Understanding the nature of bonding interactions in the carbonic acid dimers


Carbonic acid dimer, (CA)2, (H2CO3)2, helps to explain the existence of this acid as a stable species, different to a simple sum between carbon dioxide and water. Five distinct, well characterized types of intermolecular interactions contribute to the stabilization of the dimers, namely, C=O⋯H–O, H–O⋯H–O, C=O⋯C=O, C=O⋯O–H, and C–O⋯O–H. In many cases, the stabilizing hydrogen bonds are of at least the same strength as in the water dimer. We dissect the nature of intermolecular interactions and assess their influence on stability. For a set of 40 (H2CO3)2 isomers, C=O⋯H–O hydrogen bonds between the carbonyl oxygen in one CA molecule and the acidic hydrogen in the hydroxyl group at a second CA molecule are the major stabilizing factors because they exhibit the shortest interaction distances, the largest orbital interaction energies, and the largest accumulation of electron densities around the corresponding bond critical points. In most cases, these are closed-shell hydrogen bonds, however, in a few instances, some covalent character is induced. Bifurcated hydrogen bonds are a common occurrence in the dimers of carbonic acid, resulting in a complex picture with multiple orbital interactions of various strengths. Two anti–anti monomers interacting via the strongest C=O⋯H–O hydrogen bonds are the ingredients for the formation of the lowest energy dimers.

Carbonic acid dimer, (CA)2, (H2CO3)2, helps explaining the existence of this acid as a stable species, different to a simple sum between carbon dioxide and water. Five distinct, well-characterized types of intermolecular interactions contribute to the stabilization of the dimers, namely, C=O⋯H–O, H–O⋯O–H, C=O⋯C=O, C=O⋯O–C, and C–O⋯O–C. In many cases, the stabilizing hydrogen bonds are of at least the same strength as in the water dimer.

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Quantum theory of atoms in molecules.


Bond critical points.


Natural bond orbitals


  1. 1.

    Terlouw J, Lebrilla C, Schwarz H (1987) Angew Chem Int Ed Engl 26:354

    Article  Google Scholar 

  2. 2.

    Hage W, Liedl K, Hallbrucker A (1998) E Mayer Sci 279:1332

    CAS  Google Scholar 

  3. 3.

    Hage W, Hallbrucker A, Mayer E (1993) J Am Chem Soc 115:8427

    CAS  Article  Google Scholar 

  4. 4.

    Liedl K, Sekušak S, Mayer E (1997) J Am Chem Soc 119:3782

    CAS  Article  Google Scholar 

  5. 5.

    Loerting T, Tautermann CS, Kroemer R, Kohl I, Hallbrucker A, Mayer E, Liedl K (2000) Angew Chem Int Ed Engl 39:891

    CAS  Article  Google Scholar 

  6. 6.

    Al-Hosney H, Grassian V (2004) J Am Chem Soc 126:8068

    CAS  Article  Google Scholar 

  7. 7.

    Al-Hosney H, Grassian V (2005) Phys Chem Chem Phys 7:1266

    CAS  Article  Google Scholar 

  8. 8.

    Moore M, Khanna R (1991) Spectrochim Acta Part A 47A:255

    CAS  Article  Google Scholar 

  9. 9.

    Breg J, Tymoczko J, Stryer L, Biochemistry WH (2002) 5th edn. Freeman and company, New York

  10. 10.

    Lindskog S, Coleman JE (1973) Proc Natl Acad Sci USA 70:2505

    CAS  Article  Google Scholar 

  11. 11.

    Kern DM (1960) J Chem Educ 37:14

    CAS  Article  Google Scholar 

  12. 12.

    Fisher S, Maupin C, Budayova–Spano M, Govindasamy L, Tu C, Agbandje-Mckenna M, Silverman D, Voth G, McKenna R (2007) Biochemistry 46:2930

    CAS  Article  Google Scholar 

  13. 13.

    Thoms S (2002) J Theor Biol 215:399

    CAS  Article  Google Scholar 

  14. 14.

    Sabine CL, Feely RA, Gruber N, Key RM, Lee K, Bullister JL, Wanninkhof R, Wong CS, Wallace DWR, Tilbrook B, Millero FJ, Peng T, Kozyr A, Ono T, Rios AF (2004) Science 305:367

    CAS  Article  Google Scholar 

  15. 15.

    Orr JC, Fabry VJ, Aumont O, Bopp L, Doney SC, Feely RA, Gnanadesikan A, Gruber N, Ishida A, Joos F, Key RM, Lindsay K, Maier-Reimer E, Matear R, Monfray P, Mouchet A, Najjar RG, Plattner GK, Rodgers KB, Sabine CL, Sarmiento JL, Schlitzer R, Slater RD, Totterdell IJ, Weirig MF, Yamanaka Y, Yool A (2005) Nature 437:681

    CAS  Article  Google Scholar 

  16. 16.

    Dore J, Lukas R, Sadler W, Church M, Karl D (2235) Proc Natl Acad Sci USA 106(1):2009

    Google Scholar 

  17. 17.

    Kim S, Minh Y, Hyung S, Kim Y, van Dishoeck E, van der Tak F (2000) High-Resolution Optical and Infrared Observations of Molecules in Comets: Chemistry in the Envelopes around Massive Young Stars from Molecular Clouds to Planetary, pp 471

  18. 18.

    Ehrenfreund PW, Schutte W (2000) Infrared Observations of Interstellar Ices, from Molecular Clouds to Planetary, pp 135

  19. 19.

    Longhi J (2006) J Geophys Res 111:E06011

    Article  Google Scholar 

  20. 20.

    Strazzulla G, Brucato JR, Cimino G, Palumbo ME (1996) Planet Space Sci 44:1447

    CAS  Article  Google Scholar 

  21. 21.

    Mason N et al (2006) VUV Spectroscopy of extraterrestrial ices, Astrochemistry-from Laboratory Studies to Astronomical Observations, pp 128

  22. 22.

    Ghoshal S, Hazra MK (2015) RSC Adv 5:17623

    CAS  Article  Google Scholar 

  23. 23.

    Chebbi A, Carlier P (1996) Atmos Environ 30:4233

    CAS  Article  Google Scholar 

  24. 24.

    Wight C, Boldyrev A (2125) J Phys Chem 99(1):1995

    Google Scholar 

  25. 25.

    Tossell J (2006) Inorg Chem 45:5961

    CAS  Article  Google Scholar 

  26. 26.

    de Marothy SA (2013) Int J Quantum Chem 113:2306

    CAS  Article  Google Scholar 

  27. 27.

    Ghoshal S, Hazra MK (2014) J Phys Chem A 118:2385

    CAS  Article  Google Scholar 

  28. 28.

    Kumar M, Busch DH, Subramaniam B, Thompson WH (2014) J Phys Chem A 118:5020

    CAS  Article  Google Scholar 

  29. 29.

    Mitterdorfer C, Bernard J, Klauser F, Winkel K, Kohl I, Liedl K, Grothe H, Mayer E, Loerting T (2012) J Raman Spectrosc 43:108

    CAS  Article  Google Scholar 

  30. 30.

    Winkel K, Hage W, Loerting T, Price S, Mayer E (2007) J Am Chem Soc 129:13863

    CAS  Article  Google Scholar 

  31. 31.

    Ballone P, Montanari B, Jones R (2000) J Chem Phys 112:6571

    CAS  Article  Google Scholar 

  32. 32.

    Murillo J, David J, Restrepo A (2010) Phys Chem Chem Phys 12:10963

    CAS  Article  Google Scholar 

  33. 33.

    Ghoshal S, Hazra MK (2014) J Phys Chem A 118:4620

    CAS  Article  Google Scholar 

  34. 34.

    Tautermann CS, Voegele AF, Liedl K (2004) J Chem Phys 120:631

    CAS  Article  Google Scholar 

  35. 35.

    Nguyen M, Matus M, Jackson V, Ngan V, Rustad J, Dixon D (2008) J Phys Chem A 112:10386

    CAS  Article  Google Scholar 

  36. 36.

    Tossell J (2009) Environ Sci Technol 43:2575

    CAS  Article  Google Scholar 

  37. 37.

    Bader R (1990) Atoms in molecules. a quantum theory. Oxford University Press, NY

    Google Scholar 

  38. 38.

    Weinhold F, Landis CR (2012) Discovering Chemistry wit Natural Bond Orbitals. Wiley

  39. 39.

    Reed A, Curtiss L, Weinhold F (1988) Chem Rev 88(6):89

    Article  Google Scholar 

  40. 40.

    Reed A, Weinhold F (1983) J Chem Phys 78:4066

    CAS  Article  Google Scholar 

  41. 41.

    Farfán P, Echeverri A, Diaz E, Tapia J, Gómez S, Restrepo A (2017) J Chem Phys 147:044312

    Article  Google Scholar 

  42. 42.

    Salazar J, Guevara A, Vargas R, Restrepo A, Garza J (2016) Phys Chem Chem Phys 18:23508

    Article  Google Scholar 

  43. 43.

    Pérez J, Hadad C, Restrepo A (2008) Intl J Quantum Chem 108:1653

    Article  Google Scholar 

  44. 44.

    Ramírez F, Hadad C, Guerra D, David J, Restrepo A (2011) Chem Phys Lett 507:229

    Article  Google Scholar 

  45. 45.

    Hincapié G, Acelas N, Castano M, David J, Restrepo A (2010) J Phys Chem A 114:7809

    Article  Google Scholar 

  46. 46.

    Acelas N, Hincapié G, Guerra D, David J, Restrepo A (2013) J Chem Phys 139:044310

    Article  Google Scholar 

  47. 47.

    Jenkins S, Restrepo A, David J, Yin D, Kirk SR (1644) Phys Chem Chem Phys 13(1):2011

    Google Scholar 

  48. 48.

    Hadad C, Restrepo A, Jenkins S, Ramírez F, David J (2013) Theor Chem Acc 132:1376

    Article  Google Scholar 

  49. 49.

    Hadad C, Florez E, Acelas N, Merino G, Restrepo A (2018) Int J Quantum Chem 119(2). https://doi.org/10.1002/qua.25766

  50. 50.

    Yepes D, Kirk SR, Jenkins S, Restrepo A (2012) J Mol Model 18:4171

    CAS  Article  Google Scholar 

  51. 51.

    David J, Guerra D, Restrepo A (2012) Chem Phys Lett 64:539–540

    Google Scholar 

  52. 52.

    Giraldo C, Gómez S, Weinhold F, Restrepo A (2016) Chem Phys Chem 17:2022

    CAS  Article  Google Scholar 

  53. 53.

    Gomez S, Guerra D, López JG, Toro–Labbé A, Restrepo A (2013) J Phys Chem A 117:1991

    CAS  Article  Google Scholar 

  54. 54.

    Mutlay I, Restrepo A (2015) Phys Chem Chem Phys 17:7972

    CAS  Article  Google Scholar 

  55. 55.

    Rengifo E, Gómez S, Arce J, Weinhold F, Restrepo A (2018) Comp Theor Chem 1130:58

    CAS  Article  Google Scholar 

  56. 56.

    Reed A, Weinhold F (1983) J Chem Phys 78:4066

    CAS  Article  Google Scholar 

  57. 57.

    Reed A, Curtiss L, Weinhold F (1998) Chem Rev 88:899

    Article  Google Scholar 

  58. 58.

    Weinhold F, Klein R (2014) Angew Chem Intl Ed 53:11214

    CAS  Article  Google Scholar 

  59. 59.

    Grabowski SJ (2011) J Chem Rev 111:2597

    CAS  Article  Google Scholar 

  60. 60.

    Knop O, Boyd R, Choi S (1998) J Am Chem Soc 110:7299

    Article  Google Scholar 

  61. 61.

    Alkorta I, Rozas I, Elguero J (1998) Struct Chem 9:243

    CAS  Article  Google Scholar 

  62. 62.

    Keith T (2013) AIMALL version 13.05.06. http://aim.tkgristmill.com/

  63. 63.

    Espinosa E, Alkorta I, Elguero J, Mollins E (2002) J Chem Phys 117:5529

    CAS  Article  Google Scholar 

  64. 64.

    Romero–Montalvo E, Guevara–Vela J, Vallejo W, Costales A, Martin A, Rodríguez M, Rocha–Rinza T (2017) Chem Comm 53:3516

    Article  Google Scholar 

  65. 65.

    Guevara–Vela J, Romero–Montalvo E, del Rio–Lima A, Martin A, Hernández–Rodríguez M, Rocha–Rinza T (2017) Chem Eur J 21:16605

    Article  Google Scholar 

  66. 66.

    Duarte V, Rocha–Rinza T, Cuevas G (2015) J Comp Chem 36:361

    Article  Google Scholar 

  67. 67.

    Guevara–Vela J, Romero–Montalvo E, Mora V, Chávez–Calvillo R, García–Revilla M, Francisco E, Martin A, Rocha–Rinza T (2016) Phys Chem Chem Phys 18:19557

    Article  Google Scholar 

  68. 68.

    Guevara–Vela J, Romero–Montalvo E, Costales A, Martin A, Rocha–Rinza T (2016) Phys Chem Chem Phys 18:26383

    Article  Google Scholar 

  69. 69.

    Guevara–Vela J, Chávez–Calvillo R, García–Revilla M, Hernández–Trujillo J, Christiansen O, Francisco E, Martin A, Rocha–Rinza T (2013) Chem Eur J 19:14304

    Article  Google Scholar 

  70. 70.

    Lane J, Contreras–García J, Piquemal J, Miller B, Kjaergaard H (2013) J Chem Theor Comp 9:3263

    CAS  Article  Google Scholar 

  71. 71.

    Blanco M, Pendás A, Francisco E (2005) J Chem Theory Comput 1:1096

    CAS  Article  Google Scholar 

  72. 72.

    Pendás A, Francisco E, Blanco M, Gatti C (2007) Chem Eur J 13:9362

    Article  Google Scholar 

  73. 73.

    Eskandari K, Val Alsenoy CJ (2014) Comp Chem 35:1883

    CAS  Article  Google Scholar 

  74. 74.

    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery Jr JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Keith T, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox Dj (2013) Gaussian 09, Revision D.01, Gaussian, Inc., Wallingford CT

  75. 75.

    NBO 6.0, Glendening ED, Badenhoop JK, Reed A, Carpenter JE, Bohmann JA, Morales CM, Landis CR, Weinhold F (2013) Theoretical Chemistry Institute. University of Wisconsin, Madison. http://nbo6.chem.wisc.edu/

    Google Scholar 

  76. 76.

    Jackson J (1998) Electrodynamics, 3rd edn. Classical Wiley, New York

    Google Scholar 

  77. 77.

    Knop O, Rankin K, Boyd R (2001) J Phys Chem A 105:6552

    CAS  Article  Google Scholar 

  78. 78.

    Knop O, Rankin K, Boyd R (2003) J Phys Chem A 107:272

    CAS  Article  Google Scholar 

  79. 79.

    Bader R, Essen H (1984) J Chem Phys 80:1943

    CAS  Article  Google Scholar 

  80. 80.

    Reed A, Curtiss L, Weinhold F (1988) Chem Rev 88:899

    CAS  Article  Google Scholar 

  81. 81.

    Reed A, Weinhold F (1983) J Chem Phys 78:4066

    CAS  Article  Google Scholar 

  82. 82.

    Feldblum E, Arkin I (2014) Proc Natl Acad Sci 111:4085

    CAS  Article  Google Scholar 

  83. 83.

    Rozas I, Alkorta I, Elguero J (1998) J Phys Chem A 102:9925

    CAS  Article  Google Scholar 

  84. 84.

    Gilli G, Gilli P (2009) The nature of the hydrogen bond. Oxford University Press, New York

    Google Scholar 

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Financial support for this project by Colciencias via project 111571249844, contract 378–2016 is acknowledged. J.M. acknowledges CONICYT for her postdoctoral Project FONDECYT/Postdoctorado-2015 No. 3150041.


Colciencias, Colombia: Project 111571249844, contract 378–2016. Conicyt, Chile: Fondecyt project, Postdoctorado–2015 No. 3150041.

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Correspondence to Albeiro Restrepo.

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Supporting Information

Cartesian coordinates for all dimers considered in this work. QTAIM quantities evaluated at all bond critical points.

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Zapata–Escobar, A.D., Murillo–López, J.A., Hadad, C.Z. et al. Understanding the nature of bonding interactions in the carbonic acid dimers. J Mol Model 25, 20 (2019). https://doi.org/10.1007/s00894-018-3907-1

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  • Carbonic acid
  • NBOs
  • Hydrogen bonds
  • Bifurcated bonds