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Beyond Standard Charge Density Topological Analyses

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Modern Charge-Density Analysis

Abstract

The analysis and treatment of density matrices provides the decisive key for the understanding of molecular and solid state systems. The density matrices not only reflect the energetic state of the system as the whole, but also open a possibility for a decomposition of a system into parts accessible to our imagination and experience. The interplay between the density matrices and the space partitioning with the focus on chemically relevant decomposition of molecular systems from the viewpoint of energy as well as the topology and the creation of new functionals is an important subject on the long journey to the comprehension of quantum chemistry.

To their great sorrow, Angel Martín Pendás, Miroslav Kohout, and Evelio Francisco announce the death of Professor Miguel Alvarez Blanco on April 4th, 2010.

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References

  1. Alcoba DR, Lain L, Torre A, Bochicchio R (2005) A study of the partitioning of the first-order reduced density matrix according to the theory of atoms in molecules. J Chem Phys 123:144113

    Article  Google Scholar 

  2. Arnold WD, Oldfield E (2000) The chemical nature of hydrogen bonding in proteins via NMR: J-couplings, chemical shifts, and aim theory. J Am Chem Soc 122:12835–12841

    Article  CAS  Google Scholar 

  3. Bader RFW (1990) Atoms in molecules. Oxford University Press, Oxford

    Google Scholar 

  4. Bader RFW, Stephens ME (1974) Fluctuation and correlation of electrons in molecular systems. Chem Phys Lett 25:445–449

    Article  Google Scholar 

  5. Bader RFW, Stephens ME (1975) Spatial localization of the electronic pair and number distributions in molecules. J A Chem Soc 97:7391–7399

    Article  CAS  Google Scholar 

  6. Baranov AI, Kohout M (2008) Electron localizability for hexagonal element structures. J Comput Chem 29:2161–2171

    Article  CAS  Google Scholar 

  7. Becke AD (1988) A multicenter numerical integration scheme for polyatomic molecules. J Chem Phys 88:2547–2553

    Article  CAS  Google Scholar 

  8. Becke AD, Edgecombe KE (1990) A simple measure of electron localization in atomic and molecular systems. J Chem Phys 92:5397–5403

    Article  CAS  Google Scholar 

  9. Bezugly V, Wielgus P, Wagner FR, Kohout M, Grin Y (2008) Electron localizability indicators ELI and ELIA: the case of highly correlated wavefunctions for the argon atom. J Comput Chem 29:1198–1207

    Article  CAS  Google Scholar 

  10. Bezugly V, Wielgus P, Kohout M, Wagner FR (2010) Electron localizability indicators ELID and ELIA for highly correlated wavefunctions of homonuclear dimers. II. N2, O2, F2, and Ne2. J Comput Chem 31:2273–2285

    CAS  Google Scholar 

  11. Blanco MA, Martín Pendás A, Francisco E (2005) Interacting quantum atoms: a correlated energy decomposition scheme based on the quantum theory of atoms in molecules. J Chem Theory Comput 1:1096–1109

    Article  CAS  Google Scholar 

  12. Bochicchio R, Ponec R, Lain L, Torre A (2000) Pair population analysis within AIM theory. J Phys Chem A 104:9130–9135

    Article  CAS  Google Scholar 

  13. Bochicchio R, Ponec R, Torre A, Lain L (2001) Multicenter bonding within the AIM theory. Theor Chem Acc 105:292–298

    Article  CAS  Google Scholar 

  14. Buckingham AD, Fowler PW (1983) Do electrostatic interactions predict structures of Van der Waals molecules? J Chem Phys 79:6426–6428

    Article  CAS  Google Scholar 

  15. Castiglioni C, Gussoni M, Zerbi G (1984) Stabilization energies of weak hydrogen bonded molecular complexes. Comparison of simple models. J Chem Phys 80:3916–3918

    Article  CAS  Google Scholar 

  16. Chamorro E, Fuentealba P, Savin A (2003) Electron probability distribution in AIM and ELF basins. J Comput Chem 24:496–504

    Article  CAS  Google Scholar 

  17. 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. At Data Nucl Data Tables 14:177–478

    Article  CAS  Google Scholar 

  18. Cohen L (1979) Local kinetic energy in quantum mechanics. J Chem Phys 70:788–789

    Article  CAS  Google Scholar 

  19. Cooper DL, Ponec R, Thorsteinssohn T, Raos G (1996) Pair populations and effective valencies from ab initio SCF and spin-coupled wavefunctions. Int J Quantum Chem 57:501–518

    Article  CAS  Google Scholar 

  20. Costales A, Blanco MA, Martín Pendás A, Mori-Sánchez P, Luaña V (2004) Universal features of the topological bond properties of the electron density. J Phys Chem A 108:2794–2801

    Article  CAS  Google Scholar 

  21. Daudel R (1968) The fundamentals of theoretical chemistry. Pergamon Press, Oxford

    Google Scholar 

  22. Dobson JF (1991) Interpretation of the Fermi hole curvature. J Chem Phys 94:4328–4332

    Article  CAS  Google Scholar 

  23. Dominiak PM, Makal A, Mallinson PR, Trzcinska K, Eilmes J, Grech E, Chruszcz M, Minor W, Wozniak K (2006) Continua of interactions between pairs of atoms in molecular crystals. Chem Eur J 12:1941–1949

    Article  CAS  Google Scholar 

  24. Dykstra CE (1993) Electrostatic interaction potentials in molecular force fields. Chem Rev 93:2339–2353

    Article  CAS  Google Scholar 

  25. Fernández Rico J, López R, Ema I, Ludeña E (2004) Analytical representation and fast evaluation of density, electronic potential and field and forces on the nuclei. J Comput Chem 25:1355–1363

    Article  Google Scholar 

  26. Francisco E, Martín Pendás A, Blanco MA (2006) A molecular energy decomposition scheme for atoms in molecules. J Chem Theory Comput 2:90–102

    Article  CAS  Google Scholar 

  27. Francisco E, Martín Pendás A, Blanco MA (2007) Electron number probability distributions for correlated wave functions. J Chem Phys 126:094102

    Article  CAS  Google Scholar 

  28. Francisco E, Martín Pendás A, Blanco MA (2008) EDF: computing electron number probability distribution functions in real space from molecular wave functions. Comput Phys Commun 178:621–634

    Article  CAS  Google Scholar 

  29. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery Jr JA, 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 Gaussian 03, Revision C.02. Gaussian, Inc., Wallingford, CT, 2004

    Google Scholar 

  30. Giambiagi M, de Giambiagi MS, Mundim KC (1990) Definition of a multicenter bond index. Struct Chem 1:423–427

    Article  CAS  Google Scholar 

  31. Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theor Chim Acta 44:129–138

    Article  CAS  Google Scholar 

  32. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871

    Article  Google Scholar 

  33. Jayatilaka D (1998) Wave function for beryllium from x-ray diffraction data. Phys Rev Lett 80:798–801

    Article  CAS  Google Scholar 

  34. Jeffrey GA, Saenger W (1991) Hydrogen bonding in biological structures. Springer, Heidelberg

    Book  Google Scholar 

  35. Jeziorski B, Moszynski R, Szalewicz K (1994) Perturbation theory approach to intermolecular potential energy surfaces of Van der Waals complexes. Chem Rev 94:1887–1930

    Article  CAS  Google Scholar 

  36. Kaijser P, Smith VH Jr (1977) Evaluation of momentum distributions and compton profiles for atomic and molecular systems. Adv Quantum Chem 10:37–76

    Article  CAS  Google Scholar 

  37. Kato T (1957) On the eigenfunctions of many-particle systems in quantum mechanics. Commun Pure Appl Math 10:151–177

    Article  Google Scholar 

  38. Kohout M (2004) A measure of electron localizability. Int J Quantum Chem 97:651–658

    Article  CAS  Google Scholar 

  39. Kohout M (2009) DGrid 4.5. Radebeul

    Google Scholar 

  40. Kohout M (2007) Bonding indicators from electron pair density functionals. Faraday Discuss 135:43–54

    Google Scholar 

  41. Kohout M, Pernal K, Wagner FR, Grin Y (2004) Electron localizability indicator for correlated wavefunctions. I: parallel-spin pairs. Theor Chem Acc 112:453–459

    Article  CAS  Google Scholar 

  42. Kohout M, Pernal K, Wagner FR, Grin Y (2005) Electron localizability indicator for correlated wavefunctions. II: antiparallel-spin pairs. Theor Chem Acc 113:287–293

    Article  CAS  Google Scholar 

  43. Kohout M, Savin A (1996) Atomic shell structure and electron numbers. Int J Quantum Chem 60:875–882

    Article  CAS  Google Scholar 

  44. Kohout M, Wagner FR, Grin Y (2006) Atomic shells from the electron localizability in momentum space. Int J Quantum Chem 106:1499–1507

    Article  CAS  Google Scholar 

  45. Kohout M, Wagner FR, Grin Y (2008) Electron localizability indicator for correlated wavefunctions. III: singlet and triplet pairs. Theor Chem Acc 119:413–420

    Article  CAS  Google Scholar 

  46. Kollman P (1977) A general analysis of noncovalent intermolecular interactions. J Am Chem Soc 99:4875–4894

    Article  CAS  Google Scholar 

  47. Kutzelnigg W (1963) Über die Symmetrie-Eigenschaften der reduzierten Dichtematrizen. Z Naturforschg 18a:1058–1064

    CAS  Google Scholar 

  48. Kutzelnigg W (2002) In: Rychlewski J (ed) Explicitly correlated wave functions in chemistry and physics: theory and applications. Kluwer, Dordrecht, pp 14–17

    Google Scholar 

  49. Kutzelnigg W, Mukherjee D (2002) Irreducible Brillouin conditions and contracted schrödinger equations for n-electron systems. II: spin-free formulation. J Chem Phys 116:4787–4801

    Article  CAS  Google Scholar 

  50. Li L, Parr RG (1986) The atom in a molecule: a density matrix approach. J Chem Phys 84:1704–1711

    Article  CAS  Google Scholar 

  51. Löwdin PO (1955) Quantum theory of many-particle systems. I: physical interpretations by means of density matrices, natural spin-orbitals, and convergence problems in the method of configurational interaction. Phys Rev 97:1474–1489

    Article  Google Scholar 

  52. Martín Pendás A, Blanco MA, Costales A, Mori-Sánchez P, Luaña V (1999) Non-nuclear maxima of the electron density. Phys Rev Lett 83:1930–1933

    Article  Google Scholar 

  53. Martín Pendás A, Blanco MA, Francisco E (2004) Two-electron integrations in the quantum theory of atoms in molecules. J Chem Phys 120:4581–4592

    Article  Google Scholar 

  54. Martín Pendás A, Francisco E, Blanco MA (2005) Two-electron integrations in the quantum theory of atoms in molecules with correlated wavefunctions. J Comput Chem 26:344–351

    Article  Google Scholar 

  55. Martín Pendás A, Blanco MA, Francisco E (2006) The nature of the hydrogen bond: a synthesis from the interacting quantum atoms picture. J Chem Phys 125:184112

    Article  Google Scholar 

  56. Martín Pendás A, Francisco E, Blanco MA (2006) Binding energies of first row diatomics in the light of the interacting quantum atoms approach. J Phys Chem A 110:12864–12869

    Article  Google Scholar 

  57. Martín Pendás A, Blanco MA, Francisco E (2007) Chemical fragments in real space: definitions, properties, and energetic decompositions. J Comput Chem 28:161–184

    Article  Google Scholar 

  58. Martín Pendás A, Francisco E, Blanco MA (2007) Pauling resonant structures in real space through electron number probability distributions. J Phys Chem A 111:1084–1090

    Article  Google Scholar 

  59. Martín Pendás A, Francisco E, Blanco MA (2007) Spatial localization, correlation, and statistical dependence of electrons in atomic domains: the \( {x^1}\sigma_g^{ + } \) and \( {b^3}\sigma_u^{ + } \) states of h2. Chem Phys Lett 437:287

    Article  Google Scholar 

  60. Martín Pendás A, Francisco E, Blanco MA (2007) Charge transfer, chemical potentials, and the nature of functional groups: answers from a quantum chemical topology. Faraday Discuss 135:423–438

    Article  Google Scholar 

  61. Martín Pendás A, Francisco E, Blanco MA (2007) An electron number distribution view of chemical bonds in real space. Phys Chem Chem Phys 9:1087–1092

    Article  Google Scholar 

  62. Martín Pendás A, Francisco E, Blanco MA (2007) Spin-resolved electron number distribution functions: how spins couple in real space. J Chem Phys 127:144103

    Article  Google Scholar 

  63. Martín Pendás A, Francisco E, Blanco MA, Gatti C (2007) Bond paths as privileged exchange channels. Chem Eur J 13:9362–9371

    Article  Google Scholar 

  64. Martín Pendás A, Blanco MA, Francisco E (2009) Steric repulsions, rotation barriers, and stereoelectronic effects: a real space perspective. J Comput Chem 30:98

    Article  Google Scholar 

  65. Mayer I (2003) An exact chemical decomposition scheme for the molecular energy. Chem Phys Lett 382:265–269

    Article  CAS  Google Scholar 

  66. Mundim KC, Giambiagi M, de Giambiagi MS (1994) Multicenter bond index: Grassmann algebra and n-order density functional. J Phys Chem 98:6118–6119

    Article  CAS  Google Scholar 

  67. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York

    Google Scholar 

  68. Pauling L (1928) The shared-electron chemical bond. Proc Natl Acad Sci USA 14:359–362

    Article  CAS  Google Scholar 

  69. Pauling L (1960) The nature of the chemical bond, 3rd edn. Cornell University Press, Ithaca

    Google Scholar 

  70. Ponec R, Cooper DL (2007) Anatomy of bond formation. Bond length dependence of the extent of electron sharing in chemical bonds from the analysis of domain-averaged Fermi holes. Faraday Discuss 135:31–42

    Article  CAS  Google Scholar 

  71. Ponec R, Mayer I (1997) Investigation of some properties of multicenter bond indices. J Phys Chem A 101:1738–1741

    Article  CAS  Google Scholar 

  72. Rafat M, Popelier PLA (2007) The quantum theory of atoms in molecules, chapter 5. Wiley-VCH/GmbH & Co. KGaA, pp 121–140

    Google Scholar 

  73. Rendell APL, Bacskay GB, Hush NS (1985) The validity of electrostatic predictions of the shapes of Van der Waals dimers. Chem Phys Lett 117:400–408

    Article  CAS  Google Scholar 

  74. Salvador P, Mayer I (2004) Energy partitioning for fuzzy atoms. J Chem Phys 120:5046–5052

    Article  CAS  Google Scholar 

  75. Sannigrahi AB, Kar T (1990) Three-center bond index. Chem Phys Lett 173:569–572

    Article  CAS  Google Scholar 

  76. Sannigrahi AB, Kar T (2000) Ab initio theoretical study of three-centre bonding on the basis of bond index. J Mol Struct Theochem 496:1–17

    Article  CAS  Google Scholar 

  77. Savin A, Nesper R, Wengert S, Fässler TF (1997) Die Elektronenlokalierungsfunktion ELF, ELF: the electron localization function. Angew Chem Int Ed Engl 36:1808–1832

    Article  CAS  Google Scholar 

  78. Sierraalta A, Frenking G (1997) Diatomic interaction energies in the topological theory of atoms in molecules. Theor Chim Acta 95:1–12

    CAS  Google Scholar 

  79. Silvi B (2003) The spin-pair compositions as local indicators of the nature of the bonding. J Phys Chem A 107:3081–3085

    Article  CAS  Google Scholar 

  80. Smith VH Jr (1971) Cusp conditions for natural functions. Chem Phys Lett 9:365–371

    Article  CAS  Google Scholar 

  81. Spackman MA (1986) A simple quantitative model of hydrogen bonding. J Chem Phys 85:6587–6601

    Article  CAS  Google Scholar 

  82. Thompson WH, Hynes JT (2000) Frequency shifts in the hydrogen-bonded oh stretch in halide-water clusters. The importance of charge transfer. J Am Chem Soc 122:6278–6286

    Article  CAS  Google Scholar 

  83. Tsirelson V, Stash A (2002) Determination of the electron localization function from electron density. Chem Phys Lett 351:142–148

    Article  CAS  Google Scholar 

  84. Umeyama H, Morokuma K (1977) The origin of hydrogen bonding. An energy decomposition study. J Am Chem Soc 99:1316–1332

    Article  CAS  Google Scholar 

  85. Wagner FR, Bezugly V, Kohout M, Grin Y (2007) Charge decomposition analysis of the electron localizability indicator: a bridge between the orbital and direct space representation of the chemical bond. Chem Eur J 13:5724–5741

    Google Scholar 

  86. Wagner FR, Kohout M, Grin Y (2008) Direct space decomposition of ELI-D: interplay of charge density and pair-volume function for different bonding situations. J Phys Chem A 112:9814–9828

    Article  CAS  Google Scholar 

  87. Wiberg KB (1968) Application of the pople-santry-segal cndo method to the cyclopropylcarbinyl and cyclobutyl cation and to bicyclobutane. Tetrahedron 24:1083–1096

    Article  CAS  Google Scholar 

  88. Zhang Y, Zhao GY, You XZ (1997) Systematic theoretical study of structures and bondings of the charge-transfer complexes of ammonia with HX, XY, and X2 (X and Y are halogens). J Phys Chem A 101:2879–2885

    Article  CAS  Google Scholar 

  89. Ziegler T, Rauk A (1979) Carbon monoxide, carbon monosulfide, molecular nitrogen, phosphorus trifluoride, and methyl isocyanide as .sigma. donors and .pi. acceptors. A theoretical study by the Hartree-Fock-Slater transition-state method. Inorg Chem 18:1755–1759

    Article  CAS  Google Scholar 

  90. Ziegler T, Rauk A (1979) A theoretical study of the ethylene-metal bond in complexes between copper(1+), silver(1+), gold(1+), platinum(0) or platinum(2+) and ethylene, based on the Hartree-Fock-Slater transition-state method. Inorg Chem 18:1558–1565

    Article  CAS  Google Scholar 

  91. Ziesche P (2000) Many-electron densities and reduced density matrices, chapter 3. Kluwer Academic, New York, p 33

    Google Scholar 

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Acknowledgements

Financial support from the Spanish MEC, Project No. CTQ2006-02976, the MALTA Consolider program (CSD2007-00045), and the ERDF of the European Union, is acknowledged.

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Pendás, A.M., Kohout, M., Blanco, M.A., Francisco, E. (2011). Beyond Standard Charge Density Topological Analyses. In: Gatti, C., Macchi, P. (eds) Modern Charge-Density Analysis. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3836-4_9

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