RSC Advances
Paper
3110, 3015, 1660, 1545 cmꢀ1. HRMS (ESI+): m/z calcd for
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[C19H17N2O + H]+: 289.1341; found 289.1340.
5. Computational methods
The structures of all systems involved in these 13DC reactions
were optimized using the B3LYP24 functional together with the
6-31G(d) basis set.25 The nature of the stationary points were
conrmed by frequency calculations in order to distinguished
between the minimums and transition states, which have zero
and one imaginary frequency, respectively. The electronic
structures of the TSs were analyzed by the natural bond orbital
(NBO) method.26 Values of enthalpies, entropies, and Gibbs free
energies in chloroform were calculated with standard statistical
thermodynamics at 383 K and 1 atmosphere over the optimized
gas-phase structures27 All computations were carried out with
the Gaussian 09 suite of programs.28
The global electrophilicity index,29 u, is given by the
following expression, u ¼ (m2/2h), in terms of the electronic
chemical potential m and the chemical hardness h. Both quan-
tities may be approached in terms of the one-electron energies
of the Frontier molecular orbitals HOMO and LUMO, 3H and 3L,
as m z (3H + 3L)/2 and h ¼ (3L ꢀ 3H), respectively.30 The empirical
(relative) nucleophilicity index,31 N, based on the HOMO ener-
gies obtained within the Kohn–Sham scheme,32 is dened as N
¼ 3HOMO(Nu) ꢀ 3HOMO(TCE), where tetracyanoethylene (TCE) is the
reference because it presents the lowest HOMO energy in a long
series of molecules already investigated in the context of polar
organic reactions. The electrophilic P+k and nucleophilic Pkꢀ Parr
functions22 were obtained through the analysis of the Mulliken
atomic spin densities (ASD) of the corresponding radical anion
and radical cation by single-point energy calculations over the
optimized neutral geometries.
7 T. Q. Tran, V. V. Diev and A. P. Molchanov, Tetrahedron, 2011,
67, 2391.
´
´
8 A. K. Nacereddine, C. Sobhi, A. Djerourou, M. Rıos-Gutierrez
and L. R. Domingo, RSC Adv., 2015, 5, 99299.
9 E. Falkowska, M. Y. Laurent, V. Tognetti, L. Joubert,
P. Jubault, J. Bouillon and X. Pannecoucke, Tetrahedron,
2015, 71, 8067–8076.
10 K. N. Houk, Acc. Chem. Res., 1975, 8, 361.
11 (a) R. G. Parr and W. Yang, J. Am. Chem. Soc., 1984, 106, 4049;
´
(b) L. R. Domingo, M. J. Aurell, P. Perez and R. Contreras, J.
Phys. Chem. A, 2002, 106, 6871–6875.
12 H. Eyring, J. Chem. Phys., 1935, 3, 107.
13 P. Geerlings, F. De Pro and W. Langenaeker, Chem. Rev.,
2003, 103, 1793; D. H. Ess, G. O. Jones and K. N. Houk,
Adv. Synth. Catal., 2006, 348, 2337.
14 R. C. F. Jones and J. N. Martin, in Synthetic Applications of 1,3-
Dipolar Cycloaddition Chemistry Toward Heterocycles and
Natural Products, A. Padwa and W. H. Pearson, John Wiley
& Sons, New York, NY, 2002, pp. 1–81.
15 (a) M. P. S. Ishar, G. Singh, K. Kumar and R. Singh,
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and H. Huber, Chem. Ber., 1967, 100, 1802.
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Phys., 1985, 83, 735; (b) A. E. Reed, L. A. Curtiss and
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´
Acknowledgements
17 L. R. Domingo, M. J. Aurell and P. Perez, Tetrahedron, 2014,
70, 4519.
This work was supported by the Ministry of Higher Education
and Scientic Research of the Algerian Government [project
CNEPRU Code: E01620140051].
18 (a) P. Geerlings, F. De Pro and W. Langenaeker, Chem. Rev.,
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2003, 103, 1793; (b) M. Rıos-Gutierrez, F. Chafaa,
A. K. Nacereddine, A. Djerourou and L. R. Domingo, J. Mol.
Graphics Modell., 2016, 70, 296–304.
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19 L. R. Domingo and J. A. Saez, Org. Biomol. Chem., 2009, 7,
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