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Parr’s index to describe both electrophilicity and nucleophilicity
Accepted Manuscript Parr’s index to describe both electrophilicity and nucleophilicity Syun-ichi Kiyooka, Daisuke Kaneno, Ryoji Fujiyama PII: DOI: Reference:
S0040-4039(12)01969-7 http://dx.doi.org/10.1016/j.tetlet.2012.11.039 TETL 42131
To appear in:
Tetrahedron Letters
Please cite this article as: Kiyooka, S-i., Kaneno, D., Fujiyama, R., Parr’s index to describe both electrophilicity and nucleophilicity, Tetrahedron Letters (2012), doi: http://dx.doi.org/10.1016/j.tetlet.2012.11.039
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Parr’s index to describe both electrophilicity and nucleophilicity Syun-ichi Kiyooka,* Daisuke Kaneno, Ryoji Fujiyama Department of Materials Science, Faculty of Science, Kochi University, Akebono-cho, Kochi 780-8520, Japan
Corresponding author, fax: +81 88 8305 E-mail address: [email protected] Keywords: Parr’s index, Single reactivity scale, Electrophilicity, Nucleophilicity, HOMO and LUMO ABSTRACT We have disclosed a new aspect of the Parr’s value ( = 2/2, which was originally proposed as an electrophilicity index, and reformed the value as a useful single scale from electrophilicity to nucleophilicity by introducing the corresponding values (. The plot of the values against the values ( – correlation) presented a fine parabola for 65 chemical species: the order of the electrophilicity is seen at negative values and the order of nucleophilicity is seen at positive values.
The concepts of the electrophilicity and nucleophilicity of molecules are important to almost chemists. Although numerous methods have been developed to determine these concepts in understanding of the behavior of molecules,1-9 there is still possibility for discussion and improvements in this field. As far as we know, there has been no single theoretical scale valid for both electrophilicity and nucleophilicity. It is our goal to propose an effective single theoretical scale over the wide range of reactivity of chemical species (electrophiles and nucleophiles). Parr et al. considered the concept of electrophilicity on the basis of the density functional theory (DFT). 10-12 The energy change depends on electron transfer in charge-transfer models. This transfer is presented on the second-order Taylor series expansion of energy as a function of the number of electrons. The energy change is
described by (f (N) =) E = N + (/2) N2 (1) 2 2 where (= E/N) is the chemical potential and (= E/N ) is the chemical hardness.10 After the and to the two coefficients in the equation were introduced by Parr, equation (1) can be recognized to be an ordinary quadratic equation which is apart from DFT When the differentiation of f (N) equals to zero (f ’(N) = 0), N = / is obtained. The substitution of / to N of the equation results in E = 2/2where both values are situated at the extremum in the second-order parabora. For electrophilicity, Parr proposed index = 2/2) which is directly related to the energy difference for the change in electronic charge in the system containing the charge transfer process and determined a correlation between the index and the electron affinity of atoms and molecules. 11 According to Koopmans’ theorem,13 and can be represented by using the highest occupied molecular orbital, HOMO, and lowest unoccupied molecular orbital, LUMO, as follows: ≈ (ELUMO + EHOMO)/2 ≈ ELUMO EHOMO Although this approximation is not necessarily adequate to all chemical species,14 if the HOMO and LUMO energy levels of the molecules in question are approximately allowed to describe the values, the index can be used efficiently to estimate the reactivity of the species from the standpoint of the frontier orbital theory.15-17 In order to realize a simple theoretical scale, we confined our attention to the introduing process of the index for electrophilicity and recognized that the value is not independent variable. Apparently, 2/2= ) is a function of /in the second-order parabora. The value must be accompanied by the corresponding value related to /. Therefore, we decided to propose the term (). The validity of this idea was straightforwardly confirmed by the treatment of the related chemical species; hydronium cation, neutral H2O, and hydroxide anion, as shown in Figure 1. Cationic and anionic species are, a priori, directed towards electrophilicity and nucleophilicity, respectively. The cationic species has lower HOMO and LUMO energy levels while the anionic species has both higher. This fact is significant because the former has a high value (4.50 eV) with an of 0.63 and the latter has a relatively high value (1.57 eV) but with an of +0.44. This plus sign of the nucleophile suggested that the treatment makes it possible to extend the index to nucleophilicity.
Figure 1. HOMO-LUMO energy levels and and values of the related cationic, neutral, and anionic species, calculated at the HF/ 6-31G(d,p) level of theory The structures of 65 compounds were optimized at the HF/ 6-31G(d,p) level of theory. There is a comment why the Hartree-Fock molecular orbital theory (HFT) was chosen rather than DFT in this study. It is well-known that HFT provides more reliable data on MO energy levels than DFT.18-21 In practice, the energy gap is smaller using DFT than using HFT, as tabulated on hydronium cation in Table 1. Scheme 1 illustrates that the and values were obtained from the HOMO and LUMO energy levels calculated from their optimized structures. The values were then plotted against the values, as shown in Figure 2. The rank order of nucleophilicity is seen at positive values and the order of electrophilicity is seen at negative values. As might have been expected, we found that when the value is introduced, the index effectively works for both electrophilicity and nucleophilicity. Regression analysis of the – correlation presented a parabola ( = 6.032 + 0.47, R = 0.885), which is unambiguously attributable to the original equation (1) through the definition of the terms and . The coefficient of 2 should be comparable with /2 in the equation and the value of 6.03 was quite consistent with 7.60, calculated from the average of the 65 compounds.
Table 1 Comparison of HFT and DFT for the MO energy of H3O+ HF/6-31G(d,p) E = 76.3103248 a.u. HOMO LUMO 0.9500 a.u. 0.1080 a.u. 0.8420 a.u. 0.5290 a.u. 4.50 eV 0.63 B3LYP/6-31G(d,p) E = 76.7056366 a.u. HOMO LUMO 0.7382 a.u. 0.2646 a.u. 0.4736 a.u. 0.5014 a.u. 7.22 eV 1.06
Scheme 1.
The and values of 65 chemical species
6
4
2
0
−1
Figure 2.
0
1
The correlation of 65 chemical species
The dianions of 1, 2, 3, and 4 are ranked as very active nucleophiles on the parabola because of their high values and high values. Various monoanions (5, 6, 7, 8, 11, 14, 15, 16, 17, 18, 20, 22, and 23) also show considerably high nucleophilicity depending on their dominant anionic characteristics. Although the fluoride anion (9) is separated from the ideal curve, the halogen anions correlated well together (the dotted line a in Figure 2).
The leaving groups in organic reactions (21, 24, 26, and 28) lie on
the positive side of the parabola, which indicate relatively weak nucleophilicity. The silyl nucleophiles (32, 35, and 38) used in Lewis-acid catalyzed reactions do not display strong nucleophilicity and are on the negative side of the parabola.
Methyl
compounds with the leaving groups 41, 43, 47, 48, and 49 display low electrophilicity and the unsaturated compounds with electron attracting groups 50, 51, 53, and 54 display moderate electrophilicity. Benzaldehyde, activated by BCl3, (56) apparently becomes more electrophilic than either benzaldehyde (50) or BCl3 (52). The cationic species 57, 58, 59, 60, 61, and 63 possess outstanding electrophilicity. The – values of Mayr’s benzhydryl cationic compounds 62, 64, and 65 show high values and a good correlation (the dotted line b in Figure 2).22 Because the main aim of this report is to present the real meaning of and the expansion of to nucleophilicity along with the chemistry, characterized by the – correlation, is not presented in more detail. In conclusion, we have disclosed a new aspect of the Parr’s value, which was originally proposed as an electrophilicity index, and reformed the value as a useful single scale from electrophilicity to nucleophilicity by introducing the corresponding values. The theoretical index will play a role to judge unknown or indistinct reactivity of various chemical species for a wide range of chemical phenomenon. The calculation using Mller-Plesset (MP2/6-31G(d,P)) theory, incorporated electron correlation, has been carried out and gave approximately the same HOMO-LUMO gaps over the above 65 compounds with the HF data. The full paper, containing the data with higher basis sets, will be reported in due course.
Supplementary data Supplementary data (the computed data of the optimized geometries and their HOMO and LUMO energy levels of 65 chemical species) associated with this article can be found, in the online version, at.
References and notes 1. Ingold, C. K. Chem. Rev. 1934, 15, 225. 2. Swain, C. G.; Scott, C. B. J. Am. Chem. Soc. 1953, 75, 141. 3. Yang, W.; Parr,R. G. Proc. Natl. Acad. Sci. USA 1985, 82, 6723. 4. Ritchie, C. D. Acc. Chem. Rev. 1972, 5,348. 5. Geerlings, P.; De Proft, F.; Langenaeaker, W. Chem. Rev. 2003, 103, 1793.
6. Mayr, H.; Ofial, A. R. Pure Appl. Chem. 2005, 11, 1807. 7. Liu, S. Chemical Reactivity Theory: Density Functional View, (Ed.: Chattaraj, P. K.),Taylor and Francis, Boca Raton, 2009. 8. Morell, C.; Herrera, B.; Gutiérrez-Oliva, S.; Ceróa, M. -L.; Grand, A.; Tore-Labbé, A. J. Phys. Chem. A. 2012, 116, 7074. 9. Dichiarante, V.; Fagnoni, M.; Albini, A. J. Org. Chem. 2008, 73, 1282. 10. (a) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. (b) Pearson, R. G. Chemical Hardness, John Wiley-VCH, Weinheim, 1997. 11. Parr, R. G.; Szentpály, L. v.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922. 12. Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065. 13. (a) Koopmans, T. A. Physica 1933, 1, 104. (b) Pearson, R. G. Acc. Chem. Res. 1993, 26, 250: Pearson’s definition is = (ELUMO EHOMO)/2 as chemical hardness, but the factor of 2 was added arbitrarily to make and symmetrical. Recently, he used = ELUMO EHOMO (J. Chem. Sci., 2005, 117, 369). 14. Szabo, A; Osthund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Macmilian Publishing, New York, 1982. 15. (a) Fukui, K.; Yonezawa, T.; Shingu, H. J. Chem. Phys. 1952, 20, 722. (b) Fukui, K. Science, 1982, 217, 747. 16. Klopman, G. J. Am. Chem. Soc. 1968, 90, 223. 17. Salem, L. J. Am. Chem. Soc. 1968, 90, 543. 18. Janak, J. F. Phys. Rev. B 1978, 18, 7165. 19. Zhang, G.; Musgrave, C.B.; J. Phys. Chem. A 2007, 111, 1554. 20. Stein, T.; Eisenberg, H.; Kronik, L.; Baer, R. Phys. Rev. Lett. 2010, 105, 266802. 21. Rudberg, E. J. Phys.: Condens. Matter 2012, 24, 072202. 22. Schindele, C.; Houk, K. N.; Mayr, H. J. Am. Chem. Soc. 2002, 124, 11208.
Graphical Abstract
Parr’s index to describe both electrophilicity and nucleophilicity Syun-ichi Kiyooka*, Daisuke Kaneno, Ryoji Fujiyama
Parr’s values of 65 chemical species were plotted
6
as a function of the newly introduced values, = (/2)2 + The fine parabola indicates the order of
4
nucleophilicity at positive values and the order of electrophilicity at negative values.
2
0 -1
0
1
S0040-4039(12)01969-7 http://dx.doi.org/10.1016/j.tetlet.2012.11.039 TETL 42131
To appear in:
Tetrahedron Letters
Please cite this article as: Kiyooka, S-i., Kaneno, D., Fujiyama, R., Parr’s index to describe both electrophilicity and nucleophilicity, Tetrahedron Letters (2012), doi: http://dx.doi.org/10.1016/j.tetlet.2012.11.039
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Parr’s index to describe both electrophilicity and nucleophilicity Syun-ichi Kiyooka,* Daisuke Kaneno, Ryoji Fujiyama Department of Materials Science, Faculty of Science, Kochi University, Akebono-cho, Kochi 780-8520, Japan
Corresponding author, fax: +81 88 8305 E-mail address: [email protected] Keywords: Parr’s index, Single reactivity scale, Electrophilicity, Nucleophilicity, HOMO and LUMO ABSTRACT We have disclosed a new aspect of the Parr’s value ( = 2/2, which was originally proposed as an electrophilicity index, and reformed the value as a useful single scale from electrophilicity to nucleophilicity by introducing the corresponding values (. The plot of the values against the values ( – correlation) presented a fine parabola for 65 chemical species: the order of the electrophilicity is seen at negative values and the order of nucleophilicity is seen at positive values.
The concepts of the electrophilicity and nucleophilicity of molecules are important to almost chemists. Although numerous methods have been developed to determine these concepts in understanding of the behavior of molecules,1-9 there is still possibility for discussion and improvements in this field. As far as we know, there has been no single theoretical scale valid for both electrophilicity and nucleophilicity. It is our goal to propose an effective single theoretical scale over the wide range of reactivity of chemical species (electrophiles and nucleophiles). Parr et al. considered the concept of electrophilicity on the basis of the density functional theory (DFT). 10-12 The energy change depends on electron transfer in charge-transfer models. This transfer is presented on the second-order Taylor series expansion of energy as a function of the number of electrons. The energy change is
described by (f (N) =) E = N + (/2) N2 (1) 2 2 where (= E/N) is the chemical potential and (= E/N ) is the chemical hardness.10 After the and to the two coefficients in the equation were introduced by Parr, equation (1) can be recognized to be an ordinary quadratic equation which is apart from DFT When the differentiation of f (N) equals to zero (f ’(N) = 0), N = / is obtained. The substitution of / to N of the equation results in E = 2/2where both values are situated at the extremum in the second-order parabora. For electrophilicity, Parr proposed index = 2/2) which is directly related to the energy difference for the change in electronic charge in the system containing the charge transfer process and determined a correlation between the index and the electron affinity of atoms and molecules. 11 According to Koopmans’ theorem,13 and can be represented by using the highest occupied molecular orbital, HOMO, and lowest unoccupied molecular orbital, LUMO, as follows: ≈ (ELUMO + EHOMO)/2 ≈ ELUMO EHOMO Although this approximation is not necessarily adequate to all chemical species,14 if the HOMO and LUMO energy levels of the molecules in question are approximately allowed to describe the values, the index can be used efficiently to estimate the reactivity of the species from the standpoint of the frontier orbital theory.15-17 In order to realize a simple theoretical scale, we confined our attention to the introduing process of the index for electrophilicity and recognized that the value is not independent variable. Apparently, 2/2= ) is a function of /in the second-order parabora. The value must be accompanied by the corresponding value related to /. Therefore, we decided to propose the term (). The validity of this idea was straightforwardly confirmed by the treatment of the related chemical species; hydronium cation, neutral H2O, and hydroxide anion, as shown in Figure 1. Cationic and anionic species are, a priori, directed towards electrophilicity and nucleophilicity, respectively. The cationic species has lower HOMO and LUMO energy levels while the anionic species has both higher. This fact is significant because the former has a high value (4.50 eV) with an of 0.63 and the latter has a relatively high value (1.57 eV) but with an of +0.44. This plus sign of the nucleophile suggested that the treatment makes it possible to extend the index to nucleophilicity.
Figure 1. HOMO-LUMO energy levels and and values of the related cationic, neutral, and anionic species, calculated at the HF/ 6-31G(d,p) level of theory The structures of 65 compounds were optimized at the HF/ 6-31G(d,p) level of theory. There is a comment why the Hartree-Fock molecular orbital theory (HFT) was chosen rather than DFT in this study. It is well-known that HFT provides more reliable data on MO energy levels than DFT.18-21 In practice, the energy gap is smaller using DFT than using HFT, as tabulated on hydronium cation in Table 1. Scheme 1 illustrates that the and values were obtained from the HOMO and LUMO energy levels calculated from their optimized structures. The values were then plotted against the values, as shown in Figure 2. The rank order of nucleophilicity is seen at positive values and the order of electrophilicity is seen at negative values. As might have been expected, we found that when the value is introduced, the index effectively works for both electrophilicity and nucleophilicity. Regression analysis of the – correlation presented a parabola ( = 6.032 + 0.47, R = 0.885), which is unambiguously attributable to the original equation (1) through the definition of the terms and . The coefficient of 2 should be comparable with /2 in the equation and the value of 6.03 was quite consistent with 7.60, calculated from the average of the 65 compounds.
Table 1 Comparison of HFT and DFT for the MO energy of H3O+ HF/6-31G(d,p) E = 76.3103248 a.u. HOMO LUMO 0.9500 a.u. 0.1080 a.u. 0.8420 a.u. 0.5290 a.u. 4.50 eV 0.63 B3LYP/6-31G(d,p) E = 76.7056366 a.u. HOMO LUMO 0.7382 a.u. 0.2646 a.u. 0.4736 a.u. 0.5014 a.u. 7.22 eV 1.06
Scheme 1.
The and values of 65 chemical species
6
4
2
0
−1
Figure 2.
0
1
The correlation of 65 chemical species
The dianions of 1, 2, 3, and 4 are ranked as very active nucleophiles on the parabola because of their high values and high values. Various monoanions (5, 6, 7, 8, 11, 14, 15, 16, 17, 18, 20, 22, and 23) also show considerably high nucleophilicity depending on their dominant anionic characteristics. Although the fluoride anion (9) is separated from the ideal curve, the halogen anions correlated well together (the dotted line a in Figure 2).
The leaving groups in organic reactions (21, 24, 26, and 28) lie on
the positive side of the parabola, which indicate relatively weak nucleophilicity. The silyl nucleophiles (32, 35, and 38) used in Lewis-acid catalyzed reactions do not display strong nucleophilicity and are on the negative side of the parabola.
Methyl
compounds with the leaving groups 41, 43, 47, 48, and 49 display low electrophilicity and the unsaturated compounds with electron attracting groups 50, 51, 53, and 54 display moderate electrophilicity. Benzaldehyde, activated by BCl3, (56) apparently becomes more electrophilic than either benzaldehyde (50) or BCl3 (52). The cationic species 57, 58, 59, 60, 61, and 63 possess outstanding electrophilicity. The – values of Mayr’s benzhydryl cationic compounds 62, 64, and 65 show high values and a good correlation (the dotted line b in Figure 2).22 Because the main aim of this report is to present the real meaning of and the expansion of to nucleophilicity along with the chemistry, characterized by the – correlation, is not presented in more detail. In conclusion, we have disclosed a new aspect of the Parr’s value, which was originally proposed as an electrophilicity index, and reformed the value as a useful single scale from electrophilicity to nucleophilicity by introducing the corresponding values. The theoretical index will play a role to judge unknown or indistinct reactivity of various chemical species for a wide range of chemical phenomenon. The calculation using Mller-Plesset (MP2/6-31G(d,P)) theory, incorporated electron correlation, has been carried out and gave approximately the same HOMO-LUMO gaps over the above 65 compounds with the HF data. The full paper, containing the data with higher basis sets, will be reported in due course.
Supplementary data Supplementary data (the computed data of the optimized geometries and their HOMO and LUMO energy levels of 65 chemical species) associated with this article can be found, in the online version, at.
References and notes 1. Ingold, C. K. Chem. Rev. 1934, 15, 225. 2. Swain, C. G.; Scott, C. B. J. Am. Chem. Soc. 1953, 75, 141. 3. Yang, W.; Parr,R. G. Proc. Natl. Acad. Sci. USA 1985, 82, 6723. 4. Ritchie, C. D. Acc. Chem. Rev. 1972, 5,348. 5. Geerlings, P.; De Proft, F.; Langenaeaker, W. Chem. Rev. 2003, 103, 1793.
6. Mayr, H.; Ofial, A. R. Pure Appl. Chem. 2005, 11, 1807. 7. Liu, S. Chemical Reactivity Theory: Density Functional View, (Ed.: Chattaraj, P. K.),Taylor and Francis, Boca Raton, 2009. 8. Morell, C.; Herrera, B.; Gutiérrez-Oliva, S.; Ceróa, M. -L.; Grand, A.; Tore-Labbé, A. J. Phys. Chem. A. 2012, 116, 7074. 9. Dichiarante, V.; Fagnoni, M.; Albini, A. J. Org. Chem. 2008, 73, 1282. 10. (a) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, 1989. (b) Pearson, R. G. Chemical Hardness, John Wiley-VCH, Weinheim, 1997. 11. Parr, R. G.; Szentpály, L. v.; Liu, S. J. Am. Chem. Soc. 1999, 121, 1922. 12. Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065. 13. (a) Koopmans, T. A. Physica 1933, 1, 104. (b) Pearson, R. G. Acc. Chem. Res. 1993, 26, 250: Pearson’s definition is = (ELUMO EHOMO)/2 as chemical hardness, but the factor of 2 was added arbitrarily to make and symmetrical. Recently, he used = ELUMO EHOMO (J. Chem. Sci., 2005, 117, 369). 14. Szabo, A; Osthund, N. S. Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Macmilian Publishing, New York, 1982. 15. (a) Fukui, K.; Yonezawa, T.; Shingu, H. J. Chem. Phys. 1952, 20, 722. (b) Fukui, K. Science, 1982, 217, 747. 16. Klopman, G. J. Am. Chem. Soc. 1968, 90, 223. 17. Salem, L. J. Am. Chem. Soc. 1968, 90, 543. 18. Janak, J. F. Phys. Rev. B 1978, 18, 7165. 19. Zhang, G.; Musgrave, C.B.; J. Phys. Chem. A 2007, 111, 1554. 20. Stein, T.; Eisenberg, H.; Kronik, L.; Baer, R. Phys. Rev. Lett. 2010, 105, 266802. 21. Rudberg, E. J. Phys.: Condens. Matter 2012, 24, 072202. 22. Schindele, C.; Houk, K. N.; Mayr, H. J. Am. Chem. Soc. 2002, 124, 11208.
Graphical Abstract
Parr’s index to describe both electrophilicity and nucleophilicity Syun-ichi Kiyooka*, Daisuke Kaneno, Ryoji Fujiyama
Parr’s values of 65 chemical species were plotted
6
as a function of the newly introduced values, = (/2)2 + The fine parabola indicates the order of
4
nucleophilicity at positive values and the order of electrophilicity at negative values.
2
0 -1
0
1