new insights on the bridge carbon–carbon bond in propellanes: a theoretical study based on the...

New Insights on the Bridge Carbon–Carbon Bond

in Propellanes: A Theoretical Study Based on the Analysis

of the Electron Localization Function

VICTOR POLO,1JUAN ANDRES,

1BERNARD SILVI

2

1Departament de Ciencies Experimentals, Universitat Jaume I, Apartat 224,12080 Castello, Spain

2Laboratoire de Chimie Theorique, Universite Pierre et Marie Curie, 4 Place Jussieu,75252 Paris Cedex, France

Received 22 May 2006; Revised 6 June 2006; Accepted 7 June 2006DOI 10.1002/jcc.20615

Published online 19 January 2007 in Wiley InterScience (www.interscience.wiley.com).

Abstract: The nature of the bonding between bridgehead carbon atoms (Ca, Ca0) as well as the ring strain in a

family of 10 propellanes formed by three-, four-, or five-member rings: [1.1.1] (I), [2.1.1] (II), [3.1.1] (III), [2.2.1]

(IV), [3.2.1] (V), [2.2.2] (VI), [3.3.1] (VII), [3.2.2] (VIII), [3.3.2] (IX), and [3.3.3] (X) are studied by means of the

electron localization function (ELF) at the DFT level (B3LYP/cc-pVTZ). The ELF analysis of smaller propellanes

(I, II, and III) reveals the coexistence of two resonance forms: one with a nonbonding electron pair partially delocal-

ized between Ca and Ca0 atoms outside the cage (ionic) and the other with a bridge bond between the same atoms

(covalent). The weights of each form are calculated according to the ELF-basin populations, yielding 94, 88, and

53% for the ionic structure of I, II, and III, respectively, while larger propellanes (IV–X) present only the covalent

form. The question of the s-character of the bridge bond is addressed by dissecting the bridge-bond ELF basin into

the molecular orbital contributions. Finally, �-aromaticity associated to surface electron delocalization has been ana-

lyzed by means of nucleus-independent chemical shift (NICS) calculations. The results point out that the stability of

the fused ring structure of propellanes I, II, and III, can be assigned to the remarkable �-aromaticity of the involved

three-member rings.

q 2007 Wiley Periodicals, Inc. J Comput Chem 28: 857–864, 2007

Key words: propellanes; DFT calculations; electron localization function; �-aromaticity; ring strain; nucleus inde-

pendent chemical shift

Introduction

Since the successful synthesis of [1.1.1] propellane by Wiberg

and Walker,1 numerous experimental2,3 and theoretical4 studies

have been devoted to understand the unusual structure and sta-

bility of this type of compounds. The remarkable stability of this

propellane and related derivatives in spite of its considerable

ring strain yields to these compounds new properties and poten-

tial applications in technological materials, which are being

explored, such as molecular machines.3

The elucidation of the nature of the interaction between

bridgehead carbon atoms (Ca, Ca0) in [1.1.1] propellane is a

controversial issue since the study of Jackson and Allen5 until

the very recent work presented by Luger and coworkers6 using

experimentally obtained electron density. The existence of some

kind of covalent bonding between Ca and Ca0 was elegantly pro-

ven in the seminal studies of Wiberg et al.7 using atoms-in-

molecules (AIM) theory.8 However, both experimental and theo-

retical investigations along the last decade have offered different

interpretations on the nature of the bridge bond in [1.1.1] propel-

lane and derivatives. Bond order indices of 0.53,9 0.70,10 and

0.79 were calculated using Mayer, Wiberg, and quadratic

valence indices methods,11 respectively; while a natural bond

orbital (NBO) analysis study showed that 15% of �*(Ca–Ca0)orbital is populated.12 Nalewajski and Broniatowska13 using den-

Contract/grant sponsor: Ministerio de Educacion, JdC Fellowship

Contract/grant sponsors: Ministerio de Ciencia y Tecnologıa (MCyT)

and DGICYT; contract/grant numbers: BQU2003-04168-C03-03 and

CTQ2006-15447-C02-01

Contract/grant sponsors: Generalitat Valenciana; contract/grant numbers:

GRUPOS03/176 and ACOMP06/122

Correspondence to: V. Polo; e-mail: [email protected]

q 2007 Wiley Periodicals, Inc.

sity deformation maps and molecular entropy displacement have

found that the [1.1.1] and [2.1.1] propellanes exhibit a partial

‘‘through-bridge’’ bond lowering the electron density between

the bridgehead atoms, while [2.2.1] and [2.2.2] propellanes

introduce a ‘‘through-space’’ character increasing the electron

and information densities in the central bond region. Very

recently, the development of experimental measures of the

charge density by X-ray diffraction14 has provided reliable data,

which confirm the particular features of the bridge bond in a

[1.1.1] propellane derivative.6

Another controversial aspect stands on the type of hybridiza-

tion at Ca and Ca0 carbon atoms forming the central bond; dif-

ferent tools yield contradictory results. In an earlier work, New-

ton and Schulman15 found sp4.13 hybridization of bridgehead

atoms using Edmiston-Ruedenberg localized orbitals, while Jar-

ret and Cusumano,16 measuring the Ca–Ca0 NMR spin–spin cou-

pling constants (1J(Ca, Ca0)), provided an estimation of sp0.5.

More recently, this dichotomy still persists; pure p-type charac-

ter for the Ca–Ca0 bond was determined from a study based on

an NBO analysis12, while 1J(Ca, Ca0) calculations,17,18 using ex-

perimental correlations, yield normal bonding in the range of

sp2.9 to sp4.0 (using experimental or theoretical values).

The type of bridge bond in propellanes must be related with

the ring-strain energy of the corresponding three- and four-mem-

ber rings. In the seminal articles of Cremer and Gauss,19 the un-

expected similar ring-strain energies of cyclopropane (27.5 kcal/

mol) and cyclobutane (26.5 kcal/mol) were justified by the ener-

getic compensation provided by the following contributions: (i)

the von Baeyer’s angle deformation theory,20 (ii) the classical

Pitzer or torsional strain,21 (iii) the 1,3 carbon–carbon bond

repulsion, (iv) the stretching strain of the C��C bonds, (v) the

rehybridization effect associated to C��H bond strengthening,22

and (vi) the �-electron delocalization or the so-called �-aroma-

ticity in three-member rings. Recently, nucleus-independent

chemical shift (NICS)23 calculations carried out by Schleyer and

coworkers,24,25 have been proved useful for the assessment the

�-(anti-)aromaticity in cyclopropane and cyclobutane, respec-

tively. Interestingly, cage hydrocarbons were found to magnify

the �-(anti-)aromaticity in three-(four) member rings, being

qualified as ‘‘super �-(anti)aromaticity’’. However, surface deloc-

alization in propellane systems was not investigated.

The analysis based on the electron localization function

(ELF)26 has proven to be a very useful tool to interpret different

types of bonding situations, such as the recently defined bond-

shift,27 aromaticity,28 and complex electronic rearrangements

along the reaction path involving chemical bond breaking/forming

processes.29 In the framework of the ELF analysis,30 a disynaptic

basin connecting two-core basins is considered a topological sig-

nature of a covalent electron-shared interaction. Moreover, the

populations are calculated from the integrated one electron density

over any basin and it is possible to reconstruct the charge density

in terms of the superposition of weighted mesomeric Lewis struc-

tures. On the basis of the rigorous definition of electron pairing

provided by the ELF,31 the bonding of a series of propellanes will

be investigated thoroughly in this work. The following systems,

formed by all possible combinations of three-, four-, or five-mem-

ber rings, have been selected: [1.1.1] (I), [2.1.1] (II), [3.1.1] (III),

[2.2.1] (IV), [3.2.1] (V), [2.2.2] (VI), [3.3.1] (VII), [3.2.2] (VIII),

[3.3.2] (IX), and [3.3.3] (X) (Scheme 1).

The article is organized as follows. Theoretical methods are

described in the following section. The Results and Discussion

section is composed of three parts. First, an ELF analysis on I–

X propellanes is performed to investigate the character of the

electron pair associated to the bridge bond and its behavior with

respect to the ring strain, going from I to X. Second, the ques-

Scheme 1. Compounds studied in this article: propellanes formed by three-, four-, and five-member rings.

Table 1. Valence Basin Populations (N) and Covariance Matrix (cov)

Elements of CnH2n Cyclo Alkanes.

C3H6 C4H8 C5H10

N[V(C, C0)] 1.76 1.83 1.86

N[V(C, H)] 2.07 2.04 2.02

hcov(C��C0,C��C@i �0.12 �0.12 �0.12

hcov(C��C0,C��Hi �0.15 �0.15 �0.15

858 Polo, Andres, and Silvi • Vol. 28, No. 5 • Journal of Computational Chemistry

Journal of Computational Chemistry DOI 10.1002/jcc

tion of the hybridization type of the Ca–Ca0 bond is studied by

dissection of the ELF bond basin into the molecular orbital

(MO) components. Third, new insights to the stability of propel-

lanes are found from the measure of �-aromaticity by means of

NICS calculations. Finally, the main conclusions arising from

this work are summarized in the last section.

Computational Methods and

Theoretical Procedures

All quantum mechanical calculations were carried out employ-

ing density functional theory-based methods, in particular, the

B3LYP exchange-correlation potential32 together with the Dun-

ning’s cc-pVTZ basis set33 as implemented in GAUSSIAN03.34

All stationary points were confirmed as minima via vibrational

frequency calculations. The Kohn–Sham orbitals were used to

analyze topologically the electron density and the electron local-

ization function (ELF) by using AIMPAC35 and TopMod36 pro-

grams, respectively. The graphical representation was plotted

using the MOLEKEL37 and MOLDEN38 programs. Nucleus-

independent chemical shift (NICS) calculations were computed

using the gauge-independent atomic orbital (GIAO) method39

for the B3LYP/cc-PVTZ optimized structures at geometrical

ring centers (for five-member rings, the center of the four atoms

lying in the same plane was considered). Finally, reliable calcu-

lation of ring-strain energies using homodesmic reactions for

I–X propellanes was performed using the highly accurate

G3(MP2) procedure.40

To understand the different factors, which determine the

bonding in propellanes, we will briefly investigate the effect of

the ‘‘ring strain’’ in small cycloalkanes. Previous investigations,

carried out by Chevreau and Sevin,41 have shown that the strain

in carbon compounds globally preserve a VSEPR (valence shell

electron pair repulsion)42 geometry of the valence basins. This

point is clearly illustrated by the valence attractor location. The

properties of V(C, C) basins, associated with the CC bonds,

remain as constant as possible. The main effect of the strain is

to modify the maximal electron localization in each V(C, C) ba-

sin. With the availability of the covariance analysis in TopMoD,

it is now possible to have a better insight onto the bonding in

the CnH2n series. Table 1 reports the populations and the covari-

ance matrix elements of the V(C, C) and V(C, H) valence

basins, which are consistent with the superposition of a purely

covalent cyclic and of two kinds of zwitterionic open structures.

For example, in the case of cyclopropane, the mesomeric struc-

tures displayed in Scheme 2 have to be considered to explain

the V(C, C) and V(C, H) populations of Table 1.

The zwitterionic structure (b) is responsible for the excess

over 2.0 of the V(C, H) and the rather small V(C, C) population.

Scheme 2. Proposed resonance structures of cyclopropane.

Table 2. B3LYP/cc-PVTZ-Optimized Geometrical Data (dCa–Ca0 [A]and apyr [8]), AIM Topological Parameters (Density (�) [eA�3] and

Laplacian (!2�) [eA�5] at the bcp), ELF Data (Populations

of V(Ca, Ca0) and V(Ca), V(Ca0) Basins, in Electrons).

Geom. AIM ELF

dCa��Ca0 apyr �(bcp)

!2

�(bcp)

N

[V(Ca, Ca0)]N

[V(Ca)]

I [1.1.1] 1.569 58.8 0.1897 0.0783 0.13 1.27

II [2.1.1] 1.648 67.4 0.1748 0.0608 0.27 1.04

III [3.1.1] 1.549 75.0 0.2146 �0.1719 0.90 0.54

IV [2.2.1] 1.582 79.0 0.2137 �0.2560 1.17

V [3.2.1] 1.525 86.3 0.2408 �0.4484 1.56

VI [2.2.2] 1.536 90.7 0.2592 �0.6473 1.72

VII [3.3.1] 1.514 92.3 0.2448 �0.4851 1.73

VIII [3.2.2] 1.554 95.8 0.2448 �0.5671 1.79

IX [3.3.2] 1.581 100.6 0.2294 �0.4814 1.83

X [3.3.3] 1.586 105.2 0.2244 �0.4610 1.89

Figure 1. ELF representation of [1.1.1] and [2.2.2] propellanes (I

and VI) for an isocontour value of � ¼ 0.80. Disynaptic basins are

colored in green, monosynaptic in orange, and core basins in purple

(hydrogenated basins are not displayed for clarity). [Color figure can

be viewed in the online issue, which is available at www.interscience.

wiley.com.]

859New Insights on the Bridge Carbon–Carbon Bond in Propellanes


The weight of this structure decreases with the ring strain as tes-

tified by the evolution of both V(C, C) and V(C, H) populations

along the series. It should be noted that the (a) and (c) structures

would yield identical averaged populations.

Results and Discussion

Electron Localization Function Analysis

Propellanes I–X are ordered by the pyrimidalization angle (apyr)defined as the average of the three hCCaCa0 angles around the

bridgehead carbon given by the B3LYP/cc-PVTZ optimized struc-

tures. Hence, propellanes I–V present apyr values lower than 908,corresponding to the so-called ‘‘inverted’’ bridgehead carbon

atoms. Three sets of data are shown in Table 2 for each propellane:

selected geometrical parameters (the interbridgehead distance

(dCa–Ca0) and apyr), AIM topological data (values of the electron

density and its Laplacian at the bcp), and ELF-basin populations.

As it can be observed, the distance between bridgehead atoms do

not follow any trend with respect to the degree of invertedness of

the bridge atoms: smaller propellanes (I–III) can present shorter or

longer distances than larger propellanes (IV–X).

The issue of bridge bonding in propellanes using AIM meth-

odology was discussed in detail in the seminal studies of

Wiberg,4 and their particular features were revealed. The exis-

tence of a bond path on the electron density connecting bridge-

head atoms with a (3,�1) bond critical point (bcp) supports

covalent-type bonding. On the other hand, propellanes I and II

present a depletion of density charge at the bcp typical of

closed-shell interactions, as it is shown by a positive value of

the Laplacian of the charge density at the (3,�1) bcp. Examina-

tion of deformation density plots show a lowering of the elec-

tron density in the bridge-bond region (see the more recent plots

in ref. 6). This bonding signature is characteristic of covalent-

depleted bonds.43

The ELF analysis allows to differentiate three groups for the

considered propellanes. Smaller propellanes I–III are character-

ized by a very lowly populated disynaptic basin between bridge-

head carbon atoms (V(Ca, Ca0)), and two monosynaptic basins

on Ca and Ca0 atoms (V(Ca) and V(Ca0)) outside the propellane

cage (Fig. 1a, note that the maximum value of V(Ca, Ca0) basinis � ¼ 0.57 whether an isocontour value of � ¼ 0.80 has been

chosen for the sake of clarity). Propellanes IV–VII possess

depleted V(Ca, Ca0) basins but the monosynaptic ones have dis-

appeared. Finally, larger propellanes VIII–X present bridge-bond

basins of electronic population similar to � C��C single bonds.

The presence of V(Ca) (and V(Ca0)) ELF attractor correlates

well with very early studies where an accumulation of the elec-

tron density in the bridgehead axis outside the cage was found.7

Hence, topological analysis of the Laplacian in the same region

yields a (3,�3) cp located at 0.950 Bohr from Ca atom along

the bridge axis whereas ELF attractor is found at 1.593 Bohr.

The attractor on the ELF field outside the propellane cage indi-

cates the existence of a nonbonding electron pair with an ELF

integrated electron population on each monosynaptic basin of

1.29, 1.04, and 0.54 e for I, II, and III, respectively. Taking into

account the ELF-basin populations of V(Ca, Ca0) and V(Ca),

V(Ca0) exclusively, compounds I–III can be described as the

superposition of three Lewis resonance structures (among others

Scheme 3. Proposed resonance structures for [1.1.1] propellane (I).

Table 5. Basin Populations in the Ca��CcH2�Cc H2��Ca0 Bridge and

in Cyclobutane.

II IV V

C4H8 [2.1.1] [2.2.1] [3.2.1]

V(Ca, Cc) 1.83 1.86 1.90 1.93

V(Cc, Cc0) 1.83 1.88 1.85 1.83

V(Cc, H) 2.04 2.03 2.04 2.04

Table 3. Calculation of Resonance Weights of Propellanes I–III.

The Total Population of V(Ca,Ca0), V(Ca), and V(Ca0) is Normalized

to 2.00 e, the Corresponding Normalization Factors Are 0.73, 0.85,

and 1.01, Respectively.

N[V(Ca, Ca0)]N[V(Ca)]þN[V(Ca0)] Ntot w1 w2 ¼ w3

I [1.1.1] 0.13 2.54 2.67 0.06 0.47

II [2.1.1] 0.23 2.08 2.35 0.12 0.44

III [3.1.1] 0.91 1.08 1.98 0.46 0.27

Table 4. Basin Populations in the Ca��CbH2��Ca0 Bridge and

in Cyclopropane.

I II III IV V

C3H6 [1.1.1] [2.1.1] [3.1.1] [2.2.1] [3.2.1]

V(Ca, Cb) 1.76 1.73 1.77 1.85 2.23 1.95

V(Ca, Ca0) 0.13 0.26 0.89 1.17 1.56

V(Ca) 1.27 1.03 0.53

V(Cb, H) 2.07 2.08 2.07 2.07 2.06 2.07

Table 6. Basin Populations in the Ca��CdH2��CeH2��Cd0H2��Ca0 Bridge

and in Cyclopentane.

III V

C5H10 [3.1.1] [3.2.1]

V(Ca, Cd) 1.86 1.96 1.99

V(Cd, Ce) 1.86 1.85 1.85

V(Cd, H) 2.02 2.01 2.02

V(Ce, H) 2.02 2.02 2.02



in which another C��C bond is opened, but these three account

for the Ca–Ca0 bond and for the V(Ca) monosynaptic basins)

(Scheme 3).

The calculation of weights w1 and w2þw3 yields 0.06 and

0.94 for I (Table 3). This approximation is rather rough because

it neglects many other structures, which could be deduced from.

Besides the high strain of the bridge bond, the wing C��C bonds

also present a considerable strain and part of its charge density

is transferred to the V(Ca) and V(Ca0) basins. The weight of the

covalent structure (1) increases for II and III to 0.12 and 0.46,

respectively. When a first ��CH2�� bridge is substituted by a

��CH2��CH2�� one, the weight of the ionic structures is

decreased; then, the V(Ca) population decreases while the V(Ca,

Ca0) population increases. The substitution by a ��CH2

��CH2��CH2�� magnifies this effect yielding weights of 0.46

and 0.54 for the covalent and ionic structures, respectively. Sub-

stitution of a second ��CH2�� bridge makes the V(Ca) basin

disappear in compounds IV–X. Propellane IV should be, how-

ever, considered as an intermediate case in which the structure

(c) of the mesomeric scheme of cyclopropane (Scheme 2)

replaces the (b) structure, explaining why the population of

V(Ca, C) exceeds 2.00 e and why there is no V(Ca) basin.

Indeed, the V(Ca, Ca0) population appears to be a reliable

measure of the total ring strain, being an interesting aspect the

correlation between V(Ca, Ca0) population and the pyramidali-

zation angle apyr. Tables 4–6 display the populations of the

CH2-related basins in propellanes I–V (Scheme 4). The V(C,

H) basin populations of propellanes are always equal to the

corresponding cycloalkane value. The populations of the

V(Cb, Cb0) or V(Cb, Cc) of the 2 and 3 bridges are larger than

the corresponding cycloalkane in the lightest molecules, and

they decrease towards the cycloalkane value as the pyramidali-

zation angle increases.

Orbital Contributions to the Bridgehead Lone Pair

and Bridge-Bonding Basins

Once the ELF basins have been characterized, it is interesting to

analyze the orbital contribution to these basins to identify the

molecular orbitals responsible for the bridge bond, V(Ca, Ca0),and the delocalized lone pairs, V(Ca) and V(Ca0). Contrary to

the recent investigations,9,18 and in agreement with the early

studies,7 using AIM analysis of [1.1.1] propellane, the HOMO

formed by the in-phase overlap of 2p� orbitals on the bridge-

head atoms (Fig. 2a) only makes a small contribution (one-

fourth) to the total population of V(Ca, Ca0) as it can be read

from Table 7. The main contribution to V(Ca, Ca0) in com-

pounds I–III (0.58, 0.44, and 0.33, respectively) comes from the

MO formed by the overlap of 2sp atomic orbitals (Fig. 2b) in a

similar way as it occurs in cyclopropane. The charge density

belonging to the monosynaptic basins V(Ca) and V(Ca0) comes

mainly (49, 41, and 39%, for I–III, respectively) from the

HOMO orbital.

Considering the orbital contributions to the bridge-bond ba-

sin, V(Ca, Ca0) for compounds IV–X, the replacement of three-

member rings by four- and five-member rings lead to a worse

overlap between the 2sp atomic orbitals. Therefore, the corre-

sponding MO systematically lowers its contribution to the bridge

bond. Nevertheless, the s-character of the bridge bond does not

disappear. Because of the enlargement of the bridge, the degree

of ‘‘invertedness’’ of Ca and Ca0 atoms decreases allowing the

HOMO to be formed by Ca, Ca0 atomic orbitals with more sp3

character.

Hence, in spite of the pure p-character of the HOMO in

smaller propellanes, the bridge bond presents a considerable s-

character because of the contribution from the overlapping 2sp

atomic orbital. These findings are in agreement with the estima-

tion of the sp-character from calculations on the interbridgehead

spin–spin coupling constant,18 1J(Ca, Ca0), pointing out that the

bonding in the bridge bond of [1.1.1] propellane is by no means

of pure p-character (sp2.9 using experimental or sp4.0 using theo-

retical values).

Scheme 4. Atom labeling for three-, four-, and five-member rings.

Figure 2. HOMO or 2p� molecular orbital (a) and the molecular

orbital formed by the overlapping 2sp atomic orbital (b) involving

all carbon atoms for [1.1.1] propellane (I).



NICS Assessment of �-(Anti-)Aromaticity in Propellanes

The �-aromaticity associated with the delocalization of �-elec-trons in the surface of the cyclopropane ring has been estimated to

stabilize the system around 30 kcal/mol.19 Recently, Schleyer and

coworkers24 have proven the usefulness of NICS calculations to

reveal �-(anti-)-aromaticity for three-(four) member rings and

cage hydrocarbons. Henceforth, further insight into the �-aromac-

ity in propellane systems can be achieved by inexpensive NICS

calculations at each of the three-ring centers (for cyclopentanes,

the planar structure was considered). For the sake of comparison,

cyclopropane, cyclobutane, and cyclopentane are also considered.

The NICS results are gathered in Table 8, together to ring-strain

energies (RSE) calculated by means of homodesmic reactions44

using eq. (1), conveniently adjusted by the stequiometric coeffi-

cients, at the highly accurate G3(MP2) level.

Interestingly, all propellanes formed by three-member rings

present strong diatropic currents in the �-plane larger than cyclo-

propane (�43.7 ppm), which is considered to be the archetypal �-aromatic system. The more extreme NICS value corresponds to

compound I, where a value of �60.7 ppm is found at each ring

center. In contrast, four-member rings present small paratropic

values of NICS. The more �-antiaromatic system is propellane VI

displaying a paratropic NICS comparable to cyclobutane. As

expected, five-member rings present moderate diatropic NICS val-

ues. Inspection of RSE in Table 8 shows that �-antiaromatic sys-

tems present larger ring-strain energies when compared with the

aromatic analogues. It is worth noting that in comparison between

propellanes V and VI, although both possess the same total num-

ber of ��CH2�� bridge carbons, the high �-aromaticity of the for-

mer in the three-member ring and the considerable �-anti-aroma-

ticity of the latter are important factors to explain why the RSE of

VI is 28.43 kcal/mol larger than V. However, the interpretation of

the contributions to the RSE is not straightforward. In particular,

Table 7. ELF-Basin Population (N), Covariance (�2), Lambda (�), and Orbital Contributions for

the V(Ca, Ca0) and V(Ca). Orbital Percentages Are Normalized to 1, the First Column Correspond

to the HOMO Orbital (labeled also 2p�), the Second to the Orbital Formed by the Combination

of 2sp Atomic Orbitals and Other Nonnegligible Contributions Are Collected in the Third Column

(the Number of the MO is Indicated in Parenthesis).

ELF basin N �2 �

Orbital percentage

HOMO

(2p�)

Orbital

2sp

Other

MOs

I [1.1.1] V(Ca, Ca0) 0.13 0.12 0.95 0.25 0.58 0.17 (8)

V(Ca) 1.27 0.83 0.66 0.49 0.21 (9)

II [2.1.1] V(Ca, Ca0) 0.26 0.23 0.91 0.24 0.44 0.16 (10)

V(Ca) 1.03 0.72 0.7 0.41 0.16 (11) 0.10 (17)

III [3.1.1] V(Ca, Ca0) 0.89 0.67 0.75 0.26 0.33 0.13 (12)

V(Ca) 0.52 0.43 0.83 0.39 0.17 (13) 0.13 (20)

IV [2.2.1] V(Ca, Ca0) 1.17 0.81 0.69 0.28 0.27 0.14 (12)

V [3.2.1] V(Ca, Ca0) 1.56 0.96 0.61 0.29 0.23 0.10 (14)

VI [3.3.1] V(Ca, Ca0) 1.73 1 0.58 0.30 0.21 0.12 (16)

VII [2.2.2] V(Ca, Ca0) 1.72 0.98 0.57 0.30 0.21 0.15 (12)

VIII [3.2.2] V(Ca, Ca0) 1.79 0.99 0.55 0.31 0.18 0.09 (16)

IX [3.3.2] V(Ca, Ca0) 1.83 1 0.55 0.41 0.22 0.13 (15)

X [3.3.3] V(Ca, Ca0) 1.89 1.01 0.54 0.32a 0.12 0.10 (15) 0.16 (20)

aThe contribution corresponds to the HOMO-2 orbital instead of HOMO.

Table 8. NICS Values for [abc] Propellanes at the Geometrical Center

(Except Five-Member Rings) of the a-Ring, b-Ring, and c-Ring

and G3(MP2) Ring-Strain Energies (RSE, in kcal/mol) Given

by Homodesmic eq. 1.

a-ring b-ring c-ring RSE

C3H6 �43.7

C4H8 þ3.2

C5H10 �10.9

I [1.1.1] �60.6 �60.6 �60.6 100.57

II [2.1.1] �8.1 �53.2 �53.2 100.11

III [3.1.1] �17.1 �53.1 �36.5 77.07

IV [2.2.1] �2.6 �2.6 �48.8 100.68

V [3.2.1] �17.3 �7.0 �48.1 67.15

VI [2.2.2] þ3.2 þ3.3 þ3.3 95.58

VII [3.3.1] �17.3 �15.6 �48.3 41.05

VIII [3.2.2] �11.8 �0.1 þ0.4 61.25

IX [3.3.2] �10.9 �11.0 �3.1 32.56

X [3.3.3] �13.0 �13.0 �13.0 11.20



separation between bridge-bond energy and �-aromaticity in pro-

pellanes is not an easy task, as it has been pointed out in previous

studies about the determination of bond energies from Grimme45

and Exner and Schleyer.46

Conclusions

The nature of the bridge bond in propellanes has been investi-

gated by means of the ELF analysis. To obtain a consistent eval-

uation of the effect of ring strain on the electron pair forming

the bridge bond, the central ��CH2�� bridge is systematically

replaced by ��CH2��CH2�� and ��CH2��CH2��CH2�� units.

Three situations can be found: (i) larger propellanes (VIII–X)

present typical � C��C single bond, (ii) propellanes IV–VII

show depleted V(Ca, Ca0) basin population as a consequence of

the increase of the ring strain, and (iii) smaller propellanes (I–

III) present an intermediate structure between two resonance

forms: one with a nonbonding electron pair partially delocalized

between Ca and Ca0 atoms outside the cage (ionic) and the other

with a bridge bond between the same atoms (covalent). The con-

tribution of the ionic form is estimated from ELF-basin popula-

tions in 94, 88, and 54% for I, II, and III, respectively. This

finding seems to be inconsistent with early studies where a bond

dissociation energy of 65 kcal/mol was postulated for the bridge

bond of I using isodesmic reactions. An explanation for this

apparent contradiction comes from the outstanding �-aromaticity

measured at the center of the three-member rings by means of

NICS calculations. NICS values of �60.7 ppm are found at the

ring centers of [1.1.1] propellane, pointing out that a consider-

able part of the calculated bond dissociation energy must corre-

spond to the dramatic increment of �-aromaticity rather than the

proper bridge-bond strength. The issue of the sp-hybridization of

the bridge bond has been addressed by the examination of the

orbital contributions to the Ca–Ca0 ELF bonding basin to com-

plement insights given from NMR 1J(C,C) data. Two different

types of molecular orbitals (2p� along the interbridgehead axis

and 2sp atomic orbital) are found to participate in the electronic

density corresponding to the bridge-bond basin depending on the

size of the propellane.

Acknowledgments

The authors are grateful to the Servei d’Informatica, Universitat

Jaume I for generous allotment of computer time.

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new insights on the bridge carbon–carbon bond in propellanes: a theoretical study based on the...

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