Chemical Physics Letters 426 (2006) 415–421
www.elsevier.com/locate/cplett
Performance of various density functionals for the hydrogen bonds
in DNA base pairs
Tushar van der Wijst a,b, Célia Fonseca Guerra b, Marcel Swart
F. Matthias Bickelhaupt b,*
a
b
b,c,d
,
Fachbereich Chemie, Lehrstuhl für Anorganische Chemie III, Universität Dortmund, Otto-Hahn-Straße 6, D-44227 Dortmund, Germany
Theoretische Chemie, Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083, NL-1081 HV Amsterdam, The Netherlands
c
Institució Catalana de Recerca i Estudis Avançats (ICREA), E-08010 Barcelona, Catalonia, Spain
d
Institut de Quı́mica Computacional, Universitat de Girona, Campus Montilivi, E-17071 Girona, Catalonia, Spain
Received 8 June 2006; in final form 16 June 2006
Available online 23 June 2006
Abstract
We have investigated the performance of seven popular density functionals (B3LYP, BLYP, BP86, mPW, OPBE, PBE, PW91) for
describing the geometry and stability of the hydrogen bonds in DNA base pairs. For the gas-phase situation, the hydrogen-bond lengths
and strengths in the DNA pairs have been compared to the best ab initio results available in the literature (MP2). For a comparison with
the crystallographic experiments, the first crystal-environment shell was taken into account in our DNA model systems. BP86 and PW91
excellently recover both the ab initio and experimental values. B3LYP consistently underestimates hydrogen-bond strengths and overestimates hydrogen-bond distances.
2006 Elsevier B.V. All rights reserved.
1. Introduction
Hydrogen bonds are important in many fields of biological chemistry. They play, for instance, a key role in the
working of the genetic code. In DNA, the two helical
chains of nucleotides are held together by the hydrogen
bonds that occur in a selective fashion between a purine
and a pyrimidine nucleic base giving rise to the Watson–
Crick pairs adenine–thymine (AT) and guanine–cytosine
(GC), see Fig. 1.
These hydrogen bonds in DNA have been the subject of
many theoretical investigations. The incapacity of the
ab initio Hartree–Fock method to describe these hydrogen
bonds in DNA, on one hand, and the extreme computational cost of ab initio MP2 or coupled-cluster methods
*
Corresponding author. Fax: +31 20 598 7629.
E-mail address: [email protected] (F.M. Bickelhaupt).
0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2006.06.057
for systems of this size, on the other hand, make density
functional theory (DFT) an excellent alternative which
combines accuracy and computational efficiency. One of
the most widely used functionals, B3LYP, has also been
applied to the DNA base pairs. B3LYP is generally considered to be a reliable general-purpose alternative to MP2
that is to be preferred over other DFT approaches. However, it was recently shown that B3LYP does not in general
outperform all other functionals regarding the computation of chemical reaction barriers [1–6]. Often, it performs
even less accurately than popular GGA-based functionals
(e.g., OLYP and also BLYP), and in certain cases
B3LYP even fails to reproduce the barrier [1–6]. Another
peculiar phenomenon was observed by Bertran et al. [7]
in a study on DNA base pairs in the gas phase: the agreement for the hydrogen bonds in the DNA base pair AT
with crystallographic data [8,9] was excellent, however for
the other base pair GC it failed to reproduce the crystallographic data.
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T. van der Wijst et al. / Chemical Physics Letters 426 (2006) 415–421
by Sponer et al. [12] which (to our knowledge) are the most
accurate ab initio values available for these systems. Furthermore, for the gas-phase base pairs, we also examine
the performance of the DFT approaches to reproduce the
MP2 as well as coupled-cluster hydrogen bonding energies
[12,13]. In this way, an all-round picture about performance and suitability for describing DNA base pairs
emerges. Here, we anticipate that the crystal-environment
effects on the Watson–Crick structures is confirmed at
every level of theory and that B3LYP is not the method
of choice for studying DNA base pairs.
2. Theoretical methods
Fig. 1. Watson–Crick DNA base pairs AT and GC.
Previously, we have shown [10,11] that the gas-phase
structures of the Watson–Crick pairs AT and GC computed with the BP86 functional differ both markedly with
the experimental, crystallographic data. However, introducing into the model system the direct molecular environment that the base pairs experience in the crystals studied
experimentally, lead to a reconciliation of the computed
BP86 structures and the crystallographic structures. The
most striking feature in the geometrical rearrangements
from the gas phase to the crystal environment occurs for
guanine–cytosine. Here, the hydrogen-bond length pattern
of O6–N4, N1–N3 and N2–O2 (see Fig. 1) changes qualitatively from short–long–long in isolated GC to long–long–
short in our GC model system including the first shell of
the crystal environment, in exact agreement with the
X-ray structures measured for the crystal of sodium guanylyl-3 0 ,5 0 -cytidine nonahydrate (2). The molecular environment consists of crystal water, ribose OH groups of
neighbouring base pairs (modelled also by water in the
BP86 computations) and counter-ions [10,11].
In the present work, we wish to clarify if the crystalenvironment effects on the Watson–Crick structure that
we found with BP86 are reproduced with other popular
GGA and hybrid DFT approaches. This will shed light
on the question if these effects are a physically meaningful
phenomenon or rather an artefact of one particular
method, i.e., BP86. A second objective is the evaluation
of the performance of the different functionals for reproducing both gas phase and the above condensed-phase
Watson–Crick hydrogen-bond structures [8,9]. As an accurate ab initio benchmark for the gas-phase AT and GC
base pairs we employ the MP2 results recently obtained
Calculations have been performed with two different
programs: an adapted version (QUILD) [14] of the Amsterdam Density Functional Program (ADF) [15,16], which uses
a Slater-type orbital (STO) basis set and the GAUSSIAN03
program [17], which uses a Gaussian-type orbital (GTO)
basis set. Basis sets of comparable flexibility (triple-f) and
polarization were chosen: a TZ2P STO basis set and a
cc-pVTZ GTO basis set. Geometries were optimized at
the BLYP, BP86 (with the GAUSSIAN program specified as
BVP86), mPW, OPBE, PBE and PW91 level of the generalized gradient approximation (GGA), but also at the hybrid
level, B3LYP. For all GGAs the LDA part is treated by
local Slater exchange [18] and local correlation by
Vosko–Wilk–Nusair (VWN) [19] (except BLYP which
describes all correlation through LYP, vide infra), with
non-local (GGA) corrections included self-consistently as
follows: (i) BLYP: exchange corrections due to BECKE88
[20], correlation is computed by the Lee–Yang–Parr
(LYP) scheme [21], (ii) BP86: exchange corrections due to
BECKE88 [20], correlation corrections due to PERDEW86
[22], (iii) mPW: exchange corrections due to Adamo and
Barone [23], correlation corrections due to Perdew and
Wang (PW91c) [24], (iv) OPBE: exchange corrections from
Cohen and Handy (OPTX) [25], correlation corrections
from the Perdew–Burke–Ernzerhof scheme (PBEc) [26],
(v) PBE: exchange and correlation corrections both from
the Perdew–Burke–Ernzerhof scheme [26], (vi) PW91:
exchange and correlation corrections from Perdew and
Wang (PW91) [24,27], (vii) B3LYP: a hybrid functional
formed by mixing a portion of exact exchange, local Slater
exchange and non-local BECKE88 exchange corrections, and
for the correlation part a mix of local VWN and non-local
LYP correlation [21,28,29].
Geometry optimizations have been performed in CS
symmetry for the base pairs and the microsolvated crystal
model systems and in C1 symmetry for the individual bases
to account for the pyramidalisation of the amino group in
the latter [30,31]. For the crystal model systems, we have
taken into account the first shell of the crystal environment
which consists of crystal water, ribose OH groups of neighbouring base pairs (modelled also by water in the BP86
computations) and counter-ions [10,11]. The geometry
optimization of the crystal model systems was started from
T. van der Wijst et al. / Chemical Physics Letters 426 (2006) 415–421
417
tal values [8,9]. First, we address the technical issue of using
different types of basis sets in the ADF and Gaussian computations, namely, the TZ2P STO basis versus the cc-pVTZ
GTO basis. While for sufficiently large expansions both can
achieve a similar accuracy, the GTO basis set converges
more slowly. We have verified that the two basis sets perform indeed comparably well. As can be seen in Tables 1
and 2, the BLYP and BP86 results do not differ much for
the TZ2P STO and the cc-pVTZ GTO basis. Discrepancies
in hydrogen-bond distances are typically two hundredths
of an Å and hydrogen-bond energies differ by ca half a
kcal/mol. Note also that the BSSE in the various DFT
hydrogen-bond energies is more than one order of magnitude smaller than the latter (1 kcal/mol or less for the
the experimental crystal structure. Geometries were converged to 105 Hartree/Bohr. The basis-set superposition
error (BSSE), associated with the hydrogen-bond energy,
has been computed and corrected through the counterpoise
method [32], using the individual DNA bases as fragments.
3. Results and discussion
3.1. Gas-phase AT and GC
The hydrogen-bond distances and energies of the Watson–Crick base pairs AT and GC in the gas phase are given
in Tables 1 and 2, respectively, together with the MP2
benchmark results of Sponer et al. [12], and the experimen-
Table 1
Hydrogen-bond distances (in Å) and bond energies (in kcal/mol) for AT computed at various levels of theory
MADa
DEBSSEb
Method
N6–O4
N1–N3
Best ab initio
RI-MP2/aug-cc-pVQZ//RI-MP2/cc-pVTZc
‘CCSD(T)/aug-cc-pVQZ’//RI-MP2/cc-pVTZd
2.86
2.86
2.83
2.83
STO basis: TZ2P
BLYP
BP86
mPW
OPBE
PBE
PW91
2.92
2.85
2.87
3.00
2.87
2.85
2.88
2.81
2.83
2.93
2.80
2.79
0.055
0.015
0.005
0.120
0.020
0.025
11.6
13.0
12.7
6.9
14.6
15.2
0.6
0.7
0.7
0.9
0.7
0.7
11.0
12.3
12.0
6.0
13.9
14.5
GTO basis: cc-pVTZ
B3LYP
BLYP
BP86
2.93
2.94
2.87
2.88
2.90
2.83
0.060
0.075
0.005
13.0
12.5
13.7
1.4
1.7
1.5
11.6
10.8
12.2
BSSE
DE
15.1
15.1
a
Mean absolute deviation (MAD) in computed N6–O4 and N1–N3 distances between DFT and MP2.
Bond energy with inclusion of BSSE correction [32].
c
Data from Sponer et al. [12].
d
Data from Jurecka et al. [13]. The coupled-cluster energy has been obtained by adding a correction to the MP2 energies. This correction is calculated as
a difference between the coupled-cluster energy and the MP2 energy obtained with smaller basis sets as explained in Ref. [13].
b
Table 2
Hydrogen-bond distances (in Å) and bond energies (in kcal/mol) for GC computed at various levels of theory
MADa
DEBSSEb
Method
O6–N4
N1–N3
N2–O2
Best ab initio
RI-MP2/aug-cc-pVQZ//RI-MP2/cc-pVTZc
‘CCSD(T)/aug-cc-pVQZ’//RI-MP2/cc-pVTZd
2.75
2.75
2.90
2.90
2.89
2.89
STO basis: TZ2P
BLYP
BP86
mPW
OPBE
PBE
PW91
2.79
2.73
2.74
2.80
2.73
2.72
2.94
2.88
2.90
2.97
2.89
2.88
2.93
2.87
2.89
2.98
2.87
2.86
0.040
0.020
0.003
0.070
0.017
0.027
23.9
26.1
25.4
17.1
27.8
28.5
0.7
0.9
0.9
1.1
0.9
0.9
23.2
25.2
24.5
16.0
26.9
27.6
GTO basis: cc-pVTZ
B3LYP
BLYP
BP86
2.79
2.80
2.73
2.94
2.96
2.90
2.93
2.96
2.89
0.040
0.060
0.007
26.1
24.6
26.6
1.7
2.0
1.8
24.4
22.6
24.8
a
DE
BSSE
27.7
28.2
Mean absolute deviation (MAD) in computed O6–N4, N1–N3 and N2–O2 distances between DFT and MP2.
Bond energy with inclusion of BSSE correction [32].
c
Data from Sponer et al. [12].
d
Data from Jurecka et al. [13]. The coupled-cluster energy has been obtained by adding a correction to the MP2 energies. This correction is calculated as
a difference between the coupled-cluster energy and the MP2 energy obtained with smaller basis sets as explained in Ref. [13].
b
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T. van der Wijst et al. / Chemical Physics Letters 426 (2006) 415–421
TZ2P STO basis set and up to 2 kcal/mol for the cc-pVTZ
GTO basis set). This suggests that counterpoise correction
[32] is a reliable approach to correct for the BSSE. Thus,
taking the above basis-set derived differences into account,
we can compare the B3LYP results obtained with the ccpVTZ GTO basis set with those of the other functionals
that are evaluated using the TZ2P STO basis set.
Next, we examine the performance of the various methods for the Watson–Crick geometries (see Table 1). It
appears that the seemingly good performance of B3LYP
to reproduce the experimental hydrogen-bond distances is
indeed spurious, as concluded earlier on the basis of
BP86 calculations [10,11]. B3LYP yields N6–O4 and N1–
N3 hydrogen-bond distances of 2.93 and 2.88 Å which
are in close agreement with the experimental values of
2.93 and 2.85 Å (see Tables 1 and 3) [8]. For GC however,
all theoretical methods are in disagreement with experiment [9]. Thus, quantum chemistry (DFT and MP2) yields
even a qualitatively different bond-length pattern for the
GC hydrogen bonds O6–N4, N1–N3 and N2–O2 of
short–long–long whereas the experiment shows long–
long–short (see Tables 2 and 3).
The origin of the above discrepancy between theory and
experiment is not a deficiency in the density functional
approaches. This becomes clear by comparing the hydrogen-bond distances obtained with the various density functionals with the ab initio MP2/aug-cc-pVQZ results of
Sponer [12] (see Tables 1 and 2). The agreement of DFT
with MP2 is in general much better than with the experimental values. In the first place, MP2 also yields the
short–long–long pattern for the hydrogen bonds in GC.
Further comparisons reveal four density functionals that
agree excellently with MP2, namely, BP86, mPW, PBE
and PW91. The mean absolute deviation (MAD) in hydrogen-bond distances obtained with these DFT approaches
relative to the MP2 ones is smaller than 0.027 Å (see Tables
1 and 2).
As far as hydrogen-bond energies are concerned, it is the
PW91 functional that performs best with values of 14.5
and 27.6 kcal/mol for AT and GC which has to be compared with the corresponding MP2 values of 15.1 and
27.7 kcal/mol and coupled-cluster values of 15.1 and
28.2 kcal/mol, respectively (see Tables 1 and 2) [12,13].
Note that the MP2 and coupled-cluster values agree within
a few tenths of a kcal/mol. BLYP and B3LYP yield hydrogen bonds that are longer than the ones at the MP2 level
and both functionals underestimate the hydrogen-bond
energy by 3–5 kcal/mol. Our present findings agree well
with earlier studies [12,33] in which PW91 also emerged
as superior to B3LYP for describing hydrogen-bonded systems. The OPBE functional substantially overestimates the
hydrogen-bond distances (MAD larger than 0.1 Å for AT)
and underestimates the hydrogen-bond energies by a factor
2–3 (see Tables 1 and 2).
The available experimental (mass spectrometry) complexation enthalpies of 13.0 and 21.0 kcal/mol for
methylated AT and GC [34] have not been used here as a
benchmark for the various DFT approaches because a
direct comparison is not straightforward. The experimental
values were obtained by measuring the temperature dependence of the equilibrium constant at 323 and 381 K. It has
been shown by Kabelac and Hobza [35] on the basis of
molecular dynamics simulations that at such temperatures
Watson–Crick hydrogen-bonded structures are negligibly
Table 3
Hydrogen-bond lengths (in Å) for model systems of AT (1a, 1b) and GC (2a, 2b) in the crystal environment computed with various DFT methods
System
H-bond
Exp.a,b
GTO: cc-pVTZ
B3LYP
BP86
BLYP
BP86
PW91
1a
N4–O6
N1–N3
MADc,d
2.93/2.95
2.85/2.82
3.00
2.88
0.050/0.055
2.93
2.82
0.015/0.010
2.98
2.87
0.035/0.040
2.92
2.80
0.030/0.025
2.91
2.79
0.040/0.035
1b
N4–O6
N1–N3
MADc,d
3.01
2.88
0.055/0.060
2.96
2.81
0.035/0.010
2.98
2.87
0.035/0.040
2.93
2.79
0.030/0.025
2.91
2.79
0.040/0.035
2a
O6–N4
N1–N3
N2–O2
MADc
3.00
3.00
2.88
0.053
2.93
2.95
2.85
0.010
2.97
2.99
2.88
0.040
2.91
2.94
2.83
0.013
2.89
2.93
2.83
0.023
2b
O6–N4
N1–N3
N2–O2
MADc
2.93
3.01
2.93
0.050
2.87
2.97
2.89
0.030
2.93
3.01
2.91
0.043
2.86e
2.95e
2.86e
0.017
2.85
2.94
2.86
0.023
2.91
2.95
2.86
STO: TZ2P
a
X-ray crystallographic measurements of Seeman et al. [8] on sodium adenylyl-3 0 ,5 0 -uridine hexahydrate containing the Watson–Crick-type dimer
(ApU)2. There are two different values for the hydrogen-bond length because the two AU pairs in (ApU)2 have different environments. The first value of
N4–O6 and N1–N3 refers to the first pair and the second value of N4–O6 and N1–N3 refers to the second pair.
b
X-ray crystallographic measurements of Rosenberg et al. [9] on guanylyl-3 0 ,5 0 -cytidine nonahydrate containing the Watson–Crick type dimer (GpC)2.
c
Mean absolute deviation (MAD) between the calculated and the experimental hydrogen-bond distances for each system.
d
First and second MAD values refer to deviation with respect to the first and second AU pair in (ApU)2.
e
Geometry converged to 2.6 · 105 Hartree/Bohr.
T. van der Wijst et al. / Chemical Physics Letters 426 (2006) 415–421
populated by the methylated base pairs. Instead, p-stacked
complexes are the dominantly occurring species under the
experimental conditions which are not the subject of the
present study.
We conclude that BP86 and especially PW91 agree very
satisfactorily with Sponer’s MP2 benchmark on Watson–
Crick pairs, both in terms of hydrogen-bond distances
and energies. These functionals are therefore recommended
as efficient alternatives to ab initio theory for describing
hydrogen bonding in larger biologically relevant systems.
3.2. Condensed-phase AT and GC
An issue that remains is the discrepancy between theory
and experimental X-ray structures of Watson–Crick pairs.
The above agreement between DFT and MP2 for the isolated Watson–Crick pairs is strong evidence that the discrepancy with the crystallographic structures is not
419
caused by a deficiency in the density functional approaches.
In line with this, we have previously shown that reconciliation of DFT at the BP86 level and X-ray experiments
regarding Watson–Crick structures is achieved if one incorporates the effects of the molecular environment on the
Watson–Crick pairs in the crystals of sodium adenylyl3 0 ,5 0 -uridine hexahydrate (1) [8] and sodium guanylyl3 0 ,5 0 -cytidine nonahydrate (2) [9] into the theoretical model
systems [10,11].
Here, we address the question if the crystal-environment
effects on the Watson–Crick structure that we found with
BP86 are reproduced with other popular GGA and hybrid
DFT approaches. Thus, for each Watson–Crick we have
selected the two model systems from our previous work
[10,11] that most closely approach the full molecular environment in the crystallographic experiments: these model
systems are 1a and 1b for AT and 2a and 2b for GC (see
Fig. 2). They contain the sodium cation that is proximal
Fig. 2. Model systems of AT and GC with water molecules and counter ions (Na+) that simulate the crystal environment: 1a = AT with two water
molecules, 1b = AT with two water molecules and sodium cation, 2a = GC with four water molecules and a sodium cation and 2b = GC with five water
molecules and a sodium cation.
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T. van der Wijst et al. / Chemical Physics Letters 426 (2006) 415–421
to the hydrogen bonds plus up to five water molecules (for
GC) that model either crystal water or hydroxy groups of
neighboring ribose units [8,9]. Note that the sugar–phosphate back bone has been left out from our model systems.
We have previously shown [10,11] that the effect on hydrogen-bond distances of introducing methyl, sugar or phosphate–sugar groups at the purine N9 and pyrimidine N1
positions is negligible (of the order 0.01 Å) compared to
the effect of the environment that we study (of the order
0.1 Å). The geometries of 1a, 1b, 2a and 2b have been optimized with B3LYP and BP86 using the cc-pVTZ GTO
basis set in Gaussian and with BLYP, BP86 and PW91
using the TZ2P basis set in QUILD/ADF. The results are
summarized and compared with the crystallographic data
in Table 3.
First, we address again the technical issue of using different types of basis sets in the ADF and Gaussian computations by comparing the BP86 results that have been
obtained with either basis set. Again, the results do not differ much for the TZ2P STO and the cc-pVTZ GTO basis,
as can be seen in Table 3. Discrepancies in hydrogen-bond
distances are typically two hundredths of an Å, similar to
the situation for the isolated gas-phase systems discussed
in the previous section. Thus, taking these basis-set derived
differences into account, we can compare the B3LYP
geometries obtained with the cc-pVTZ GTO basis set with
the BLYP, BP86 and PW91 geometries that are computed
with the TZ2P STO basis set.
The main result of these computations is that at all levels
of theory, the same effect is observed when going from the
isolated Watson–Crick pairs (Tables 1 and 2) to those
embedded in a model of the crystal environment (Table
3): for AT, the N6–O4 bond elongates about 0.1 Å and
the N1–N3 bond remains essentially unchanged, and for
GC, the O6–N4 and N1–N3 bonds elongate approximately
0.1 Å and the N2–O2 bond remains again approximately
equal. The consistent reproduction of the environment
effect on the Watson–Crick geometries with all theoretical
methods is strong evidence that these effects represent
physically meaningful phenomena and not an artefact of
one particular method (e.g., BP86 used previously [10,11]).
The environment effects in our crystal model systems
lead for BP86 (both with GTO and STO basis) to excellent
agreement with the crystallographic results: the MAD in
bond distances in 1b and 2a relative to those in the experiments is below 0.035 Å (see Table 3). This has to be compared with the MAD in bond distances in isolated AT and
GC, also computed at BP86, relative to those in the experiments of up to 0.086 Å (not shown in the tables). The next
best functional is PW91 with MAD in bond distances in 1b
and 2a relative to those in the experiments is below 0.040 Å
(see Table 3). The BLYP and especially the B3LYP functionals yield again too long hydrogen bonds (see Table
3), just as for the isolated gas-phase systems (see Tables 1
and 2). Thus, the MAD between computed and the crystallographic hydrogen-bond distances increases to 0.043 Å for
BLYP and up to 0.060 Å for B3LYP.
We conclude that BP86 and also PW91 agree very satisfactorily with the crystallographically obtained hydrogenbond distances. The good agreement that B3LYP achieves
between the geometry of the gas-phase AT pair and the
crystallographic structure of this base pair (i.e., sodium
adenylyl-3 0 ,5 0 -uridine hexahydrate (1) [8]) is the result of
the cancellation between a physical effect (the N6–O4 bond
in the crystal 1 is longer than in the isolated gas-phase AT)
and an error in B3LYP (which overestimates the N6–O4
distance and underestimates the hydrogen-bond strength
in AT, and in general).
4. Conclusion
We have investigated the performance of seven popular
density functionals (B3LYP, BLYP, BP86, mPW, OPBE,
PBE, PW91) for describing the geometry and stability of
the hydrogen bonds in DNA base pairs. For the gas-phase
situation, the hydrogen-bond lengths and strengths in the
DNA pairs have been compared to the best ab initio results
available in the literature (MP2). For a comparison with the
crystallographic experiments, the first crystal-environment
shell was taken into account in our model systems by introducing water molecules and counter ions. The structural
deformation that the environment induces in the Watson–
Crick base pairs is confirmed at any level of theory. The
standard BP86 and PW91 functionals furthermore appear
to excellently recover both the ab initio and experimental
values. B3LYP consistently underestimates hydrogen-bond
strengths for both AT and GC and it furnishes significantly
too long hydrogen-bond distances for the gas phase as well
as for the condensed-phase model systems.
Acknowledgements
We thank Professor B. Lippert for helpful discussions.
We thank the International Max Planck Research School
in Chemical Biology (IMPRS-CB) in Dortmund for a doctoral fellowship for T.v.d.W., the National Research
School Combination – Catalysis (NRSC-C) for a postdoctoral fellowship for C.F.G., and the Deutsche Forschungsgemeinschaft (DFG) and the Netherlands organization for
Scientific Research (NWO-CW and NWO-NCF) for financial support.
Appendix A. Supplementary data
Cartesian coordinates of all species occurring in this
study are available from the internet. Supplementary data
associated with this article can be found, in the online version, at doi:10.1016/j.cplett.2006.06.057.
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