Abstract
In this work some possibilities for deriving a local electrophilicity are studied. First, we consider the original definition proposed by Chattaraj, Maiti, and Sarkar (J Phys Chem A 107:4973, 2003), in which the local electrophilicity is given by the product of the global electrophilicity, and the Fukui function for charge acceptance is derived by two different approaches, making use of the chain rule for functional derivatives. We also modify the proposals based on the electron density so as to have a definition with the same units of the original definition, which also introduces a dependence in the Fukui function for charge donation. Additionally, we also explore other possibilities using the tools of information theory and the temperature dependent reactivity indices of the density functional theory of chemical reactivity. The poor results obtained from the last two approaches lead us to conjecture that this is due to the fact that the global electrophilicity is not a derivative, like most of the other reactivity indices. The conclusion is that Chattaraj’s suggestion seems to be the simplest, but at the same time a very reliable approach to this important property.
Similar content being viewed by others
References
Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York
Chermette H (1998) Density functional theory: a powerful tool for theoretical studies in coordination chemistry. Coord Chem Rev 180:699–721
Geerlings P, De Proft F, Langenaeker W (2003) Conceptual density functional theory. Chem Rev 103:1793–1873. https://doi.org/10.1021/cr990029p
Ayers PW, Anderson JSM, Bartolotti LJ (2005) Perturbative perspectives on the chemical reaction prediction problem. Int J Quantum Chem 101:520–534. https://doi.org/10.1002/qua.20307
Gázquez J (2008) Perspectives on density functional theory of chemical reactivity. J Mex Chem Soc 52:3–10
Ayers PW, Yang WT, Bartolotti LJ (2009) Fukui function. In: Chattaraj PK (ed) Chemical reactivity theory: a density functional view. CRC, Boca Raton, pp 255–267
Liu S-B (2009) Conceptual density functional theory and some recent developments. Acta Phys -Chim Sin 25:590–600
Fuentealba P, Cardenas C (2015) Density functional theory of chemical reactivity. In: Springborg M, Joswig OJ (eds) Chemical modelling, vol 11. The Royal Society of Chemistry, pp 151-174. https://doi.org/10.1039/9781782620112-00151
Parr RG, Donnelly RA, Levy M, Palke WE (1978) Electronegativity: the density functional viewpoint. J Chem Phys 68:3801–3807. https://doi.org/10.1063/1.436185
Parr RG, Pearson RG (1983) Absolute hardness - companion parameter to absolute electronegativity. J Am Chem Soc 105:7512–7516
Cárdenas C, Heidar-Zadeh F, Ayers PW (2016) Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series. Phys Chem Chem Phys 18:25721–25734. https://doi.org/10.1039/C6CP04533B
Parr RG, Yang WT (1984) Density functional approach to the frontier-electron theory of chemical reactivity. J Am Chem Soc 106:4049–4050
Yang WT, Parr RG, Pucci R (1984) Electron density, Kohn-sham frontier orbitals, and Fukui functions. J Chem Phys 81:2862–2863. https://doi.org/10.1063/1.447964
Yang WT, Parr RG (1985) Hardness, softness, and the Fukui function in the electron theory of metals and catalysis. Proc Natl Acad Sci USA 82:6723–6726. https://doi.org/10.1073/pnas.82.20.6723
Pearson RG (1987) Recent advances in the concept of hard and soft acids and bases. J Chem Ed 64:561–567
Pearson RG (1963) Hard and soft acids and bases. J Am Chem Soc 85:3533–3539
Pearson RG (1966) Acids and bases. Science 151:172–177
Pearson RG (1967) Hard and soft acids and bases. Chem Britain 3:103–107
Chattaraj PK, Lee H, Parr RG (1991) HSAB principle. J.Am Chem Soc 113:1855–1856
Parr RG, Chattaraj PK (1991) Principle of maximum hardness. J Am Chem Soc 113:1854–1855
Pearson RG, Palke WE (1992) Support for a principle of maximum hardness. J Phys Chem 96:3283–3285. https://doi.org/10.1021/j100187a020
Gázquez JL (1993) Hardness and softness in density functional theory. Struct Bond 80:27–43
Gázquez JL, Méndez F (1994) The hard and soft acids and bases principle - an atoms in molecules viewpoint. J Phys Chem 98:4591–4593. https://doi.org/10.1021/j100068a018
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
Gázquez JL (1997) Bond energies and hardness differences. J Phys Chem A 101:9464–9469
Gázquez JL (1997) The hard and soft acids and bases principle. J Phys Chem A 101:4657–4659
Chattaraj PK (2001) Chemical reactivity and selectivity: local HSAB principle versus frontier orbital theory. J Phys Chem A 105:511–513
Torrent-Sucarrat M, Luis JM, Duran M, Sola M (2001) On the validity of the maximum hardness and minimum polarizability principles for nontotally symmetric vibrations. J Am Chem Soc 123:7951–7952
Ayers PW (2005) An elementary derivation of the hard/soft-acid/base principle. J Chem Phys 122:141102
Chattaraj PK, Ayers PW (2005) The maximum hardness principle implies the hard/soft acid/base rule. J Chem Phys 123:086101
Ayers PW, Parr RG, Pearson RG (2006) Elucidating the hard/soft acid/base principle: a perspective based on half-reactions. J Chem Phys 124:194107
Ayers PW (2007) The physical basis of the hard/soft acid/base principle. Faraday Discuss. 135:161–190
Chattaraj PK, Ayers PW, Melin J (2007) Further links between the maximum hardness principle and the hard/soft acid/base principle: insights from hard/soft exchange reactions. Phys Chem Chem Phys 9:3853–3856
Chattaraj PK (2007) A minimum electrophilicity perspective of the HSAB principle. Indian J Phys 81:871–879
Reed JL (2012) Hard and soft acids and bases: structure and process. J Phys Chem A 116:7147–7153. https://doi.org/10.1021/jp301812j
Ayers PW, Cardenas C (2013) Communication: a case where the hard/soft acid/base principle holds regardless of acid/base strength. J Chem Phys 138:181106
Cardenas C, Ayers PW (2013) How reliable is the hard-soft acid-base principle? An assessment from numerical simulations of electron transfer energies. Phys Chem Chem Phys 15:13959–13968. https://doi.org/10.1039/c3cp51134k
Miranda-Quintana RA, Kim TD, Cárdenas C, Ayers PW (2017) The HSAB principle from a finite-temperature grand-canonical perspective. Theor Chem Accounts 136:135
Parr RG, Von Szentpaly L, Liu SB (1999) Electrophilicity index. J Am Chem Soc 121:1922–1924
Chattaraj PK, Sarkar U, Roy DR (2006) Electrophilicity index. Chem Rev 106:2065–2091. https://doi.org/10.1021/cr040109f
Chattaraj PK, Roy DR (2007) Update 1 of: Electrophilicity index. Chem Rev 107:PR46–PR74
Chattaraj PK, Chakraborty A, Giri S (2009) Net electrophilicity. J Phys Chem A 113:10068–10074
Chattaraj PK, Giri S, Duley S (2011) Update 2 of: electrophilicity index. Chem Rev 111:PR43–PR75. https://doi.org/10.1021/cr100149p
Chattaraj PK, Maiti B, Sarkar U (2003) Philicity: a unified treatment of chemical reactivity and selectivity. J Phys Chem A 107:4973–4975
Perdew JP, Parr RG, Levy M, Balduz JL (1982) Density-functional theory for fractional particle number - derivative discontinuities of the energy. Phys Rev Lett 49:1691–1694. https://doi.org/10.1103/PhysRevLett.49.1691
Yang WT, Zhang YK, Ayers PW (2000) Degenerate ground states and a fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett 84:5172–5175. https://doi.org/10.1103/PhysRevLett.84.5172
Ayers PW (2008) The dependence on and continuity of the energy and other molecular properties with respect to the number of electrons. J Math Chem 43:285–303. https://doi.org/10.1007/s10910-006-9195-5
Berkowitz M, Parr RG (1988) Molecular hardness and softness, local hardness and softness, hardness and softness kernels, and relations among these quantities. J Chem Phys 88:2554–2557
Franco-Pérez M, Gázquez JL, Ayers PW, Vela A (2015) Revisiting the definition of the electronic chemical potential, chemical hardness, and softness at finite temperatures. J Chem Phys 143:154103
Yang WT, Mortier WJ (1986) The use of global and local molecular-parameters for the analysis of the gas-phase basicity of amines. J Am Chem Soc 108:5708–5711
Contreras RR, Fuentealba P, Galvan M, Perez P (1999) A direct evaluation of regional Fukui functions in molecules. Chem Phys Lett 304:405–413
Fuentealba P, Perez P, Contreras R (2000) On the condensed Fukui function. J Chem Phys 113:2544–2551
Ayers PW, Morrison RC, Roy RK (2002) Variational principles for describing chemical reactions: condensed reactivity indices. J Chem Phys 116:8731–8744
Bultinck P, Fias S, Van Alsenoy C, Ayers PW, Carbo-Dorca R (2007) Critical thoughts on computing atom condensed Fukui functions. J Chem Phys 127:034102
Domingo LR, Aurell MJ, Perez P, Contreras R (2002) Quantitative characterization of the local electrophilicity of organic molecules. Understanding the regioselectivity on Diels- Alder reactions. J Phys Chem A 106:6871–6875
Pérez P, Toro-Labbé A, Aizman A, Contreras R (2002) Comparison between experimental and theoretical scales of electrophilicity in benzhydryl cations. J Org Chem 67:4747–4752
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
Chattaraj PK, Cedillo A, Parr RG (1995) Variational method for determining the Fukui function and chemical hardness of an electronic system. J Chem Phys 103:7645–7646
Gázquez JL, Cedillo A, Vela A (2007) Electrodonating and electroaccepting powers. J Phys Chem A 111:1966–1970. https://doi.org/10.1021/jp065459f
Cedillo A, Contreras R (2012) A local extension of the electrophilicity index concept. J Mex Chem Soc 56:257–260
Morell C, Gázquez JL, Vela A, Guegan F, Chermette H (2014) Revisiting electroaccepting and electrodonating powers: proposals for local electrophilicity and local nucleophilicity descriptors. Phys Chem Chem Phys 16:26832–26842. https://doi.org/10.1039/c4cp03167a
Morell C, Grand A, Toro-Labbé A (2005) New dual descriptor for chemical reactivity. J Phys Chem A 109:205–212. https://doi.org/10.1021/jp046577a
Morell C, Grand A, Toro-Labbé A (2006) Theoretical support for using the Delta f(r) descriptor. Chem Phys Lett 425:342–346. https://doi.org/10.1016/j.cplett.2006.05.003
Heidar-Zadeh F, Fias S, Vöhringer-Martinez E, Verstraelen T, Ayers PW (2017) The local response of global descriptors. Theor Chem Accounts 136:19
Tognetti V, Morell C, Joubert L (2015) Quantifying electro/nucleophilicity by partitioning the dual descriptor. J Comput Chem 36:649–659. https://doi.org/10.1002/jcc.23840
Franco-Pérez M, Ayers PW, Gázquez JL, Vela A (2015) Local and linear chemical reactivity response functions at finite temperature in density functional theory. J Chem Phys 143:244117
Franco-Pérez M, Ayers PW, Gázquez JL, Vela A (2017) Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory. Phys Chem Chem Phys 19:13687–13695
Franco-Pérez M, Heidar-Zadeh F, Ayers PW, Gázquez JL, Vela A (2017) Going beyond the three-state ensemble model: the electronic chemical potential and Fukui function for the general case. Phys Chem Chem Phys 19:11588–11602
Polanco-Ramírez CA, Franco-Pérez M, Carmona-Espíndola J, Gázquez JL, Ayers PW (2017) Revisiting the definition of local hardness and hardness kernel. Phys Chem Chem Phys 19:12355–12364. https://doi.org/10.1039/c7cp00691h
Franco-Perez M, Polanco-Ramirez CA, Gazquez JL, Ayers PW (2018) Reply to the ‘Comment on “Revisiting the definition of local hardness and hardness kernel”’ by C. Morell, F. Guegan, W. Lamine, and H. Chermette, Phys Chem Chem Phys, 2018, 20, doi:10.1039/C7CP04100D. Phys Chem Chem Phys 20:9011–9014. https://doi.org/10.1039/c7cp07974e
Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev B 136:B864–B871
Ayers PW, Parr RG (2008) Local hardness equalization: exploiting the ambiguity. J Chem Phys 128:184108
Ayers PW, Parr RG (2008) Beyond electronegativity and local hardness: higher-order equalization criteria for determination of a ground-state electron density. J Chem Phys 129:054111
Gázquez JL, Vela A, Chattaraj PK (2013) Local hardness equalization and the principle of maximum hardness. J Chem Phys 138:214103
Heidar-Zadeh F, Fuentealba P, Cardenas CA, Ayers P (2014) An information-theoretic resolution of the ambiguity in the local hardness. Phys Chem Chem Phys 16:6019-6060-6026
Nalewajski RF, Parr RG (2000) Information theory, atoms in molecules, and molecular similarity. Proc Natl Acad Sci USA 97:8879–8882
Nalewajski RF, Parr RG (2001) Information theory thermodynamics of molecules and their Hirshfeld fragments. J Phys Chem A 105:7391–7400
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22:79–86
Kullback S (1997) Information theory and statistics. Dover, Mineola
Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge-densities. Theor Chim Acta 44:129–138
Heidar-Zadeh F, Vinogradov I, Ayers PW (2017) Hirshfeld partitioning from non-extensive entropies. Theor Chem Accounts 136:54
Heidar-Zadeh F, Ayers PW (2017) Fuzzy atoms in molecules from Bregman divergences. Theor Chem Accounts 136:92
Heidar-Zadeh F, Ayers PW, Verstraelen T, Vinogradov I, Vöhringer-Martinez E, Bultinck P (2017) Information-theoretic approaches to atoms-in-molecules: Hirshfeld family of partitioning schemes. J Phys Chem A 122:4219–4245
Heidar Zadeh F (2017) Variational information-theoretic atoms-in-molecules. McMaster University, Hamilton
Gonzalez MM, Cardenas C, Rodríguez JI, LIU S, Heidar-Zadeh F, Miranda-Quintana RA, Ayers PW, Martínez GM, Carlos C, Juan IR (2017) Quantitative electrophilicity measures. Acta Phys Chim Sin 34:662–674
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 MJ, Heyd J, Brothers EN, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell AP, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, 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 Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09. Gaussian Inc., Wallingford
Kohn W, Sham LJ (1965) Self-consistent equations including exchange and correlation effects. Phys Rev 140:1133–1138
Becke AD (1993) Density functional thermochemistry. III. The role of exact exchange. J Chem Phys 98:5648–5652
Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem 98:11623–11627
Kim K, Jordan KD (1994) Comparison of density functional and MP2 calculations on the water monomer and dimer. J Phys Chem 98:10089–10094
Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys Rev A 38:3098–3100
Lee CT, Yang WT, Parr RG (1988) Development of the Colle-Salvetti correlation-energy formula into a functional of the electron-density. Phys Rev B 37:785–789
Breneman CM, Wiberg KB (1990) Determining atom-centered monopoles from molecular electrostatic potentials - the need for high sampling density in formamide conformational-analysis. J Comput Chem 11:361–373
Reed AE, Weinstock RB, Weinhold F (1985) Natural-population analysis. J Chem Phys 83:735–746. https://doi.org/10.1063/1.449486
Acknowledgments
This work was financed by: i) FONDECYT through projects No 1181121 and 1180623, and ii) Centers Of Excellence With Basal/Conicyt Financing, Grant FB0807. This paper is dedicated to Professor Patrim Chattaraj on the occasion of his 60th birthday.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper belongs to Topical Collection International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday
Rights and permissions
About this article
Cite this article
Robles, A., Franco-Pérez, M., Gázquez, J.L. et al. Local electrophilicity. J Mol Model 24, 245 (2018). https://doi.org/10.1007/s00894-018-3785-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00894-018-3785-6