probing the mechanism of morita–baylis–hillman reaction in dichloromethane by density functional...
TRANSCRIPT
Probing the mechanism of Morita–Baylis–Hillman reaction
in dichloromethane by density functional theory
Jianhua Xu
Department of Chemistry, Fuling Normal College, Chongqing 408003, China
Received 19 January 2006; received in revised form 26 April 2006; accepted 29 April 2006
Available online 11 May 2006
Abstract
The mechanism of Morita–Baylis–Hillman reaction was investigated at B3LYP/6-311CG(d) level combined with Tomasi’s IEF-PCM solvent
model. The computational results indicate that the catalytic cycle of Morita–Baylis–Hillman involves the following steps: 1,4-addition of PMe3,
aldolic addition, hydrogen transfer, and elimination of product. The hydrogen transfer step is predicted to be the rate-limiting step for the whole
process. And the predicted rate expression is in agreement with the previous kinetic studies. The computational results make clear that the Morita–
Baylis–Hillman process is equilibrated and it is in good agreement with the previous experimental results. The entropy plays a crucial role in the
1,4-addition and aldolic steps. The CN group in the whole process mainly serves as an electronic charge acceptor to delocalize the electronic
charge on carbon through the p–p interaction between C and the CN group.
q 2006 Elsevier B.V. All rights reserved.
Keywords: PMe3-catalyzed; Morita–Baylis–Hillman reaction; Mechanism; SCRF; DFT
1. Introduction
The Baylis–Hillman reaction is an atom economical
coupling of an activated alkene and an aldehyde in the presence
of a nucleophilic catalyst (Scheme 1). The reaction was first
reported by Morita and coworkers [1] in 1968 and by Baylis
and Hillman in 1972. [2] The nucleophilic catalyst employed
by Morita was tricyclohexylphosphine, while Baylis and
Hillman used tertiary amines such as DABCO. Activated
alkenes include acrylic esters, acrylonitrile, vinyl ketones,
phenyl vinyl sulfone, phenyl vinyl sulfonate ester, vinyl
phosphonate and acrolein. b-Substituted alkenes required
more forcing conditions due to the slow addition of the
phosphine catalyst. A variety of coupling partners such as
aliphatic, aromatic and a,b-unsaturated aldehydes have been
successfully employed [3–8].
Unfortunately, the applications of the Morita–Baylis–
Hillman reaction had been limited in complex syntheses by
low rates and conversions as well as high substrate-dependent
yields. The rate-determining step is typically the bimolecular
coupling of the zwitterionic intermediate and the aldehyde.[3]
The Morita–Baylis–Hillman reaction remained relatively
0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.theochem.2006.04.044
E-mail address: [email protected]
undeveloped for many years, despite of its obvious synthetic
potential. In the 1980s research on the tertiary amine-
catalyzed variant escalated [4–6]. Although tertiary amines
are cheaper and less toxic than phosphines, the latter some-
times give higher yields in shorter reaction time. The
phosphine-catalyzed variant was explored only sporadically,
with an improvement in reaction efficiency reported by
Kawanisi using the cocatalysts tributylphosphine and triethyl-
aluminum in dichloromethane. [7]
Several mechanistic considerations and kinetic studies led
to the general acceptance of the Baylis–Hillman catalytic cycle
was summarized in Scheme 2. This mechanism was initially
proposed by Hill and Isaacs [9], and later refined by others [10–
12]. According to Scheme 2, the first reaction step I consists of
the 1,4-addition of the catalytic tertiary phosphine 1 to the
activated alkene 2, which generates the zwitterion intermediate
3. In step II, 3 adds to aldehyde 4 by an aldolic addition to yield
intermediate 5. Step III involves an intramolecular prototropic
shift within 5 to form intermediate 6, and in step IV forms the
final Baylis–Hillman adduct 7 through E2 or E1cb elimination
in the presence of a Lewis base. The last step IV regenerates
catalyst 1 to complete the catalytic cycle. The reaction rate
seems to be determined by step II because the dipole moment is
increased by further charge separation. Drewes et al. [13]
carried out the reaction of methyl acrylate with 2-hydroxyben-
zaldehyde in dichloromethane at 0 8C in the presence of
DABCO, isolated a type-6 intermediate (Scheme 2) as a
Journal of Molecular Structure: THEOCHEM 767 (2006) 61–66
www.elsevier.com/locate/theochem
C
X
R1
R1
R2
EWG
EWG
XHR2
Lewis base
catalysts
X = O,NTS,NCOR,NSO2PhR1 = HR2 = alkyl or arylEWG = COOR,CN,POEt2,CHO,COR,SO2Ph
Scheme 1.
J. Xu / Journal of Molecular Structure: THEOCHEM 767 (2006) 61–6662
coumarin salt, and characterized the salt by X-ray
crystallography.
Despite the considerable importance of the Baylis–Hillman
reaction for organic synthesis, there had been a remarkable lack
of theoretical studies published on the mechanism. Therefore,
density functional theory (DFT) calculations had been carried
out for PMe3-catalyzed Morita–Baylis–Hillman reaction at
B3LYP/6-311CG(d) level. These calculations aim to provide
specific help for the design and development of new selective
catalytic transformations proceeding through Baylis–Hillman
by amine and phosphine catalysts.
2. Models and computational detail
Our models are based on the PCy3-catalyzed Motira–
Baylis–Hillman reaction of acrylonitrile and ethanal in
CH2Cl2 [4]. The PCy3 is modeled by PMe3.
All computations were performed by the use of GAUSSIAN 03
package [14]. Geometries for all intermediates and transition
states were optimized by means of the density functional theory
(DFT) with Becke’s three-parameter functional (B3) [15] plus
Lee, Yang, and Parr (LYP) [16] correlation functional
combined with Tomasi’s IEF-PCM solvent [17–20] model
implemented in GAUSSIAN 03 with CH2Cl2 as solvent. The
6-311CG(d) [21–24] basis sets were utilized for all atoms.
The vibrational analysis and the natural bond orbital (NBO)
analysis [25,26] were performed at the same computational
level. The optimized transition states were characterized by a
sole imaginary frequency, whereas other optimized structures
had only real frequencies.
PMe3
1
CN2
Me3P+
-O CH3
CNMe3P
+
HO CH3
CNMe3P
+-
CN
H3C
OH
3
4
56
7 CH3CHO
Step I
Step II
Step III
Step IV
1
2
3
4
5
-CN
Scheme 2.
3. Results and discussions
As shown in Scheme 2, the complete catalytic cycle for the
title reaction was investigated. The total energy and free energy
profiles at 298.15 K and 1 atm are shown in Fig. 1. The
corresponding geometries and selected parameters are listed
in Figs. 2–5 and Table 1.
3.1. The process of the Morita–Baylis–Hillman reaction
As shown in Scheme 2, there exist four steps for the Morita–
Baylis–Hillman reaction. Because of the pro-chirality in
ethanal and intermediates 3, there are two chiral centers in
intermediate 5. Therefore, there have four enantiomers for 5,
RR, SR, SS and RS. The energies of SS and RS are equal to RR
and SR, respectively. For intermediate 6, there is only one
chiral center, and S configuration is connected to the RS and SS
isomers of the intermediate 5. Therefore, in the present paper,
only the pathways leading to S configuration were calculated
and the RS and SS were denoted R and S, respectively.
3.1.1. PMe3 addition to the activated alkenes
As displayed in Scheme 2, the first step of Morita–Baylis–
Hillman is trimethylphosphine 1 addition to the activated
alkene acrylonitrile 2 to form the zwitterionic phosphonium
intermediate 3. The transition state (TS1/3) of this step is
shown in Fig. 2.
Going from trimethylphosphine and acrylonitrile to inter-
mediate 3 via TS1/3, there involves formation of the P1–C2
bond and cleavage of p bond of the C2–C3. As shown in Fig. 1,
the C2–C3 bond varies from 1.336 A in 2 to 1.430 A in TS1/3
and finally 1.481 A in 3. These indicate that the C1–C2 bond
changes to single bond in intermediate 3 from the double bond
in acrylonitrile. The C1 becomes to sp3 hybridization while C2
remains sp2 hybridizated character. Interestingly, the three P–C
bonds in the PMe3 moiety of intermediate 3 and transition state
TS1/3 are shorter than that of the free PMe3 due to the positive
charges on phosphorus in 3 and TS1/3.
The C–N bonds of the acrylonitrile moiety in 3 and TS1/3
are longer than that of the free PMe3 because the p–pinteraction between 2p orbital of C3 and p bond of the CN
group. This p–p interaction also causes the electronic charge
on C3 to delocalizate to the CN group (the charges on the CN
group in 2, TS1/3 and 3 are K0.07, K0.16 and K0.33 a.u.,
respectively) and thus it stabilizes the zwitterionic phos-
phonium intermediate 3. At the same time, the variation of
the C3–CN bond in this process also demonstrates the p–pinteraction in 3 and TS1/3.
The formation of 3 causes the electronic charge transfer
from the PMe3 moiety to the acrylonitrile moiety. The
transferred charges are 0.58 and 0.96 a.u. for TS1/3 and 3
(Table 1), respectively. Therefore, the PMe3 can be considered
as a nucleophilic reagent. This also indicates that the formation
of zwitterionic phosphonium intermediate 3 results in a
markedly charge separation and the dipole moment of the
intermediate 3 is very large. The calculated dipole moments
of intermediate 3 (4.77 and 1.55 debye for 2 and 1 compared to
TS1/3+4
1+2+4
0.00(0.00)
3+4
TS3/5R
TS3/5S
5R
5S6
TS6/7
7+1
TS5/6S
TS5/6R
15.01(26.05)
14.05(25.33)
14.54(37.12)
15.91(38.77)
12.49(36.23)
14.01(37.86)
41.66(66.77)
38.50(63.20)
14.84(38.34)
17.85(40.87)
–1.21(10.18)
Er/GrKcal/mol
Fig. 1. The total energy and free energy profiles (298.15 K and 1 atm) of Marita–Baylis–Hillman reaction at B3LYP/6-311CG(d)/SCRF level. (The free energies are
in parentheses). Unit is in kilocalories/mol.
P
C
C
C
CC
C
N
1.8851.816
1.481
1.380
1.179P
CC
C
1
1.862
C C
C
N
1.336 1.429
1.157
2
3
NC
CC
P
C
C
C
1.846
2.1161.4301.394
1.172
TS1/3
Fig. 2. The optimized geometries and selected parameters of reactants,
intermediate and transition state involved in 1,4-addition step. Bond lengths
are in angstrom.
J. Xu / Journal of Molecular Structure: THEOCHEM 767 (2006) 61–66 63
12.10 and 14.56 debye for TS1/3 and 3) justify this point. The
natural charges on selected atoms (Table 1) indicate that the
nucleophilic site is C3.
The predicted energy barrier for the 1,4-addition step is
15.01 kcal/mol while the free energy of activation is
26.05 kcal/mol. Therefore the entropy plays a crucial role in
the process of the 1,4-addition to acrylonitrile of PMe3. The
formation of intermediate 3 is endothermic 14.05 kcal/mol.
The TS1/3 occurs late on the PES according to the parameters
shown in Fig. 2.
3.1.2. The aldolic addition reaction
Because of the pro-charilty of C3 in intermediate 3 and C4
in reactant ethanal 4, the addition of intermediate 3 to ethanal
will generate four pathways, RR, SR, RS and SS. The stationary
points on RR and SR potential energy surfaces (PES) are the
same as that of SS and RS PESs. So we only calculated the SS
and RS pathways and the related species were denoted as S and
R. The optimized structures and selected parameters are
depicted in Fig. 3.
The barrier heights for the two pathways are 0.49 and
1.86 kcal/mol, while the free energies of activation are 11.79
and 13.44 kcal /mol for S and R pathways. Therefore, this step is
easier than the first step. The two pathways are predicted to be
exothermic by 0.04 and 1.56 kcal/mol while the reaction free
energies are endothermic 10.90 and 12.53 kcal/mol, respect-
ively. So the entropy also plays an important role in this process.
The process of intermediate 3 addition to ethanal 4 involves
the formation of the C3–C4 bond and the cleavge of the p bond
of the C4–O5 double bond. It is also a nucleophilic addition.
Because of the large charge separation in intermediates 5R and
5S, the lengths of C3–C4 bonds are longer than that of normal
C–C bond. The P1–C2 bond becomes stronger from the
reactant intermediate 3 to TS3/5 and finally intermediate 5
(Figs. 1 and 2). This change results from the electronic charge
transfer from C2 and C3 to the O5. Interestingly, the P–C
methyl bonds in PMe3 moiety lengthen in the process of 3 to
TS3/5 and then shorten from TS3/5 to 5. In this process, the
hybridizations of C2 and C3 vary from sp2 to sp3.
The natural charges shown in Table 1 indicate that the
positive charge is gradually concentrated on P1 in this
process. The electronic charge on C3 transfer to O5 and this
point also predicts that this process is nucleophilic addition.
The electronic charges on the CH3CHO moiety are 0.34, 0.39,
0.75 and 0.75 a.u. for TS3/5R, TS3/5S, 5R and 5S, respect-
ively, and the positive charges of the PMe3 moiety are also
concentrated in the process of the nucleophilic addition. The
charges of the CN group increase because of the cleavage of
the p–p interaction between C3 and the CN group. The dipole
moments of 5R and 5S are 16.29 and 16.79 debye. The
variation of dipole moments in this process is smaller than
the above 1,4-addition step.
3.1.3. Hydrogen transfer
In the hydrogen transfer step, two transition states have been
located and they are both connected to the intermediate 6. The
optimized structures and selected parameters involved in this
step are depicted in Fig. 4.
The transition states TS5/6R and TS5/6S are connected with
5R and 5S, respectively. The energy barriers of the two
pathways are 29.17 and 24.49 kcal/mol while the activation
1.5081.212
O
CC
4
C CO C
CN
C
P
TS3/5R
1.522
1.257
2.1471.505
1.829
1.820
CC
O
CC
N
C
PC
1.526 1.261
2.114
1.4112.576
1.5101.827
1.820
TS3/5S
C
CO
CN
C C
P
C
5R
1.811
1.816
1.534
1.6671.449
1.160
1.3281.544
5S
P
C
CC
C
NO
C
C
1.814
1.814
1.538
1.451
1.159
1.6721.326
1.547
Fig. 3. The optimized geometries and selected parameters of reactants, intermediates and transition states involved in aldolic addition step. Bond lengths are in
angstrom.
J. Xu / Journal of Molecular Structure: THEOCHEM 767 (2006) 61–6664
free energies are 30.84 and 25.34 kcal/mol, respectively. From
the energy barrier point, the path S is more favorable than path
R. This process is endothermic slightly.
The hydrogen transfer process involves the cleavage of the
C2–H bond and formation of the O5–H bond. On going from
5R and 5S to 6 through TS5/6R and TS5/6S, the C3–C4 bond
shortens gradually. In 5R and 5S, the C3–C4 bonds are close to
the normal C–C bond length. Natural charges shown in Table 1
indicate that hydrogen transfer can be considered as a proton
transfer process (the hydrogen atoms being transferred are
positively charged 0.40 a.u. in both two transitions states).
Fig. 4. The optimized geometries and selected parameters of intermediate and tran
In this hydrogen transfer process, the hybridization of C3
changes from sp3 to sp2 and hence causes the increase of the
electronic charge of the CN group. The positive charge of the
PMe3 moiety also decrease slightly. An analysis the atomic
motions corresponding to the imaginary frequency of TS5/6R
and TS5/6S, indicates that the displacement of the H atom is
the main contribution to the transition vectors.
3.1.4. Product elimination
The last step of the Morita–Baylis–Hillman reaction is
elimination of product 7 from 6 and regenerates the catalyst
sition states involved in hydrogen transfer step. Bond lengths are in angstrom.
P
C
C
CC
N C
O
C
C
O
C
C
N
C
C
1.843
2.155
1.4291.398
1.172 1.5051.533
1.462
TS6/7 7
1.337
1.437
1.157
1.519
1.431
1.530
Fig. 5. The optimized geometries and selected parameters of product and
transition state involved in the elimination step. Bond lengths are in angstrom.
J. Xu / Journal of Molecular Structure: THEOCHEM 767 (2006) 61–66 65
PMe3. The optimized geometries of the transition state of the
elimination step and product are shown in Fig. 5.
The variation of the relative parameters in the elimination is
similar to the reverse process of the 1,4-addition. The C3–C4
and C4–O5 bonds shorten gradually. In TS6/7, the charge on
the PMe3 moiety is 0.69 a.u. The C4–CN bond weakens while
the CbN bond strengthens due to the disappearance of the p–pinteraction between C3 and the CN group.
The energy barrier and activation free energy of this process
are 3.01 and 2.54 kcal/mol, therefore the elimination process is
kinetically very favorable. From the thermodynamic point
(Fig. 1), the elimination process is also very favorable.
3.2. The overview of whole catalytic cycle
From the above discussions, the catalytic cycle of Morita–
Baylis–Hillman involves four steps: initially, PMe3 1,4-
addition to the activated alkene forms the zwitterionic phos-
phonium intermediate 3 via TS1/3; then, the zwitterionic
phosphonium intermediate 3 attacks the ethanal to give rise
to 5R and 5S through TS3/5R and TS3/5S, respectively; the
next step is an intramolecular hydrogen transfer to generate 6
via TS5/6R and TS5/6S and finally the product 7 is formed by
elimination from 6 and the catalyst PMe3 is regenerated.
Table 1
The natural charges (au) on selected atoms and groups at B3LYP/6-311CG(d) lev
Species P1 C2 C3 C
1 0.73 – – –
2 – K0.25 K0.33 –
3 1.44 K0.63 K0.68 –
4 – – – 0
5R 1.52 K0.72 K0.40 0
5S 1.51 K0.73 K0.40 0
6 1.49 K0.65 K0.50 0
7 – K0.17 K0.25 0
TS2/3 1.23 K0.48 K0.60 –
TS3/5R 1.50 K0.70 K0.55 0
TS3/5S 1.50 K0.70 K0.53 0
TS5/6R 1.51 K0.67 K0.53 0
TS5/6S 1.52 K0.66 K0.52 0
TS6/7 1.21 K0.45 K0.42 0
The total barrier heights for the R and S pathways are 41.66
and 38.50 kcal/mol and hence the S pathway is favorable
slightly in this process. The potential energy profile and free
energy profile shown in Fig. 1 indicate that the Morita–Baylis–
Hillman process is equilibrated and it is in good agreement
with the previous experimental works [5]. The computational
results also indicted that the hydrogen transfer is the rate-
limiting step energetically while the 1,4-addition or hydrogen
transfer may be the rate-determining step under various
conditions from free energy point. If the hydrogen transfer is
the rate-limiting step, the rate can be written as the following
formula:
PMe3 CCH2CHCN%k1
kK1
3 (1)
3CCH3CHO%k2
kK2
5 (2)
5%k3
kK3
6 (3)
6%k4
kK4
7CPMe3 (4)
Rate Zðk1k2k3Þ
ðkK1kK2Þ
� �½PMe3�½CH2CHCN�½CH3CHO� (5)
This rate expression is in agreement with the previous
kinetic studies [5] on the similar reaction.
4. Conclusion
From the above discussions, the following conclusions are
obtained:
(1) The catalytic cycle of Morita–Baylis–Hillman involves
four steps: initially, PMe3 1,4-addition to the activated
alkene forms the zwitterionic intermediate, then the
zwitterionic phosphonium adduct attacks the ethanal.
The next step is an intramolecular hydrogen transfer and
el in CH2Cl2 solvent
4 O5 CN PMe3
– – 0.0
– K0.07 K
– K0.33 0.96
.45 K0.56 – –
.20 K0.94 K0.11 1.10
.19 K0.94 K0.10 1.10
.11 K0.79 K0.29 1.03
.11 K0.75 K0.06 –
– K0.16 0.58
.34 K0.77 K0.21 1.06
.32 K0.78 K0.22 1.07
.14 K0.91 K0.17 1.09
.11 K0.91 K0.15 1.09
.12 K0.77 K0.22 0.69
J. Xu / Journal of Molecular Structure: THEOCHEM 767 (2006) 61–6666
finally the product eliminates from product complex and
the catalyst PMe3 is regenerated.
(2) The hydrogen transfer step is predicted to be the rate-
limiting step for the whole reaction. At the same time, the
predicted rate expression is in agreement with the previous
kinetic studies.
(3) The computational results make clear that the Morita–
Baylis–Hillman process is equilibrated and it is in good
agreement with the previous experimental works. The
entropy plays a crucial role in the 1,4-addition and
aldolic steps.
(4) The CN group in the whole process mainly serves as an
electronic charge acceptor to delocalize the electronic
charge on carbon through the p–p interaction between C
and CN group.
To the best of our knowledge, this work is the first
comprehensive computational study of the Baylis–Hillman
reaction. However, this work left unanswered the questions
related to the role of protonic solvent and product. These
questions are a subject of ongoing work and will be reported
elsewhere.
Acknowledgements
This work is supported by the project of science and
technology of Chongqing education council, People’s Republic
of China (No. KJ051302). I are grateful to the reviewers for
their pertinent comments and good suggestions concerning my
original manuscript.
References
[1] K. Morita, Z. Suzuki, H. Hirose, Bull. Chem. Soc. Jpn 41 (1968) 2815.
[2] A.B. Baylis, M.E.D. Hillman, German Patent 2155113, 1972 [Chem.
Abstr. 1972, 77, 34174q].
[3] M.L. Bode, P.T. Kaye, Tetrahedron Lett. 32 (1991) 5611.
[4] S.E. Drewes, G.H.P. Roos, Tetrahedron 44 (1988) 4653.
[5] D. Basavaiah, P. Dharma Rao, R. Suguna Hyma, Tetrahedron 52 (1996)
8001.
[6] E. Ciganek, in: L.A. Paquette (Ed.), Organic Reactions, vol. 51, Wiley,
New York, 1997, p. 201.
[7] D. Basavaiah, A. Jaganmohan Rao, T. Satyanarayana, Chem. Rev. 103
(2003) 811.
[8] T. Imagawa, K. Uemura, Z. Nagai, M. Kawanisi, Synth. Commun. 14
(1984) 1267.
[9] J.S. Hill, N.S. Isaacs, J. Phys. Org. Chem. 3 (1990) 285.
[10] H.M.R. Hoffman, J. Rabe, Angew. Chem. 95 (1983) 795;
H.M.R. Hoffman, J. Rabe, Angew. Chem. Int. Ed. Engl. 22 (1983) 796.
[11] P.T. Kaye, L. Bode, Tetrahedron Lett. 32 (1991) 5611.
[12] Y. Fort, M.-C. Berthe, P. CaubMre, Tetrahedron 48 (1992) 6371.
[13] E. Drewes, O.L. Njamela, N.D. Emslie, N. Ramesar, J.S. Field, Synth.
Commun. 23 (1993) 2807.
[14] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R.
Cheeseman, J.A. Montgomery, Jr., T. Vreven, K.N. Kudin, J.C. Burant,
J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, M. Cossi,
G. Scalmani, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara,
K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O.
Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross,
C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J.
Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma,
G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich,
A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K.
Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S.
Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P.
Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A.
Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill,
B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, GAUSSIAN 03,
Revision C.02, Gaussian, Inc., Pittsburgh, PA, 2003.
[15] A.D. Becke, Phys. Rev. A 38 (1988) 3098.
[16] C. Lee, W. Yang, G. Parr, Phys. Rev. B 37 (1988) 785.
[17] M.T. Cances, B. Mennucci, J. Tomasi, J. Chem. Phys. 107 (1997) 3032.
[18] M. Cossi, V. Barone, B. Mennucci, J. Tomasi, Chem. Phys. Lett. 286
(1998) 253.
[19] B. Mennucci, J. Tomasi, J. Chem. Phys. 106 (1997) 5151.
[20] M. Cossi, G. Scalmani, N. Rega, V. Barone, J. Chem. Phys. 117 (2002)
43.
[21] A.D. McLean, S. Chandler, J. Chem. Phys. 72 (1980) 5639.
[22] R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem. Phys. 72 (1980)
650.
[23] T. Clark, J. Chandrasekhar, G.W. Spitznagel, P.v.R. Schleyer, J. Comp.
Chem. 4 (1983) 294.
[24] M.J. Frisch, J.A. Pople, S. Binkley, J. Chem. Phys. 80 (1984) 3265.
[25] E.D. Glendening, A.E. Reed, J.E. Carpenter, F. Weinhold, NBO Version
3.1 (1993).
[26] A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899.