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Electron Density and Bonding at Inverted Carbon Atoms An Experimental Study of a [1.1.1]Propellane Derivative

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Electron Density and Bonding at Inverted Carbon
Atoms: An Experimental Study of a
[1.1.1]Propellane Derivative**
Marc Messerschmidt, Stephan Scheins, Lutz Grubert,
Michael Ptzel, Gnter Szeimies, Carsten Paulmann,
and Peter Luger*
tion from ref. [2]). An experimental investigation of the
electron density of two [1.1.1]propellane derivatives agreed
qualitatively with the theoretical results.[4] Since no quantitative topological analysis was applied, a conclusion on the
existence of a bond critical point could not been drawn from
the experiments. Therefore, it was necessary to readdress the
issue of electron density in [1.1.1]propellanes, and we present
here quantitative results of a synchrotron experiment carried
out with propellane 5 (Scheme 1).
Propellane 5 was prepared in four steps from tricycloheptane 1[6] (Scheme 1). After metalation of 1 with butyl-
The most exciting problem in the chemistry of small-ring
propellanes is the nature of the central bond that connects the
two “inverted” bridgehead carbon atoms common to the
three “wings” of the cage structure (see Figure 1). For several
Figure 1. Structure of [1.1.1]propellane. The dashed line connects the
inverted carbon atoms.
[1.1.1]propellanes, the X-ray structures showed distances of
1.59 ( 0.01) [1] between these atoms—only slightly longer
than the standard CC bond length in saturated hydrocarbons.
The results of intensive theoretical work devoted to the
question of covalent bonding seem to converge to the
conclusion that the inverted carbon atoms are covalently
bonded; this is supported by the existence of a bond critical
point.[2] On the other hand, the electron deformation density
is not accumulated in this region,[3] which was, however,
regarded by Wiberg et al. “as an artefact of the promolecule
density distribution and not as a reflection of the relative
properties of the two charge distributions of interest” (quota[*] Dr. M. Messerschmidt, Dipl.-Chem. S. Scheins, Prof. Dr. P. Luger
Institut fr Chemie/Kristallographie
Freie Universitt Berlin
Takustrasse 6, 14195 Berlin (Germany)
Fax: (+ 49) 30-838-53464
Dr. L. Grubert, Dr. M. Ptzel, Prof. Dr. G. Szeimies
Institut fr Chemie
Humboldt-Universitt zu Berlin
Brook-Taylor-Strasse 2, 12489 Berlin (Germany)
Dr. C. Paulmann
Mineralogisch-Petrographisches Institut
Universitt Hamburg
Grindelallee 48, 20146 Hamburg (Germany)
[**] This research was supported by the Deutsche Forschungsgemeinschaft (grant Lu 222/24-1 and Lu 222/24-3).
Angew. Chem. Int. Ed. 2005, 44, 3925 –3928
Scheme 1. a) BuLi (0.8 equiv Et2O), 0 8C!RT, 72 h, b) adamantan2-one (0.9 equiv in Et2O), 0 8C!RT; c) BuLi (2.25 equiv in Et2O),
0 8C!RT, 72 h, d) para-toluenesulfonyl bromide (0.55 equiv), RT;
e) Me2S (1.0 equiv in CH2Cl2), NCS (1.0 equiv in CH2Cl2), 25 8C!RT;
f) chromatography, silica gel, hexane; g) MeLi (1.25 equiv in Et2O),
25 8C!RT.
lithium, the resulting lithium species was treated with
adamantan-2-one to afford the tertiary alcohol 2. The
substitution of the second bridgehead hydrogen atom by
bromine was achieved by twofold lithiation of 2 followed by
reaction with tosyl bromide. Reaction of 3 with the dimethyl
sulfide/N-chlorosuccinimide reagent furnished the olefin 4
bearing a geminal halogen moiety. The key step of the
synthesis is the intramolecular addition of the carbene, [5]
generated by treatment of 4 with methyllithium, to the CC
double bond, to afford the target propellane 5 in 10 % overall
Single crystals of 5 were obtained from a cold pentane
solution at 258 K. The rather small crystals, which did not
diffract sufficiently in the outer regions of reciprocal space
with our laboratory setup, made it necessary to collect highresolution data at a synchrotron beam line.[7] Propellane 5
crystallizes in the space group Pmmn and is situated at an
mm2 site of symmetry in the crystal; this results in nine
independent carbon atoms (Figure 2). This symmetry is
possible only with a 1:1 disorder for one methylene group
(C1/C1a, see Figure 2).[8]
For comparison of the experimentally obtained electron
density with the theoretical, ab initio calculations, which
DOI: 10.1002/anie.200500169
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 3. Static deformation densities in the [1.1.1]propellane cage.
Left/middle: Experimental distribution in the wing containing C3/C5.
Right: Distribution from the B3LYP/6-311G** calculation. Contour interval 0.1 e 3, solid/dotted/dashed lines: positive/zero/negative values.
Figure 2. ORTEP representation[19] of the molecular structure of 5 in
the crystal with atom numbering (not identical to the numbering in
keeping with IUPAC nomenclature). The C1/C1a methylene groups
exhibit the 1:1 disorder. Displacement ellipsoids (at 100 K) are shown
at a 50 % probability.
initially were performed by Wiberg et al.[2] with HF methods,
were now completed at the density functional B3LYP level of
The deformation densities visualize the difference
Figure 4. Laplace distributions in the same sections as defined in
between the multipol model and a promolecule that consists
Figure 3. Contour interval 5 e 5, blue/red: positive/negative values.
of neutral spherical atoms. Therefore, it is open whether they
reproduce properly the charge accumulation in strained
Quantitative results were obtained from the bond critical
systems, as was already pointed out in Wibergs statement
points (bcps), all of which were found in the experimental
cited above.[2] For the two experimentally independent wings
density of 5 and characterized using Baders theory of “Atoms
of the propellane cage of 5 the static deformation densities are
in Molecules”.[12] They are summarized in Table 1, where also,
shown in Figure 3 along with the corresponding densities
derived from theory. The features of the two experimental
for comparison, corresponding topological data are given for
maps show some differences, which can be caused by the
the cage of a [1.1.1]bicyclopentane derivative, of which the
different crystal environments or by the fact that the C3experimental electron density was described earlier.[11] There
containing map displays a region close to the disordered part
is a relationship between the two types of cages, in that
of the molecule. Nevertheless, the major features are
formally the addition of two substituents to the propellane
comparable. The bonding densities on the wings have
bridgehead atoms breaks the bond in question and yields the
maxima clearly outside the direct internuclear vectors, showcorresponding bicyclopentane molecule, where the intracage
ing the so-called banana bonds that are typically found in very
distance increases to 1.8–1.9 .[1]
[10, 11]
strained ring systems.
The second common feature is the
As shown in Table 1 the bonds in the wings are described
absence of density accumulation in the region between the
by experiment and theory as covalent. The experimental
inverted carbon atoms, as is also
shown in the theoretical distribution (Figure 3, right).
Table 1: Summary of selected topological parameters of 5 and a [1.1.1]bicyclopentane derivative.
Regardless of whether the
Distance []
1 [e 3]
521 [e 5]
deformation density is an artefact
of the promolecule distribution,
the Laplacian 521(r), which is
directly obtained from the total
electron density, should provide
more reliable and detailed inforC4-C4a-C3
mation on the bonding situation.
As shown in Figure 4, the bonds on
the wings have saddle-shaped
2) [1.1.1]Bicyclopentane derivative[11]
regions with a clear charge accuwing bonds:
mulation over the whole bond, as is
9.7(1)– 13.1(1)
characteristic for covalent bonds.
In contrast, the central bond
through the cage shows, in good
agreement with theory, no charge
accumulation at the center.
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2005, 44, 3925 –3928
densities on the bond critical points fall roughly in the range
also found for the six wing bonds in the [1.1.1]bicyclopentane
derivative, although these bonds are slightly shorter in 5. In
total, the agreement for the wing bonds is reasonable for the
two compounds; both 1bcp and 521bcp, and experimental and
theoretical descriptions are all in good agreement as well.
Of major interest is the central bond through the cage.
While for the bicyclopentane only a cage critical point (ccp)
could be located inside the cage, a bond critical point is found
unambiguously also in the experimental electron density of
the propellane 5. For the much shorter contact between the
bridgehead atoms, the bcp has nearly twice the density of the
bicyclopentane ccp, which is in good agreement with theoretical calculations. The Laplacian at this bond critical point is
positive, as is seen normally for noncovalent interactions. Its
higher value in the experiment indicates that the experimental bond path has a stronger curvature than the theoretical.
By using an exponential relation introduced by Bader
et al.,[13] a bond order n can be derived from the electron
density at the bond critical point. For C4C4a and the
experimental value 1bcp = 1.31(3) e 3 we obtained a bond
order of n = 0.71, which is in line with n = 0.73 determined by
Wiberg et al.[2] in earlier theoretical studies and comparable
to n = 0.69(1) recently reported for the lengthened bond in
the cyclopropane ring of a barbaralane derivative.[14] It
should, however, be noted that the determination of bond
orders smaller than one is uncertain because the extrapolation to zero bond order is not well defined. The existence of a
bond path is further supported by the location of ring critical
points (rcps) in the two crystallographically independent
wings of 5 with densities found very close to theoretical values
(see Table 1). Such ring critical points were not located in the
bicyclopentane cage.
This study shows that a high-resolution data set could be
obtained even from otherwise weakly diffracting crystals
thanks to the use of very intense synchrotron primary
radiation. This data set served as the experimental basis for
the determination of the electron density of the [1.1.1]propellane 5 and its topological analysis. Although a small part of
the molecule was affected by disorder, all expected topological descriptors in terms of critical points could be located and
a general good agreement was seen between experiment and
theory. In contrast to a related [1.1.1]bicyclopentane derivative,[11] a bond critical point was found between the bridgehead atoms in 5. This bond is unusual according to topological
analysis: it has a bond path with a bond critical point of
significant density, as is characteristic for a covalent bond, but
no charge accumulation is evident at the bond critical point
where the Laplacian is positive. These findings, confirming
small-ring propellanes as a unique class of hydrocarbons, have
been obtained for the first time by quantitative topological
results derived from experimental electron density distribution.
Experimental Section
2: The solvent was removed from a solution of butyllithium (50 mL,
1.6 m in hexane, 80 mmol) under reduced pressure and under nitrogen. The residue was dissolved in about the same volume of Et2O. To
Angew. Chem. Int. Ed. 2005, 44, 3925 –3928
this first solution was added a solution of 1 (9.4 g, 100 mmol) in Et2O
(100 mL) at 0 8C within 30 min. The reaction solution was allowed to
warm to room temperature and was stirred for further 72 h. Then the
reaction mixture was cooled to 0 8C, and adamantan-2-one (11.25 g,
75 mmol) dissolved in Et2O (100 mL) was added dropwise. After
stirring for 5 h the mixture was hydrolyzed with 1m NaOH. The ether
phase was washed twice with 1m NaOH, the organic layer was dried
(MgSO4), and the solvent was removed under reduced pressure. The
solid residue was dissolved in diisopropyl ether. Recrystallization at
10 8C afforded 2 (16.5 g, 84 %) as colorless crystals. M.p. 122–124 8C
(diisopropyl ether). 1H NMR (600 MHz, CDCl3, TMS): d = 2.45 (m,
2 H, H-6’ and H-2’), 2.19 (m, 2 H, H-4a and H-9a), 2.11 (m, 2 H, H-8a
and H-10a), 1.88 (m, 1 H, H-5), 1.81 (m, 1 H, H-7), 1.74 (m, 7 H, H-1, 3,
6, 8b, 10b and H-7’), 1.58 (m, 2 H, H-4b and H-9b), 1.42 (m, 1 H,
H-3a’), 1.38 (m, 4 H, H-3b’, 4’, 5b’), 1.31 (m, 1 H, H-5a’), 1.03 ppm (s,
1 H, OH); 13C NMR (75 MHz, CDCl3, TMS): d = 73.9 (C-2), 39.5 (2 C,
C-2’ and C-6’), 38.1 (C-6), 38.0 (2 C, C-1 and C-3), 34.9 (2 C, C-8 and
C-10), 33.0 (2 C, C-4 and C-9), 27.5 (C-5), 27.1 C-7), 26.7 (C-1’), 20.8
(C-4’), 19.9 (2 C, C-3’ and C-5’) 13.5 ppm (C-7’).
3: Carbinol 2 (5.76 g, 40 mmol) in Et2O (100 mL) was added
dropwise with stirring at 0 8C to butyllithium (56 mL, 1.6 m in Et2O,
90 mmol). Stirring was continued for 72 h at room temperature. The
reaction mixture was again cooled in an ice bath, charged with 4toluenesulfonyl bromide (11.75 g, 50 mmol) in small portions, stirred
for 5 h at room temperature, and then hydrolyzed with 1n NaOH in
an ice bath. The layers were separated, the aqueous part extracted
three times with Et2O, and the combined ether layers dried with
MgSO4. After filtration and removal of the solvents and volatile
products under reduced pressure (5 105 Torr) and elevated bath
temperature (up to 80 8C), the solid residue was dissolved in Et2O.
Recrystallization at 10 8C afforded 3 (2.5 g, 33 %) as colorless
crystals. M.p. 77–78 8C (Et2O). MS (CI) m/z (%): 322//324 (0.5) [M+C],
243 (23) [MBr+C], 171//173 (6) [MAd-OH+], 162 (58), 151 (42), 91
(100), 79 (64), 77 (45), 67 (35), 55 (40), 41 (55), 39 (33); 1H NMR
(300 MHz, CDCl3, TMS): d = 2.85 (m, 2 H, H-6’ and H-2’), 2.28 (m,
2 H, H-4a and H-9a), 1.99 (m, 2 H, H-8a and H-10a), 1.88 (s 1 H, OH),
1.82 (m, 4 H, H-1, 3, 5, 7), 1.72 (m, 4 H, H-6, 8b, 10b), 1.57 (m, 2 H, H4b and H-9b), 1.54 (m, 2 H, H-3a’ and H-5a’), 1.38 ppm (m, 4 H, H-3b’,
4’, 5b’); 13C NMR (75 MHz, CDCl3, TMS): d = 75.8 (C-2), 46.6 (2 C, C2’ and C-6’), 38.4 (2 C, C-1 and C-3), 38.0 (C-6), 34.6 (2 C, C-8 and C10), 33.0 (C-7’), 32.6 (2 C, C-4 and C-9), 27.9 (C-1’), 27.3 (C-5), 27.0
(C-7), 19.9 (C-4’), 19.0 ppm (2 C, C-3’ and C-5’).
4: N-Chlorosuccinimide (2.4 g, 0.018 mol) and dimethyl sulfide
(1.32 mL, 0.018 mol) were mixed at 0 8C in dichloromethane (75 mL).
The milky suspension was cooled to 25 8C, and a solution of 3
(4.83 g, 0.015 mol) in 25 mL dichloromethane was added dropwise
with stirring. The bath temperature was increased to 25 8C, and
stirring was continued for 4 h. The dichloromethane solution was
extracted three times with 1m NaOH and twice with brine, dried with
MgSO4, and filtered, and the solvent was removed under reduced
pressure. The volatile products were removed in vacuo (105 Torr,
40 8C). The residue was purified by chromatography (silica gel, nhexane) The solvent was removed and the target compound 4 (2.5 g,
49 %) was obtained as colorless crystals. M.p. 55 8C (n-hexane). MS
(CI) m/z (%): 340/342/344 (3/4/1) [M+C], 213 (100), 131 (16), 91 (36),
H NMR (600 MHz, CDCl3, TMS): d = 3.39 (d, 2 H, H-1’ and H-5’),
2.53 (s, br, 2 H, H-1 and H-3), 2.30 (m 2 H, H-2’ and H-4’) 1.93 (m, 2 H,
H-5 and H-7) 2.85 (m 10 H, H-2’, 4’, 4, 6, 8, 9, 10), 1.71 (d, br., 2 H, H-4
and H-9) 1.63 (m, 1 H, H-3’), 1.45 ppm (m, 1 H, H-3’); 13C NMR
(75 MHz, CDCl3, TMS): d = 140.2 (C-6’), 121,4 (C-2), 70.9 (C-7’), 59.1
(2 C, C-1’ and C-5’) 39.2 (2 C, C-4 and C-9), 38.3 (2 C, C-8 and C-10),
37.1 (C-6), 33.9 (2 C, C-1 and C-3), 29.6 (2 C, C-2’ and C-4’) 28.3 (2 C,
C-5 and C-7), 14.7 ppm (C-3’).
5: Methyllithium in Et2O (6.1 mL, 1.5 m, 9.1 mmol MeLi) was
diluted at 0 8C with Et2O (10 mL) and cooled down to 25 8C. This
solution was stirred and a solution of dihalide 4 (2.5 g, 7.25 mmol) in
Et2O (40 mL) was added dropwise. The mixture was allowed to warm
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
to room temperature and kept at this temperature for 5 h. The
reaction mixture was cooled in an ice bath, then 2 n NaOH (5 mL)
was added with stirring. After separation of the phases, the organic
layer was extracted twice with water and dried with MgSO4. Removal
of the solvent afforded a crystalline residue. Recrystallization yielded
5 (1.25 g, 76 %) as colorless needles. M.p. 81–83 8C (n-pentane at
10 8C). 1H NMR (600 MHz, CDCl3, TMS): d = 3.25 (s, 2 H, H-2’ and
H-6’), 1.70 (br s, 2 H, H-1 and H-3), 1.57 (br s, 2 H, H-5 and H-7), 1.55
(br s, 4 H, H-4, 8, 9, 10), 1.45 (m, 6 H, H-4, 8, 9, 10 and H-6), 1.34 (m,
4 H, H-3’ and H-5’), 0.96 ppm (m, 2 H, H-4’); 13C NMR (75 MHz,
CDCl3, TMS): d = 102.2 (C-8’=C-2), 80.8 (2 C, C-2’ and C-6’), 40.0
(4 C, C-4, 8, 9, 10), 39.1 (C-6), 29.2 (2 C, C-5 and C-7), 28.7 (2 C, C-1
and C-3), 22.3 (2 C, C-3’ and C-5’), 20.8 (C-4’), 20.2 ppm (2 C, C-1’ and
Received: January 17, 2005
Published online: May 13, 2005
Keywords: density functional calculations · electron density ·
propellanes · solid-state structures · strained molecules
[1] M. D. Levin, P. Kaszynski, J. Michl, Chem. Rev. 2000, 100, 169 –
234; see Table 2 on p. 176.
[2] K. B. Wiberg, R. F. W. Bader, C. D. H. Lau, J. Am. Chem. Soc.
1987, 109, 985 – 1001, and references therein.
[3] See ref. [1] and references therein.
[4] P. Seiler, J. Belzner, U. Bunz, G. Szeimies, Helv. Chim. Acta 1988,
71, 2100.
[5] M. Kenndorf, A. Singer, G. Szeimies, J. Prakt. Chem. 1997, 339,
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[7] Crystal structure analysis of 5, C17H22, at 100 K: Crystal size 0.4 0.2 0.1 mm3, orthorhombic, Pmmn, a = 6.706(1), b = 7.332(1),
c = 12.521(2) , V = 608.99(14) 3, 1calcd = 1.240 g cm3, sinq/
lmax = 1.18 1. The structure was solved by direct methods
and at first spherically refined using full matrix least squares
methods (SHELXTL).[20] The synchrotron experiments were
carried out at beamline F1 (k-axis geometry) at Desy/Hasylab. A
Bruker CCD area detector and Oxford Cryosystem N2 gas
stream device were used. The measurement strategy was
determined with ASTRO,[15] the measurement was controlled
with SMART,[15] and the integration and correction of the data
was done with SAINT[15] and SORTAV.[16] Si double-crystal
monochromator, l = 0.5600 , T = 100 K, 26 569 reflections
measured, 4087 unique (Rint = 4.4 %), 2371 reflections with (I >
3s(I)) were included in multipole refinements which were
carried out then based on the formalism of Hansen and
Coppens[17] with the program system XD.[18] Hexadecapoles
were used for the heavy atoms and dipoles for the H atoms.
Atomic site symmetry was applied according to corresponding
special positions in the crystal structure. The disorder was
considered by a 1:1 population. After convergence R(F) =
3.56 % for 217 parameters, Rw(F) = 3.47 %, min./max. residual
density: 0.23/0.28 e 3. The topological analysis, derivation of
electronic properties, and graphical visualization (Figures 3 and
4) were also done with XD. CCDC 257891 contains the
supplementary crystallographic data for this paper. These data
can be obtained free of charge from the Cambridge Crystallographic Data Centre via
[8] Attempts to solve and refine the structure in the corresponding
acentric space group Pmn21 confirmed the disorder, although it
is not forced by the symmetry of this space group.
2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
[9] To predict the influence of the substituents on the propellane
cage, several calculations at HF and B3LYP level of theory were
performed with the basis set 6-311G**.[21] All calculations
resulted in an almost D3h-symmetric propellane cage and
showed no significant influence of the substituents on the
interesting bond features of the propellane cage. Therefore
results of the unsubstituted propellane were used for all further
comparisons. These are in line with earlier calculations,[2] except
for minor quantitative differences in the bond topological
descriptors. The partitioning procedure which uses the zeroflux surfaces of 51(r) to obtain atomic properties was applied to
the theoretical density of propellane[22] derived from the abovementioned calculation. It yielded practically zero charges for all
atoms and volumes of 13.5 3 and 10.1 3 for the bridgehead
and the wing carbon atoms, respectively.
[10] T. Koritsnszky, J. Buschmann, P. Luger, J. Phys. Chem. 1996,
100, 10 541 – 10 553.
[11] P. Luger, M. Weber, G. Szeimies, M. Ptzel, J. Chem. Soc. Perkin
Trans. 2 2001, 1956 – 1960.
[12] R. F. W. Bader, Atoms in Molecules, A Quantum Theory,
Clarendon, Oxford, 1990; R. F. W. Bader, P. Lode, A. Popelier. T. A. Keith, Angew. Chem. 1994, 106, 647; Angew. Chem.
Int. Ed. Engl. 1994, 33, 620.
[13] R. F. W. Bader, T. S. Slee, D. Cremer, E. Kraka, J. Am. Chem.
Soc. 1983, 105, 5061 – 5068.
[14] P. Luger, M. Messerschmidt, S. Scheins, A. Wagner, Acta
Crystallogr. Sect. A 2004, 60, 390 – 396.
[15] Programs of ASTRO 1995 – 1996, SMART 1996, SAINT 1994 –
1996, Bruker-ASS Inc. Madison, WI (USA).
[16] R. H. Blessing, Acta Crystallogr. Sect. A 1995, 51, 33.
[17] N. K. Hansen, P. Coppens, Acta Crystallogr. Sect. A 1978, 34, 909.
[18] T. Koritsnszky, T. Richter, P. Macchi, A. Volkov, C. Gatti, S.
Howard, P. R. Mallinson, L. Farrugia, Z. W. Su, N. K. Hansen,
XD—A Computer Program Package for Multipole Refinement
and Analysis of Electron Densities from Diffraction Data. User
Manual. Tech. rep., Freie Universitt Berlin, 2003.
[19] M. N. Burnett, C. K. Johnson, ORTEP-III, Oak Ridge Thermal
Ellipsoid Plot Program for Crystal Structure Illustrations. Tech.
rep., Oak Ridge National Laboratory Report ORNL-6895, Oak
Ridge, TN, 1996.
[20] G. M. Sheldrick, Acta Crystallogr. Sect. A 1990, 46, 467; G. M.
Sheldrick, SHELX-TL 5.03, Software Package for the Crystal
Structure Determination, Siemens Analytical X-ray Instrument
Division, Madison, WI, USA, 1994.
[21] Gaussian 98 (Revision A.7), M. J. Frisch, G. W. Trucks, H. B.
Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G.
Zakrzewski, J. A. M. Jr., 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,
A. D. Rabuck, K. Raghavachari, J. B. Foresman, J. Cioslowski,
J. V. Ortiz, A. G. Baboul, 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.
Gonzalez, M. Challacombe, P. M. W. Gill, B. Johnson, W.
Chen, M. W. Wong, J. L. Andres, C. Gonzalez, M. HeadGordon, E. S. Replogle, J. A. Pople, Gaussian, Inc., Pittsburgh,
PA, 1998.
[22] P. Popelier, R. Bone, MORPHY, a program written by P. L. A.
Popelier with a contribution from R. G. A. Bone, Tech. rep.
UMIST, Manchester, England, EU, 1998.
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bonding, experimentov, propellanes, inverted, stud, atom, electro, carbon, density, derivatives
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