1290
A. Baeza et al. / Tetrahedron: Asymmetry 22 (2011) 1282–1291
in the Spartan package.29 Electron correlation was incorporated, in
part, to our studies by means of density functional theory (DFT),30
by using the non-local hybrid three-parameter functional devel-
oped by Becke and denoted B3LYP exchange-correlation func-
tional.31,32 It should be noted that optimizations have been
carried out with keywords for tight convergence criteria as well
as for using the ultrafine integration grid of the program. Vibra-
tional analysis was applied to all B3LYP/6-31G⁄ stationary points
by diagonalization of their Hessian matrices (vibrational analy-
sis).33 Ground state equilibrium geometries on the potential energy
surface were recognized as having real frequencies only, whereas
transition structures were recognized as having only one negative
eigenvalue (visualized with the help of an appropriate application).
Unless otherwise noted only electronic energies are given in the
text. In all cases, the zero-point vibrational energies (ZPVE) were
computed at the same level, though were not scaled. Cartesian
coordinates of the stationary points found in this study are avail-
able upon request.
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Acknowledgments
This work is supported by MICINN (Spain) through projects
CTQ2007-62952/BQU, CTQ2007-62771/BQU, CTQ 2010-17339,
CTQ2010-20387, and Consolider INGENIO 2010 CSD2007-00006.
We also thank the computing facilities generously provided by
the UIB, CESCA, CESGA and CIEMAT.
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