Synthesis of new tetraethyl(N-alkyl-1-aminoethan-1,1-diyl)bisphosphona-tes and ESR analysis of chemical exchange of derived nitroxides of acyclic aminobisphosphonates

Article abstract of DOI:10.1080/10426500701441499

The synthesis and the full characterization of two new linear bisphosphonates (tetraethyl(N-tert-butyl-1-aminoethan-1,1-diyl)bisphosphonate and tetraethyl(N-sec-butyl-1-aminoethan-1,1-diyl)bisphosphonate), and the first analysis of the ESR spectra of the corresponding nitroxides is reported. The preliminary results of theoretical calculations on model compounds suggest a small B0 (in the McConnell equation). The results of bisphosphonate ester and bisphosphonic acid are similar. The discrepancies of P coupling for the diphosphorus compound stems from B2 that is different when the dihedral angle is larger than 90.

Full text of DOI:10.1080/10426500701441499

This article was downloaded by: [Dalhousie University]
On: 15 September 2013, At: 00:38
Publisher: Taylor & Francis
Informa Ltd Registered in England and Wales Registered Number: 1072954
Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,
UK
Phosphorus, Sulfur, and Silicon
and the Related Elements
Publication details, including instructions for
authors and subscription information:
http://www.tandfonline.com/loi/gpss20
Synthesis of New Tetraethyl(N-
alkyl-1-aminoethan-1,1-
diyl)bisphosphona-tes and ESR
Analysis of Chemical Exchange
of Derived Nitroxides of Acyclic
Aminobisphosphonates
Gilles Olive a , Antal Rockenbauer a , Xavier
Rozanska c , Alain Jacques d , Daniel Peeters d
Anton German a
&
a Department of Polymer Chemistry and Coatings
Technology, Eindhoven University of Technology,
Eindhoven, The Netherlands
b Chemical Research Center, Institute of Structural
Chemistry, Budapest, Hungary
c Schuit Institute of Catalysis, Laboratory of
Inorganic Chemistry and Catalysis, Eindhoven
University of Technology, Eindhoven, The
Netherlands
d Unité CSTR, Université Catholique de Louvain,
Bâtiment Lavoisier, Louvain-la-Nueve, Belgium
Published online: 23 Aug 2007.
To cite this article: Gilles Olive , Antal Rockenbauer , Xavier Rozanska , Alain
Jacques , Daniel Peeters & Anton German (2008) Synthesis of New Tetraethyl(N-
alkyl-1-aminoethan-1,1-diyl)bisphosphona-tes and ESR Analysis of Chemical Exchange
of Derived Nitroxides of Acyclic Aminobisphosphonates, Phosphorus, Sulfur, and Silicon
and the Related Elements, 182:10, 2359-2369

To link to this article: http://dx.doi.org/10.1080/10426500701441499
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the
information (the “Content”) contained in the publications on our platform.
However, Taylor & Francis, our agents, and our licensors make no
representations or warranties whatsoever as to the accuracy, completeness,
or suitability for any purpose of the Content. Any opinions and views
expressed in this publication are the opinions and views of the authors, and
are not the views of or endorsed by Taylor & Francis. The accuracy of the
Content should not be relied upon and should be independently verified with
primary sources of information. Taylor and Francis shall not be liable for any
losses, actions, claims, proceedings, demands, costs, expenses, damages,
and other liabilities whatsoever or howsoever caused arising directly or
indirectly in connection with, in relation to or arising out of the use of the
Content.
This article may be used for research, teaching, and private study purposes.
Any substantial or systematic reproduction, redistribution, reselling, loan,
sub-licensing, systematic supply, or distribution in any form to anyone is
expressly forbidden. Terms & Conditions of access and use can be found at
http://www.tandfonline.com/page/terms-and-conditions

Phosphorus, Sulfur, and Silicon, 182:2359–2369, 2007
Copyright © Taylor & Francis Group, LLC
ISSN: 1042-6507 print / 1563-5325 online
DOI: 10.1080/10426500701441499
Synthesis of New Tetraethyl(N-alkyl-1-aminoethan-1,1-
diyl)bisphosphona-tes and ESR Analysis of Chemical
Exchange of Derived Nitroxides of Acyclic
Aminobisphosphonates
Gilles Olive
Department of Polymer Chemistry and Coatings Technology, Eindhoven
University of Technology, Eindhoven, The Netherlands
Antal Rockenbauer
Institute of Structural Chemistry, Chemical Research Center, Budapest,
Hungary
Xavier Rozanska
Schuit Institute of Catalysis, Laboratory of Inorganic Chemistry and
Catalysis, Eindhoven University of Technology, Eindhoven, The
Netherlands
Alain Jacques
Daniel Peeters
Unite´ CSTR, Universite´ Catholique de Louvain, Baˆtiment Lavoisier,
Louvain-la-Nueve, Belgium
Anton German
Department of Polymer Chemistry and Coatings Technology, Eindhoven
University of Technology, Eindhoven, The Netherlands
The synthesis and the full characterization of two new linear bisphosphonates
(tetraethyl(N-tert-butyl-1-aminoethan-1,1-diyl)bisphosphonate and tetraethyl(N-
sec-butyl-1-aminoethan-1,1-diyl)bisphosphonate), and the first analysis of the ESR
spectra of the corresponding nitroxides is reported. The preliminary results of the-
oretical calculations on model compounds suggest a small B0 (in the McConnell
equation). The results of bisphosphonate ester and bisphosphonic acid are similar.
The discrepancies of P coupling for the diphosphorus compound stems from B2 that
is different when the dihedral angle is larger than 90◦.
Received January 26, 2007; accepted April 30, 2007.
We thank the Hungarian Scientific Research Fund OTKA T-046953 for the financial
support. We also thank M. David Riffont from EICVN for his help.
This manuscript is dedicated to the memory of Jean-Pierre Finet.
Address correspondence to Gilles Olive, Ecole Industrielle et Commerciale de la Ville
de Namur, Rue Pe´pin 2B, Namur 5000, Belgium. E-mail: gilles.olive@excite.com.
2359

2360
G. Olive et al.
Keywords Bisphosphonates; diphosphorylation; ESR; McConnell equation; nitroxide;
theoretical calculations
INTRODUCTION
The radical polymerization has interesting property as it is more
tolerant towards traces of impurities than ionic or coordination
polymerization.1 It requires absence of oxygen but can be carried
out in the presence of water.2 Unfortunately, the control over the
macromolecules is worse in radical polymerization than in ionic
polymerization.2 To increase the polymerization control, the use of ni-
troxides has been suggested.1 Nitroxyl radicals are observed to result
in a better control of the molecular weight, polydispersity, and ter-
mination processes. The action of a nitroxyl radical occurs through a
reversible coupling between the nitroxide and the growing polymeric
chain (Scheme 1).
SCHEME 1 Controlled radical polymerization involving nitroxides.
To clarify the role of nitroxyl radical in the polymerization pro-
cess, some information about its conformational behavior needs to be
known. We have already demonstrated it for geminally diphosphory-
lated pyrrolidinoxyl radicals3 where the combination of ring pseudo-
rotation with the internal rotation of phosphoryl groups produces at
least four nonequivalent sites.
In this article, we describe the synthesis of two new bis-
phosphonates, namely the tetraethyl(N-tert-butyl-1-aminoethan-1,1-
diyl)bisphosphonate 1 and the tetraethyl(N-sec-butyl-1-aminoethan-
1,1-diyl)bisphosphonate 2 molecules (Scheme 2) and perform the full

ESR Analysis of Nitroxides of Aminobisphosphonates
2361
ESR4 analysis of the chemical exchange of various nitroxides formed
from the oxidation of 1 and 2 (Scheme 2).
SCHEME 2 Compounds studied.
RESULTS AND DISCUSSION
Synthesis
The synthesis of 1 and 2 is described in Scheme 3. It uses a one step
reaction that has been described elsewhere.5−7 At −7.5◦C under ni-
trogen atmosphere POCl3 (2 mol) is slowly added to a mixture of the
corresponding amide (1 mol eq) and triethylphosphite (2 mol eq). Af-
ter stirring the mixture for one hour at room temperature, it is poured
over a cold aqueous solution saturated with NH4OH. After work-up, the
corresponding aminobisphosphonates are obtained with several yields.
(Table I) Compounds 3 and 4 are prepared using the procedure of Beube
and Lessard8 and of Lock and Sagar,9 respectively.
Using the same procedure, Grimaldi10 prepared the tetraethyl N-
tert-butyl aminomethylene bisphosphonate 5 with a yield of 56%.
TABLE I Yields and 31P Chemical Shifts for Some
Aminobisphosphonates
Yield/%
(isolated compound)
Product
δ
31P/ppm in CDCl3
1
2
5
29
23
56
22.5
23.3
See ref6 or 10

2362
G. Olive et al.
SCHEME 3 Reaction pathway for the one-pot procedure of bisphosphonates.
Compared to 1 and 2, which have one additional methyl group on the
carbon bearing the two phosphonate groups, the yield is twice as high
with 5.
ESR Study
Analysis of the Radical Derived from 1
The main lines of the spectra can be interpreted as a doublet of a
triplet (AP = 53.2 G, AN = 13.8 G) and all lines show a further small
doublet with an AX = 1.7 G coupling (Figure 1). Even at high temper-
atures, there is no sign of line width alternation (LWA). In principle,
this lack and the very small second phosphorus coupling could be ex-
plained by a rigid geometry. However, this contradicts our observations
for other geminally diphosphorylated nitroxide radicals where a chem-
ical exchange always occurs. No other example with the phosphorus in
β-position can be found in the literature where the coupling is smaller
than 20 G, which in fact is caused by the anomeric effect stabilizing the
axial preference of the CP bond. Furthermore, the spectra contain addi-
tional satellites of low intensity that can be attributed to a radical with
two phosphorus couplings of 40 G on average; the lines reveal the usual
LWA. The major product is thus assigned to a mono-phosphorylated
radical (1aNO), whereas the satellites are interpreted as the lines of
the radical (1bNO). The assignment of 1aNO is supported by the small
coupling of 1.7 G typical for N-methine hydrogen. This attribution is
sustained by the appearance of the impurity lines present in the spec-
tra of the nitroxide obtained by the oxidation of 5 in pentane, which
have parameters similar to the major product in the spectra of 1. A
computer simulation of the altꢀeꢀ rnating lines11 from 1bNO gives data
ꢀ
as AN = 14.1 G, AP = 55.2 G, AP = 14.5 G, τ = 0.525 ns [exchange time
at 293 K), and ꢀE = 15 kJ/mol (potential barrier computed from the
slope on the Arrhenius plot (not shown)].
Using the simplified McConnell equation12 [Ap=Bp cos2 θ (Scheme
4) and AH = BH cos2 θ, with Bp = 56 G and BH = 24 G for linear

ESR Analysis of Nitroxides of Aminobisphosphonates
2363
SCHEME 4 Explanation of θ in the McConnell equation.
nitroxide13], we found θP = 12.9◦ and θH = 72.9◦ for 1aNO, θP < 6◦
ꢀ
and θP = 59.4◦ for 1bNO.
ꢀꢀ
A more elaborate study of this thermal evolution and a discussion of
the coalescences and the frozen states will be published elsewhere
Analysis of the Radical Derived from 214
Above room temperature, the ESR spectra show nine major lines (see
Figure 9 in ref14 and Figure 2 in this article). The phosphorus central
lines have smaller amplitudes than the outer lines, revealing a fast
chemical exchange. At 363 K in toluene the outer triplet splits into a
smaller doublet pattern of 1.44 G that can be attributed to the beta
proton of the sec-butyl group. The three central lines display a 1:2:1
triplet which is credited with the chirality of the sec-butyl group. Plain
FIGURE 1 Experimental ESR spectra of radical obtained during the oxidation
of 1 in toluene at 213 and 363 K.

2364
G. Olive et al.
FIGURE 2 Experimental ESR spectra of radical 2 in dichloromethane at se-
lected temperatures (in K).
simulations have provided AN = 13.96 G, AP1 = 35.63 G, and AP2
=
38.20 G coupling constants.
A significant line broadening is noticed at lower temperatures; the
corresponding two coalescences happen below 333 K and at 293 K in
toluene, below 343 K and at 283 K in dichloromethane (Figure 2). Start-
ing from 213 K in toluene and 203 K in dichloromethane, the spectra
have an anisotropic behavior due to the presence of frozen conformers.
In order to see small coupling, new experiments using pump-freeze
cycle instead bubbling helium, as well as new oxidants reagents (like
lead dioxide or silver dioxide) will be carried out.
Theoretical Calculations
Many simulations were performed to analyze the ESR spectra. All sim-
ulated spectra show a perfect fit with the experimental ones. However,
their interpretation is more complicated. The presence of two different
phosphorus atoms allows to determine separately B and B in the di-
0
2
hedral relation of McConnell12 by analysis of P-hfs couplings, if the ꢁ
PCP angle is known.14 B and B are estimated to be 25 and 35 G, re-
0
2
spectively, if ꢁ = 120◦. B describes direct and indirect polarization, and
0
B describes hyperconjugation.15 This contradicts the values of B = 0
2
0
and B = 60 G that were proposed by Tordo, indicating a significant
2
angular distortion of the PCP group.14 According to quantum chemical
computations, B should actually be small, i.e., never larger than 6 G.16
0

ESR Analysis of Nitroxides of Aminobisphosphonates
2365
To investigate an alternative possibility causing anomalous B
0
and B values, we performed several ab initio calculations on model
2
molecules similar to 1bNO and 2NO using the Gaussian 9817 software.
Model molecules are CH3-NO-CH2-PO3H2 6, CH3-NO-CH2-PO3(CH3)2
7 for monophosphonated species, and CH3-NO-CH-(PO3H2)2 8 for
diphosphonated species. All results were obtained after full optimiza-
tion at UHF(6-31G) level but constraining the value of the dihedral
angle θ.18,19 In 6, the PO3H2 hydrogen atoms were oriented to avoid
hydrogen bonding with the NO oxygen. This configuration was main-
tained in all the compounds. The second molecule was studied in order
to establish that the previous results are independent of the nature of
the substituents.
The preliminary results show that i) B is generally small; ii) the
0
values of the energy or of the spin density at 0◦ and 180◦ and at 90◦ and
270◦ are slightly different; iii) the results for 6 and 7 are very similar;
and iv) in case of two PO3H2 groups (compound 8), result ii is more
important (Figure 3), and the behavior of the two groups is sensibly
different, leading to different B and B in the McConell relation (com-
0
2
pared to monophosphonated species).
These results are in agreement with a model in which B is different
2
for the angles larger than 90◦. This model can explain the discrepan-
cies of P coupling for the diphosphorus compound even if small B is
0
assumed. Since the B asymmetry is supposed to be related to the level
2
of pyramidal distortion, it was interesting to look into this property.
Three angles—the valence angles (C(H3)-N-O (A1) and C(P)-N-O (A2)
completed by the elevation angle at the O atom above the CNC plane
(B)—are reported here for the most stable structures:
6 A1 = 119.0, A2 = 117.2, B = 13.2,
7 A1 = 119.0, A2 = 117.3, B = 13.6, and
8 A1 = 119.8, A2 = 117.0, B = 12.0.
(1)
(2)
(3)
The model we developed14 is now supported by the quantum chemical
calculations.
Ab initio calculations on 1bNO and 2NO are under way and all rel-
evant results will be published in a forthcoming paper.
CONCLUSION
In this article, we have described the synthesis and the full character-
ization of two new linear bisphosphonates and the preliminary results
of the analysis of the ESR spectra of the corresponding nitroxides. We
also report the results of theoretical calculations on model compounds.

2366
G. Olive et al.
FIGURE 3 (a) Calculated spin density of the two phosphorus atoms and, (b)
energy (in kJ/mol) as a function of θ (in degree) for 8.
With this approach we can claim that B0 is generally small and that
the results of bisphosphonate ester and bisphosphonic acid are similar.
Because of the asymmetry, at 0◦ and 180◦ for example, the constants
in the McConnell relation are different in the case of mono and diphos-
phorylated species. For diphosphonate molecules, the constant for the
simplified relation must be determined. The discrepancies of P coupling
for the diphosphorus compound stems from B2 that is different when
the sign of dihedral angle is changed.
EXPERIMENTAL
NMR spectra were acquired on a Bruker AM 400 (1H, 400 MHz; 13C,
100.61 MHz; 31P, 161.98 MHz) spectrometer. The chemical shifts (δ) are

ESR Analysis of Nitroxides of Aminobisphosphonates
2367
given in ppm and referred to internal TMS for 1H and 13C and to exter-
nal 85% H3PO4 for 31P. 15N NMR spectra were recorded on a Varian In-
ova 500 at 50.649 MHz (Inverse gated method) and the δ values in ppm
are referred to external CD3NO2. All J values are given in Hz. Elemen-
tal analyses were performed at the Eindhoven University of Technology.
UV spectra were acquired on a HP 8453 UV-VIS spectrophotometer.
IR spectra were acquired on a Mattson Polaris spectrophotometer. Ra-
man spectra were acquired on a Labram Dilor spectrophotometer. In-
dex of refraction were determined on an Atago refractometer at 20◦C.
ESR measurements were performed on a Bruker ESP 300E spectrom-
eter equipped with an X-band resonator (9.41 GHz). All ESR spectra
were recorded at 100 kHz magnetic field modulation. Solvents were
purchased from Biosolve. Phosphorus oxychloride, ammonia solution
(ca. 28–30%), hydrochloric solution (ca. 32%), triethyl phosphite and
all compounds for the synthesis of 3 and 4 were used as purchased
from Aldrich. m-CPBA (m-chloroperbenzoic acid) (70–75%) was used as
purchased from Acros. Sodium hydroxide was used as purchased from
Fluka.
General Procedure
In a double walled flask, under nitrogen, phosphorus oxychloride
(20 mL, 0.22 mol) was added during 1 h to a mixture at −7.5◦C of
amide 3 or 4 (0.11 mol) and triethylphosphite (34.9 g, 0.21 mol). The re-
action mixture was stirred for 1 h at room temperature and then poured
over a mixture of ice (200 g) and ammonia 30% (400 mL). The aqueous
layer was extracted with methylene chloride (3 × 100 mL) and then the
latter was removed to obtain a yellow oil. The oil was dissolved in 100
mL of methylene chloride. An aqueous solution of hydrochloric acid (10
mL of 32% HCl solution, 190 mL of water) was added (pH 1) and the
aqueous layer was washed with methylene chloride (3 × 100 mL). A
solution of sodium hydroxide (20 g of NaOH in 200 mL of water) was
added up to pH 10 and the aqueous layer was extracted with methylene
chloride (4 × 100 mL). The organic layer was dried over sodium sulfate
and filtered. Removal of the solvent afforded 1 or 2.
Tetraethyl(N-tert-butyl-1-aminoethan-1,1-diyl)-
bisphosphonate (1)
(11.3 g, 29%). 1H NMR (CDCl3): δ 1.24 (s, 9H, CH C), 1.33 (t, J = 7.0,
3
12H, CH CH2O), 1.74 (t, J = 18.4, 3H, CH CP2), 2.70 (s, 1H, NH), 4.1-
3
3
4.3 (m, 8H, CH3CH O). 13C NMR (CDCl3): δ 15.8 (t, J = 5.5, CH3CP2),
2
16.3 (t, J = 3.5, CH3CH2O), 32.4 (CH3C), 52.6 (t, J = 5.7, CH3C),

2368
G. Olive et al.
58.9 (t, J = 145.0, CP2), 62.5 (t, J = 4.1, CH3CH2O), 64.0 (t, J = 3.7,
CH3CH2O). 31P NMR (CDCl3): δ 22.5. 15N NMR (C6D6): δ −324.3 (t,
J
= 6.1). IR (CCl4): 3466 (νNH), 1251 (P=O), 1164 (POC2H5) cm−1
.
PN
Raman: 2978 (νCH3 As.); 2934 (νCH2 As.); 2908 (νCH3 Sym.); 2875 (νCH2
Sym.); 2776; 2726; 1479; 1456 (δCHsp3 As.); 1446; 1396 or 1369 (δCHsp3
Sym.); 1288; 1239 (P=O); 1099 (νC−N); 1028; 923; 767; 686; 639; 537;
313; 213 cm−1. Anal. Calcd. for C14H33NO6P2: C, 45.04; H, 8.91; N, 3.75.
Found: C, 44.80; H, 8.49; N, 3.55. UV (Ethanol, 25◦C, 10−3 M): λmax
207 (εmax 492 mol−1·dm3·cm−1), 260 (εmax 309 mol−1·dm3·cm−1) nm. nD20
21
21
1.4463. d 1.12. MRExp 88.9.
Tetraethyl(N-sec-butyl-1-aminoethan-1,1-diyl)-
bisphosphonate (2)
1
(9.0 g, 23%). H NMR (CDCl3): δ 0.68 (t, J = 7.4, 3H, CH CH2CH)
3
0.87 (d, J = 6.4, 3H, CH CH), 1.05 (m, 1H, CH3CH HbCH), 1.15 (t,
3
a
J = 7.2, 12H, CH CH2O), 1.35 (m, 1H, CH3CHa H CH), 1.41 (t, J =
3
b
17.4, 3H, CH CP2), 2.9 (m, 1H, CHN), 4.02 (m, 8H, CH3CH O). 13C
3
2
NMR (CDCl3): δ 10.1 (CH3CH), 15.6 (t, J = 4.2, CH3CP2), 16.2 (t, J =
3.0, CH3CH2O), 22.3 (CH3CH2CH), 32.1 (CH3CH2CH), 48.4 (t, J = 6.1,
CHN), 57.5 (t, J = 143.0, CP2), 62.3 (t, J = 3.8, CH3CH2O), 63.2 (t, J =
3.8, CH3CH2O). 31P NMR (CDCl3): δ 23.3. 15N NMR (C6D6): δ −330.8
(t, J = 5.2). IR (CCl4): 3447 (νNH), 1246 (P=O), 1163 (POC2H5) cm−1
.
PN
Raman: 2975 (νCH3 As.); 2934 (νCH2 As.); 2905 (νCH3 Sym.); 2875 (νCH2
Sym.); 2773; 2723; 1481; 1457 (δCHsp3 As.); 1371; 1292; 1249 (P=O);
1100 (νC−N); 1031; 949; 844; 813; 765; 648; 535; 327; 242 cm−1. Anal.
Calcd. for C14H33NO6P2.H2O: C, 42.96; H, 9.01; N, 3.58. Found: C,
42.91; H, 8.50; N, 3.64. UV (Ethanol, 25◦C, 10−3 M): λmax 204 (εmax
1202 mol−1.dm3.cm−1) nm. nD20 1.4461. d2211 1.13. MRExp 88.1.
ESR Study of Nitroxides 1aNO, 1bNO and 2NO
Compounds 1 or 2 (0.03 mmol) were dissolved in 100 μL of solvent
(dichloromethane or toluene). m-CPBA (7.2 mg, 0.03 mmol) was added
and the spectrum was recorded immediately after helium bubbling.
REFERENCES
[1] G. Moad and D. H. Solomon, The Chemistry of Free Radical Polymerization, (Perg-
amon, Oxford, 1995), 1st ed.
[2] K. Matyjaszewski, S. Gaynor, D. Greszta, D. Mardare, and T. Shigemoto, J. Phys.
Org. Chem., 8, 306 (1995).
[3] A. Rockenbauer, A. Mercier, F. Le Moigne, G. Olive, and P. Tordo, J. Phys. Chem. A,
101, 7965 (1997).

ESR Analysis of Nitroxides of Aminobisphosphonates
2369
[4] J. A. Weil and J. R. Bolton, Electron Paramagnetic Resonance—Elementary Theory
and Practical Applications, (John Wiley, New York, 1994).
[5] G. Olive, F. Le Moigne, A. Mercier, A. Rockenbauer, and P. Tordo, J. Org. Chem., 63,
9095 (1998).
[6] G. Olive, F. Le Moigne, A. Mercier, and P. Tordo, Synth. Commun., 30, 619 (2000).
[7] G. Olive and A. Jacques, Phosphorus, Sulfur, and Silicon, 178, 33 (2003).
[8] D. Berube and J. Lessard, Can. J. Chem., 60, 1127 (1982).
[9] M. V. Lock and B. F. Sagar, J. Chem. Soc. (B), 690 (1966).
[10] S. Grimaldi, Ph.D. Thesis, Universite´ d’Aix Marseille III, Marseille, France (1997).
[11] A. Rockenbauer and L. Korecz, Appl. Magn. Reson., 10, 29 (1996).
[12] C. Heller and H. M. McConnell, J. Chem. Phys., 32, 1535 (1960).
[13] A. S. Mukhtarov, A. V. Il’yasov, Y. A. Levin, I. P. Gozman, M. S. Skorobogatova, and
E. I. Zoroatskaya, Theor. Exp. Chem. (Eng. Transl.), 12, 656 (1976).
[14] A. Rockenbauer, G. Olive, X. Rozanska, A. Jacques, D. Gigmes, F. Le Moigne, D.
Peeters, A. German, and P. Tordo, J. Phys. Chem. A, 108, 5484 (2004).
[15] A. R. Sornes, E. Sagstuen, and A. Lund, J. Phys. Chem., 99, 16867 (1995).
[16] P. Tordo, Unpublished results.
[17] M. J. Frisch, G. W. Trucks, H. B. Schlegel, M. A. Scuseria, M. A. Robb, J. R. Cheese-
man, X. Zakrzewski, J. A. Montgomery, R. E. Stratmann, J. C. Burant, S. Dapprich, J.
M. Millam, A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone,
M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski,
G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma, D. K. Malick, D. K. Rabuck, K.
Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A.
Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith,
M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzales, M. Challacombe, P. M.
W. Gill, B. G. Johnson, W. Chen, M. W. Wong, J. L. Andress, M. Head-Gordon, E. S.
Replogle, and J. A. Pople, Graussian 98 (Gaussian, Inc., Pittsburg, PA, 1998).
[18] J. A. Pople and R. K. Nesbet, J. Chem. Phys., 22, 571 (1954).
[19] J. S. Binkley, J. A. Pople, and W. J. Hehre, J. Am. Chem. Soc., 102, 939 (1980).