theoretical studies of unusually short bond lengths in oxirane · pdf file ·...

Theoretical studies of unusually short bond lengths inoxirane and derivativesq

M. HoÃÁ 1, W.A. Szarek, V.H. Smith Jr.*

Department of Chemistry, Queen's University, Kingston, Ont., Canada K7L 3N6

Received 1 June 2000; accepted 28 June 2000

Abstract

The p-Complex-Back-Donation model (p-cbd) has been used together with the topological analysis of the ab initio and semi-

empirical densities to investigate bond lengths in the oxirane molecule and derivatives. Both models offer similar conclusions.

The shortenings of the C±C bond in the oxirane ring and of the neighbouring C±C bond arise mainly from the substituent

groups. However, neither the p-cbd model nor the atoms in molecules model offers a satisfactory explanation for the elongation

of one of the C±O bonds. q 2001 Elsevier Science B.V. All rights reserved.

Keywords: Oxirane molecule; p-Complex-Back-Donation model; Oxirane derivatives; Three-membered ring model; Charge density analysis;

Walsh orbitals; Molecular orbitals; Atoms in molecules

1. Introduction

The X-ray structure of 1,2-Anhydro-3,4:5,6-di-O-

isopropylidene-1-C-nitro-d-mannitol (1) has been

determined by Szarek et al. [1] (see Fig. 1). Their

result shows that the bond lengths of C(1)±C(2) (in

the oxirane ring) and C(2)±C(3) are unusually short.

The C(1)±C(2) bond distance is 1.441(4) AÊ , a value

which is unusually small compared to that of a typical

C±C bond length of oxirane of 1.462(3) AÊ [2±4]. The

observed C±C bond is also shorter than the compar-

able bond of oxirane derivatives such as 2-(¯uoro-

methyl)-2-((p-tolysul®nyl)methyl)oxirane (1.453 AÊ ) [5],

(1aa, 2b, 2ab, 4a, 7a, 7ab, 8b, 8aa)-octahydro-4,7-

epoxy-2,8-methanooxireno [h][3] benzoxepin-3(4H)-one

(1.462 AÊ ) [6] and 1,2:5,6-dianhydrogalactitol

(1.452(5) AÊ ) [7], and is similar to that estimated for

tetra¯uorooxirane [8] and that of methyl 3,4-anhydro-

1,6-bis-O-(p-tolylsulfonyl)-b-d-tagatofurano-

side (1.45(1) AÊ ) [9]. The C(2)±C(3) bond distance is

1.484(4) AÊ ; this is shorter than the corresponding C±

C bonds of certain isopropylidene substituents of

carbohydrates [10±13].

Saebo and Kavana [14] optimized three confor-

mers of epi¯uorohydrin at the HF/6-311Gpp level

and reported an average bond length of 1.453 AÊ

for the C±C bond in the oxirane ring, 1.402 AÊ for

the C±O bond, and 1.499 AÊ for the neighbouring

C±C bond.

In this paper, we applied two approaches in an

attempt to elucidate the unusually short bonds that

occur in oxirane and its derivatives.

Journal of Molecular Structure (Theochem) 537 (2001) 253±264

0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.

PII: S0166-1280(00)00682-5

www.elsevier.nl/locate/theochem

q Dedicated to Professor SerafõÂn Fraga on the occasion of his 70th

birthday.

* Corresponding author.

E-mail address: [email protected] (V.H. Smith Jr.).1 Present address: Universidad AutoÂnoma del Edo de Morelos,

Centro de Investigaciones QuõÂmicas, Av. Universidad No. 1001

Col. Chamilpa. Cuernavaca, Mor. C. P. 62210, MexõÂco.

2. Results and discussions

The chemistry and structure of three-membered rings

(3MRs) including ethylene oxide have been the subject

of many theoretical and experimental studies [15±25].

Among these studies, there are two theoretical models,

which have proved to be satisfactory in explaining the

behaviour of the 3MR and oxirane in particular. The p-

complex-back-donation (p-cbd) model, ®rst proposed

by Dewar and Ford [26], and later expanded by others

[8,27±33], has been used to rationalize the substituent

effect on the 3MR. The second model, based on the

theory of atoms in molecules [34], was applied to

3MRs by Cremer and Kraka [19,20].

2.1. The p -complex-back-donation model

In the Molecular Orbital framework, one thinks of

MOs as the result of the mutual overlap of several

atomic orbitals. Since atomic and molecular orbitals

in principle are the same, as each represents an orbital

space that accommodates two electrons, it is possible

that MOs can also overlap with different AOs to form

new MOs. While s MOs are unable to overlap

ef®ciently with other AOs for steric reasons; the

same is not true for the p MOs. This idea is the essen-

tial one behind the p-cbd model. This model consid-

ers the 3MR as being composed of two parts: the

ole®n fragment (basal) and the acceptor (apical) (see

Fig. 2). The ole®n can use its ®lled p MO to form a

dative bond with the acceptor. The acceptor, on the

other hand, has ®lled p or d AOs that can be used to

form a reverse dative bond with the vacant (antibond-

ing) pp MO of the ole®n. Thus, the formation of the

3MR can be thought of as the interaction between two

opposed dative bonds resulting in an increase in the

overall bonding between the ole®n fragment and

the acceptor.

It has been shown [35] that the electronegativity of the

apical group will affect the degree of back donation. If

the apical group is very electronegative, due to the

difference in the energy between thepp MO of the ethy-

lene fragment and the ®lled AO of the apical fragment,

the back donation will be negligible and the predomi-

nant effect will be the electron transfer from thepMO to

the empty AO of the apical group. The resulting struc-

ture will behave as a simple p-complex. If the apical

group is weakly electronegative, the back donation will

M. HoÃÁ et al. / Journal of Molecular Structure (Theochem) 537 (2001) 253±264254

Fig. 1. 1,2-Anhydro-3,4:5,6-di-O-isopropylidene-1-C-nitro-d-mannitol (1).

be more signi®cant; the result will be the conventional

3MR.

Dewar and Ford [26] showed that it is arbitrary to

decide whether a compound is a p-complex or a 3MR,

and that the distinction is based entirely on the suitability

for the interpretation of the experimental data. One

should note, however, that, in examining thep-complex

character according to this model, the essential criterion

is not the electron density associated with the apical

group but rather the ratio of electron transfer in the

forward and reverse directions. Therefore, any change

in the geometry of the molecule should be the result of

both p-donation and the back-donation changes.

Hoffmann and coworkers [27±29] and Allen and

coworkers [8,30±32] extended this model using the

Walsh orbital scheme [36], which deduces the mole-

cular geometry based on the symmetries and energy

orders of the AOs, to explain the geometric behaviour

of cyclopropane and of some other heterocyclic

compounds, although they did not treat oxirane and

derivatives systematically. Analysis based on this

scheme classi®es the substituents into four groups:

s-withdrawing, s-donating, p-withdrawing, and p-

donating, depending on the symmetry and relative

energy levels of the interacting MOs belonging to

these substituents. One still has to determine which

MOs of the 3MR will be affected by the substituents.

The interaction of an electron-donor MO from the

substituent with a bonding MO of the 3MR will

increase the bonding characteristic, and, therefore,

will shorten the bond. On the other hand, if the

same substituent interacts with an antibonding orbital

of a particular bond, it will enhance the antibonding

characteristic of that bond, and, as a result, lengthen it.

The electron-withdrawing substituents also work in an

analogous fashion.

The determination of which MO will be affected by

the substituent is a non-trivial task. For large mole-

cules, there are many more MOs involved in the

Walsh orbital picture, and, furthermore, these MOs

are much closer together energetically and the extent

of mixing of orbitals having the same symmetry and

compatible energy is enhanced greatly [37]. As will

be shown below, the matter is further complicated by

the fact that calculations at different levels of theory

can reverse the order of close-lying MOs, particularly

the HOMO±LUMO levels.

An HF/STO-3G calculation by McAlduff and Houk

[38] for the oxirane molecule using an experimentally

determined structure shows that the ®rst four

HOMO ionization potentials are as follows:

2b1 , 4a1 , 2b2 . 1a2. Our result, also at the same

level of theory using the same geometry, shows that

the order is 4a1 , 2b1 , 1a2 . 2b2. This order is

consistent with that of Pople and coworkers [39]

M. HoÃÁ et al. / Journal of Molecular Structure (Theochem) 537 (2001) 253±264 255

Fig. 2. The MO model of the three-membered ring according to

Dewar and Ford [26].

Table 1

Ionization potential order of oxirane at the HF level using different

basis sets

Basis set Ionization potential order Reference

STO-3G 2b1 , 4a1 , 2b2 , 1a2 McAlduff and Houk [38]

STO-3G 4a1 , 2b1 , 2b2 , 1a2 This work

6-31Gp 4a1 , 2b1 , 2b2 , 1a2 Pople et al. [39]

6-31Gpp 4a1 , 2b1 , 2b2 , 1a2 This work

DZ 2b1� 4a1 , 2b2 , 1a2 Basch et al. [40]

Expt. 2b1 , 4a1 , 2b2 , 1a2 Basch et al. [40]

Expt. 2b1 , 4a1 , 2b2� 1a2 Bieri et al. [44],

Potts et al. [45]

HF/6-31Gp calculation and our HF/6-31Gpp calcula-

tion. An earlier Hartree±Fock calculation using a

Double Zeta basis set by Basch et al., [40] predicted

an almost degenerate MO: 2b1� 4a1 , 2b2 , 1a2 (see

Table 1). Basch et al. removed the degeneracy by

further modifying the calculation, yielding the MO

order 2b1 , 4a1 , 2b2 , 1a2.

Within the Hartree±Fock scheme, Koopmans'

theorem [41] is employed to approximate the ioniza-

tion energies of the molecules as the negative of the

SCF orbital eigenvalues. The differences between

Koopmans' theorem ionization potentials and the

experimentally derived vertical ionization potentials

are due to the frozen orbital approximation. This

approximation does not allow the ionized cation to

stabilize itself by reorganizing its MOs after losing

the electron. Since orbital relaxation is inherent in an

ionization process, the MO levels predicted by Koop-

mans' theorem may not be the same as those predicted

by experimentally derived photoelectron spectra.

Basch et al. also used photoelectron data to support

their assignment of the MO levels. In subsequent

investigations [38,42,43] on ethylene oxide and deri-

vatives, interpretations were made assuming that

Basch et al.'s assignments were correct. However,

further experimental data from Bieri et al. [44] and

Potts et al. [45] show a different ionization potential

order for oxirane: 2b1 , 4a1 , 1a2� 2b2.

To determine which MOs will interact with the

substituent is even more complicated. For cyclopro-

pane, Clark et al. [21] argue that the Walsh orbital

having the largest coef®cient is the one most affected

by the electronegativity of the substituent, an aspect

which was not discussed in other similar studies. Even

though symmetry and energy compatibility are the

aspects that determine the interactions between

MOs, the ®nal assignment should come from the

experimental data.

2.1.1. Oxirane and derivatives

The p-acceptor substituents, such as CH21 CN,

NO2, Li, BeH, and BH2, having low-lying MOs will

withdraw charge from the 2b2 HOMO of the oxirane

molecule. This MO is bonding with respect to C±C

and antibonding for C±O (see Fig. 3). Thus, removing

charge from this MO will shorten the C±O bond and

lengthen the C±C bond. The experimentally deter-

mined geometry of tetracyanoethylene oxide [46]

shows that the C±C bond of tetracyanoethylene

oxide is 0.024 AÊ longer than that of oxirane, and

that the C±O bonds are 0.012 AÊ shorter than the C±

O bonds of oxirane.


Fig. 3. The HOMO 2b2 of oxirane.

In the case of the s-acceptor substituents, the main

interaction could come from the 1a2 orbital of oxirane.

This MO has a large coef®cient on the C atom and

show C±X bonding characteristics (see Fig. 4). The

2b2 MO also has C±X bonding characteristics, but

with a smaller coef®cient at the C atom (see Fig. 3).

The 1a2 MO has antibonding characteristics for the

C±C bond; thus, s-acceptor substituents, such as F,

should shorten the C±C bond. The experimentally

determined structure of cis-1,2 di¯uorooxirane [47]

exhibits a shortening of the C±C bond by 0.021 AÊ

compared to that of oxirane. The shortening of the

C±O bonds by 0.027 AÊ in cis-1,2 di¯uorooxirane is

probably due to the contribution of the C±O antibond-

ing 2b2 MO mentioned above. Other s-acceptor

substituents are Cl, OH, and NH3. According to

Clark et al. [21] the CH3 group can also be considered

as a s-acceptor group. A study of the crystal structure

of methyloxirane [48] indicates that the CH3 substitu-

ent indeed shortens both vicinal C±O and C±C bonds

of the oxirane ring in the same manner as ¯uorine

does. By interpreting photoelectron spectra, McAlduff

and Houk [38] also con®rmed that the interaction

between an oxirane ring and alkyl substituents arises

mainly from the 1a2 and 2b2 MOs.

Strong p-donor substituents can transfer charge to

the low-lying 4b1 LUMO of oxirane. This MO has

antibonding characteristics for both the C±O and

C±C bonds (see Fig. 5). Thus p-donor substituents

such as CH22 and O2 would lengthen all three bonds

in the 3MR. s-Donor substituents (e.g. Li) can also

interact with the 4b1 MO of oxirane. Obviously, those

substituents have strong C±X bond characteristics,

and can interact in a manner similar to those of the

s-acceptor substituents. The situation becomes more

complicated, and requires more calculations and

experimental data, if one wishes to assign the proper

contributions of particular MOs. Currently, there have

been few investigations about the effect of s-donor

substituents on 3MR system.


Fig. 4. The 1a2 Molecular Orbital of oxirane.

Fig. 5. The LUMO 4b1 of oxirane.

2.1.2. 1,2-Anhydro-3,4:5,6-di-O-isopropylidene-1-C-

nitro-d-mannitol (1)

Following the Walsh orbital picture discussed

above, one can look at (1) as an oxirane derivative

having two substituent groups: the NO2 group and one

comprised of two O-isopropylidene rings. Both

groups will affect the geometry of the oxirane ring

in (1) in a different way. NO2, being a p-acceptor

substituent, will shorten the vicinal C±O bond and

lengthen the C±C bond. The fragment containing

the two isopropylidene rings is a s-acceptor substitu-

ent and thus would shorten both vicinal C±C and C±O

bonds. The combined effect is that the C±O bond

adjacent to the NO2 group in (1) is shortened by

0.048 AÊ compared to that in oxirane. The C±O bond

adjacent to the di-O-isopropylidene fragment on the

other hand is lengthened by 0.017 AÊ , an observation

which contradicts the predictions made above. A possi-

ble explanation is that the interaction of the 2b2 MO

which is responsible for the shortening of this C±O

bond could be diminished by the perpendicular orien-

tation of the 3,4-O-isopropylidene ring. Furthermore,

CNDO calculations by Furman and Meleshevich [49]

on the effect of an NO2 group on oxirane show weak-

ening (therefore lengthening) of this C±O bond.

2.2. The Laplacian of the charge density model

The p-cbd model for oxirane can be viewed from a

different perspective. While the Walsh orbital scheme

is convenient computationally and visually, the theory

of atoms in molecules [34] provides a more quantita-

tive approach for the oxirane ring. From the p-cbd

model, one can see that, for the dative donation,

there is a charge build-up along the C2 axis of oxirane.

Therefore, the resulting bond path would be from the

apical oxygen to the midpoint of the basal ethylene.

According to the catastrophe theory as applied to the

topological approach (see, for example, chapter 4 of

Ref. [34]), such a structure is known as the T-structure

and is topologically unstable. Any in®nitesimal

change in the symmetry of the molecule will alter

its geometry signi®cantly.

For the back donation, the charge build-up from the

occupied p orbital of oxygen to the empty antibonding

MO of ethylene will result in two convex bond paths

from oxygen to the carbon atoms. It is now possible to

determine the predominant donation based solely on

the molecular path of the molecule. If the apical group

is more electronegative than the basal group, a

concave molecular path will occur. A convex mole-

cular path exhibits a strong dative donation in which

the apical group is less electronegative than the basal

group. This approach is a quanti®cation of the intui-

tive orbital picture proposed by Dewar and Ford.

Cremer and Kraka [19,20] studied a series of

heterocyclic 3MRs to support this model. From Fig.

6 one can see the changes of the molecular paths with

respect to the p-complex character of the molecules.

Beryllocyclopropyne (BeC2, structure n) possesses

a T-structure, since the main charge build-up comes

from the 2s orbital of the Be atom to the s bonding

orbital of the basal fragment [50]. Due to its extreme

electronegativity, the ¯uoroethyl cation (structure 1)

shows a very concave molecular path, which is almost

a T-structure. Protonation of oxygen in oxirane makes

it even more electronegative, as can be seen by the

molecular path of the protonated oxirane (k) being


Fig. 6. Changes in molecular paths with respect to the p-complex

character of the molecule (after Cremer and Kraka [19]).

more concave than that of the neutral oxirane mole-

cule (j). The importance of the back donation is

demonstrated clearly in oxirane, cyclopropane (i),and, particularly, beryllocyclopropane (m) where the

back donation has outweighed the dative donation due

to the electropositivity of the beryllium atom.

The effect of the substituent group on the oxirane

ring can be investigated using the Laplacian of the

charge density. According to topological de®nitions,

the integration of the Laplacian of the charge density

over the subspace V , de®ned by the zero-¯ux surface

of r (r), vanishes:ZV7 2r�~r� d~r �

I~7r�~r�´~n dS � 0: �1�

Any changes in the Laplacian of r are accompanied

by other changes within the subspace V boundary in

order to satisfy Eq. (1). The physical interpretation of

this equation can be explained by the example of an

A±X molecule. If X is more electronegative than A,

there will be a shift of the location of the bond critical

point toward A due to the fact that the valence sphere

of A is being pulled toward X. This deformation

causes a decrease in the charge concentration of A

in the direction of X; thus, Eq. (1) indicates that

there must be an increase in the charge concentration

at A in the opposite direction.

An increase of the charge concentration in the inter-

nuclear region shields the nuclei from repelling each

other, and, hence, a shortened bond results. Similarly,

a decrease in the charge concentration in this region

will increase the nuclear±nuclear repulsion, causing a

bond elongation.

The Laplacian of the charge density indicates the

locally electron-depleted and locally electron-concen-

trated areas on the valence sphere of the substituents.

The effect of these electronic holes and electronic

lumps allows one to distinguish the substituents as

s-attractor, s-repeller, p-attractor, or p-repeller.

The s-attractor substituents, which transmit their

effect through the bond path, withdraw electrons

from the 3MR, and thereby create an electronic hole

in the adjacent carbon atom. According to Eq. (1)

there will be electronic lumps toward the direction

of the oxygen and the distal carbon atoms. These

electronic lumps will deshield the vicinal carbon

from the oxygen atom and the distal carbon. Conse-

quently, shortening of the vicinal bond occurs. The

electronic lumps also become staggered in order to

avoid each other, thus making the distal bond longer.

F, OH and NH2 are substituents that have s-attracting

ability, even though they also have stronger p-repel-

lent effect.

In the same manner, a s-repeller such as Li and

BeH donates electrons to the adjacent carbon of the

3MR, thereby forming an electronic lump between

itself and this carbon atom. Elongation of the vicinal


Fig. 7. Model derivatives of (1).

bonds occurs, due to the electron holes, toward the

oxygen and the distal carbon atoms. The distal C±O

bond contracts because of the reduction of the

nuclear±nuclear repulsion.

The p-attractors possess electronic holes in their

valence spheres and the effects are transmitted

through space rather than through the bond paths.

CN, NO2, and phenyl act as p-attractors and cause a

decrease of the charge density in the vicinal bond

region, and, hence, shorten the distal bond and stretch

the vicinal bonds.

Strong p-repellers such as F, OH and NH2 have the

reverse effect on the 3MR, namely contraction of the

vicinal bonds and expanding of the distal one.

2.2.1. 1,2-Anhydro-3,4:5,6-di-O-isopropylidene-1-C-

nitro-d-mannitol (1)

To study the effect of the substituents on compound

(1), its structure and six more derivatives were opti-

mized using the AM1 method [51]. The starting

geometry of (1) was taken from the X-ray structure

[1]. In order to study the effect of the substituents, the

NO2 and isopropylidene groups were also replaced or

removed, and the structures were optimized indepen-

dently (Fig. 7). Missing experimental parameters were

replaced mainly with data from Pople et al. [52].

The results from the AM1 optimized geometry

show good agreement with those from the crystal

structural determination (see Tables 2±5). For the

most part, the optimized bond lengths agree within

2% with the experimental ones. The discrepancies

of the C(1)±C(2) and C(2)±C(3) bond lengths are

reasonable within the AM1 approximation. Bond

lengths involving the methyl groups, for example,

C(7)±C(9) and C(10)±C(11), give large deviations.

However, the similar type of bond in C(7)±C(8) and

C(10)±C(12) shows better agreement. In general, the

C±O bond lengths are reproduced satisfactorily.

The bond angles show an average deviation of

2.5%. The largest deviation comes from the angle


Table 2

Bond lengths of AM1 optimized structure of (1)

Bond Distance (AÊ ) Bond Distance (AÊ ) Bond Distance (AÊ )

O(1)±C(1) 1.425 O(5)±C(5) 1.430 C(4)±C(5) 1.533

O(1)±C(2) 1.442 O(5)±C(10) 1.438 C(5)±C(6) 1.531

O(1N)±N 1.199 O(6)±C(6) 1.428 C(7)±C(8) 1.522

O(2N)±N 1.198 O(6)±C(10) 1.431 C(7)±C(9) 1.522

O(3)±C(3) 1.431 N±1C(1) 1.515 C(10)±C(11) 1.522

O(3)±C(7) 1.435 C(1)±C(2) 1.498 C(10)±C(12) 1.520

O(4)±C(4) 1.430 C(2)±C(3) 1.507

O(4)±C(7) 1.434 C(3)±C(4) 1.539

Table 3

Bond angles of AM1 optimized structure of (1)

Bonds Angle (8) Bonds Angle (8) Bonds Angle (8)

C(1)±O(1)±C(2) 62.968 O(1)±C(2)±C(3) 116.053 O(3)±C(7)±O(4) 105.788

C(3)±O(3)±C(7) 110.957 C(1)±C(2)±C(3) 120.954 O(3)±C(7)±C(8) 109.153

C(4)±O(4)±C(7) 110.888 O(3)±C(3)±C(2) 110.148 O(3)±C(7)±C(9) 109.853

C(5)±O(5)±C(10) 110.933 O(3)±C(3)±C(4) 105.305 O(4)±C(7)±C(8) 108.813

C(6)±O(6)±C(10) 110.431 C(2)±C(3)±C(4) 112.323 O(4)±C(7)±C(9) 110.700

O(1N)±N±O(2N) 123.232 O(4)±C(4)±C(3) 104.988 C(8)±C(7)±C(9) 112.311

O(1N)±N±C(1) 117.175 O(4)±C(4)±C(5) 109.150 O(5)±C(10)±O(6) 105.843

O(2N)±N±C(1) 119.563 C(3)±C(4)±C(5) 112.446 O(5)±C(10)±C(11) 109.332

O(1)±C(1)±N 116.766 O(5)±C(5)±C(4) 108.479 O(5)±C(10)±C(12) 109.384

O(1)±C(1)±C(2) 59.084 O(5)±C(5)±C(6) 105.141 O(6)±C(10)±C(11) 108.998

N±C(1)±C(2) 120.266 C(4)±C(5)±C(6) 112.561 O(6)±C(10)±C(12) 110.630

O(1)±C(2)±C(1) 57.948 O(6)±C(6)±C(5) 105.124 C(11)±C(10)±C(12) 112.434

C(6)±O(6)±C(10) of the isopropylidene ring; surpris-

ingly, the angles C(3)±O(3)±C(7) and C(5)±O(5)±

C(7) are accurately reproduced. These results indicate

a distortion of one side of each of the isopropylidene

rings. The dihedral angles show the largest deviations.

However, from Fig. 8 one can see that the optimized

structure of (1) is less-closely packed than is the crys-

tal one. This deviation could come from the fact that

(1) is optimized in the gas phase, an approach which

involves a structure, which has none of the intermo-

lecular forces present in a crystal structure.

The topological properties of these molecules were

obtained using the semi-empirical wavefunctions

produced with the AM1 method. The bond critical

points of the oxirane moiety of (1) and derivatives

were used to analyse the effects of the NO2 group

and the fragment containing the two isopropylidene

groups. It should be noted that, in this method, energy

contributions arising from core electrons and their

interactions with valence electrons are represented

only in a parameterized form. Consequently, no expli-

cit charge distribution associated with these electrons

can be given. The AM1 wavefunctions, therefore,

contain only valence orbitals resulting in profound

consequences for their topological analysis (see Fig.

9). We have addressed this question by studying the

topological properties of various valence type wave-

functions [53]. We found that there are problems for

only a few systems, mostly of a p-bonded nature,

having short bond lengths and large differences in

atomic charges. In these systems, the bond critical

points could not be located. The bond critical point

by de®nition is the minimum in the charge density

along the internuclear path. The short bond lengths

plus the high atomic charges of the atoms suppress

these minima. This feature is not due to the inability of

AM1 to calculate the charge density in the bonding

region of these molecules, or to the direct contribution

of the core orbitals to the charge density in this region.

In fact, we have shown [53] that topological proper-

ties of AM1 wavefunctions are consistent with those

of the Hartree±Fock calculations at the split-valence

(6-31G) basis level. Furthermore, the missing core

orbitals can be replaced with those from Near

Hartree±Fock atomic wave functions [54] of the

corresponding atoms. For the molecules studied

here, this implementation was not necessary.

NO2 is a p-attractor group, a feature which shortens

the C(2)±O bond and lengthens the C(1)±O and

C(1)±C(2) bonds. A 1,3-dioxolanyl group can be

considered both as a s-attractor and a p-repeller


Table 4

Difference in bond lengths (%) between optimized structure of (1)

and crystal structure

Bond Bond Bond

O(1)±C(1) 2.66 O(5)±C(5) 21.22 C(4)±C(5) 1.93

O(1)±C(2) 20.74 O(5)±C(10) 1.30 C(5)±C(6) 0.54

O(1N)±N 21.42 O(6)±C(6) 22.07 C(7)±C(8) 1.37

O(2N)±N 2.00 O(6)±C(10) 20.32 C(7)±C(9) 2.05

O(3)±C(3) 20.23 N±C(1) 1.82 C(10)±C(11) 2.83

O(3)±C(7) 0.86 C(1)±C(2) 3.92 C(10)±C(12) 0.26

O(4)±C(4) 0.41 C(2)±C(3) 1.58

O(4)±C(7) 0.84 C(3)±C(4) 20.20

Table 5

Difference in bond angles (%) between optimized structure of (1) and crystal structure

Bonds Bonds Bonds

C(1)±O(1)±C(2) 3.4 O(1)±C(2)±C(3) 21.3 O(3)±C(7)±O(4) 20.1

C(3)±O(3)±C(7) 1.3 C(1)±C(2)±C(3) 21.6 O(3)±C(7)±C(8) 0.4

C(4)±O(4)±C(7) 3.3 O(3)±C(3)±C(2) 20.5 O(3)±C(7)±C(9) 20.1

C(5)±O(5)±C(10) 0.7 O(3)±C(3)±C(4) 1.5 O(4)±C(7)±C(8) 1.0

C(6)±O(6)±C(10) 5.0 C(2)±C(3)±C(4) 20.3 O(4)±C(7)±C(9) 0.4

O(1N)±N±O(2N) 22.4 O(4)±C(4)±C(3) 2.7 C(8)±C(7)±C(9) 1.3

O(1N)±N±C(1) 1.0 O(4)±C(4)±C(5) 1.3 O(5)±C(10)±O(6) 0.4

O(2N)±N±C(1) 1.5 C(3)±C(4)±C(5) 21.7 O(5)±C(10)±C(11) 20.8

O(1)±C(1)±N 1.6 O(5)±C(5)±C(4) 1.1 O(5)±C(10)±C(12) 0.9

O(1)±C(1)±C(2) 24.4 O(5)±C(5)±C(6) 0.7 O(6)±C(10)±C(11) 1.1

N±C(1)±C(2) 1.0 C(4)±C(5)±C(6) 0.0 O(6)±C(10)±C(12) 20.2

O(1)±C(2)±C(1) 1.1 O(6)±C(6)±C(5) 2.9 C(11)±C(10)±C(12) 21.3

group, features which cause the expansion of the

C(1)±O and the contraction of the C(1)±C(2) and

C(2)±O bonds. Thus, the combined effect of a p-

attractor and a s-attractor is a shifting of the bond

critical point toward the C(2) atom. The location of

the bond critical point of the C(1)±C(2) bond of (1)

(see Table 6) shows a shift of 0.0646 AÊ compared to

that of oxirane.

Replacement of NO2 in (1) with CH3 to give (1a), a

group which is a weak s- and p-repeller, indeed

shows a shift of 0.0071 AÊ in the location of the

bond critical point toward the opposite direction, i.e.

toward C(1). The tri¯uoromethyl group in (1b) is

similar, although it is a weaker s-attractor and p-

repeller than is a 1,3-dioxolanyl group, and hence a

shift of 0.0503 AÊ in the bond critical point position

toward C(2) is observed.

The amino substituent in (1c), being a weak p-repel-

ler, also exhibits a shift of 0.0088 AÊ in the bond critical

point position toward C(2). The COOH substituent in

(1d) causes a larger shift of 0.0395 AÊ in the same direc-

tion. The most pronounced effect is the removal of the

3,4-dioxolanyl group in (1). The corresponding bond

critical point in (1e) shifts by 0.0934 AÊ toward

C(2), demonstrating a strong p-repelling effect


Fig. 8. Crystal structure (upper right) and AM1 optimized structure of (1).

Fig. 9. The charge density of a substituted oxirane resulted from the

AM1 method.

whereby the density is pushed towards the C(1)

and O(1) atoms by the electron lumps in the

1,3-dioxolane ring. Removing the second O-

isopropylidene group to give (1f) shows a similar

effect but to a lesser extent (0.0597 AÊ ). Similar

behaviour is observed for the C(2)±C(3) bond,

again showing the signi®cant effect of

the fragment containing the two isopropylidene

rings.

Comparing the topological changes in the C(1)±O,

C(2)±O, and C±C bonds one can see that the NO2

group has more effect on the C(1)±O and C(2)±O

bonds. However, changes in the bond critical point

of C(1)±O and C(2)±O are not as signi®cant. The

NO2 group in¯uences the 72r (r) of C(1)±O and

C(1)±C(2) mostly, and changes in the C(2)±O bond

come mainly from the immediate O-isopropylidene

group.

3. Conclusions

Using both the p-cbd model with the Walsh orbitals

scheme and the Laplacian of the charge density, the

structure of (1) has been analyzed to explain the beha-

viour of the oxirane ring and the C(2)±C(3) bond. The

®rst model requires little computation and relies on

experimental data. The theory of atoms in molecules

also allows one to use the inexpensive AM1 method.

Both models come to the same conclusion. The short-

enings of the C(1)±C(2) and C(2)±C(3) bonds arose

mainly from the two O-isopropylidene groups,

whereas the NO2 is responsible for the contraction

of the C(1)±O bond. Neither the p-cbd model nor

the Laplacian of the charge density model offers a

satisfactory explanation for the elongation of the

C(2)±O bond.

In larger molecules, the Walsh picture becomes

increasingly complicated and thus more MO inter-

actions should be considered. This aspect, however,

makes the model lose its attractive features of

being simple and convenient. The Laplacian

model on the other hand does not really differenti-

ate between various 3MR compounds in claiming

that the substituents will in¯uence all 3MRs in the

same fashion. From the molecular orbital point of

view, this claim is not the case for cyclopropane

and oxirane. The experimental structures of simple

derivatives of these two compounds do not support

the model completely. A systematic study of the

Laplacian and p-cbd together with experimentally

determined structures and spectra should minimize

these defects.

Acknowledgements

This research was supported in part by the Natural

Sciences and Engineering Research Council of

Canada (NSERCC). We would like to thank Dr Hart-

mut L. Schmider for valuable discussions.


Table 6

Topological properties of (1) and derivatives (from top to bottom:

(1), (1a)±(1f)) from AM1 wavefunctions

Bond Location of r b (AÊ ) r b (ea023) 72r b (ea0

25)

C(1)±C(2) 0.8006 0.2239 20.4703

C(1)±O 0.5439 0.2637 20.3911

C(2)±O 0.5457 0.2516 20.3376

C(2)±C(3) 0.7961 0.2397 20.5787

C(1)±C(2) 0.7755 0.2289 20.5024

C(1)±O 0.5474 0.2566 20.3429

C(2)±O 0.5421 0.2528 20.3407

C(2)±C(3) 0.8008 0.2400 20.5759

C(1)±C(2) 0.7448 0.2274 20.5028

C(1)±O 0.5564 0.2412 20.2522

C(2)±O 0.5457 0.2576 20.3627

C(2)±C(3) 0.7771 0.2408 20.5856

C(1)±C(2) 0.7289 0.2302 20.5090

C(1)±O 0.5435 0.2530 20.3402

C(2)±O 0.5462 0.2571 20.3516

C(2)±C(3) 0.7693 0.2409 20.5888

C(1)±C(2) 0.7862 0.2298 20.5034

C(1)±O 0.5449 0.2638 20.3871

C(2)±O 0.5466 0.2537 20.3412

C(2)±C(3) 0.7929 0.2400 20.5812

C(1)±C(2) 0.8294 0.2215 20.4403

C(1)±O 0.5456 0.2641 20.3845

C(2)±O 0.5420 0.2487 20.3277

C(2)±C(3) 0.8090 0.2453 20.5981

C(1)±C(2) 0.7975 0.2243 20.4735

C(1)±O 0.5428 0.2637 20.3929

C(2)±O 0.5466 0.2514 20.3320

C(2)±C(3) 0.8075 0.2389 20.5646

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