Rehybridization as a General Mechanism for Maximizing
Chemical and Supramolecular Bonding and a Driving
Force for Chemical Reactions
IGOR V. ALABUGIN, MARIAPPAN MANOHARAN
Department of Chemistry and Biochemistry, Florida State University, Tallahassee,Florida 32306-4390
Received 30 April 2006; Revised 6 June 2006; Accepted 7 June 2006DOI 10.1002/jcc.20524
Published online in Wiley InterScience (www.interscience.wiley.com).
Abstract: Dynamic variations in hybridization patterns (rehybridization) were analyzed at B3LYP/6–31G** and
MP2/6–31þG* levels. Computations clearly illustrate the generality of rehybridization in a variety of chemical phe-
nomena, which involve structural reorganization in hydrogen-bonded complexes, nonhyperconjugative stereoelec-
tronic effects in saturated heterocycles, Mills-Nixon effect, and contrasting substituent effects in cycloaromatization
reactions.
q 2006 Wiley Periodicals, Inc. J Comput Chem 28: 373–390, 2007
Key words: rehybridization; s-character; hybridization; hydrogen bonding; stereoelectronic effects; cycloaromatiza-
tion; strain
Introduction
Hybridization,1 or mixing of orbitals at an atom, adds direction-
ality to the classic Lewis concept of covalent bond as a shared
electron pair.2 In the most familiar example, one s and three p
orbitals blend in the textbook picture of the four sp3-hybridized
orbitals that point to the corners of regular tetrahedron and form
the four identical bonds in methane. Expansion of this model
describes chemical bonding and geometries of other saturated or-
ganic systems whereas sp2 and sp hybridization patterns readily
explain structural features of alkenes and alkynes. The concept
is equally useful for elements other than carbon.3
Didactically, hybridization can be described using the
sequence of electron promotion and orbital mixing as shown in
Figure 1. Although electron promotion of valence s-electrons to
the respective p-subshell is energetically unfavorable (It is re-
markable that all organic chemistry derives from an excited state
of a carbon atom!), its cost is more than compensated by the
subsequent formation of stronger chemical bonds made possible
by the directionality of newly available set of singly occupied
hybrid orbitals. In a classic work, Kutzelnigg also outlined two
other reasons for isovalent hybridization displacement of lone
pairs in the opposite direction to the s-bonds and increase of the
valence angle. Both changes decrease ‘‘Pauli repulsion’’ (‘‘Fermi
repulsion’’ between occupied orbitals).4 Since hybrid orbitals are
simply a linear combination of the original atomic orbitals
(AOs), their formation (hybridization per se) at an isolated atom
is just a mathematical operation that does not involve an energy
cost. This model illustrates both the cost paid for the involve-
ment of low energy s electrons in chemical bonding and the role
of hybridization as a mechanism to maximize chemical bonding.
As a consequence, hybridization changes in response to external
or internal perturbations when such a change increases stability
of a molecular or supramolecular system. These dynamic devia-
tions from the common hybridization patterns are translated into
structural changes and energetic consequences, and can be often
probed experimentally through secondary kinetic isotope effects.
We will call such effects rehybridization, the phenomenon that
will be the topic of this article. After a general analysis of rehy-
bridization trends in saturated and unsaturated compounds using
DFT and ab initio calculations, we will illustrate diversity and
generality of rehybridization in organic and supramolecular
chemistry and the utility of this concept in the design of organic
reactions.
Computational Methods
All computations were performed using Gaussian 03.5 Trends in
hybridization were estimated at two computational levels. Intra-
molecular effects were analyzed at the B3LYP/6–31G** level6
whereas MP2/6–31þG* calculations better suited for the
description of noncovalent interaction were used to describe
Correspondence to: I. V. Alabugin; e-mail: [email protected]
q 2006 Wiley Periodicals, Inc.
hydrogen bonded complexes.7 Reaction profiles for Bergman
cyclizations were calculated using Broken-Spin (BS) unrestricted
B3LYP/6–31G** level.8 Second order force constant matrix
indicated that all equilibrium geometries are true minima
whereas the transition state structures have first order saddle
point character. X��H � � �Y geometry scans of red- and blue-
shifting H-bonds were performed by constraining the H � � �Ydistance in 0.3 A steps with the Opt ¼ ModRedundant option,
and allowing all other structural variables to be optimized.
Hybridization was analyzed quantitatively using natural bond or-
bital (NBO) analysis,9 which is implemented in Gaussian. NBO
analysis involves sequential transformation of nonorthogonal
AOs to the complete and orthonormal sets of ‘‘natural’’ atomic
orbitals (NAOs), hybrid orbitals (NHOs), and bond orbital
(NBOs). These localized basis sets describe electron density and
other properties by the smallest number of filled orbitals in the
most rapidly convergent fashion. These orbitals are closely
related to the localized orbitals (bonds and lone pairs) used by
organic chemists and, thus become increasingly useful in trans-
lating quantum mechanical results into the language of organic
chemistry (For an illustrative rather than an exhaustive list of
recent applications of NBO method for analysis of chemical
bonding, see ref. 10.) and for reintroduction of VB concepts
such as hybridization for the analysis of ab initio and DFT
results. Importantly, NBO analysis does not enforce �–� separa-
tion or otherwise treat it in an arbitrary fashion. Thus, the natu-
ral localized orbitals (NLMOs) and underlying NBOs are free to
adopt optimal hybridized forms that maximize descriptions of
electron density.9 Other popular localization methods11 may pro-
vide slightly different numbers but all general trends should
remain valid.
Monosubstituted Ethane (sp3), Ethylene (sp2),
and Acetylene (sp)
Direct Rehybridization
We will lay the foundation for the following discussion with
analysis of the general hybridization trends in monosubstituted
ethanes, ethylenes, and ethynes with C��X bonds to group III–
VII, first row substituents (BH2 to F in Tables1 and 2). The major
effect is concentrated at the carbon hybrid orbital directed to-
ward the substituent s-character at the carbon hybrid orbital di-
rected to substituent X decreases as electronegavity of X in-
creases (Tables 1 and 2). This trend reflects a general correlation
between hybridization and electronegativity (commonly referred
to as the Bent’s rule) that states that ‘‘atomic s-character tends
to concentrate in orbitals that are directed toward electropositive
groups and atomic p-character tends to concentrate in orbitals
that are directed toward electronegative groups.’’ A modified
Bents’ rule accommodates bonding in heavier main group ele-
ments and transition metals. See ref. 3. for a more detailed dis-
cussion.12,13 These values illustrate that hybridization is not set
in stone and can deviate considerably from the textbook values
when such deviations are stabilizing. For example, the carbon
orbitals of the C��F bonds are about sp4-hybridized in alkanes,
sp3-hybridized in alkenes, and sp2-hybridized in alkynes. For an
illustrative example of structural and energetic consequences of
rehybridization by an electropositive (Li) substituent, see ref. 14.
The direct rehybridization effects are especially significant in
alkynes where the electron acceptors show the most significant
effects (16.8% difference in the s-character of hybrids directed
to BH2 and F). In line with the Bent’s rule, attachment of a fluo-
rine atom at a sp-hybridized carbon (*50% s-character) is more
unfavorable than formation of C��F bond at a sp2-hybridized
carbon of an alkene (*33% s-character) or at a sp3-hybridized
carbon of an alkane (*25% s-character).
Interestingly, even these simple molecules show nontrivial
structural effects. For example, the classic linear geometry of
alkenes and linear geometry of alkynes are about 1 kcal/mol
higher than the global energy minimum for several model unsat-
urated systems with acceptor substituents. In fact, these
‘‘classic’’ geometries are not even local minima. The geometrical
distortions are not large: the HCCN dihedral in aminoethene is
3.98 whereas the CCX angles in aminoethyne and hydroxyethyne
are 177.08 and 176.88, respectively. However, NBO analysis
suggests that electronic distortions and changes in hybridization,
in particular, are significant as illustrated by the respective devi-
ations from the almost perfect correlations shown in Figure 2.
NBO analysis also shows that such deviations from the clas-
sic VSEPR geometries are accompanied by the breakdown of
the �, �-separation (Indeed, �–� separation is enforced (or oth-
erwise treated in rather arbitrary fashion) in some LMO meth-
ods, whereas NLMOs (and underlying NBOs) are inherently free
to adopt optimal hybridized forms that maximize description of
electron density.), which can be traced back to the Bent’s rule.
Since allocating significant amount of s-character to the sigma
bonds with acceptor substituents is unfavorable, carbon
‘‘borrows’’ some of the p-character from the p-orbital allocated
to the �-bonds.Such partial rehybridization leads to pyramidalization at the
substituted carbon.15 and, most interestingly, to the NBO
description of the C¼¼C moiety as two banana bonds with 44–
568 orbital deviations from line of nuclear centers (as also ana-
lyzed recently by Weinhold and Landis).16 Both of the two ba-
nana bonds interact strongly with the lone pair on nitrogen with
the combined energy of n(N) ? �*(CC) interactions in the order
of 15 kcal/mol, according to the perturbational NBO analysis.
The fully planar aminoethylene is only 1.2 kcal/mol higher in
energy than the global minimum. Since fluoroethene and fluo-
Figure 1. Formation of sp3 hybrid orbitals from the valence atomic
orbitals of an isolated carbon atom.
374 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
Table 1. The s-Character of C in C��R and C��C Bonds, the Average s-Character of C in C��H Bonds, the
Energies of Hyperconjugative Interactions (C��R Behaves as Donor as well as Acceptor) Along With the
C��C Bond Distances in 1-Substituted Ethanes and Ethylenes Calculated at the B3LYP/6–31G** Level.
s-char of C in,
C��R (%)
s-char of C
in C��Ha (%)
s-char of C
in C��Hb (%)
s-char of C
in C��Hc (%)
s-char of C
in C(R)��C (%)apol of C in
C(R)��C (%)b
Energy
(�CH ? �*CR)
(kcal/mol)
Energy
(�CR ? �*CH)
(kcal/mol)
r(C��C)
(A)
R ¼¼ H 23.97 23.97 23.97 23.97 28.10, 28.10 50.00 2.68 2.68 1.5301
R ¼¼ BH2 30.21 22.87 24.31 24.22 25.97, 27.15 50.96 2.08 2.61 1.5578
R ¼¼ CH3 27.05 22.97 23.73 24.06 27.05, 28.47 49.94 3.12 1.64 1.5317
R ¼¼ NH2 23.87 23.78 23.70 24.13 28.67, 28.47 50.79 4.11 1.14 1.5340
R ¼¼ OH 20.95 25.14 24.19 23.86 28.94, 27.76 50.26 3.90 1.42 1.5191
R ¼¼ F 18.66 25.69 24.28 23.91 30.07, 27.54 49.04 4.72 1.26 1.5153
R¼¼ H 30.22 30.22 30.22 30.22 39.54, 39.54 50.00 4.36 4.36 1.3299
R¼¼ BH2 36.29 25.27 30.12 30.58 38.32, 39.29 51.51 3.41 4.73 1.3375
R ¼¼ CH3 32.73 28.17 29.98 30.36 39.08, 39.63 50.74 5.88 2.53 1.3328
R ¼¼ NH2(np)c 29.08 29.37 30.40 31.00 25.71, 23.47d 48.60 7.34 1.50 1.3388
R ¼¼ NH2(p)c 29.16 29.09 30.60 31.15 41.82, 38.22 51.43 7.53 1.35 1.3415
R ¼¼ OH 25.37 31.68 31.07 30.88 43.03, 38.02 50.44 7.52 1.51 1.3312
R ¼¼ F 22.72 33.31 31.26 30.97 44.01, 37.73 49.57 8.05 1.55 1.3242
aFirst value belongs to the carbon attached to the R group whereas the second one to the unsubstituted carbon.bPolarization for the carbon with R group.cWhere np is nonplanar structure and p is planar geometry.dThis unusual s-character in aminoethylene is due to the breakdown of the sigma-pi-separation discussed above. The
s-characters in the 1.18 kcal/mol less stable planar alkene with a single imaginary frequency fits very well to the cor-
relations shown in Figure 2.
Table 2. Carbon s-Character in C��R, C��C, and C��H Bonds Along with the C��C Bond Length in
Monosubstituted Ethynes at the B3LYP/6–31G** Level.
s-char of C
in C��R (%)
s-char of C
in C��H (%)
s-char of C
in C(R)��C (%)apol C in
C(R)��C (%)b r (C��C) (A)
R ¼¼ H 48.05 48.05 51.83, 51.83 50.00 1.2053
R ¼¼ BH2 53.08 47.53 46.91, 52.33 50.75 1.2183
R ¼¼ CH3 47.53 48.18 52.39, 51.69 50.80 1.2074
R ¼¼ NH2 (bent) 42.83 49.08 42.93, 36.70c 49.59 1.2097
R ¼¼ NH2 42.70 49.26 57.20, 50.58 50.90 1.2115
R ¼¼ OH (bent) 38.66 49.92 52.01, 41.70c 50.06 1.2059
R ¼¼ OH 38.54 49.98 61.19, 49.92 50.78 1.2081
R ¼¼ F 36.27 50.54 63.54, 49.29 48.77 1.2005
aThe first value is for the substituted carbon. The second value is for the unsubstituted carbon.bPolarization of C��C bond (NBO coefficient the substituted carbon).cThe unusual hybridization of amino and hydroxyacetylenes is due to the non-linearity of the CCX moiety and the
breakdown of the �—� separation. The s-character in the less stable (1.18 and 0.96 kcal/mol, respectively) planar
systems with single imaginary frequency fits very well to the correlations in Figure 2.
375Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
roethyne do not show unusual hybridization patterns and fall
back at the correlation shown in Figure 2, hybridization changes
in the above NH2�� and OH�� substituted systems are likely to
be assisted by the �-donor effects that involve lone pairs of N
and O.16
Although it would be very interesting to analyze these struc-
tures with other localization techniques, (12c) the parallel be-
tween electronic and structural changes strongly supports gener-
ality of the above phenomena. Importance of such rehybridization-
promoted breakdowns of �, �-separation is further underscored
by a recently reported rehybridization effect that leads to mixing
of s-character in �*-orbitals of single-walled carbon nanotubes
that lowers energy of states in the conduction band, ‘‘exactly the
same mechanism contributes to the high electron affinity of the
fullerenes.’’17 The rehybridization effects in such simple closed
shell neutral molecules are further amplified in highly reactive
species. For the significant role of rehybridization in stabilization
of spin and charge in distorted radical cations, see ref. 18.
Secondary Rehybridization
A set of more subtle second order effects involve changes at
hybrid carbon orbitals in C��H and C��C bonds. These changes
occur in response to change in s-character in C��(R) hybrid (pri-
mary rehybridization) because of the conservation of total s-
character at a given carbon (s-character should add up to 100%,
or one s-orbital, for the four hybrid orbitals taken together). Of
course, the total amount of p-character at a given atom is also
conserved. We assume that contribution of d-orbitals is negligi-
ble for the first row elements. In general, if an atom is only
using one s and three p orbitals to form hybrid AOs (in other
words, when d-orbitals are not involved in bonding), then all
hybrid AOs will be just linear combinations of the initial four
AOs and thus neither s- nor p-character can disappear during the
hybridization process.
As electronegativity of R increases and amount of s-character
at carbon hybrid orbital in the C��R bond decreases, the com-
bined amount of s-character in other hybrids at this carbon
increases to compensate for the C��R bond reorganization (see
Fig. 4). Since this secondary effect directly results from the con-
servation of s- and p-character, it is also an indirect consequence
of the Bent’s rule. Interestingly, the secondary rehybridization is
not distributed in the remaining three bonds equally. Even
though all geminal bonds get more s-character and become more
polar when electronegative substituents are introduced (Table 1),
the net variation in the s-character in the hybrid orbital directed
to the second carbon is twice of that in each of the �-C��H
bonds. Increased rehybridization of the C(R)��C bond is quite
likely to be facilitated by the fact that unlike hydrogens in the
C��H bonds, the carbon-centered orbital at the other end of the
C��C bond can also adjust hybridization. This change, in turn,
changes hybridization of other orbitals at the �-carbon etc.
Although the rehybridization effects do not spread far in the
neutral hydrocarbon systems, these simple molecules illustrate
how hybridization effects propagate through the sigma frame-
work contributing to the inductive effect.
In alkanes, rehybridization at each carbon is distributed
between four orbitals. In contrast, as long as the �-separation is
preserved in alkenes and alkynes (As follows from the previous
section, this is not always a safe assumption!), these unsaturated
molecules have only three and two hybrid orbitals, respectively,
at each carbon. In the classic picture where the �- and �-systems
of alkenes and alkynes are clearly separated, p-orbitals constitut-
ing the �-bonds still retain 100% of p-character, thus preserving
parallel arrangement of the two p-orbitals in the �-bonds. Thedifference in number of participating hybrids translates in differ-
ences in the efficiency of rehybridization.
Although the overall change in the carbon s-character in the
alkene C��R bonds is comparable with that in alkanes (13.6%
vs. 11.6), secondary rehybridization in the remaining hybrids at
the substituted carbons is noticeably different. Unlike alkanes,
�-C��H bonds in alkenes rehybridize slightly more than �-car-bon in the C��C bond (6.0 vs. 5.7%). Overall, the change in
hybridization of �-C��H bonds is twice of that in each �-C��H
bond of respective alkanes. Such dependence should lead to sig-
nificantly larger effects of substituents on acidity, strengths, and
geometry of �-C��H bonds in alkenes than in alkanes.
Since there are no �-C��H bonds at the substituted carbon of
alkynes in Table 2, the internal hybrid at this carbon (forming
the C��C bond) has to rehybridize to the same extent but in the
opposite direction as the external carbon, thus achieving the un-
Figure 2. Correlation of electronegativity of atom and substituent in
R with s-character of hybrid orbitals at C1 in C1��R and C1��C2
bonds of monosubstituted ethanes, ethenes, and ethynes at the
B3LYP/6–31G** level. Deviations for the three ‘‘anomalous’’ systems
shown in Figure 3 are indicated with the empty diamond and squares.
376 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
usual sp0.6 character in fluoroethyne. These unfavorable hybrid-
ization patterns are associated with the extreme instability and
scarcity of fluoroalkynes.19
Hybridization and rehybridization trends become more com-
plicated beyond the first row where valence p-orbitals become
considerably more diffused than the corresponding s-type AOs
and ‘‘hybridization defects’’ become more important as analyzed
in detail by Kutzelnigg.4 Applicability of simple rehybridization
models to heavier elements should be analyzed carefully in the
future. However, for carbon compounds such deviations are
unlikely to be large (3c) and a discussion of hybridization, direc-
tionality, and conservation rules based on the NBO method
should be of general importance.
In summary, it is clear that the efficiency of rehybridization
depends on initial hybridization and, thus, is different in alkanes,
alkenes, and alkynes. Two examples from the selection given
below will illustrate how hybridization trends characteristic for
alkyne moiety render an otherwise unfavorable transformation
(the Bergman cyclization) exothermic and explains why blue-
shifting, or improper, H-bonding is uncharacteristic for alkynes,
even though respective alkanes and alkenes readily form analo-
gous blue-shifted C��H � � �Y complexes. Other examples will
illustrate ubiquity of rehybridization in stereoelectronic, reso-
nance, and strain effects.
Hybridization and Stereoelectronic Effects
Although hybridization is an atomic property, its importance
extends to interaction of orbitals located at different atoms such
Figure 3. Computed geometries of the global minima for aminoethylene, aminoacetylene, and hydroxy-
acetylene at the B3LYP/6–31G** level. NBO hybridization of C in C��C and the energy (kcal/mol)
of interaction of lone pair with �* (C¼¼C) (in green) obtained for optimized as well as constrained
structures of the above three systems and also for the optimized hydroxyethylene, fluoroethylene, and
fluoroacetylene.
Figure 4. Correlation of electronegativity with the s-character of C in
selected C��H bonds in monosubstituted ethanes (bold line), ethenes
(normal line), and ethynes (dashed line) (�-bonds for alkanes and
alkenes and �-bonds for alkynes) at the B3LYP/6–31G** level.
377Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
as stereoelectronic effects. Stereoelectronic effects develop
through interaction of electronic orbitals in space and are maxi-
mized at certain spatial arrangements. Thus, such effects provide
a connection between structure and reactivity. Six-membered
saturated heterocycles are convenient, conformationally defined
model systems for understanding of structural, spectroscopic,
and energetic consequences of stereoelectronic interactions.20,21
Hybridization and Energies of Lone Pairs
Particularly interesting is the effect on hybridization on shapes
and energies of lone pairs—donor orbitals that play dominant
role in stereoelectronic effects.22
Table3 and Figure 5 summarize these effects in a family of
saturated heterocycles derived from cyclohexane. Differences in
hybridization impact stereoelectronic interactions in several
ways. First, hybridization determines the direction in which non-
bonding orbitals are projected in space (the valence angles) and,
thus, controls the overlap with the respective acceptor orbitals.
Second, hybridization determines the relative size of the two
lobes of a lone pair. The front and back lobes are equivalent
only in purely p-lone pairs whereas increase in the s-character in
Table 3. The NBO s-Character, Hybridization and Energy of all Lone Pairs (X ¼¼ N, O, S, Se) in
Heterocyclohexanes Calculated at the B3LYP/6–31G** Level, the NBO Plots of the Lone Pairs and
s-Character in C��X Bonds.a
s-character in n(X) (%)b spn (X) E(X) (a.u.)a n(X)axc n(X)eqc s-character in C��X (%)c
0.03 (44.16) p (sp1.26) �0.27 (�0.54) 20.53 (C); 27.89 (O)
0.03 (69.89) p (sp0.43) �0.22 (�0.61) 20.54 (C); 15.18 (S)
0.05 (76.66) p (sp0.30) �0.21 (�0.67) 18.51 (C); 11.74 (Se)
17.99 sp4.55 �0.27 – 23.51 (C); 29.94 (N)
17.86 sp4.59 �0.27 – 23.62 (C); 29.65 (N)
aThe axial and equatorial lone pairs are plotted as dissected by Hax��C3��X1 or Heq��C3��X1 planes, respectively.bFor X¼¼O, S, Se, the data for the equatorial lone pairs are given in parentheses.cs-Character in hybrid orbitals forming C¼¼X (X¼¼N, O, S, Se) bonds.
Figure 5. Hybridization effects at the energies (NBO values in har-
trees) of equatorial lone pairs in oxa-, thia-, selena-, and azacyclo-
hexane calculated at the B3LYP/6–31G** level. Energies of respec-
tive axial lone pairs are given for comparison.
378 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
hybrid spn lone pairs adds directionality to these orbitals and
decrease the size of the back lobe. Third, hybridization of a do-
nor orbital influences its absolute energy (see Fig. 5). Increase in
the p-character raises orbital energy and decreases energy gap
between the donor lone pair and an acceptor �*- or �*-orbital.As a result, lone pairs with 100% p-character are intrinsically
better donors than related spn hybrids. These, sometimes subtle
effects, are associated with interesting electronic consequences.
For example, lone pairs of the oxygen atom in water rehybridize
upon H-bond formation from a p- and a spn lone pairs into a
pair of spm hybrids.3a,23
Energies of Lone Pairs
The interplay between hybridization (percentage of s-character)
and electronegativity of X leads to interesting relative trends in
the orbital energies. Because orbital energies of lone pairs can
be lowered through either an increase in electronegativity or
through a decrease in p-character, the purely p (pseudo) axial
lone pair on oxygen has essentially the same energy as the sp5
nitrogen lone pairs, despite greater electronegativity of oxygen.
In this case, effects of hybridization and electronegativity com-
pensate each other. Another interesting trend is observed for the
lone pairs of chalcogens: the energies (and donor ability) of
axial lone pairs increase when going from oxygen to selenium
(O < S < Se), whereas the energies and donor ability of equato-
rial lone pairs follow the opposite direction (O > S > Se).16
The first trend is explained by the difference in electronegativity
and the period number, the second trend by the increase in the
s-character for S and Se relative to that of O. As a result of
these two effects, the energy gap between the axial and equato-
rial lone pairs of chalcogens increases with their atomic number.
In every case, the higher energy axial orbitals with 100% p-char-
acter should be intrinsically better donors than the respective
equatorial spn hybrids. These fundamentally important effects
are analyzed in more detail in our recent article,24 which illus-
trates that O- and S-heterocycles are considerably different from
their N-analogues and, thus, stereoelectronic effects observed in
O-heterocycles cannot be automatically transferred to the N-het-
erocycles and vice versa.
Table 4. Effect of Heteroatom X on Hybridization (s-Character in Carbon Hybrids) in the
X(1)��C(2)H2��C(3)H2 moiety, C(3)H Bond Lengths and Polarization at the B3LYP/6–31G** Level.
a (s-char)a b (s-char)a c (s-char) d (s-char) r (C���H)ax r (C���H)eq
pop �*
(C���H)ax
pop �*
(C���H)eq
pol
(C���H)axb
pol
(C���H)eqb
Group 1
X¼¼Y¼¼CH2 22.58 23.55 22.58 23.55 1.0996 1.0968 0.0154 0.0105 38.44 37.94
X¼¼NHax¼¼Y¼¼CH2 23.47 24.36 22.65 23.77 1.0998 1.0975 0.0154 0.0119 38.57 37.92
X¼¼Y¼¼NHax 23.53 24.63 22.77 24.01 1.0997 1.0979 0.0154 0.0128 38.68 37.91
Group 2
X¼¼NHeq, Y¼¼CH2 24.07 24.44 23.10 23.60 1.0970 1.0965 0.0155 0.0103 37.92 38.02
X¼¼O, Y¼¼CH2 24.70 25.35 23.11 23.77 1.0973 1.0969 0.0152 0.0112 37.97 37.88
X¼¼S, Y¼¼CH2 24.85 24.79 23.10 23.32 1.0969 1.0982 0.0151 0.0137 37.72 37.80
X¼¼Se, Y¼¼CH2 25.59 25.49 23.01 23.22 1.0969 1.0990 0.0153 0.0150 37.67 37.80
X¼¼NHax, Y¼¼NHeq 23.59 24.60 23.17 23.82 1.0972 1.0971 0.0153 0.0114 38.05 37.98
X¼¼O, Y¼¼NHax 24.20 25.20 23.23 24.03 1.0973 1.0973 0.0151 0.0122 38.09 37.87
X¼¼S, Y¼¼NHax 24.21 24.71 23.17 23.43 1.0971 1.0986 0.0151 0.0143 37.83 37.75
Group 3
X¼¼Y¼¼NHeq 24.12 24.70 23.65 23.66 1.0947 1.0959 0.0154 0.0096 37.38 38.05
X¼¼Y¼¼O 24.85 25.82 23.71c 24.07c 1.0951 1.0965 0.0147 0.0114 37.46 37.80
X¼¼Y¼¼S 24.88 24.68 23.64 23.11 1.0948 1.0991 0.0150 0.0156 37.02 37.62
X¼¼O, Y¼¼S 24.88 25.30 23.62 23.42 1.0950 1.0983 0.0148 0.0140 37.20 37.70
X¼¼O,Y¼¼NHeq 24.50 25.24 23.66 23.82 1.0949 1.0963 0.0150 0.0107 37.43 37.94
X¼¼S, Y¼¼NHeq 24.50 24.69 23.60 23.32 1.0948 1.0979 0.0152 0.0132 37.20 37.86
aAverage s-character of both �-carbons is provided for the unsymmetrically substituted systems.bPolarization of carbon at the C��H bond.cThe slight deviation for X, Y¼¼O requires further analysis.
Figure 6. The nonstabilizing through-space stereoelectronic interac-
tion of equatorial N lone pair and with the axial �-C��H bond. The
destabilizing through space stereoelectronic interaction of equatorial
N lone pair and with the axial �-C��H bond is shown.
379Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
Rehybridization and Anomalous StereoelectronicEffects on Nitrogen
In our recent study of homoanomeric effects,24a we found an inter-
esting trend at �-CH2 groups relative to heteroatoms (Table 4).
While the equatorial C��H bond lengths are mostly controlled by
the combined energy of delocalizing hyperconjugative interactions
that involve these bonds, data for the systems shown in Figure 6
cluster in the three groups separated by an additional factor (not
hyperconjugation). The situation is even more interesting for axial
C��H bonds at the �-carbon where hyperconjugative energies
shown in Figure 6 are hardly different but results still cluster in the
same three groups. Most interestingly, a �-CH2 group and an equa-
torial nitrogen lone pair have a similar ‘‘C��H bond lengthening
effect’’ and the �-C��H bonds are considerably elongated for the
three compounds where two such moieties are present simultane-
Figure 7. The contrasting correlations between NBO deletion energies for all hyperconjugative inter-
actions (both vicinal and homoanomeric) involving axial (top) and equatorial (bottom) �-CH bonds
with the respective C��H bonds lengths at the B3LYP/6–31G** level. E(del)ax and E(del)eq are defined
as the sum of all homoanomeric and vicinal � ? �* interactions involving the respective C��H
bonds.16
380 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
ously (X, Y ¼ CH2 or NHax). The second group of seven com-
pounds possesses a single CH2 moiety or equatorial nitrogen lone
pair at the �-position relative to the analyzed C��H bond whereas
such structural elements are absent for the 3rd group of molecules
in Figure 6.
The equatorial nitrogen lone pair effect is due to rehybridiza-
tion of C��H bond, which is likely to be caused by a direct
through space electrostatic interaction of the two moieties (see
Fig. 7). This somewhat surprising stereoelectronic effect, which
is not associated with hyperconjugative stabilization, was first
suggested in 2003.24 This work outlined contrasting hybridiza-
tion of oxygen, sulfur, selenium, and nitrogen lone pairs dis-
cussed in the previous section (Table 3) and extended this analy-
sis to explain trends in homoanomeric interactions involving
these heterocycles (Table 4). The equatorial lone pair of nitrogen
is approximately sp5-hybridized and, thus, possesses a relatively
large back lobe. However, it is directed to the node of the
�*(C��Hax) orbital and, thus, the net stabilization is close to
zero because of the unfavorable symmetry of this orbital over-
lap. At the same time, substantial 4-electron Pauli interaction
between the lone pair and the occupied �(C��Hax) orbital results
in repolarization and rehybridization of the C��H bond. Recent
work of Cuevas, Perrin, and Juaristi found further examples of
stereoelectronic effects of nonhyperconjugative origin attributed
to electrostatic interactions.25
The ‘‘lengthening effect’’ at the axial �-C��H bond, which is
caused by substitution of a heteroatom by a X¼¼CH2 group, can
be traced to changes in hybridization. In short, the �-carbonatom in heterocyclohexanes has to use a hybrid orbital with
more p-character to form the C��C bond with the �-carbonatom. This is a result of �-C��X bond polarization and a direct
consequence of Bent’s rule for X¼¼O and N. The situation for
the elements from the lower periods is more complicated and
exact reasons for this behavior have to be analyzed in a separate
study. The differences in electronegativity seem to be less im-
portant than the effects of orbital size mismatch between C and
S (Se). Polarization effects propagate through bonds and lead to
rehybridization and to increased p-character (decreased s-charac-
ter) in the C���C� bond forming hybrid at C� (in other words,
the �-C atom becomes more electronegative than the �-C atom).
Because the total s- and p-characters at every carbon atom are
conserved, this decrease in the s-character leads to an automatic
increase in the total s-character in other hybrid orbitals at C�
including the two C���H bonds. This increase is larger for the
axial C��H bonds, which may lead to their shortening compared
to the axial C��H bonds in cyclohexane. The same effect can
explain the anomalously short C2Heq bond length in 1,3-diox-
ane.
Interestingly, rehybridization parallels repolarization (the
same connection exists for H-bonded complexes discussed in
one of the following sections). As a consequence, the �-CHax
bond length for a set of compounds correlates very well with the
positive charge on hydrogen of the C��H bond (see Fig. 8).
The Mills-Nixon Effect
Annelation of benzene to saturated rings leads to ring deformation
with strain induced bond localization (the Mills-Nixon effect).26
Deformation of the benzene framework in these strained systems27
is accompanied by rehybridization,28 which we analyzed quantita-
tively at the B3LYP/6–31G** level in this section, using a family
of benzenes fused with saturated rings (A–G in Table5).
Generally, annelation of benzene by saturated ring in A–G
affects both the �-system and the �-bonds. We will not analyze
this thoroughly studied29 relationship here but limit ourselves to
a purely phenomenological illustration of the intimate connec-
tion between �- and �-effects in these systems. With the
increase in ring strain, hybridization of �-bonds increases from
sp2 to sp3 for the endocyclic bond (R1) and decreases from sp2
to sp at the other end (Table 5). Clearly, the Mills-Nixon bond
Figure 8. The correlation between NBO charges at axial hydrogen atom in �-CH2 groups with the re-
spective C��H bond lengths at the B3LYP/6–31G** level.
381Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
alternation DR in ring-annelated benzenes correlates well both
with the changes in s-character (the tris-cyclopropane C being
the most significant deviation) and in �-delocalization as illus-
trated in Figure 9. Along the same lines, the difference in endo-
and exocyclic angles �1 and �2 also defined in Table 5 correlates
well with the Ds-character for all compounds. From a practical
perspective, changes in s-character should be reflected in increased
acidity of aryl C��H bonds adjacent to fused strained ring.30
Table 5. The Difference in Endocyclic and Exocyclic C��C Bond Bonds (A), the Difference in Angle found
Between Endocycle and Exocycle, the Average s-Characters (%)(including spa Hybridization) of C in Each
Type of Bond, the Difference in the s-Character of C in Both Bonds, NICS(1) Values (ppm). Energy of
�-Delocalization (kcal/mol) in the Benzene Ring Calculated for Different Saturated Ring-Fused Benzenes at
the B3LYP/6–31G** Level.
DRa D0a s-char(C)R1b s-char(C)R2
b D(s-char)c NICS(1) S1d E(�)dele
0.000 0.00 35.18; sp1.84 35.18; sp1.84 0.00 �11.00 0.0 23.80
0.023 114.74 23.96; sp3.17 43.48; sp1.30 19.52 �13.39 27.5 17.87
0.024 53.54 31.25; sp2.30 38.04; sp1.57 7.79 �10.48 26.5 18.96
0.004 16.90 33.14; sp2.02 36.20; sp1.70 3.06 �10.70 6.2 21.07
�0.013 �2.19 34.95; sp1.86 34.55; sp1.89 �0.40 �10.61 0.0 20.70
0.076 36.06 29.76; sp2.36 39.52; sp1.53 9.76 �8.38 29.6 14.75
0.041 27.32 31.17; sp2.21 37.93; sp1.64 6.76 �11.11 7.0 17.40
0.018 14.22 32.55; sp2.07 36.49; sp1.74 3.94 �11.57 0.0 19.01
aThis is estimated from a difference in the bond distances (R1–R2) and angles (02–01) on endo and exocyclic bonds.bThe s-character of carbons in the both bonds.cA difference between the average s-character of carbons in R1 bond and that in R2 bond.dExperimental strain energies for the corresponding simple cyclo and bicycloalkanes.eThis is the average energy of six � � �� interactions in the benzene ring found from NBO ouput.
382 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
Hybridization Effects in Supramolecular Chemistry:
H-Bonding
Importance of rehybridization extends beyond intramolecular
effects. In particular, rehybridization explains the origin of blue-
shifted or ‘‘improper’’ H-bonds,31 an interesting class of H-bonds
that contradicts the conventional wisdom that formation of
X��H � � �Y hydrogen bond always leads to the X��H bond elon-
gation and concomitant red shift of the X��H IR stretching fre-
quency. We suggested a chemical mechanism for the electronic
reorganization involved in the X��H bond contraction, which is
based on continuous increase in the s-character of X and polar-
ization of the X��H bond in the process of X��H � � �Y hydrogen
bond formation.31
Computational support for this model is provided by data
shown in Figure 10. As electron density of Y is approaching
hydrogen atom of the X��H bond, the H atom becomes more elec-
tropositive and electron density in the C��H bonds shifts toward
carbon. As a direct consequence of the Bent’s rule, this change
increases s-character at X hybrid of the X��H bond. Rehybridiza-
tion and repolarization result in the X��H bond shortening, which
under certain conditions is capable of compensating for the X��H
bond elongation caused by of n(Y)?�*(X��H) hyperconjugative
interaction and concomitant increases in the �*(X��H) population.
Thus, the overall direction of the X��H bond length upon the for-
mation of a X��H. . .Y hydrogen bonded complex depends on the
balance of two effects acting in the opposite direction: rehybrid-
ization and hyperconjugation. A blue-shift (We will use the terms
‘‘blue shift’’ and ‘‘bond contraction’’ interchangeably in this part
since the correlation between these two spectroscopic and struc-
tural parameters is well-established. For exceedingly small
changes in the bond lengths, it may become harder to predict the
effect of such structural change on the direction of the spectro-
scopic effect. Despite a recent literature claim, this region of
uncertainty exists for only very small changes.)32a,b is observed
when rehybridization/repolarization is dominant, whereas the
‘‘normal’’ red-shift occurs31 when hyperconjugation is significant.
Value of this model is in its simplicity, direct relation to structural
organic chemistry and agreement with a large number of experi-
mental and theoretical results. In particular, rehybridization model
readily rationalizes concomitant structural changes that occur in
those parts of the molecule that are not directly involved in H-
bond formation.31 For example, secondary rehybridization
(increase in the p-character) in C��F bonds of fluoroform explains
why the H��C��F bond angles widen upon the F3CH. . .Y H-bond
formation (see Fig. 10).
Since rehybridization is essential for the development of
blue-shift, inefficient rehybridization should render the C��H
bond contraction more difficult. As a consequence, the trends in
H-bonding in C��H. . .Y systems strongly depend on the original
hybridization of C��H bonds. This notion explains a collection
of interesting observations reported in the literature. For exam-
ple, Scheiner and coworkers found that the improper character
in C��H. . .Y H-bonds is weakened in sp2 C��H bonds when
compared with sp3 C��H bonds and that the trend is further
enhanced for sp-hybridized C��H bonds, which show only clas-
sic H-bonding patterns.33 These findings were confirmed in thor-
ough studies by the groups of Radom,34 Hobza,35 and Dannen-
berg.36
These results can be explained by considering two H-bond
complexes with two C��H bonds of comparable acidity (In addi-
tion, one has to bear in mind that sp �*(C��H) orbitals are, in
general, better hyperconjugative acceptors than sp3 �*(C��H)
orbitals because they have lower energy and more favorable
polarization of �*(C��H) towards H. Thus, with less acidic
C��H bonds than that in fluoroform, the differences between
alkanes and alkynes should become even greater.) but different
hybridization (F3C��H and HCBC��H). Electrostatic component
is also different for these H-complexes (charges at the H- and O
atom involved in the H-bonds are 0.21/�1.02, 0.27/�1.01 and
0.28/�1.01 for the complexes of water with F3CH, HCBC��Hand FCBC��H, respectively). Whereas F3CH can form either
red-shifting or blue-shifting H-bonds depending of the properties
of H-bond acceptor (Table6), even those H-bond acceptors from
blue-shifting complexes with fluoroform show only normal red-
shifted behavior in respective complexes with acetylene and flu-
oroacetylene (Table7) at the MP2/6–31þG* level.
Analysis of electronic changes that accompany H-bond for-
mation shows that the relative changes in hybridization upon
formation of H-bonds are less pronounced in these systems when
compared with similar complexes involving C��H bonds of
alkanes and alkenes. For example, the hybridization of the C��H
bond in CHF3 changes from sp2.12 to sp1.97 while the hybridiza-
Figure 9. Correlation of DR (see Table 5) with both D(s-character of C) and �-delocalization energy
of benzene ring and that of D� with D(s-character of C) calculated at the B3LYP/6–31G** level.
383Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
Table 6. The C��H and C��F Bond Distances (D), s-Character (%) of C in Both C��H and C��F (average
Values) Bonds and the Enerfy (kcal/mol) of Hyperconjugative Interaction Between Y Donor and C��H
Acceptor in F3C��H Moiety Calculated for Blue and Red-Shifting F3CH � � �Y Hydrogen Bonded Complexes
Calculated at the MP2/6-31þG* Level.
r(C��H) r(C��F)a r(H��Y) 0(H��C��F)a s-char (C)C��H s-char (C)C��F E(n?�*)
F3CH 1.0876 1.3507 – 110.58 31.94 22.75 0.00
F3CH��FH 1.0856 1.3528 2.266 110.83 32.75 22.48 3.62
F3CH��CH 1.0861 1.3520 2.776 110.73 32.56 22.53 4.58
F3CH��Cl2 1.0861 1.3512 2.955 110.63 32.58 22.46 4.12
F3CH��OB2 1.0860 1.3554 2.143 111.08 33.31 22.24 8.60
F3CH��SH2 1.0863 1.3531 2.788 110.82 32.91 22.47 6.56
F3CH��OMe2 1.0867 1.3556 2.123 111.07 33.36 22.23 8.48
F3CH��SMe2 1.0856 1.3532 2.986 110.87 32.70 22.51 3.95
F3CH��Cl 1.0949 1.3643 2.273 112.16 36.10 21.37 24.94
F3CH��Br 1.0928 1.3623 2.493 111.97 35.44 21.61 18.51
F3CH��NC5H5b 1.0886 1.3563 2.240 111.14 33.88 22.10 9.77
F3CH��NH3 1.0888 1.3567 2.234 111.19 34.07 22.04 11.66
F3CH��NH2Me 1.0897 1.3568 2.216 111.18 34.09 22.03 11.00
F3CH��NHMe2 1.0902 1.3570 2.207 111.16 34.05 22.04 9.81
F3CH��NMe3 1.0907 1.3572 2.208 111.13 33.99 22.08 7.58
F3CH��NC4H9c 1.0910 1.3574 2.201 111.20 34.17 22.02 12.14
aThe average value of three C��F bonds.bPyridine.cPyrrolidine.
Figure 10. Correlations of C��H distance, H��C��F angle, and NBO energy of nY?�C��H* hypercon-
jugation in F3C��H � � �Y hydrogen bonded complexes (see Table 6) with the s-character of C (MP2/6–
31þG**) in C��H and C��F bonds.
384 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
tion of the C��H bond in HFCBCH and FCBCH changes only
from sp1.05 to sp1.03 and sp0.96 to sp0.92 upon formation of com-
plexes of these two fluorocarbons with water. The striking dif-
ference between the two types of C��H bonds is illustrated in
Figure 11 that clearly shows that the ‘‘blue-shifted’’ region only
exist for fluoroform but not for acetylene.
The ultimate example of a bond, which is not capable of re-
hybridization, is the H��H bond. According to the above model,
formation of H��H � � �Y (Y ¼ H2O, Me2O, Cl�) complexes31a
should always lead to the red-shift even though the �*HH orbital
is a relatively weak acceptor and energies of the corresponding
n(Y)?�*HH interactions are low. This notion is an excellent
agreement with the computational finding that even H��H � � �Ycomplexes with relatively strong electron donors Y are red-
shifted!31
An interesting problem addressed recently by Wang et al.37
and by us38 was the role of rehybridization in H-bonded
X��Rg��H � � �Y complexes where Rg is a rare gas element.
Although Wang et al. was not able to fit the finding of red-shift
in such complexes to our rehybridization model, it is not surpris-
ing that an attempt to directly transfer model developed for the
classic 2c,2e-bonds of Lewis to hypervalent 3c,4e-bonds was
futile. We found that unusual electronic properties of hyperva-
lent molecules open a new mechanism for the red-shift, which is
not available for the classic X-H bonds and compensate for the
lack of rehybridization. This mechanism is based on rebalancing
of dominant resonance contributions and a switch from H-bond-
ing to He-bonding. It is remarkable, however, that it leads to
repolarization of Rg��H bond, which is analogous to that
observed in classic 2c,2e bonds.38
Contrasting Effects of Acceptor Substituents on the
Bergman Cyclization
The final part of this article gives an example of a rehybridiza-
tion effect that controls chemical reactivity. As a direct conse-
quence of the Bent’s rule, carbon compounds with significantamount of s-character in their bonds to an acceptor element,e.g., fluoroalkynes are unstable.19 Thus, reactions that involvechange in hybridization at a reactive atom bearing such anacceptor can be promoted when amount of s-character at the re-active atom decreases. An illustrative example of such an effectis provided by interesting substituent effects in the Bergman cy-
clization39 of enediynes (see Fig. 12).
Figure 11. Correlation of C��H bond length with.. . .Y (Y¼¼O) distance in CF3H��OH2 (blue dia-
mond) and HCCH��OH2 (red circle) complexes (MP2/6–31þG* level). The equilibrium distances are
shown with arrows.
Table 7. The C��H Bond Distance (A), s-Character (%) of C in Both
C��H Bond and the Energy (kcal/mol) of Hyperconjugative Interaction
Between Y Donor C��H Acceptor in RCCH Moiety Calculated for
RCCH � � �Y Hydrogen Bonded Complexes Calculated at the
MP2/6-31þG* Level.
RCBCH��Y r(C��H) r(H��Y) s-char (C)C��H E(n?�*)
HCCH 1.0676 – 48.60 –
HCCH��FH 1.0693 2.256 49.11 3.3
HCCH��OH2 1.0723 2.141 49.54 7.1
HCCH��SH2 1.0680 2.827 48.87 1.9
HCCH��OMe2 1.0744 2.095 49.63 7.7
HCCH��SMe2 1.0721 2.753 49.32 3.2
FCCH 1.0660 – 51.00 –
FCCH��FH 1.0679 2.229 51.52 4.0
FCCH��OH2 1.0716 2.120 51.99 8.1
FCCH��SH2 1.0665 2.801 51.31 2.5
FCCH��OMe2 1.0740 2.071 52.10 8.7
FCCH��SMe2 1.0716 2.686 51.77 4.7
385Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
The Bergman cyclization transforms the enediyne moiety into
a highly reactive diradical species (p-benzynes) that play a key
role in the mechanism of biological activity of natural ene-
diynes.40 Although the cyclization, which can be considered as a
Cope rearrangement interrupted by aromatic stabilization,41 is
simple topologically (a new sigma bond is formed at the
expense of two �-bonds), it is complex from the electronic per-
spective42 because relative changes in the two orthogonal �-sys-tems proceed asynchronously. In general, ‘‘cyclization’’ precedes
‘‘aromatization’’ in the cycloaromatization process43 because
reorganization of the in-plane �-orbitals occurs well before the
out-of-plane effects become important. As a result, one needs to
address the sigma system directly in order to control thermal
cycloaromatization reactions (Note however that this limitation
is removed in radical anionic cycloaromatizations).44
Recently, we showed that it is possible to influence the in-plane
orbitals through steric and electronic effects of ortho-substituents,
even though the effect of analogous para substituents is very
small.45 An alternative approach to activating sigma effect for
control of Bergman cyclization is based on rehybridization. This
approach was first applied by Schreiner and coworkers who found
significant acceleration of the Bergman cyclization upon intro-
duction of sigma acceptors at the terminal carbons of (Z)-1,5-
hexadiyne-3-ene.46 In particular, cyclization of the enediynes
with terminal fluoro-substituents was predicted to have the lowest
barrier and be significantly exothermic. A subsequent experimen-
tal study found that the reverse reaction (retro-Bergman ring
opening) in this system is endothermic, thus confirming the ear-
lier computational predictions.47 In contrast, computational work
of Jones and Warner found that acceptor substituents positioned
at the ene part of the enediyne moiety decelerate the reaction48 in
a full accord with the earlier experimental results of Jones and
coworkers.49
We reanalyzed the parent systems of Schreiner and Jones and
extended this study to the benzannelated fluorinated enediynes
as shown in Figure 13. This analysis revealed that hybridization
Figure 12. (a) Comparison of potential energy profile for the formal Cope rearrangement of 3,4-
difluorohexa-1,5-diyne-3-ene with that of (Z)-hexa-1,5-diyne-3-ene, (b) rehybridization in the C(F)
bond along the reaction path. ED1, 3,4-difluoro-hex-3-ene-1,5-diyne; ED2, 1,6-difluoro-hex-3-ene-1,5-
diyne; BZY, difluoro-1,4-didehydrobenzezne; TSBC, the transition state for the Bergman cyclization;
TSRBC, the transition state for the retro Bergman cyclization (UB3LYP/6-31G** data).
386 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
plays a crucial role in the cyclizations explaining not only the
accelerating effect of terminal fluorine substitution but also the
less predictable decelerating effect of vinyl fluorine substitution.
Combining the two Bergman reactions into a formal Cope rear-
rangement of 3,4-difluorohexa-1,5-diyne-3-ene to 1,6-difluoro-
hexa-1,5-diyne-3-ene (Fig. 12) most clearly illustrates the effect
of rehybridization in this system. In short, the further the reac-
tion progresses toward the ‘‘anti-Bent’’ 1,6-difluorohexa-1,5-
diyne-3-ene, the more unfavorable rehybridization of C��F bond
is. This trend explains continuous increase in energy along rela-
tive to that for the formal Cope rearrangement of the parent (Z)-
hexa-1,5-diyne-3-ene. Remarkably, 1,6-difluorohexa-1,5-diyne-3-
ene is about 21 kcal/mol less stable than 3,4-difluorohexa-1,5-
diyne-3-ene at the B3LYP/6–31G** level.
Since we concentrate on relative trends in reactivity, the
choice of DFT functional is not crucial. For example both
B3LYP and BLYP functionals (such as the extensively discussed
performance of B3LYP vs. BLYP)46,48 show similar trends in
describing reactivity of the family of fluorinated enediynes as
shown in Figure 12. The results clearly show significant increase
in reactivity for enediynes II and VI with fluorine substituents at
the terminal carbons in accordance with the earlier results of
Schreiner.46 In contrast, direct substitution at the vinyl part of
the enediyne moiety slows the reaction in accordance with the
experimental data of Jones and coworkers49 and theoretical anal-
ysis of Jones and Warner.48 Comparison of the Bergman activa-
tion barriers for enediynes III and VII clearly shows that direct
acceptor substitution at the vinyl carbons is much more efficient
than attachment of four fluorines at a more remote position. This
observation suggests that the effect of F-substituents at the cen-
ter is mostly transmitted through the sigma framework. This
reactivity trend can be seen from computed activation barriers in
Figure 13. Comparison of perfluoro enediynes IV and VIII illus-
trates that, surprisingly, the effect of terminal substituents can be
completely compensated by the effect of acceptor substitution at
the central double bond. In contrast, the four sigma acceptors
attached to the benzene ring of VIII are not able to interfere
with the accelerating effect of the directly attached terminal sub-
stituents.
Since transition state is reactant-like43 and TS and reactant
have the same dominant Lewis structures, application of NBO
for the analysis of transition state is straightforward (Table8).
The hybrid orbital h that connects terminal acetylene carbon to
the substituent undergoes the most significant rehybridization
(sp?sp2 or 48%?33%) in the Bergman cyclization of enediyne
I (see Fig. 12). According to the Bent’s rule, terminal fluorine
substitution destabilizes the reagent by preventing this hybrid or-
bital from attaining its ‘‘natural’’ sp-hybridization (in other
words, it is unfavorable to direct hybrid with 50% of s-character
toward a strong acceptor). As a result, hybrid h has only 36–
37% of s-character in the reactant—a dramatic effect of F sub-
stitution! However, the differences in hybridization decrease in
the TS, illustrating that the destabilizing effect of electron
acceptor in the reactant is removed by rehybridization in the TS.
Similar underappreciated hybridization effects may be quite
common in chemistry as further illustrated by a recent study of
Lewis and Glaser that illustrated synergism of catalysis and
rehybridization at the reaction center in hydrolysis of carbodii-
mide50 and called for reinvestigation of chemistry promoted by
human carbonic anhydrase, environmentally important hydrolysis
of SO3 involved in acid rain and numerous proton transfers in
proteins. In a different example, rehybridization plays important
role in electronic reorganization at an incipient radical center X
in the process of X��H bond dissociation where lone pair(s)
‘‘acquire more s-character, to the detriment of the orbital
involved in the breaking bond,’’51 thus explaining the well-
known ‘‘lone pair bond weakening effect.’’
Figure 13. The Bergman cyclizations of parent and fluoro-substi-
tuted enediynes with the triple bond and the incipient bond lengths
and the activation energies calculated at the BS-UB3LYP/6–31G**
level.
387Rehybridization as a Mechanism for Maximizing Chemical and Supramolecular Bonding
Journal of Computational Chemistry DOI 10.1002/jcc
Conclusion
The Lewis concept of localized chemical bond amplified by
hybridization is still a useful tool that enables better understand-
ing of chemical structure and helps to develop efficient
approaches for the control of chemical reactivity. The dynamic
ability of hybridization patterns to adjust (rehybridize) in
response to external and internal perturbation provides a unify-
ing conceptual framework for understanding of such diverse
topics as structural reorganization in red-shifting and blue-shift-
ing H-bonded complexes, nonhyperconjugative stereoelectronic
effects in saturated heterocycles, competition between �- and �-effects in strained polycyclic structures and contrasting substitu-
ent effects in cycloaromatization reactions.
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390 Alabugin and Manoharan • Vol. 28, No. 1 • Journal of Computational Chemistry
Journal of Computational Chemistry DOI 10.1002/jcc
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