Rehybridization as a general mechanism for maximizing chemical and supramolecular bonding and a...

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


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.



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.



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.



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.



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



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.



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.



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.



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.



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



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).



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.



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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Table 8. The s-Character of C in All Bonds of Enediyne Framework from Both Reactant and Transition State

Structures Calculated at the BS-UB3LYP/6–31G** Level.

s-char(a)R s-char(b)R s-char(c)R s-char(d)R s-char(e)R s-char(f)R s-char(g)R s-char(h)R

I 51.45 52.17 47.67 32.58 38.33 0.00 0.00 48.41

II 63.21 49.85 50.00 32.22 38.55 0.00 0.00 36.59

III 51.27 53.32 46.52 36.53 40.35 0.00 0.00 48.60

IV 62.99 51.05 48.79 36.24 40.61 0.00 0.00 36.80

V 51.50 52.50 47.40 31.26 33.94 0.00 0.00 48.36

VI 63.27 50.17 49.76 30.90 34.07 0.00 0.00 36.53

VII 51.37 52.94 46.92 32.42 34.24 0.00 0.00 48.49

VIII 63.10 50.61 49.28 32.14 34.38 0.00 0.00 36.68

Transition state s-char(a)TS s-char(b)TS s-char(c)TS s-char(d)TS s-char(e)TS s-char(f)TS s-char(g)TS s-char(h)TSI 44.35 48.57 45.30 33.79 36.47 11.56 3.92 33.74

II 49.24 48.94 47.62 33.42 37.01 17.47 3.34 33.07

III 41.60 51.26 44.24 38.26 38.27 11.35 4.47 46.75

IV 46.40 50.52 44.92 7.55 38.64 20.37 4.48 32.94

V 42.46 50.38 45.69 32.85 31.73 11.41 3.87 33.43

VI 48.62 49.33 46.95 32.47 32.02 18.29 3.60 32.84

VII 43.53 49.33 44.14 33.98 31.98 11.03 3.98 32.96

VIII 49.14 47.45 45.43 33.54 32.33 16.76 3.73 32.82



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