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Hardness maximization or equalization? New insights and quantitative relations between hardness increase and bond dissociation energy

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Abstract

It has been overlooked that the change of hardness, η, upon bonding is intimately connected to thermochemical cycles, which determine whether hardness is increased according to Pearson’s “maximum hardness principle” (MHP) or equalized, as expected by Datta’s “hardness equalization principle” (HEP). So far the performances of these likely incompatible “structural principles” have not been compared. Computational validations have been inconclusive because the hardness values and even their qualitative trends change drastically and unsystematically at different levels of theory. Here I elucidate the physical basis of both rules, and shed new light on them from an elementary experimental source. The difference, Δη = η mol – <η at>, of the molecular hardness, η mol, and the averaged atomic hardness, <η at>, is determined by thermochemical cycles involving the bond dissociation energies D of the molecule, D + of its cation, and D − of its anion. Whether the hardness is increased, equalized or even reduced is strongly influenced by ΔD = 2D – D + − D −. Quantitative expressions for Δη are obtained, and the principles are tested on 90 molecules and the association reactions forming them. The Wigner-Witmer symmetry constraints on bonding require the valence state (VS) hardness, η VS, instead of the conventional ground state (GS) hardness, η GS. Many intriguingly “unpredictable” failures and systematic shortcomings of said “principles” are understood and overcome for the first time, including failures involving exotic and/or challenging molecules, such as Be2, B2, O3, and transition metal compounds. New linear relationships are discovered between the MHP hardness increase Δη VS and the intrinsic bond dissociation energy D i . For bond formations, MHP and HEP are not compatible, and HEP does not qualify as an ordering rule.

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References

  1. Mulliken RS (1952) Molecular compounds and their spectra, II. J Am Chem Soc 74:811–824

    Article  CAS  Google Scholar 

  2. Pearson RG (1963) Hard and soft acids and bases. J Am Chem Soc 85:3533–3539

    Article  CAS  Google Scholar 

  3. Pearson RG (1966) Acids and bases. Science 151:172–177

    Article  CAS  Google Scholar 

  4. Parr RG, Pearson RG (1983) Absolute hardness: companion parameter to absolute electronegativity. J Am Chem Soc 105:7512–7516

    Article  CAS  Google Scholar 

  5. Pearson RG (1988) Absolute electronegativity and hardness: application to inorganic chemistry. Inorg Chem 27:734–740

    Article  CAS  Google Scholar 

  6. Pearson RG (1989) Absolute electronegativity and hardness: applications to organic chemistry. J Org Chem 54:1423–1430

    Article  CAS  Google Scholar 

  7. Pearson RG (1990) Hard and soft acids and bases – the evolution of a chemical concept. Coord Chem Rev 100:403–425

    Article  CAS  Google Scholar 

  8. Hati S, Datta D (1992) Anomeric effect and hardness. J Org Chem 57:6056–6057

    Article  CAS  Google Scholar 

  9. Pearson RG (1993) The principle of maximum hardness. Acc Chem Res 26:250–255

    Article  CAS  Google Scholar 

  10. Parr RG, Zhou Z (1993) Absolute hardness: unifying concept for identifying shells and subshells in nuclei, atoms, molecules, and metallic clusters. Acc Chem Res 26:256–258

    Article  CAS  Google Scholar 

  11. Pearson RG (1997) Chemical hardness. Wiley-VCH, Weinheim

    Book  Google Scholar 

  12. Chermette H (1999) Chemical reactivity indexes in density functional theory. J Comput Chem 20:129–154

    Article  CAS  Google Scholar 

  13. Pearson RG (2005) Chemical hardness and density functional theory. J Chem Sci 117:369–377

    Article  CAS  Google Scholar 

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

    Google Scholar 

  15. Geerlings P, De Proft F, Langenacker W (2003) Conceptual density functional theory Chem Rev 103:1793–1874

    Article  CAS  Google Scholar 

  16. De Proft F, Ayers PW, Geerlings P (2014) In: The Chemical bond. Fundamental aspects of chemical bonding. Frenking G, Shaik S (eds) Wiley-VCH, Weinheim, pp 233–269

  17. Chattaraj PK (ed.) (2009) Chemical reactivity theory: a density functional view. CRC, Boca Raton

    Google Scholar 

  18. Parr RG, von Szentpály L, Liu S (1999) Electrophilicity index. J Am Chem Soc 121:1922–1924

    Article  CAS  Google Scholar 

  19. Parr RG, Chattaraj PK (1991) Principle of maximum hardness. J Am Chem Soc 113:1854–1855

    Article  CAS  Google Scholar 

  20. Sebastian KL (1994) On the proof of the principle of maximum hardness. Chem Phys Lett 231:40–42

    Article  CAS  Google Scholar 

  21. Chattaraj PK, Liu GH, Parr RG (1995) The maximum hardness principle in the Gyftopoulos-Hatsopoulos three-level model for an atomic or molecular species and its positive and negative ions. Chem Phys Lett 237:171–176

    Article  CAS  Google Scholar 

  22. Ayers PW, Parr RG (2000) Variational principles for describing chemical reactions: the Fukui function and chemical hardness revisited. J Am Chem Soc 122:2010–2018

    Article  CAS  Google Scholar 

  23. Torrent-Sucarrat M, Luis JM, Duran M, Solà M (2002) Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations? J Chem Phys 117:10561–10570

    Article  CAS  Google Scholar 

  24. Ordon P, Tachibana A (2007) Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: a new formula for the energy third derivative γ. J Chem Phys 126:234115

    Article  CAS  Google Scholar 

  25. Poater J, Swart M, Solà M (2012) An assessment of the validity of the maximum hardness principle in chemical reactions. J Mex Chem Soc 56:311–315

    CAS  Google Scholar 

  26. Pan S, Chattaraj PK (2013) Favorable direction in a chemical reaction through the maximum hardness principle. J Mex Chem Soc 57:23–24

    CAS  Google Scholar 

  27. Pan S, Solà M, Chattaraj PK (2013) On the validity of the maximum hardness principle and the minimum Electrophilicity principle during chemical reactions. J Phys Chem A 117:1843–1852

    Article  CAS  Google Scholar 

  28. Datta D (1986) Geometric mean principle for hardness equalisation: a corollary of Sanderson’s geometric mean principle of electronegativity equalization. J Phys Chem 90:4216–4217

    Article  CAS  Google Scholar 

  29. Chattaraj PK, Giri S, Duley S (2010) Electrophilicity equalization principle. J Phys Chem Lett 1:1064–1067

    Article  CAS  Google Scholar 

  30. Noorizadeh S (2007) Is there a minimum Electrophilicity principle in chemical reactions? Chin J Chem 25:1439–1444

    Article  CAS  Google Scholar 

  31. Chaquin P (2008) Absolute electronegativity and hardness: an analogy with classical electrostatics suggests an interpretation of the Parr ‘electrophilicity index as a ‘global energy index’ leading to the ‘minimum electrophilicity principle’. Chem Phys Lett 458:231–234

    Article  CAS  Google Scholar 

  32. von Szentpály L (2011) Ruling out any Electrophilicity equalization principle. J Phys Chem A 115:8528–8531

    Article  CAS  Google Scholar 

  33. von Szentpály L (2012) Reply to “comment on ‘Ruling out any electrophilicity equalization principle’”. J Phys Chem A 116:792–795

    Article  CAS  Google Scholar 

  34. Shee NK, Datta D (2014) Failure of principle of equalization of atomic hardnesses on molecule formation: implications. Int J Chem Model 6:507–519

    Google Scholar 

  35. Pal S, Roy R, Chandra AK (1994) Change of hardness and chemical potential in chemical binding: a quantitative model. J Phys Chem 98:2314–2317

    Article  CAS  Google Scholar 

  36. Wigner E, Witmer EE (1928) Über die Struktur der zweiatomigen Molekelspektren nach der Quantenmechanik. Z Phys 51:859–886

    Article  CAS  Google Scholar 

  37. Herzberg G (1950) Molecular spectra and molecular structure, vol.1. Spectra of diatomic molecules. Van Nostrand, Princeton, pp 315–322

    Google Scholar 

  38. Herzberg G (1966) Molecular spectra and molecular structure, vol.3. Electronic spectra and electronic structure of polyatomic molecules. Van Nostrand, Princeton

    Google Scholar 

  39. Russon LM, Heidecke SA, Birke MK, Conceicao J, Morse MD, Armentrout PB (1994) Photodissociation measurements of bond dissociation energies: Ti2 +, V2 +, Co2 +, and Co3 +. J Chem Phys 100:4747–4755

    Article  CAS  Google Scholar 

  40. von Szentpály L (2015) Physical basis and limitations of equalization rules and principles: valence-state electronegativity and valence-pair-affinity versus operational chemical potential. Quantum Matter 4:47–55

    Article  Google Scholar 

  41. von Szentpály L (2015) Symmetry laws improve electronegativity equalization by orders of magnitude and call for a paradigm shift in conceptual density functional theory. J Phys Chem A 119:1715–1722

    Article  CAS  Google Scholar 

  42. von Szentpály L (2016) Comment on “a new equation based on ionization energies and electron affinities of atoms for calculating of group electronegativity” by S. Kaya and C. Kaya [Comput Theoret Chem 1052 (2015) 42–46]. Comput Theoret Chem 1083:72–74

    Article  CAS  Google Scholar 

  43. Mulliken RS (1978) Chemical bonding. Annu Rev Phys Chem 29:1–30

  44. Mulliken RS (1934) A new Electroaffinity scale; together with data on valence states and on valence ionization potentials and electron affinities. J Chem Phys 2:782–793

    Article  CAS  Google Scholar 

  45. Pritchard HO, Skinner HA (1955) The concept of electronegativity. Chem Rev 55:745–786

    Article  CAS  Google Scholar 

  46. Hinze J, Jaffé HH (1962) Electronegativity. I. Orbital electronegativity of neutral atoms. J Am Chem Soc 84:540–546

    Article  CAS  Google Scholar 

  47. Bergmann D, Hinze J (1987) Electronegativity and charge distribution. In: Sen KD, Jørgensen CK (eds) Structure & bonding vol 66. Springer, Berlin, pp 145–190

    Google Scholar 

  48. Bratsch G (1988) Revised Mulliken electronegativities: I. Calculation and conversion to Pauling units. J Chem Educ 65:34–41

    Article  CAS  Google Scholar 

  49. Bergmann D, Hinze J (1996) Electronegativity and molecular properties. Angew Chem Int Ed Eng 35:150–163

    Article  CAS  Google Scholar 

  50. von Szentpály L (1991) Studies on electronegativity equalization: part 1. Consistent diatomic partial charges. J Mol Struct (THEOCHEM) 233:71–81

    Article  Google Scholar 

  51. von Szentpály L (2000) Modeling the charge dependence of total energy and its relevance to electrophilicity. Int J Quantum Chem 76:222–234

    Article  Google Scholar 

  52. Datta D, Shee NK, von Szentpály L (2013) Chemical potential of molecules contrasted to averaged atomic electronegativities: alarming differences and their theoretical rationalization. J Phys Chem A 117:200–206

    Article  CAS  Google Scholar 

  53. Miliordos E, Mavridis A (2010) An accurate first principles study of the geometric and electronic structure of B2, B2 −, B3, B3 −, and B3H: ground and excited states. J Chem Phys 132:164307

    Article  CAS  Google Scholar 

  54. Bruna PJ, Wright JS (1990) Theoretical study of the ionization potentials of boron dimer. J Phys Chem 94:1774–1781

    Article  CAS  Google Scholar 

  55. Tzeli D, Miranda U, Kaplan IG, Mavridis A (2008) First principles study of the electronic structure and bonding of Mn2. J Chem Phys 129:154310

    Article  CAS  Google Scholar 

  56. Barborini M (2016) Neutral, anionic, and cationic manganese dimers through density functional theory. J Phys Chem A 120:1716–1726

    Article  CAS  Google Scholar 

  57. Huber KP, Herzberg G (1979) Molecular spectra and molecular structure, vol.4. Constants of diatomic molecules. Van Nostrand, New York

    Book  Google Scholar 

  58. Åsbrink L (1970) The photoelectron Spectrum of H2. Chem Phys Lett 7:549–5652

    Article  Google Scholar 

  59. Rudnev V, Schlösser M, Telle HH, González-Ureňa Á (2015) First experimental photo-detachment spectrum of H2 −. Chem Phys Lett 639:41–46

    Article  CAS  Google Scholar 

  60. von Szentpály L (1982) Potential curves for the alkali dimers and their cations: a new sectroscopic rule and its predictions. Chem Phys Lett 88:321–324

    Article  Google Scholar 

  61. Fuentealba P, Preuss H, Stoll H, von Szentpály L (1982) A proper account of core-polarization with pseudopotentials: single valence-electron alkali compounds. Chem Phys Lett 89:418–422

    Article  CAS  Google Scholar 

  62. von Szentpály L, Fuentealba P, Preuss H, Stoll H (1982) Pseudopotential calculations on Rb2 +, Cs2 +, RbH+, CsH+ and the mixed alkali dimer ions. Chem Phys Lett 93:555–559

    Article  Google Scholar 

  63. Chen ES, Chen ECM (2003) Semiempirical characterization of homonuclear diatomic ions: 6. Group VI and VII anions. J Phys Chem A 107:169–177

    Article  CAS  Google Scholar 

  64. Van Lonkhuyzen H, De Lange CA (1984) High-resolution UV photoelectron spectroscopy of diatomic halogens. Chem Phys 89:313–322

    Article  Google Scholar 

  65. Kalemos A, Kaplan IG, Mavridis A (2010) The Sc2 dimer revisited. J Chem Phys 132:024309

    Article  CAS  Google Scholar 

  66. Kalemos A, Mavridis A (2011) The electronic structure of Ti2 and Ti2 +. J Chem Phys 135:134302

    Article  CAS  Google Scholar 

  67. Rienstra-Kiracofe JC, Tschumper GS, Schaefer III HF, Nandi S, Ellison GB (2002) Atomic and molecular electron affinities: photoelectron experiments and theoretical computations. Chem Rev 102:231–282

    Article  CAS  Google Scholar 

  68. Goebbert DJ (2012) Photoelectron imaging of CH–. Chem Phys Lett 551:19–25

    Article  CAS  Google Scholar 

  69. Turner DW, Baker C, Baker AD, Brundle CR (1970) Molecular photoelectron spectroscopy. Wiley-Interscience, London

    Google Scholar 

  70. Kimura K, Katsumata S, Achiba Y, Yamazaki T, Iwata S (1981) Handbook of HeI photoelectron spectra of fundamental organic molecules. Halsted, New York

    Google Scholar 

  71. Albritton DL, Schmeltekopf AL, Zare RN (1979) Potential energy curves for NO+. J Chem Phys 71:3271–3279

    Article  CAS  Google Scholar 

  72. Dyke JM, Lewis AE, Morris A (1984) A photoelectron spectroscopic study of the ground state of CF+ via the ionization process CF+(X 1Σ+)←CF(X 2Π). J Chem Phys 80:1382–1386

    Article  CAS  Google Scholar 

  73. Zhang X, Zhai H, Liu Y, Sun J (2013) Extensive ab initio calculation on low-lying excited states of CCl+ including spin–orbit interaction. J Quant Spectrosc Radiat Transf 119:23–31

    Article  CAS  Google Scholar 

  74. Antonov IO, Barker BJ, Bondybey VE, Heaven MC (2010) Spectroscopic characterization of Be2 + X 2Σu + and the ionization energy of Be2. J Chem Phys 133:074309

    Article  CAS  Google Scholar 

  75. Heaven MC, Bondybey VE, Merritt JM, Kaledin AL (2011) The unique bonding characteristics of beryllium and the group IIA metals. Chem Phys Lett 506:1–14

    Article  CAS  Google Scholar 

  76. Kaplan IG, Dolgounitcheva O, Watts JD, Ortíz JV (2002) Nondipole bound anions: Be2 − and Be3 −. J Chem Phys 117:3687–3693

    Article  CAS  Google Scholar 

  77. Mulliken RS (1966) The bonding characteristics of diatomic MOs. In: Löwdin P-O (ed) Quantum theory of atoms, molecules and the solid state. Academic, New York, p 231-241

  78. Moore CE (1954) Atomic energy levels as derived from the analysis of optical spectra, U. S. Natl. Bur. Stand. Circ. 467. Washington, 1949–1954

  79. Watts JD, Bartlett RJ (1992) Coupled-cluster calculations on the C2 molecule and the C2 + and C2 − molecular ions. J Chem Phys 96:6073–6084

    Article  CAS  Google Scholar 

  80. Haynes WM, Lide DR (eds.) (2011) Handbook of chemistry and physics, 92nd edn. CRC, Boca Raton

    Google Scholar 

  81. Greeff CW, Lester WA, Jr, Hammond BL (1996) Electronic states of Al and Al2 using quantum Monte Carlo with an effective core potential. J Chem Phys 104:1973–1978

  82. Meier U, Peyerimhoff SD, Grein F (1990) Ab initio MRD-CI study of neutral and charged Ga2, Ga3 and Ga4 clusters and comparison with corresponding boron and aluminum clusters. Z Phys D 17:209–224

    Article  CAS  Google Scholar 

  83. Bruna PJ, Petrongolo C, Buenker RJ, Peyerimhoff SD (1981) Theoretical prediction of the potential curves for the lowest-lying states of the CSi+ and Si2+ molecular ions. J Chem Phys 74

  84. van Lonkhuyzen H, de Lange CA (1984) U.V. Photoelectron spectroscopy of OH and OD radicals. Mol Phys 51:551–568

    Article  Google Scholar 

  85. Dunlavey SJ, Dyke JM, Fayad NK, Jonathan N, Morris A (1979) Vacuum ultraviolet photoelectron spectroscopy of transient species, part 10. The SH (x,2IIi) radical and the S(3P) atom. Mol Phys 38:729–738

    Article  CAS  Google Scholar 

  86. Miliordos E, Mavridis A (2010) Electronic structure and bonding of the early 3d-transition metal diatomic oxides and their ions: ScO0,±, TiO0,±, CrO0,±, and MnO0,±. J Phys Chem A 114:8536–8572

    Article  CAS  Google Scholar 

  87. Leopold DG, Murray KK, Stevens Miller AE, Lineberger WC (1985) Methylene: a study of the X 3 B 1 and A 1 A 1 states by photoelectron spectroscopy of CH2 − and CD2 −. J Chem Phys 83:4849–4865

    Article  CAS  Google Scholar 

  88. Johnson III RD (ed.) (2015) NIST computational chemistry comparison and benchmark database. NIST standard reference database number 101, release 17b, September 2015

  89. Boldyrev AI, Simons J, Zakrzewski VG, von Nissen W (1994) Vertical and adiabatic ionization energies and electron affinities of new SinC and SinO (n = 1-3) molecules. J Phys Chem 98:1427–1435

    Article  CAS  Google Scholar 

  90. Sakellaris CN, Papakondylis A, Mavridis A (2010) Ab initio study of the electronic structure of zinc oxide and its ions. Ground and excited states. J Phys Chem A 114:9333–9341

    Article  CAS  Google Scholar 

  91. Trofinov AB, Schirmer J (2005) Molecular ionization energies and ground-and ionic-state properties using a non-Dyson electron propagator approach. J Chem Phys 123:144115

    Article  CAS  Google Scholar 

  92. Jonkers G, Van Der Kerk SM, Mooyman R, De Lange CA (1982) UV photoelectron spectroscopy of transient species: germanium difluoride (GeF2). Chem Phys Lett 90:252–255

    Article  CAS  Google Scholar 

  93. Allan M (2001) Selectivity in the excitation of Fermi-coupled vibrations in CO2 by impact of slow electrons. Phys Rev Lett 87:033201

    Article  CAS  Google Scholar 

  94. Takahata Y, Chong DP (1999) Density-functional calculations of molecular electron affinities. J Braz Chem Soc 10:354–358

    Article  CAS  Google Scholar 

  95. Dyke J, Jonathan N, Lee E, Morris A (1976) Vacuum ultraviolet photoelectron spectroscopy of transient species. Part 7—The methyl radical. J Chem Soc Faraday Trans 2(72):1385–1396

    Article  Google Scholar 

  96. Dyke JM, Jonathan N, Morris A, Ridha A, Winter MJ (1983) Vacuum ultraviolet photoelectron spectroscopy of transient species. XVII. The SiH3 (X, 2A1) radical. Chem Phys 481–488

  97. Ortíz JV (1987) Many-body theory of the ionization energies of CH3 −, SiH3 −, and GeH3 −. J Am Chem Soc 109:5072–5076

    Article  Google Scholar 

  98. Brundle CR, Robin MB, Basch H (1970) Electronic energies and electronic structures of the fluoromethanes. J Chem Phys 53(1970):2196–2213

    Article  CAS  Google Scholar 

  99. Meunier M, Quirke N, Binesti D (1999) The calculation of the electron affinity of atoms and molecules. Mol Simul 23:109–125

    Article  CAS  Google Scholar 

  100. Grein F (2015) Structure and properties of the anions MF4 −, MCl4 − and MBr4 − (M = C, Si, Ge). Mol Phys 113:790–800

    Article  CAS  Google Scholar 

  101. Jordan KD, Burrow PD (1987) Temporary anion states of polyatomic hydrocarbons. Chem Rev 87:557–588

    Article  CAS  Google Scholar 

  102. Bieri G, Åsbrink LJ (1980) 30.4-nm he (II) photoelectron spectra of organic molecules: part I. Hydrocarbons Electron Spectrosc Relat Phenom 20:149

    Article  CAS  Google Scholar 

  103. Damrauer R, Noble AL (2008) Ions related to silynes and disilynes: computational studies. Organometallics 27:1707–1715

    Article  CAS  Google Scholar 

  104. von Szentpály L (2010) Universal method to calculate the stability, electronegativity, and hardness of dianions. J Phys Chem A 114:10891–10896

    Article  CAS  Google Scholar 

  105. Boltalina OV, Ioffé IN, Sidorov LN, Seifert G, Vietze K (2000) Ionization energy of fullerenes. J Am Chem Soc 122:9745–9749

    Article  CAS  Google Scholar 

  106. Roduner E (2006) Nanoscopic materials: size-dependent phenomena. RSC, London

    Google Scholar 

  107. Assadollahzadeh B, Thierfelder C, Schwerdtfeger P (2008) From clusters to the solid state: global minimum structures for cesium clusters Cs n (n = 2–20, ∞) and their electronic properties. Phys Rev B 78:245423

    Article  CAS  Google Scholar 

  108. Buckman SJ, Clark CW (1994) Atomic negative-ion resonances. Rev Mod Phys 66:539–655

    Article  CAS  Google Scholar 

  109. Peterson KA, Shepler BC, Singleton JM (2007) Mol Phys 105:1139–1155

    Article  CAS  Google Scholar 

  110. von Szentpály L (2008) Atom-based thermochemistry: predictions of the sublimation enthalpies of group 12 chalcogenides and the formation enthalpies of their polonides. J Phys Chem A 112:12695–12701

    Article  CAS  Google Scholar 

  111. Cremer D, Wu A, Larsson A, Kraka E (2000) Some thoughts about bond energies, bond lengths, and force constants. J Mol Model 6:396–412

    Article  CAS  Google Scholar 

  112. Pauling L (1960) The nature of the chemical bond and the structure of molecules and crystals: an introduction to modern structural chemistry. Cornell University Press, Ithaca

    Google Scholar 

  113. Caddeo C, Malloci G, De Angelis F, Colombo L, Mattoni A (2012) Optoelectronic properties of (ZnO)60 isomers. Phys Chem Chem Phys 14:14293–14298

    Article  CAS  Google Scholar 

  114. Assadollahzadeh B, Schwerdtfeger P (2009) A systematic search for minimum structures of small gold clusters Aun (n= 2–20) and their electronic properties. J Chem Phys 131:064306

    Article  CAS  Google Scholar 

  115. Gázquez JL (1997) Bond energies and hardness differences. J Phys Chem A 101:9464–9469

    Article  Google Scholar 

  116. Primas H (1981) Chemistry, quantum mechanics and reductionism. Springer, Berlin, p 26

    Book  Google Scholar 

  117. Feynman RP (1993) The meaning of it all: thoughts of a citizen scientist. Addison-Wesley, Reading

    Google Scholar 

  118. Chamorro E, Chattaraj PK, Fuentealba P (2003) Variation of the Electrophilicity index along the reaction path. J Phys Chem A 107:7068–7072

    Article  CAS  Google Scholar 

  119. Morell C, Labet V, Grand A, Chermette H (2009) Minimum electrophilicity principle: an analysis based upon the variation of both chemical potential and absolute hardness. Phys Chem Chem Phys 11:3417–3423

    Article  CAS  Google Scholar 

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Acknowledgements

This article is dedicated to Professor Henry Chermette on the occasion of his 70th birthday. It is a pleasure to thank Professor Michael C. Boehm (Darmstadt) for useful discussions, and Professor Hans-Joachim Werner for continued kind hospitality at the Institut für Theoretische Chemie. The constructive comments of a reviewer are gratefully acknowledged.

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    László von Szentpály

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This paper belongs to Topical Collection Festschrift in Honor of Henry Chermette

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von Szentpály, L. Hardness maximization or equalization? New insights and quantitative relations between hardness increase and bond dissociation energy. J Mol Model 23, 217 (2017). https://doi.org/10.1007/s00894-017-3383-z

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