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Quantum Cluster Equilibrium

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Many-Electron Approaches in Physics, Chemistry and Mathematics

Part of the book series: Mathematical Physics Studies ((MPST))

Abstract

The Quantum Cluster Equilibrium model which has been developed within the past two decades is presented. It constitutes an alternative for the investigation of fluid phases and phase transitions. In that contribution, a conceptual overview is given. It is explained, how a limited number of molecular clusters is employed for the description of the liquid phase and the computation of thermodynamic properties. Herein, high-level electronic structure methods may be transferred to macroscopic phases via statistical mechanics. The suggested method is employed so that liquid water may be treated at the coupled-cluster level including single, double and perturbative triple excitations.

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Notes

  1. 1.

    The definitions of H-bonding to be found in freshman chemistry textbooks employ near-identical language to express concurrence with the classical “dipole-dipole” picture, viz., “a special type of dipole-dipole force”  [74, “particularly strong dipole-dipole forces”  [95], “an extreme form of dipole-dipole interaction”  [39], “unique dipole-dipole attractions”  [8], “a sort of super dipole-dipole force”  [82] and the like.

References

  1. Ahlrichs, R., Bär, M., Häser, M., Horn, H., Kölmel, C.: Electronic-structure calculations on workstation computers–the program system turbomole. Chem. Phys. Lett. 162, 165 (1989)

    Article  ADS  Google Scholar 

  2. Andrews, T.: The Bakerian lecture: on the continuity of the gaseous and liquid states of matter. Philos. T. Roy. Soc. Lond. 159, 575–590 (1869). doi:10.1098/rstl.1869.0021. http://rstl.royalsocietypublishing.org/content/159/575.short

  3. Bates, D.M., Smith, J.R., Janowski, T., Tschumper, G.S.: Development of a 3-body: many-body integrated fragmentation method for weakly bound clusters and application to water clusters \(({\rm {H}}_2 {\rm {O}})_{n = 3--10,16,17}\). 135(4), 044123 (2011). doi:10.1063/1.3609922. http://link.aip.org/link/?JCP/135/044123/1

  4. Bischoff, F.A., Wolfsegger, S., Tew, D.P., Klopper, W.: Assessment of basis sets for f12 explicitly-correlated molecular electronic-structure methods. Mol. Phys. 107(8–12), 963–975 (2009). doi:10.1080/00268970802708942. http://www.tandfonline.com/doi/abs/10.1080/00268970802708942

  5. Boese, A.D., Jansen, G., Torheyden, M., Hofener, S., Klopper, W.: Effects of counterpoise correction and basis set extrapolation on the MP2 geometries of hydrogen bonded dimers of ammonia, water, and hydrogen fluoride. Phys. Chem. Chem. Phys. 13, 1230–1238 (2011). doi:10.1039/C0CP01493A. http://dx.doi.org/10.1039/C0CP01493A

  6. Borowski, P., Jaroniec, J., Janowski, T., Wolinski, K.: Quantum cluster equilibrium theory treatment of hydrogen-bonded liquids: water, methanol and ethanol. Mol. Phys. 101(10), 1413–1421 (2003). doi:10.1080/0026897031000085083

    Article  ADS  Google Scholar 

  7. Briant, C.L., Burton, J.J.: A molecular model for nucleation of water on Ions. J. Atmos. Sci. 33, 1357–1361 (1976)

    Article  ADS  Google Scholar 

  8. Brown, T.L., LeMay Jr, H.E., Bursten, B.E., Burdge, J.R.: Chemistry: the Central Science, p. 413, 9th edn. Prentice-Hall, Upper Saddle River, NJ (2003)

    Google Scholar 

  9. Brüssel, M., Perlt, E., Lehmann, S.B.C., von Domaros, M., Kirchner, B.: Binary systems from quantum cluster equilibrium theory. J. Chem. Phys. 135, 194113 (2011)

    Article  ADS  Google Scholar 

  10. Brüssel, M., Perlt, E., von Domaros, M., Brehm, M., Kirchner, B.: A one-parameter quantum cluster equilibrium approach. J. Chem. Phys. 137(16), 164107 (2012). doi:10.1063/1.4759154. http://link.aip.org/link/?JCP/137/164107/1

  11. Brüssel, M., Zahn, S., Hey-Hawkins, E., Kirchner, B.: Theoretical investigation of solvent effects and complex systems: toward the calculations of bioinorganic systems from ab initio molecular dynamics simulations and static quantum chemistry. Adv. Inorg. Chem. 62, 111–142 (2010)

    Article  Google Scholar 

  12. Burton, J.J.: Configuration, energy, and heat capacity of small spherical clusters of atoms. J. Chem. Phys. 52(1), 345–352 (1970)

    Article  ADS  Google Scholar 

  13. Burton, J.J.: Free energy of small face centered cubic clusters of atoms. J. Chem. Soc. Faraday Trans. I I (69), 540–550 (1973)

    Article  Google Scholar 

  14. Curtiss, L.A., Redfern, P.C., Raghavachari, K.: Gaussian-4 theory. J. Chem. Phys. 126(8), 084108 (2007). doi:10.1063/1.2436888. http://link.aip.org/link/?JCP/126/084108/1

  15. di Dio, P.J., Zahn, S., Stark, C.B.W., Kirchner, B.: Understanding selectivities in ligand-free oxidative cyclizations of 1,5- and 1,6-dienes with RuO\(_4\) from density functional theory. Z. Naturforsch. 65b, 367–375 (2010)

    Google Scholar 

  16. Dunning, T.H.: Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 90(2), 1007–1023 (1989). doi:10.1063/1.456153. http://link.aip.org/link/?JCP/90/1007/1

  17. Foster, J.P., Weinhold, F.: Natural hybrid orbitals. J. Am. Chem. Soc. 102(24), 7211–7218 (1980). doi:10.1021/ja00544a007. http://pubs.acs.org/doi/abs/10.1021/ja00544a007

  18. Friedrich, J.: Incremental scheme for intermolecular interactions: benchmarking the accuracy and the efficiency. J. Chem. Theor. Comput. 8(5), 1597–1607 (2012). doi:10.1021/ct200686h. http://pubs.acs.org/doi/abs/10.1021/ct200686h

  19. Friedrich, J., Dolg, M.: Implementation and performance of a domain-specific basis set incremental approach for correlation energies: applications to hydrocarbons and a glycine oligomer. J. Chem. Phys. 129(24), 244105 (2008). doi:10.1063/1.3043797. http://link.aip.org/link/?JCP/129/244105/1

  20. Friedrich, J., Dolg, M.: Fully automated incremental evaluation of MP2 and CCSD(T) energies: Application to water clusters. J. Chem. Theor. Comput. 5(2), 287–294 (2009). doi:10.1021/ct800355e. http://pubs.acs.org/doi/abs/10.1021/ct800355e

  21. Friedrich, J., Hanrath, M., Dolg, M.: Energy screening for the incremental scheme: application to intermolecular interactions. J. Phys. Chem. A 111(39), 9830–9837 (2007). doi:10.1021/jp072256y. http://pubs.acs.org/doi/abs/10.1021/jp072256y

  22. Friedrich, J., Hanrath, M., Dolg, M.: Fully automated implementation of the incremental scheme: application to CCSD energies for hydrocarbons and transition metal compounds. J. Chem. Phys. 126(15), 154110 (2007). doi:10.1063/1.2721538. http://link.aip.org/link/?JCP/126/154110/1

  23. Friedrich, J., Walczak, K.: Incremental csd(t)(f12)-mp2-f12a method to obtain highly accurate CCSD(T) energies for large molecules. J. Chem. Phys. 9(1), 408–417 (2013). doi:10.1021/ct300938w. http://pubs.acs.org/doi/abs/10.1021/ct300938w

  24. Gibbs, J.W.: Elementary principles in statistical mechanics: developed with especial reference to the rational foundations of thermodynamics. Yale bicentennial publications. C. Scribner’s sons (1902). http://books.google.de/books?id=2oc-AAAAIAAJ

  25. Halkier, A., Helgaker, T., Jørgenson, P., Klopper, W., Koch, H., Olsen, J., Wilson, A.K.: Basis-set convergence in correlated calculations on Ne, \({\text{ N }}_2\), and \({\text{ H }}_2\)O. Chem. Phys. Lett. 286, 243–252 (1998)

    Google Scholar 

  26. Halkier, A., Klopper, W., Helgaker, T., Jorgensen, P., Taylor, P.R.: Basis set convergence of the interaction energy of hydrogen-bonded complexes. J. Chem. Phys. 111(20), 9157–9167 (1999). doi:10.1063/1.479830. http://link.aip.org/link/?JCP/111/9157/1

  27. Hansen, M.J., Wendt, M.A., Weinhold, F.: Tests of quantum cluster equilibrium (QCE)-based computational methods for describing formic acid clustering. Mol. Phys. 101(8), 1147–1153 (2003). doi:10.1080/0026897031000075679

    Article  ADS  Google Scholar 

  28. Hättig, C., Klopper, W., Köhn, A., Tew, D.P.: Explicitly correlated electrons in molecules. Chem. Rev. 112(1), 4–74 (2012). doi:10.1021/cr200168z. http://pubs.acs.org/doi/abs/10.1021/cr200168z

  29. Helgaker, T., Jørgensen, P., Olsen, J.: Molecular Electronic-Structure Theory. Wiley-VCH, Chichester (2004).

    Google Scholar 

  30. Huber, H., Dyson, A.J., Kirchner, B.: Calculation of bulk properties of liquids and supercritical fluids from pure theory. 28, 121–133 (1999)

    Google Scholar 

  31. Huelsekopf, M., Ludwig, R.: Temperature dependence of hydrogen bonding in alcohols. J. Mol. Liq. 85(1–2, Sp. Iss. SI), 105–125 (2000).

    Google Scholar 

  32. Huelsekopf, M., Ludwig, R.: Correlations between structural, NMR and IR spectroscopic properties of N-methylacetamide. Magn. Reson. Chem. 39(Sp. Iss. SI), S127–S134 (2001).

    Google Scholar 

  33. Huelsekopf, M., Ludwig, R.: Hydrogen bonding in a sterically hindered alcohol. J. Mol. Liq. 98–99(Sp. Iss. SI), 163–171 (2002)

    Google Scholar 

  34. Kendall, R.A., Dunning, T.H., Harrison, R.J.: Electron affinities of the first-row atoms revisited. systematic basis sets and wave functions. J. Chem. Phys. 96(9), 6796–6806 (1992). doi:10.1063/1.462569. http://link.aip.org/link/?JCP/96/6796/1

  35. Kirchner, B.: Cooperative versus dispersion effects: what is more important in an associated liquid like water? J. Chem. Phys. 123, 204116 (2005)

    Article  ADS  Google Scholar 

  36. Kirchner, B.: Theory of complicated liquids. Phys. Rep. 440(1–3), 1–111 (2007)

    Article  ADS  Google Scholar 

  37. Kirchner, B., Ermakova, E., Solca, J., Huber, H.: Chemical accuracy obtained in an ab initio molecular dynamics simulation of a fluid by including a three-body potential. 4, 383–388 (1998)

    Google Scholar 

  38. Kirchner, B., Spickermann, C., Lehmann, S.B.C., Perlt, E., Langner, J., von Domaros, M., Reuther, P., Uhlig, F., Kohagen, M., Brüssel, M.: What can clusters tell us about the bulk? peacemaker: Extended quantum cluster equilibrium calculations. Comp. Phys. Comm. 182, 1428–1446 (2011)

    Article  ADS  MATH  Google Scholar 

  39. Kotz, J.C., Treichel, P.M., Townsend, J.R.: Chemistry and Chemical Reactivity, p. 562, 7th edn. Brooks-Cole, Belmont, CA (2009)

    Google Scholar 

  40. Lehmann, S.B.C., Spickermann, C., Kirchner, B.: Quantum cluster equilibrium theory applied in hydrogen bond number studies of water. Part I: Assessment of the quantum cluster equilibrium model for liquid water. J. Chem. Theor. Comput. 5, 1640–1649 (2009)

    Google Scholar 

  41. Lehmann, S.B.C., Spickermann, C., Kirchner, B.: Quantum cluster equilibrium theory applied in hydrogen bond number studies of water. Part II: Icebergs in a two-dimensional water continuum? J. Chem. Theor. Comput. 5, 1650–1656 (2009)

    Google Scholar 

  42. Lenz, A., Ojamae, L.: A theoretical study of water clusters: the relation between hydrogen-bond topology and interaction energy from quantum-chemical computations for clusters with up to 22 molecules. Phys. Chem. Chem. Phys. 7(9), 1905–1911 (2005). doi:10.1039/b502109j

    Article  Google Scholar 

  43. Lenz, A., Ojamae, L.: A theoretical study of water equilibria: the cluster distribution versus temperature and pressure for (H2O)(n), n=1-60, and ice. J. Chem. Phys. 131(13), 134302 (2009). doi:10.1063/1.3239474

    Article  ADS  Google Scholar 

  44. Linstrom, P.J., Mallard, W.G. (eds.): NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD, 20899 (http://webbook.nist.gov), Jan 2011

  45. Ludwig, R.: Isotopic quantum effects in liquid methanol. ChemPhysChem 6(7), 1376–1380 (2005). doi:10.1002/cphc.200400664

    Article  Google Scholar 

  46. Ludwig, R.: The structure of liquid methanol. ChemPhysChem 6(7), 1369–1375 (2005). doi:10.1002/cphc.200400663

    Article  Google Scholar 

  47. Ludwig, R.: The importance of tetrahedrally coordinated molecules for the explanation of liquid water properties. ChemPhysChem 8(6), 938–943 (2007)

    Article  MathSciNet  Google Scholar 

  48. Ludwig, R., Behler, J., Klink, B., Weinhold, F.: Molecular composition of liquid sulfur. Angew. Chem. Int. Ed. 41(17), 3199–3202 (2002). doi:10.1002/1521-3773(20020902)41:17<3199::AID-ANIE3199>3.0.CO;2-9. http://onlinelibrary.wiley.com/doi/10.1002/1521-3773%2820020902%2941:17%3C3203::AID-ANIE3203%3E3.0.CO;2-K/full

  49. Ludwig, R., Reis, O., Winter, R., Weinhold, F., Farrar, T.C.: Quantum cluster equilibrium theory of liquids: temperature dependence of hydrogen bonding in liquid N-methylacetamide studied by IR spectra. J. Phys. Chem. B 102(46), 9312–9318 (1998)

    Article  Google Scholar 

  50. Ludwig, R., Weinhold, F.: Quantum cluster equilibrium theory of liquids: freezing of QCE/3-21G water to tetrakaidecahedral “Bucky-ice”. J. Chem. Phys. 110(1), 508–515 (1999)

    Article  ADS  Google Scholar 

  51. Ludwig, R., Weinhold, F.: Quantum cluster equilibrium theory of liquids: light and heavy QCE/3-21G model water. Phys. Chem. Chem. Phys. 2(8), 1613–1619 (2000)

    Article  Google Scholar 

  52. Ludwig, R., Weinhold, F.: Quantum cluster equilibrium theory of liquids: Isotopically substituted QCE/3-21G model water. Z. Phys. Chem. 216(Part 5), 659–674 (2002)

    Google Scholar 

  53. Ludwig, R., Weinhold, F., Farrar, T.C.: Experimental and theoretical determination of the temperature-dependence of deuteron and oxygen quadrupole coupling-constants of liquid water. J. Chem. Phys. 103(16), 6941–6950 (1995)

    Article  ADS  Google Scholar 

  54. Ludwig, R., Weinhold, F., Farrar, T.C.: Experimental and theoretical studies of hydrogen bonding in neat, liquid formamide. J. Chem. Phys. 102(13), 5118–5125 (1995). doi:10.1063/1.469237. http://link.aip.org/link/?JCP/102/5118/1

  55. Ludwig, R., Weinhold, F., Farrar, T.C.: Temperature-dependence of hydrogen-bonding in neat, liquid formamide. J. Chem. Phys. 103(9), 3636–3642 (1995)

    Article  ADS  Google Scholar 

  56. Ludwig, R., Weinhold, F., Farrar, T.C.: Structure of liquid N-methylacetamide: temperature dependence of NMR chemical shifts and quadrupole coupling constants. J. Phys. Chem. A 101(47), 8861–8870 (1997). doi:10.1063/1.474411. http://link.aip.org/link/?JCP/107/499/1

  57. Ludwig, R., Weinhold, F., Farrar, T.C.: Theoretical study of hydrogen bonding in liquid and gaseous N-methylformamide. J. Chem. Phys. 107(2), 499–507 (1997)

    Article  ADS  Google Scholar 

  58. Ludwig, R., Weinhold, F., Farrar, T.C.: Quantum cluster equilibrium theory of liquids part I: molecular clusters and thermodynamics of liquid ammonia. Ber. Bunsen-Ges. Phys. Chem. Chem. Phys. 102(2), 197–204 (1998)

    Article  Google Scholar 

  59. Ludwig, R., Weinhold, F., Farrar, T.C.: Quantum cluster equilibrium theory of liquids part II: temperature dependent chemical shifts, quadrupole coupling constants and vibrational frequencies in liquid ammonia. Ber. Bunsen-Ges. Phys. Chem. Chem. Phys. 102(2), 205–212 (1998)

    Article  Google Scholar 

  60. Ludwig, R., Weinhold, F., Farrar, T.C.: Quantum cluster equilibrium theory of liquids: molecular clusters and thermodynamics of liquid ethanol. Mol. Phys. 97(4), 465–477 (1999)

    Article  ADS  Google Scholar 

  61. Ludwig, R., Weinhold, F., Farrar, T.C.: Quantum cluster equilibrium theory of liquids: Temperature dependent chemical shifts, quadrupole coupling constants and vibrational frequencies in liquid ethanol. Mol. Phys. 97(4), 479–486 (1999)

    Article  ADS  Google Scholar 

  62. Matisz, G., Fabian, W.M.F., Kelterer, A.-M., Kunsagi-Mate, S.: Weinhold’s QCE model–A modified parameter fit. Model study of liquid methanol based on MP2 cluster geometries. Theochem-J. Mol. Struct. 956(1–3), 103–109 (2010). doi:10.1016/j.theochem.2010.07.003

  63. Mayer, J.E., Mayer, M.G.: Statistical Mechanics. Wiley (1947). http://books.google.de/books?id=VuMNAQAAIAAJ

  64. McQuarrie, D.A.: Statistical Mechanics. University Science Books (1973). http://books.google.de/books?id=itcpPnDnJM0C

  65. McQuarrie, D.A., Simon, J.D.: Molecular Thermodynamics. University Science Books (1999)

    Google Scholar 

  66. Mhin, B.J., Lee, S.J., Kim, K.S.: Water-cluster distribution with respect to pressure and temperature in the gas-phase. Phys. Rev. A 48(5), 3764–3770 (1993)

    Article  ADS  Google Scholar 

  67. Nesbet, R.K.: Atomic Bethe-Goldstone Equations, pp. 1–34. Wiley (2007). doi:10.1002/9780470143599.ch1. http://dx.doi.org/10.1002/9780470143599.ch1

  68. Neugebauer, J., Reiher, M., Kind, C., Hess, B.A.: Quantum chemical calculation of vibrational spectra of large molecules–raman and ir spectra for buckminsterfullerene. J. Comput. Chem. 23(9), 895–910 (2002). doi:10.1002/jcc.10089

    Article  Google Scholar 

  69. Ohlinger, W.S., Klunzinger, P.E., Deppmeier, B.J., Hehre, W.J.: Efficient calculation of heats of formation. J. Phys. Chem. A 113(10), 2165–2175 (2009). doi:10.1021/jp810144q. http://pubs.acs.org/doi/abs/10.1021/jp810144q

  70. Perlt, E., Friedrich, J., von Domaros, M., Kirchner, B.: Importance of structural motifs in liquid hydrogen fluoride. ChemPhysChem 12, 3474–3482 (2011)

    Article  Google Scholar 

  71. Pfleiderer, T., Waldner, I., Bertagnolli, H., Tödheide, K., Kirchner, B., Huber, H., Fischer, H.E.: The structure of fluid argon from high-pressure neutron diffraction and ab initio md-simulation. J. Chem. Phys. 111, 2641–2646 (1999)

    Article  ADS  Google Scholar 

  72. Reed, A.E., Curtiss, L.A., Weinhold, F.: Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem. Rev. 88(6), 899–926 (1988). doi:10.1021/cr00088a005. http://pubs.acs.org/doi/abs/10.1021/cr00088a005

  73. Schäfer, A., Horn, H., Ahlrichs, R.: Fully optimized contracted Gaussian basis sets for atoms Li to Kr. J. Chem. Phys. 97, 2571–2577 (1992)

    Article  ADS  Google Scholar 

  74. Silberberg, M.: Chemistry: The Molecular Nature of Matter and Change, p. 452. McGraw-Hill Education, 5th edn. (2009). http://books.google.de/books?id=NcL3kQAACAAJ

  75. Silla, E., Tuñón, I., Pascual-Ahuir, J.L.: Gepol: An improved description of molecular surfaces ii. computing the molecular area and volume. J. Comput. Chem. 12(9), 1077–1088 (1991). doi:10.1002/jcc.540120905. http://dx.doi.org/10.1002/jcc.540120905

  76. Solca, J., Dyson, A.J., Steinebrunner, G., Kirchner, B., Huber, H.: Melting curves for neon calculated from pure theory. J. Chem. Phys. 108, 4107–4111 (1998)

    Article  ADS  Google Scholar 

  77. Song, H.-J., Xiao, H.-M., Dong, H.-S., Huang, Y.-G.: Intermolecular interactions and nature of cooperative effects in linear cis, cis-cyclotriazane clusters (n=2-8). Theochem-J. Mol. Struct. 767(1–3), 67–73 (2006). doi:10.1016/j.theochem.2006.04.045

    Article  Google Scholar 

  78. Spickermann, C., Lehmann, S.B.C., Kirchner, B.: Introducing phase transitions to quantum chemistry: from Trouton’s rule to first principles vaporization entropies. J. Chem. Phys. 128(24), 244506 (2008)

    Article  ADS  Google Scholar 

  79. Stoll, H.: The correlation energy of crystalline silicon. Chem. Phys. Lett. 191(6), 548–552 (1992). http://dx.doi.org/10.1016/0009-2614(92)85587-Z, http://www.sciencedirect.com/science/article/pii/000926149285587Z

  80. Stoll, H.: Correlation energy of diamond. Phys. Rev. B 46, 6700–6704 (Sep 1992). doi:10.1103/PhysRevB.46.6700. http://link.aps.org/doi/10.1103/PhysRevB.46.6700

  81. Stoll, H.: On the correlation energy of graphite. J. Chem. Phys. 97(11), 8449–8454 (1992). doi:10.1063/1.463415. http://link.aip.org/link/?JCP/97/8449/1

  82. Tro, N.J.: Chemistry: A Molecular Approach, p. 464, 2nd edn. Prentice-Hall, Boston (2011)

    Google Scholar 

  83. van der Waals, J.D.: Over de Continuiteit van den Gas-en Vloeistoftoestand. Ph.D. thesis, Leiden University, The Netherlands (1873)

    Google Scholar 

  84. Van der Waals, J.H.: The equation of state for gases and liquids. In: Nobel Lecture (1910). http://www.nobelprize.org/nobel_prizes/physics/laureates/1910/waals-lecture.pdf

  85. Weinhold, F.: Quantum cluster equilibrium theory. In: First US-Israel Meeting on Theoretical Chemistry, Berkeley, California. Lawrence Berkeley Laboratory (1991)

    Google Scholar 

  86. Weinhold, F.: Nature of H-bonding in clusters, liquids, and enzymes: an ab initio, natural bond orbital perspective. Theochem-J. Mol. Struct. 398, 181–197 (1997)

    Article  Google Scholar 

  87. Weinhold, F.: Quantum cluster equilibrium theory of liquids: general theory and computer implementation. J. Chem. Phys. 109(2), 367–372 (1998)

    Article  ADS  Google Scholar 

  88. Weinhold, F.: Quantum cluster equilibrium theory of liquids: illustrative application to water. J. Chem. Phys. 109(2), 373–384 (1998)

    Article  ADS  Google Scholar 

  89. Weinhold, F.: Resonance character of hydrogenbonded species. In: Baldwin, R.L., Baker, D. (eds.) Peptide Solvation and HBonds, Volume 72 of Advances in Protein Chemistry, pp. 121–155. Academic Press (2005). doi:10.1016/S0065-3233(05)72005-2. http://www.sciencedirect.com/science/article/pii/S0065323305720052

  90. Weinhold, F.: Classical and Geometrical Theory of Chemical and Phase Thermodynamics, Chap. 13.3.4. Wiley (2009). http://books.google.de/books?id=Byi1W_lYLbgC

  91. Weinhold, F., Klein, R.A.: What is a hydrogen bond? Mutually consistent theoretical and experimental criteria for characterizing h-bonding interactions. Mol. Phys. 110(9–10), 565–579 (2012). doi:10.1080/00268976.2012.661478. http://www.tandfonline.com/doi/abs/10.1080/00268976.2012.661478

  92. Weinhold, F., Landis, C.R.: Valency and Bonding: A Natural Bond Orbital Donor-Acceptor Perspective, Chap. 5. Cambridge University Press (2005). http://books.google.de/books?id=6153Kt2ikggC

  93. Wendt, M.A., Meiler, J., Weinhold, F., Farrar, T.C.: Solvent and concentration dependence of the hydroxyl chemical shift of methanol. Mol. Phys. 93(1), 145–152 (1998). doi:10.1080/002689798169537. http://www.tandfonline.com/doi/abs/10.1080/002689798169537

  94. Wendt, M.A., Weinhold, F., Farrar, T.C.: Critical test of quantum cluster equilibrium theory: formic acid at B3LYP/6-31+G* hybrid density functional level. J. Chem. Phys. 109(14), 5945–5947 (1998)

    Article  ADS  Google Scholar 

  95. Zumdahl, S.S., DeCoste, D.J.: Chemical Principles, p. 779. Textbooks Available with Cengage YouBook Series. Cengage Learning, 6th edn. (2009). http://books.google.de/books?id=hsuV9JTGaP8C

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Authors and Affiliations

  1. Mulliken Center for Theoretical Chemistry, Institute for Physical and Theoretical Chemistry, University of Bonn, Beringstr. 4, 53115, Bonn, Germany

    Barbara Kirchner

  2. Department of Chemistry, University of Wisconsin, 1101 University Avenue, Madison, WI, 53706-1322, USA

    Frank Weinhold

  3. Fakultät für Naturwissenschaften, Institute für Chemie, Technische Universität Chemnitz, Straße der Nationen 62, 09111, Chemnitz, Germany

    Joachim Friedrich

  4. Wilhelm-Ostwald-Institute for Physical and Theoretical Chemistry, University of Leipzig, Linnéstr. 2, 04103, Leipzig, Germany

    Eva Perlt & Sebastian B. C. Lehmann

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    Volker Bach

  2. Institute for Mathematics, Freie Universität Berlin, Berlin, Germany

    Luigi Delle Site

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Kirchner, B., Weinhold, F., Friedrich, J., Perlt, E., Lehmann, S.B.C. (2014). Quantum Cluster Equilibrium. In: Bach, V., Delle Site, L. (eds) Many-Electron Approaches in Physics, Chemistry and Mathematics. Mathematical Physics Studies. Springer, Cham. https://doi.org/10.1007/978-3-319-06379-9_4

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