Chemistry Reference
In-Depth Information
Acknowledgments
We are grateful for financial support from the Spanish MICINN (projects
CTQ2011-23156/BQU and CTQ2011-25086/BQU), the Catalan DIUE (projects 2009SGR637,
2009SGR528, and XRQTC), the FEDER fund for the grant UNGI08-4E-003. M.G.-B. thanks the
Spanish MECD for a PhD fellowship (AP2010-2517) and S.O. thanks the European Community
for a postdoctoral fellowship (PIOF-GA-2009-252856). Excellent service by the CESCA is ac-
knowledged. The authors are also grateful to the computer resources and assistance provided by
the BSC-CNS. M. Solà thanks the Catalan DIUE for the ICREA Academia 2009 Award.
Appendix: Computational Details
All Density Functional Theory (DFT) calculations were performed with the Ams-
terdam Density Functional (ADF) program (Baerends et al.
2010
). The molecular
orbitals (MOs) were expanded in an uncontracted set of Slater type orbitals (STOs)
of double-
(TZP) quality containing diffuse functions and one set
of polarization functions. In order to reduce the computational time needed to carry
out the calculations, the frozen core approximation has been used (te Velde et al.
2001
). In this approximation, the core density is obtained and included explicitly,
albeit with core orbitals that are kept frozen during the SCF procedure. It was shown
that the frozen core approximation has a negligible effect on the optimized equilib-
rium geometries (Swart and Snijders
2003
). Scalar relativistic corrections have been
included self-consistently using the Zeroth Order Regular Approximation (ZORA)
(van Lenthe et al.
1993
). An auxiliary set of
s
,
p
,
d
,
f
, and
g
STOs was used to fit the
molecular density and to represent the Coulomb and exchange potentials accurately
for each SCF cycle (Baerends et al.
1973
). Energies and gradients were calculated
using the local density approximation (Slater exchange) with non-local corrections
for exchange (Becke88) (Becke
1988
) and correlation (Lee-Yang-Parr) (Lee et al.
1988
) included self-consistently (i.e. the BLYP functional). In some cases, energies
and gradients were calculated using the local density approximation (Slater exchange
and VWN correlation) (Vosko et al.
1980
) with non-local corrections for exchange
(Becke
1988
) and correlation (Perdew
1986
) included self-consistently (i.e. the BP86
functional). Also in some studies, we performed single point energy calculations at
the B3LYP-D
2
/TZP level of theory (Becke
1993
; Lee et al.
1988
; Stephens et al.
1994
) (i.e., B3LYP-D
2
/TZP//BLYP-D
2
/DZP). Open-shell systems were treated with
the unrestricted formalism.
Moreover, energy dispersion corrections were introduced using Grimme's
methodology (Grimme
2006
; Grimme et al.
2010
)(D
2
/D
3
) implemented in ADF
2010.01 version (Baerends et al.
2010
). All the structures were fully optimized using
these corrections in each optimization step. It was shown that dispersion corrections
are essential for a correct description of the thermodynamics and kinetics of fullerene
and nanotube reactions (Osuna et al.
2010
; Garcia-Borràs et al.
2012a
).
The actual geometry optimizations and transition state (TS) searches were
performed with the QUILD (Swart and Bickelhaupt
2008
) (QUantum-regions In-
terconnected by Local Descriptions) program, which functions as a wrapper around
the ADF program. The QUILD program constructs all input files for ADF, runs ADF,
ζ
(DZP) and triple-
ζ
