. Technical report, University of Delaware/University of WarsawGoogle Scholar
  115. 115.
    Szalewicz K, Patkowski K, Jeziorski B (2005) Intermolecular forces and clusters II. Struct Bond 116(Springer):43–117Google Scholar
  116. 116.
    Mirsky K (1976) Interatomic potential functions for hydrocarbons from crystal data: transferability of the empirical parameters. Acta Crystallogr A 32:199Google Scholar
  117. 117.
    Kitaigorodskii AI (1965) The principle of close packing and the condition of thermodynamic stability of organic crystals. Acta Crystallogr 18:585Google Scholar
  118. 118.
    Demartin F, Filippini G, Gavezzotti A, Rizzato S (2004) X-ray diffraction and packing analysis on vintage crystals: Wilhelm Koerner’s nitrobenzene derivatives from the School of Agricultural Sciences in Milano. Acta Crystallogr B 60:609Google Scholar
  119. 119.
    Li T, Feng S (2006) Empirically augmented density functional theory for predicting lattice energies of aspirin, acetaminophen polymorphs, and ibuprofen homochiral and racemic crystals. Pharm Res 23:2326Google Scholar
  120. 120.
    Gilli G (2000) Molecules and molecular crystals. In: Giacovazzo C (ed) Fundamentals of crystaphy. Oxford University Press, New York, pp 465–534Google Scholar
  121. 121.
    Karamertzanis PG, Day GM, Welch GWA, Kendrick J, Leusen FJJ, Neumann MA, Price SL (2008) Modeling the interplay of inter- and intramolecular hydrogen bonding in conformational polymorphs. J Chem Phys 128:244708Google Scholar
  122. 122.
    Rivera SA, Allis DG, Hudson BS (2008) Importance of vibrational zero-point energy contribution to the relative polymorph energies of hydrogen-bonded species. Cryst Growth Des 8:3905Google Scholar
  123. 123.
    Tsirel’son VG, Kuleshova LN, Ozerov RP (1982) The electrostatic term in lattice-energy calculations for lithium formate monodeuterate: determination from the experimental electron density. Acta Crystallogr A 38:707Google Scholar
  124. 124.
    Su Z, Coppens P (1995) On the calculation of the lattice energy of ionic-crystals using the detailed electron-density distribution. 1. Treatment of spherical atomic distributions and application to NaF. Acta Crystallogr A 51:27Google Scholar
  125. 125.
    Overgaard J, Hibbs DE (2004) The experimental electron density in polymorphs a and b of the anti-ulcer drug famotidine. Acta Crystallogr A 60:480Google Scholar
  126. 126.
    Bianchi R, Gervasio G, Marabello D (2000) Experimental electron density analysis of Mn2(CO)10: metal-metal and metal-ligand bond characterization. Inorg Chem 39:2360Google Scholar
  127. 127.
    Cummins PG, Dunmur DA, Munn RW, Newham RJ (1976) Applications of the Ewald method. I. Calculation of multipole lattice sums. Acta Crystallogr A 32:847Google Scholar
  128. 128.
    De Leeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants. Proc R Soc A 373:27Google Scholar
  129. 129.
    De Leeuw SW, Perram JW, Smith ER (1980) Simulation of electrostatic systems in periodic boundary conditions. II. Equivalence of boundary conditions. Proc R Soc A 373:57Google Scholar
  130. 130.
    Makov G, Payne MC (1995) Periodic boundary conditions in ab initio calculations. Phys Rev B 51:4014Google Scholar
  131. 131.
    Marshall SL (2000) A periodic Green function for calculation of coloumbic lattice potentials. J Phys Condens Matter 12:4575Google Scholar
  132. 132.
    Catti M (1978) Electrostatic lattice energy in ionic crystals: optimization of the convergence of Ewald series. Acta Crystallogr A 34:974Google Scholar
  133. 133.
    Ángyán JG, Silvi B (1987) Electrostatic interactions in three-dimensional solids. Self-consistent Madelung potential (SCMP) approach. J Chem Phys 86:6957Google Scholar
  134. 134.
    Ferenczy GG, Csonka G, Náray-Szabó G, Ángyán JG (1998) Quantum mechanical/molecular mechanical self-consistent Madelung potential method for the treatment of molecular crystals. J Comput Chem 19(1):38Google Scholar
  135. 135.
    Ferenczy GG, Párkányi L, Ángyán JG, Kálmán A, Hegedüs B (2000) Crystal and electronic structure of two polymorphic modifications of famotidine. An experimental and theoretical study. J Mol Struct (Theochem) 503:73Google Scholar
  136. 136.
    Ferenczy GG, AÁngyán JG (2001) Intra- and intermolecular interactions of polar molecules. A study by the mixed quantum mechanical/molecular mechanical SCMP-NDDO method. J Comput Chem 22:1679Google Scholar
  137. 137.
    Stewart R (1979) On the mapping of electrostatic properties from Bragg diffraction data. Chem Phys Lett 65:335Google Scholar
  138. 138.
    Spackman MA, Stewart RF (1981) In: Politzer P, Truhlar DG (eds) Chemical applications of atomic and molecular electrostatic potentials. Plenum Press, New York, pp 407–425Google Scholar
  139. 139.
    Stewart R (1982) Mapping electrostatic potentials from diffraction data. God Jugosl Cent Kristalogr 17:1Google Scholar
  140. 140.
    Coppens P (1997) X-ray charge densities and chemical bonding. Oxford University Press, New YorkGoogle Scholar
  141. 141.
    Gavezzotti A (1994) Are crystal structures predictable? Acc Chem Res 27:309Google Scholar
  142. 142.
    Gavezzotti A (2002) Modeling hydrogen bonded crystals. J Mol Struct 615:5Google Scholar
  143. 143.
    Gavezzotti AT (2002) Ten years of experience in polymorph prediction: what next? CrystEngComm 4:343Google Scholar
  144. 144.
    Gavezzotti A (2005) Calculation of lattice energies of organic crystals: the pixel integration method in comparison with more traditional methods. Z Kristallogr 220:499Google Scholar
  145. 145.
    Spackman MA, Weber HP, Craven BM (1988) Energies of molecular interactions from Bragg diffraction data. J Am Chem Soc 110:775Google Scholar
  146. 146.
    Abramov YA (1997) On the possibility of kinetic energy density evaluation from the experimental electron-density distribution. Acta Crystallogr A 53:264Google Scholar
  147. 147.
    March NH (1957) The Thomas-Fermi approximation in quantum mechanics. Adv Phys 6:1Google Scholar
  148. 148.
    von Weizsäcker C (1935) Zur Theorie der Kernmassen. Z Phys 96:431Google Scholar
  149. 149.
    Kirzhnits DA (1957) Quantum corrections to the Thomas-Fermi equation. Soviet Phys JETP-USSR 5:64Google Scholar
  150. 150.
    Espinosa E, Molins E, Lecomte C (1998) Hydrogen bond strengths revealed by topological analyses of experimentally observed electron densities. Chem Phys Lett 285:170–173Google Scholar
  151. 151.
    Espinosa E, Souhassou M, Lachekar H, Lecomte C (1999) Topological analysis of the electron density in hydrogen bonds. Acta Crystallogr B 55:563Google Scholar
  152. 152.
    Espinosa E, Alkorta I, Rozas I, Elguero J, Molins E (2001) About the evaluation of the local kinetic, potential and total energy densities in closed-shell interactions. Chem Phys Lett 336:457Google Scholar
  153. 153.
    Espinosa E, Lecomte C, Molins E (1999) Experimental electron density overlapping in hydrogen bonds: topology vs. energetics. Chem Phys Lett 300:745Google Scholar
  154. 154.
    Espinosa E, Alkorta I, Elguero J, Molins E (2002) From weak to strong interactions: a comprehensive analysis of the topological and energetic properties of the electron density distribution involving X-H…F-Y systems. J Chem Phys 117:5529Google Scholar
  155. 155.
    Matta CF, Castillo N, Boyd RJ (2006) Extended weak bonding interactions in DNA: π-stacking (base-base), base-backbone, and backbone-backbone interactions. J Phys Chem B 110:563Google Scholar
  156. 156.
    Lyssenko KA, Borissova AO, Burlov AS, Vasilchenko IS, Garnovskii AD, Minkin VI, Antipin MY (2007) Interplay of the intramolecular N-H…N bond and π-stacking interaction in 2-(2-tosylaminophenyl)benzimidazoles. Mendeleev Commun 14:164Google Scholar
  157. 157.
    Nelyubina YV, Antipin MY, Lyssenko KA (2009) Hydrogen bonds between zwitterions: intermediate between classical and charge-assisted ones. a case study. J Phys Chem A 113:3615Google Scholar
  158. 158.
    Lyssenko KA, Barzilovich PY, Aldoshin SM, Antipin MY, Dobrovolsky YA (2008) The role of H-bonds in charge transfer in the crystal of 1,5-naphthalenedisulfonic acid tetrahydrate. Mendeleev Commun 18:312Google Scholar
  159. 159.
    Nelyubina YV, Troyanov SI, Antipin MY, Lyssenko KA (2009) Why oxonium cation in the crystal phase is a bad acceptor of hydrogen bonds: a charge density analysis of potassium oxonium bis(hydrogensulfate). J Phys Chem A 113:5151Google Scholar
  160. 160.
    Lyssenko KA, Nelubina YV, Safronov DV, Haustova OI, Kostyanovsky RG, Lenev DA, Antipin MY (2005) Intermolecular N3⋯N3 interactions in the crystal of pentaerythrityl tetraazide. Mendeleev Commun 15:32Google Scholar
  161. 161.
    Korlyukov AA, Lyssenko KA, Antipin MY, Grebneva EA, Albanov AI, Trofimova OM, Zel’bst EA, Voronkov MG (2009) Si-Fluoro substituted quasisilatranes (N → Si)FYSi(OCH2CH2)2NR. J Organomet Chem 694:607Google Scholar
  162. 162.
    Nelyubina YV, Lyssenko KA, Kostyanovsky RG, Bakulin DA, Antipin MY (2008) ClO⋯ClO3interactions in crystalline sodium chlorate. Mendeleev Commun 18:29Google Scholar
  163. 163.
    Nelyubina YV, Lyssenko KA, Golovanov DG, Antipin MY (2007) NO3⋯NO3 and NO3π interactions in the crystal of urea nitrate. CrystEngComm 9:991Google Scholar
  164. 164.
    Nelyubina YV, Antipin MY, Lyssenko KA (2007) Are Halide⋯Halide contacts a feature of rock-salts only? J Phys Chem A 111:1091Google Scholar
  165. 165.
    Borissova AO, Antipin MY, Perekalin DS, Lyssenko KA (2008) Crucial role of Ru⋯H interactions in the crystal packing of ruthenocene and its derivatives. CrystEngComm 10:827Google Scholar
  166. 166.
    Lyssenko KA, Korlyukov AA, Golovanov DG, Ketkov SY, Antipin MY (2006) Estimation of the barrier to rotation of benzene in the (η6–C6H6)2Cr crystal via topological analysis of the electron density distribution function. J Phys Chem A 110:6545Google Scholar
  167. 167.
    Borissova AO, Korlyukov AA, Antipin MY, Lyssenko KA (2008) Estimation of dissociation energy in donor-acceptor complex AuCl-PPh3 via topological analysis of the experimental electron density distribution function. J Phys Chem A 112:11519Google Scholar
  168. 168.
    Peganova TA, Valyaeva A, Kalsin AM, Petrovskii PV, Borissova AO, Lyssenko KA, Ustynyuk NA (2009) Synthesis of aminoiminophosphoranate complexes of palladium and platinum and X-ray diffractional investigation of the weak C-H…Pd interactions affecting the geometry of the PdNPN metallacycles. Organometallics 10:3021Google Scholar
  169. 169.
    Puntus LN, Lyssenko KA, Antipin MY, Bünzli JCG (2008) Role of inner- and outer-sphere bonding in the sensitization of Eu-III-luminescence deciphered by combined analysis of experimental electron density distribution function and photophysical data. Inorg Chem 47:11095Google Scholar
  170. 170.
    Bushmarinov IS, Antipin MY, Akhmetova VR, Nadyrgulova GR, Lyssenko KA (2008) Stereoelectronic effects in N-C-S and N-N-C systems: Experimental and ab initio AIM study. J Phys Chem A 112:5017Google Scholar
  171. 171.
    Espinosa E, Molins E (2000) Retrieving interaction potentials from the topology of the electron density distribution: the case of hydrogen bonds. J Chem Phys 113:5686Google Scholar
  172. 172.
    Wong PTT, Whalley E (1976) Raman-spectrum of ice-8. J Chem Phys 64:2359Google Scholar
  173. 173.
    Kuhs WF, Finney JL, Vettier C, Bliss DV (1984) Structure and hydrogen ordering in ice-VI, ice-VII, and ice-VIII by neutron powder diffraction. J Chem Phys 81:3612Google Scholar
  174. 174.
    Ojamäe L, Hermansson K, Dovesi R, Roetti C, Saunders VR (1994) Mechanical and molecular-properties of ice-VIII from crystal-orbital ab-initio calculations. J Chem Phys 100:2128Google Scholar
  175. 175.
    Gatti C, Silvi B, Colonna F (1995) Dipole moment of the water molecule in the condensed phase: a periodic Hartree-Fock estimate. Chem Phys Lett 247:135Google Scholar
  176. 176.
    Morse MD, Rice SA (1982) Tests of effective pair potentials for water. Predicted ice structures. J Chem Phys 76:650Google Scholar
  177. 177.
    Yoon BJ, Morokuma K, Davidson ER (1985) Structure of ice-Ih ab initio 2-body and 3-body water-water potentials and geometry optimization. J Chem Phys 83:1223Google Scholar
  178. 178.
    Matsuoka O, Clementi E, Yoshimine M (1976) CI study of the water dimer potential surface. J Chem Phys 64:1351Google Scholar
  179. 179.
    Whalley E (1957) The difference in the intermolecular forces of H2O and D2O. Trans Faraday Soc 53:1578Google Scholar
  180. 180.
    Bukalov SS, Leites LA, Lyssenko KA, Aysin RR, Korlyukov AA, Zubavichus JV, Chernichenko KY, Balenkova ES, Nenajdenko VG, Antipin MY (2008) Two modifications formed by sulflower C16S8 molecules, their study by XRD and optical spectroscopy (Raman, IR, UV-Vis) methods. J Phys Chem A 112:10949Google Scholar
  181. 181.
    Lyssenko KA, Korlyukov AA, Antipin MY (2005) The role of intermolecular H⋯H and C⋯H interactions in the ordering of [2.2]paracyclophane at 100 K: estimation of the sublimation energy from the experimental electron density function. Mendeleev Commun 15:90Google Scholar
  182. 182.
    Ashby MF (1992) Materials selection in mechanical design. Pergamon, OxfordGoogle Scholar
  183. 183.
    Mata I, Alkorta I, Molins E, Espinosa E (2010) Universal features of the electron density distribution in hydrogen-bonding regions: a comprehensive study involving H⋯X (X = H, C, N, O, F, S, Cl, π) interactions. Chem Eur J 16:2442Google Scholar
  184. 184.
    Gatti C, May E, Destro R, Cargnoni F (2002) Fundamental properties and nature of CH⋯O interactions in crystals on the basis of experimental and theoretical charge densities. The case of 3,4-bis(dimethylamino)-3-cyclobutene-1,2-dione (DMACB) crystal. J Phys Chem A 106:2707Google Scholar
  185. 185.
    Gatti C (2005) Chemical bonding in crystals: new directions. Z Kristallogr 220:399Google Scholar
  186. 186.
    Kitaigorodsky AI (1973) Molecular crystals and molecules. Academic, New YorkGoogle Scholar
  187. 187.
    Mata I, Molins E, Alkorta I, Espinosa E (2009) Effect of an external electric field on the dissociation energy and the electron density properties: the case of the hydrogen bonded dimer HF ⋯ HF. J Chem Phys 130:044104Google Scholar
  188. 188.
    Dunitz J, Gavezzotti A (2005) Molecular recognition in organic crystals: directed intermolecular bonds or nonlocalized bonding? Angew Chem Int Ed 44(12):1766Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of WarsawWarszawaPoland
  2. 2.CRM2, CNRS and Nancy-UniversityVandœuvre-lès-NancyFrance

Personalised recommendations