Mechanistic investigation of the one-pot formation of amides by oxidative coupling of alcohols with amines in methanol

Article abstract of DOI:10.1016/j.cattod.2012.04.026

The one-pot formation of amides by oxidative coupling of alcohols and amines via intermediate formation of methyl ester using supported gold and base as catalysts was studied using the Hammett methodology. Determining the relative reactivity of four different para-substituted benzyl alcohol derivatives showed that the first step of the reaction generates a partial positive charge in the benzylic position (i.e. by hydride abstraction), while the second step of the reaction builds up negative charge in the rate determining step. The aminolysis of the methyl ester intermediate was further investigated by means of DFT/B3LYP. The transition state structures and energies were determined for both a concerted and a neutral two-step reaction mechanism. As expected, the base-promoted two-step mechanism was found to be the most energetically favourable and this reaction mechanism was used to construct a theoretical Hammett plot that was in good agreement with the one obtained experimentally.

Full text of DOI:10.1016/j.cattod.2012.04.026

Catalysis Today 203 (2013) 211–216
Contents lists available at SciVerse ScienceDirect
Catalysis Today
journal homepage: www.elsevier.com/locate/cattod
Mechanistic investigation of the one-pot formation of amides by oxidative
coupling of alcohols with amines in methanol
Jerrik Mielbya,b, Anders Riisagera,b, Peter Fristrup , Søren Kegnæsa,b,∗∗
b,∗
a
Centre for Catalysis and Sustainable Chemistry
Department of Chemistry, Technical University of Denmark, Building 207, DK-2800 Kgs. Lyngby, Denmark
b
a r t i c l e i n f o
a b s t r a c t
Article history:
The one-pot formation of amides by oxidative coupling of alcohols and amines via intermediate formation
of methyl ester using supported gold and base as catalysts was studied using the Hammett methodology.
Determining the relative reactivity of four different para-substituted benzyl alcohol derivatives showed
that the first step of the reaction generates a partial positive charge in the benzylic position (i.e. by hydride
abstraction), while the second step of the reaction builds up negative charge in the rate determining step.
The aminolysis of the methyl ester intermediate was further investigated by means of DFT/B3LYP. The
transition state structures and energies were determined for both a concerted and a neutral two-step
reaction mechanism. As expected, the base-promoted two-step mechanism was found to be the most
energetically favourable and this reaction mechanism was used to construct a theoretical Hammett plot
that was in good agreement with the one obtained experimentally.
Received 20 November 2011
Received in revised form 17 April 2012
Accepted 23 April 2012
Available online 23 June 2012
Keywords:
Gold catalysis
Oxidative coupling
Amide formation
Mechanism
Hammett study
© 2012 Elsevier B.V. All rights reserved.
1
. Introduction
Formation of amides is a fundamental reaction in chemical
groups to further develop this reaction [7,8], the special handling
of expensive metal complexes and ligands remains a limitation
that may prevent general application. In contrast, the handling of a
heterogeneous catalyst is usually more straightforward [9].
Since the first fundamental studies by Bond et al. [10], Hutch-
ings [11], Haruta et al. [12], and Prati and Rossi [13], supported
gold nanoparticles have been recognised as surprisingly active and
selective heterogeneous catalysts for a number of aerobic oxida-
tions using molecular oxygen (or even air) as the terminal oxidant
[14,15]. From the standpoint of green and sustainable chemistry
these oxidations are attractive, because oxygen is a cheap and abun-
dant oxidant that produces water as the only by-product.
Recently, we reported that the combination of supported gold
nanoparticles and base forms an efficient and highly selective
catalytic system for the one-pot synthesis of amides by aero-
bic oxidative coupling of alcohols or aldehydes with amines in
methanol [16] (see Scheme 1).
synthesis and is used in the production of a broad range of
bulk commodities, high-value fine chemicals, agrochemicals, and
pharmaceuticals [1]. Amides are usually prepared by coupling of
carboxylic acids and amines using a coupling reagent or by acti-
vation of the carboxylic acid. Alternative procedures include the
Staudinger ligation [2], aminocarbonylation of aryl halides [3],
and oxidative amidation of aldehydes [4]. Unfortunately, all these
methods require the use of stoichiometric amounts of reagents,
making them generally expensive and wasteful reactions [5]. In the
search for a more sustainable chemical production, great efforts
have been put into replacing the stoichiometric reagents with
catalytic processes. This approach is not only cheaper and more
environmentally friendly but also facilitates the possibility of start-
ing from substrates other than carboxylic acids, thus paving the way
for previously unavailable synthetic routes to amides [5].
In the first step of this reaction, a methyl ester is obtained by
the gold-catalysed aerobic oxidation of the alcohol or aldehyde in
methanol [17,18]. It is notable that in this step the methanol serves
as both solvent and reactant. In the second step of the reaction,
addition of amine affords the amide by base-catalysed aminolysis
of the methyl ester. As the same base promotes both steps of the
reaction, the oxidative coupling can be performed in a convenient
In 2007 Milstein and co-workers [6] reported the first direct acy-
lation of amines by alcohols under liberation of molecular hydrogen
using a homogeneous ruthenium catalyst. Although this simple and
highly atom-efficient reaction have inspired several other research
◦
one-pot procedure under mild reaction conditions (25–65 C, atmo-
∗
Corresponding author. Tel.: +45 45 25 21 23; fax: +45 45 88 31 36.
Corresponding author at: Centre for Catalysis and Sustainable Chemistry.
spheric pressure). It is important to mention that this approach
is conceptually different from the gold-catalysed reactions previ-
ously reported by Wang et al. [19] and Soulé et al. [20], which are
∗
∗
Tel.: +45 45 25 24 02; fax: +45 45 88 31 36.
E-mail addresses: pf@kemi.dtu.dk (P. Fristrup), skk@kemi.dtu.dk (S. Kegnæs).
0
920-5861/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.cattod.2012.04.026

2
12
J. Mielby et al. / Catalysis Today 203 (2013) 211–216
Scheme 1. Synthesis of amides by aerobic oxidative coupling of alcohols or aldehy-
des with amines using supported gold and base as catalysts.
proposed to involve the formation and subsequent oxidation of a
hemiaminal intermediate to the desired amide.
To study the structure-reactivity relationship we employed the
well-known Hammett methodology [21] and focused our atten-
tion on a range of para-substituted benzyl alcohol derivatives (see
Scheme 2).
Fig. 1. Kinetic plot for the first step of the reaction showing the relative reactivity
of four different para-substituted derivatives relative to benzyl alcohol.
In line with previous work [22,23], the results were obtained
by performing competition experiments rather than establish-
ing absolute kinetics. There were several reasons to choose this
approach. First of all, a competition experiment is more robust
towards small variations in the reaction conditions and allows
the reaction to be followed to relatively high conversion with-
out deviation from linearity. Secondly, a competition experiment
can be designed to investigate a different step than the overall
rate-determining step. In this study, we were interested in the
elementary steps of the reaction that are directly involved in the
activation of the substrates. It was therefore desirable to disregard
any effects from steps involving, e.g. activation of dioxygen.
2.2. Results and discussion
In the first series of experiments, the conversion of all benzyl
alcohols followed first order kinetics, which allowed the construc-
tion of the kinetic plots shown in Fig. 1. From these plots the relative
reactivity could be determined as the slopes of the lines found
by linear regression [24]. The assumption that the oxidation of all
methyl esters followed first order kinetics could be justified from
2
the good correlation coefficients (R > 0.98).
With the relative reactivity of the four different para-substituted
methyl esters at hand, the Hammett plot could be constructed using
three distinct sets of ␴-values from literature [25,26] (Fig. 2).
Fig. 2 shows that the best linear correlation of log(kX/kH) was
obtained with the ꢀ -values (R = 0.922), which resulted in a rel-
atively large negative slope (ꢁ = −0.680). A negative slope in the
Hammett plot indicates that a positive charge is built up during
substrate activation, which suggests that the reaction proceeded
through the generation of a partial cation in the benzylic position,
i.e. by ˇ-hydride elimination.
Fristrup et al. [27] have previously reported a similar result
from the gold-catalysed oxidation of benzyl alcohol to benzalde-
hyde (ꢁ = −1.10). In that study the involvement of the ˇ-hydride
abstraction step was further confirmed by a significant kinetic iso-
tope effect (KIE), when benzyl alcohol with deuterium incorporated
in the ˛-position was employed as substrate. Furthermore, Fristrup
et al. [28] have investigated the conversion of benzaldehyde to
methyl benzoate and found here a positive ꢁ value (ꢁ = 2.51). These
results suggest that the gold-catalysed esterification of alcohols
with methanol occurs through the formation of an aldehyde inter-
mediate and that this is the rate-determining step. The formation
of an aldehyde intermediate also explains the formation of imines
when the oxidation is carried out in presence of both methanol and
amine [29].
2
. Experimental study
2.1. Reaction procedure and analysis
+
2
A series of competition experiments were performed to investi-
gate the structure-reactivity relationship of the two consecutive
steps of the oxidation-aminolysis reaction. In these experi-
ments, anisole (0.5 mmol), potassium methoxide (1.25 mmol), and
methanol (50 mmol) were charged to a reaction tube together with
benzyl alcohol (2.5 mmol) and either (4-methylphenyl)methanol,
(
(
4-methoxyphenyl)methanol, (4-chloro-phenyl)methanol, or (4-
trifluoro-methyl)phenyl)methanol (2.5 mmol). The reaction tubes
were connected to a reaction station providing stirring, heating
and dioxygen gas for the oxidative esterification (atmospheric pres-
sure). The system was flushed with O before 197 mg 1 wt% Au/TiO2
catalyst (Mintek) was added, corresponding to an Au/substrate
molar ratio of 1/500. During the following two days, samples of
2
0.1 ml were periodically collected, filtered, and analysed by GC-FID
and GC–MS using anisol as internal standard. When all reactions
had reached full conversion, hexane-1-amine (10 mmol) was added
and the temperature was increased to 65 C (reflux temperature of
methanol). During the following two days additional samples were
collected and analysed.
◦
Scheme 2. Overview of the competition experiments carried out to determine the
relative reactivity of the various para-substituted benzyl methyl esters.
Fig. 2. Hammett plot obtained using the relative reactivity determined during the
oxidation of the benzyl alcohols.

J. Mielby et al. / Catalysis Today 203 (2013) 211–216
213
Fig. 5. Energy diagram for the concerted and two-step reaction mechanism, respec-
tively.
Fig. 3. Kinetic plot for the second step of the reaction showing the relative reactivity
of four different para-substituted derivatives relative to methyl benzoate.
of theory. Transition states were found to have one negative eigen-
frequency, as required. Furthermore, the transition state structures
were investigated by relaxation following the Intrinsic Reaction
Coordinate (IRC), which lead to structures resembling pre-reactive
and post-reactive complexes, as expected. Single-point solvation
energies (methanol) were calculated for the structures optimised
in gas phase. In order to avoid direct comparison between neutral
and charged species we decided only to include neutral species in
the investigated mechanisms (vide infra). Although recent devel-
opments have improved implicit solvation model tremendously,
it is still doubtful whether a comparison between a neutral and a
charged species is sufficiently accurate [39].
When all the oxidation reactions had reached full conversion,
hexane-1-amine was added to the reactions and data for a sec-
ond Hammett study could be obtained. Also here linear kinetic
plots could be constructed from the conversion of substrate, which
allowed determination of the relative reactivity (see Fig. 3). The
corresponding Hammett plot is shown in Fig. 4.
Fig. 4 shows that the best linear correlation was obtained with
the neutral ꢀ-values (R = 0.980), which resulted in a relatively large
positive slope (ꢁ = 1.738). The positive slope shows that a negative
charge is building up during the reaction. A Hammett study was also
performed starting with pure methyl benzoate esters. As expected
these experiments showed that the water formed from the oxida-
tion of the benzyl alcohols to the methyl esters had no significant
effect on the relative reactivity (see Supporting information).
Comparison of Figs. 2 and 4 shows that the effect of the sub-
stituents are opposite in the two reactions. For instance, electron
withdrawing substituents decrease the reactivity in the oxidation
step but increase the reactivity in the consecutive aminolysis step
3.2. Results and discussion
Initially, two possible mechanistic pathways were examined for
the aminolysis of methyl benzoate with ammonia [40]. In the first
reaction mechanism all bond forming and -breaking interactions
were assumed to occur in a single step. The transition state of
–
and vice versa.
this “concerted” reaction mechanism involves simultaneous C
N
bond formation, C O cleavage and a proton transfer, as shown in
Scheme 3.
3
. Computational study
In the second mechanism under consideration the aminolysis
was assumed to occur in two steps (Scheme 4). In the first step,
a C N bond is formed as a proton is transferred from ammonia
to the oxygen atom of the C O double bond. In the second step of
the mechanism, the tetrahedral intermediate [41] is converted into
benzamide and methanol by cleavage of the C O bond, reformation
of the C O double bond, and a proton transfer between the two
oxygen atoms.
The optimised structures of transition states; TS, TS1 and TS2 are
shown in the supporting information together with the structure of
the tetrahedral intermediate. A comparison of the relative energies,
with and without a solvent model, is shown in Fig. 5.
Fig. 5 shows that the concerted reaction is predicted to be the
most energetically favourable mechanistic scenario. As expected,
the implementation of the solvent model results in lowering of the
relative energies.
3
.1. DFT calculations
In order to understand the observed structure-reactivity rela-
tionship, the second step of the synthesis was modelled by means of
Density Functional Theory (DFT) using the B3LYP functional [30,31]
in line with earlier work [32,33]. The 6-31G** basis set [34] was
applied and solvation energies calculated using the built-in PCM
model [35,36] with parameters suitable for methanol [37] as incor-
porated in Jaguar v. 7.8 release 109 from Schrodinger Inc. [38] All
structures were optimised in gas phase and characterised by com-
putations of the harmonic vibrational frequencies at the same level
Schaefer and co-workers [40] have previously investigated the
aminolysis of methyl benzoate by DFT and ab initio methods and
proposed a model, where considerable energy savings are realised
by including an additional ammonia molecule in the computa-
tions. In this model, the additional NH3 molecule serves as an
H-bridge that opens up the four-membered ring intermediate and
favours the H-transfer between the hydroxylic oxygen atom and
the methoxy group. The optimised transition state structures with
an additional ammonia molecule are shown in Figs. 6 and 7, respec-
tively.
Fig. 8 shows the effect of including an additional ammonia
molecule in the model. Compared to the energy diagram in Fig. 5,
Fig. 4. Hammett plot obtained from the relative reactivity of the para-substituted
methyl benzoates.

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J. Mielby et al. / Catalysis Today 203 (2013) 211–216
Scheme 3. Concerted reaction mechanism.
Scheme 4. Two-step reaction mechanism.
Fig. 6. The optimised transition state structure TS for the concerted mechanism.
Fig. 8. Energy diagram for the concerted mechanism with an additional ammonia
molecule.
Table 1
Relative energies for the para-substituted methyl benzoate derivatives along the
two-step mechanistic pathway.
Substituent
TS1 [kJ/mol]
Intermediate [kJ/mol]
TS2 [kJ/mol]
p-CF3
p-Cl
p-H
p-CH3
p-OCH3
79.4
82.9
88.5
91.8
95.0
31.3
34.4
37.8
40.8
44.4
87.0
100.0
104.5
107.3
111.0
the figure shows that besides stabilising the intermediate, the
ammonia molecule also lowers the relative energy of the transition
states. Interestingly, this effect is most profound for the two-
step mechanism, which now becomes the energetically favourable
mechanism. Furthermore, the figure shows that the second step of
the mechanism is predicted to be rate-determining.
Fig. 8 shows how the additional ammonia molecule promotes
both steps of the reaction and results in considerable lowering of
the relative energies along the reaction pathway. Methanol has
the same effect as ammonia, but although the first step is slightly
lower in energy (4 kJ/mol) the ammonia-promoted mechanism is
Fig. 9. Energy diagram showing the promoting effect of ammonia and methanol.
the most favourable when it comes to the second step (13 kJ/mol)
(see Fig. 9).
In order to compare the theoretical calculations with the exper-
imental results, the ammonia molecule was replaced with an
amine. To limit the number of possible conformations we chose
methylamine instead of hexane-1-amine (which was used for the
Fig. 7. The optimised structure of TS1 (left), the intermediate (middle) and TS2 (right) for the two-step mechanism.

J. Mielby et al. / Catalysis Today 203 (2013) 211–216
215
mechanism was found to be the most energetically favourable
route, and using this mechanism it was possible to construct a
theoretical Hammett plot that was in good agreement with the
experimental results. The overall good correspondence between
theory and experiment gives hope for the use of DFT calculations
as a predictive tool to improve the reaction protocol, for instance by
calculating the relative energy barriers when using ethanol instead
of methanol. Furthermore, it could be envisioned that possible
additives may be screened in silico to avoid time-consuming and
waste-producing experiments.
Appendix A. Supplementary data
Fig. 10. Theoretically calculated Hammett plot.
Supplementary data associated with this article can be
found, in the online version, at http://dx.doi.org/10.1016/
j.cattod.2012.04.026.
Hammett study). Table 1 compiles the relative energies computed
from the transition state structures of the five para-substituted
derivatives that were used in the experimental Hammett
study.
The energies in Table 1 were used to construct the Hammett
plot in Fig. 10 using the Arrhenius equation. The best linear corre-
References
[
[
1] E. Valeur, M. Bradley, Chemical Society Reviews 38 (2009) 606.
2] M. Köhn, R. Breinbauer, Angewandte Chemie International Edition 43 (2004)
3106.
2
lation of log(kX/kH) was obtained with the ꢀ-values (R = 0.945)
which resulted in a line with a relatively large positive slope
[3] J.R. Martinelli, T.P. Clark, D.A. Watson, R.H. Munday, S.L. Buchwald, Angewandte
Chemie International Edition 46 (2007) 8460.
[
4] W.-J. Yoo, C.-J. Li, Journal of the American Chemical Society 128
2006) 13064.
(
ꢁ = 2.855). On the other hand, poor correlations were obtained
(
−
2
+
with the corresponding ꢀ -values (R = 0.883, ꢁ = 2.476) and ꢀ -
[5] C.L. Allen, J.M.J. Williams, Chemical Society Reviews 40 (2011) 3405.
[6] C. Gunanathan, Y. Ben-David, D. Milstein, Science 317 (2007) 790.
2
values (R = 0.877, ꢁ = 1.762).
[
7] L.U. Nordstrøm, H. Vogt, R. Madsen, Journal of the American Chemical Society
30 (2008) 17672.
The limitations of the B3LYP functional are well known and
have been addressed earlier by adding either classical dispersion
terms [42] or by using improved exchange-correlation function-
als that incorporates kinetic energy–density terms [43]. However,
recalculation of the relative reaction rates in Fig. 10 using the
M06 functional only resulted in a slight change of the correspond-
ing reaction constant (from ꢁcal = 2.856 to 2.894). As expected,
these results show that the main contribution to the relative
energies comes from electrostatic forces rather than dispersion
forces. Compared with the experimental results described in the
previous section (ꢁexp = 1.724), the Hammett plot in Fig. 10 has
a larger slope (ꢁcal = 2.856). However, the resulting lines both
have positive slopes in the same order of magnitude, which
shows that the experiments and the model are in relatively good
agreement.
1
[8] Y. Zhang, C. Chen, S.C. Ghosh, Y. Li, S.H. Hong, Organometallics 29
(2010) 1374.
[
9] S.K. Klitgaard, K. Egeblad, U.V. Mentzel, A.G. Popov, T. Jensen, E. Taarning, I.S.
Nielsen, C.H. Christensen, Green Chemistry 10 (2008) 419.
[
10] G.C. Bond, P.A. Sermon, G. Webb, D.A. Buchanan, P.B. Wells, Journal of the
Chemical Society, Chemical Communications (1973) 444b.
[
11] G.J. Hutchings, Journal of Catalysis 96 (1985) 292.
[
12] M. Haruta, N. Yameda, T. Kobayashi, S. Iijima, Journal of Catalysis 115 (1989)
301.
[13] L. Prati, M. Rossi, Journal of Catalysis 176 (1998) 552.
[
[
[
[
[
14] A.S.K. Hashmi, G.J. Hutchings, Angewandte Chemie International Edition 45
(
2006) 7896.
15] K.T. Højholt, A.B. Laursen, S. Kegnæs, C.H. Christensen, Topics in Catalysis 54
(2011) 1026.
16] S. Kegnæs, J. Mielby, U.V. Mentzel, T. Jensen, P. Fristrup, A. Riisager, Chemical
Communications 48 (2012) 2427.
17] C. Marsden, E. Taarning, D. Hansen, L. Johansen, S.K. Klitgaard, K. Egeblad, C.H.
Christensen, Green Chemistry 10 (2008) 168.
18] A.B. Laursen, K.T. Højholt, S.B. Simonsen, L.F. Lundegaard, S. Helveg, F. Schüth,
M. Paul, J.-D. Grunwaldt, S. Kegnæs, C.H. Christensen, K. Egeblad, Angewandte
Chemie International Edition 49 (2010) 3504.
4
. Conclusion
[
19] Y. Wang, D. Zhu, L. Tang, S. Wang, Angewandte Chemie International Edition
5
0 (2001) 1.
The one-pot synthesis of amides was investigated in two consec-
[
20] J.-F. Soulé, H. Miyamura, S. Kobayashi, Journal of the American Chemical Society
133 (2011) 18550.
21] L.P. Hammett, Journal of the American Chemical Society 59 (1937) 96.
22] P. Fristrup, S. Le Quement, D. Tanner, P.-O. Norrby, Organometallics 23 (2004)
utive Hammett studies. The studies were performed by competition
experiments rather than by establishing absolute reaction kinet-
ics and the investigated substrates were para-substituted benzyl
alcohol derivatives.
The result from the first Hammett study suggested that the
gold-catalysed oxidation of benzyl alcohol occurs with build-up
of positive charge in the benzylic position, which corresponds
[
[
6160.
[23] L. Keinicke, P. Fristrup, P.-O. Norrby, R. Madsen, Journal of the American Chem-
ical Society 127 (2005) 15756.
24] P. Fristrup, D. Tanner, P.-O. Norrby, Chirality 15 (2003) 360.
25] C. Hansch, A. Leo, R. Taft, Chemical Reviews 91 (1991) 165.
[26] C. Hansch, H. Gao, Chemical Reviews 97 (1997) 2995.
27] P. Fristrup, L.B. Johansen, C.H. Christensen, Catalysis Letters 120 (2007) 184.
28] P. Fristrup, L.B. Johansen, C.H. Christensen, Chemical Communications (2008)
[
[
[
[
to
a ˇ-hydride abstraction step. The negative slope of the
Hammett plot (ꢁ = −0.680) was in good agreement with the
generally accepted perception that the gold catalysed esterifica-
tion of alcohols with methanol occurs through the formation of
an aldehyde intermediate and that this is the rate-determining
step.
The result from the second Hammett study showed that the
reaction rate was very sensitive to the substituents and that nega-
tive charge is formed during the reaction (ꢁ = 1.738). The aminolysis
of the methyl ester intermediate was further investigated by
means of Density Functional Theory. The transition state structures
and energies were determined for both a concerted and a neu-
tral two-step reaction mechanism. The base-promoted two-step
2750.
[29] S. Kegnæs, J. Mielby, U.V. Mentzel, C.H. Christensen, A. Riisager, Green Chem-
istry 12 (2010) 1437.
30] A.D. Becke, Journal of Chemical Physics 98 (1993) 5648.
31] C. Lee, W. Yang, R.G. Parr, Physical Review B 37 (1988) 785.
[32] P. Fristrup, M. Kreis, A. Palmelund, P.-O. Norrby, R. Madsen, Journal of the
American Chemical Society 130 (2008) 5206.
[
[
[
33] J.H. Dam, P. Fristrup, R. Madsen, Journal of Organic Chemistry 73
2008) 3228.
34] R. Ditchfield, W.J. Hehre, J.A. Pople, Journal of Chemical Physics 54 (1971) 724.
(
[
[35] B. Marten, K. Kim, C. Cortis, R.A. Friesner, R.B. Murphy, M.N. Ringnalda, D. Sitkoff,
B. Honig, Journal of Physical Chemistry 100 (1996) 11775.
36] D.J. Tannor, B. Marten, R. Murphy, R.A. Friesner, D. Sitkoff, A. Nicholls, M. Ring-
nalda, W.A. Goddard III, B. Honig, Journal of the American Chemical Society 116
(1994) 11875.
[

2
16
J. Mielby et al. / Catalysis Today 203 (2013) 211–216
[
[
[
37] Continuum dielectric constant: 33.62; Solvent probe molecule radius: 2.000 A˚ .
[41] M.L. Bender, Chemical Reviews 60 (1960) 53.
[42] S. Grimme, Journal of Computational Chemistry 25 (2004) 1463.
[43] Y. Zhao, D.G. Truhlar, Theoretical Chemistry Accounts 120 (2008) 215.
38] Jaguar, version 7.8, Schrodinger, LLC, New York, NY, 2010.
39] For a discussion, see P. Fristrup, M. Ahlquist, D. Tanner, P.-O. Norrby, Journal of
Physical Chemistry A 112 (2008) 12862.
[40] B. Galabov, Y. Atanasov, S. Ilieva, H.F. Schaefer, Journal of Physical Chemistry A
1
09 (2005) 11470.