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Stationary points found on the PES were optimized without
any geometrical constraint by the Berny analytical gradient
optimization algorithm.21 Harmonic frequencies were
computed at the full-optimized geometries, allowing the
assignment of stationary points as minima or transition
states and the determination of zero-point vibrational
energies and thermal vibrational contributions (TZ183
and 195 K). To verify that each saddle point connects two
putative minima, intrinsic reaction coordinate (IRC)
calculations were performed in forward and backward
directions, that is, by following the eigenvector associated to
´ ´
4. Domingo, L. R.; Arno, M.; Contreras, R.; Perez, P. J. Phys.
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the unique negative eigenvalue of the Hessian matrix, using
´
22
the Gonzalez and Schlegel integration method. The
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electronic structures of stationary points were analyzed by
the natural bond orbital method,23 and global electronically
indexes,17 defined in the context of the DFT, were also
computed for the reactants. In addition, solvent effects have
been considered by performing, on top of the optimized
geometries, single-point energy calculations using the self-
consistent reaction field method based on the polarizable
continuum model of Tomasi and co-workers.24 The
dielectric constants used in the latter calculations, 3Z7.58,
8.93 and 38.3, correspond to the solvents employed in the
experiments, namely tetrahydrofuran, dichloromethane and
dimethylformamide, respectively. Finally, thermodynamic
properties were evaluated at the experimental temperatures
TZ183 and 195 K. All calculations were carried out with
Gaussian 98 package of programs.25
8. Houk, K. N.; Loncharich, R. J.; Blake, J. F.; Jorgensen, W. L.
J. Am. Chem. Soc. 1989, 111, 9172.
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Chem. 1997, 62, 1775.
13. Sustmann, R.; Tappanchai, S.; Bandmann, H. J. Am. Chem.
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14. Alves, C. N.; da Silva, A. B. F.; Marti, S.; Moliner, V.; Oliva,
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M.; Andres, J.; Domingo, L. R. Tetrahedron 2002, 58, 2695.
15. Garcia, J. I.; Martinez-Merino, V.; Mayoral, J. A.; Salvatella,
L. J. Am. Chem. Soc. 1998, 120, 2415.
16. Bernstein, Z.; Ben-Ishai, D. Tetrahedron 1977, 33, 881.
17. (a) Domingo, L. R.; Aurell, M. J.; Perez, P.; Contreras, R.
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Acknowledgements
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Andres, J. J. Org. Chem. 1999, 64, 5867. (c) Domingo, L. R.;
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Andres, J.; Alves, C. N. Eur. J. Org. Chem. 2002, 15, 2557. (d)
The authors would like to thank the Xunta de Galicia and
also the Ministry of Education of Portugal for financial
support of this work under project XUGA
PGIDT02BTF20305PR and Program PRODEP III/action
3.2, respectively.
Domingo, L. R. J. Org. Chem 2001, 66, 3211.
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