DFT-HSAB prediction of regioselectivity in 1,3-dipolar cycloadditions: Behavior of (4-substituted)benzonitrile oxides towards methyl propiolate

Article abstract of DOI:10.1002/chem.200500739

The regioselectivity of 1.3-di-polar cycloadditions between (4-substituted)benzonitrile oxides and methyl propiolate cannot be rationalized on the basis of the electron demand of the reactants or frontier molecular-orbital theory. To this problem, we have

Full text of DOI:10.1002/chem.200500739

DOI: 10.1002/chem.200500739
DFT-HSAB Prediction ofRegioselectivity in 1,3-Dipolar Cycloadditions:
Behavior of(4-Substituted)benzonitrile Oxides towards Methyl Propiolate**
Alessandro Ponti*[a] and Giorgio Molteni[b]
Abstract: The regioselectivity of 1,3-di-
polar cycloadditions between (4-substi-
tuted)benzonitrile oxides and methyl
propiolate cannot be rationalized on
the basis of the electron demand of the
reactants or frontier molecular-orbital
theory. To this problem, we have ap-
plied a quantitative formulation of the
hard–soft acid–base principle devel-
oped within the density functional
theory. Global and local reactivity indi-
ces were computed at B3LYP/6-
311+G(d,p) level. The details of charge
transfer upon the reactive encounter
have been elucidated, and the comput-
ed regioselectivity has been shown to
be in good agreement with experimen-
tal data.
Keywords: cycloaddition · density
functional calculations
·
HSAB
principle · nitrile oxide
Introduction
of coefficients in the frontier LCAO-MO (LCAO=linear
combination of atomic orbitals) to describe regioselectivity,
suffers from the fact that MOs are defined to within a rota-
tion in the orbital basis set, so that the MO coefficients are
not uniquely defined, even in a minimal basis calculation.
Furthermore, when modern multiple-zeta polarized basis
sets are used, it is far from clear how MO coefficients
should be handled. As a consequence, even in a recent com-
parative study of theoretical tools to predict regioselectivi-
ty,[11] FMO coefficients were taken from HF/STO-3G calcu-
lations, although large-basis, high-level calculations were
used throughout the study.
In the last decade, many important concepts and indices
that are useful for the understanding of chemical reactivity
have been rationalized within the framework of density
functional theory.[12] Well-known examples[13] are the elec-
tron chemical potential m=(@E/@N)n(r), which is defined as
the “marginal” electronic energy and represents the escap-
ing tendency of molecular electrons (E=molecular energy
and N=the number of molecular electrons), and the global
softness S=(@N/@m)n(r), which describes the ability of the
molecule to take or loose electrons in response to a change
in m. Within DFT, any reaction can be considered to be split
in two steps as follows:[14,15] 1) As soon as reactant mole-
cules approach each other they form a weakly-interacting,
promoted complex[16–18] in which charge is transferred be-
tween the reactants to equalize the electron chemical poten-
tial at constant external (nuclear) potential. 2) A charge re-
shuffling at constant electron chemical potential occurs in
which the promoted complex either evolves toward the
product(s) or back to the reactants. If the second step can
Since the first isoxazole synthesis in 1936,[1] nitrile oxide cy-
cloaddition chemistry has been continuously developed.[2]
The astonishing array of latent functionalities presented by
isoxazole cycloadducts make them versatile starting materi-
als in the synthesis of acyclic structures,[3] aldols,[4] enones,[5]
g-aminoalcohols,[6] and so on.[7] Later, stereoselective nitrile
oxide cycloaddition methodologies[8] provided further valua-
ble targets in the field of isoxazole synthesis. Most of the
successful applications of nitrile oxide cycloaddition chemis-
try in synthesis are intimately linked with theory. Early find-
ings by Houkꢀs group were based on a frontier molecular or-
bital (FMO) theory[9] that worked well for monosubstituted
ethylenic dipolarophiles.[10]
In general, FMO theory has been successfully applied to
many organic reactions and is still one of the most preferred
theoretical tools utilized by the organic chemist. However,
despite its broad success, it is an approximate theory deeply
rooted in the Hartree–Fock approach. For instance, the use
[a] Dr. A. Ponti
Consiglio Nazionale delle Ricerche
Istituto di Scienze e Tecnologie Molecolari
via Golgi 19, 20133 Milano (Italy)
Fax : (+39)02-5031-4300
E-mail: alessandro.ponti@istm.cnr.it
[b] Dr. G. Molteni
Università degli Studi di Milano,
Dipartimento di Chimica Organica e Industriale
via Venezian 21, 20133 Milano (Italy)
[**] HSAB=hard–soft acid–base principle
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Chem. Eur. J. 2006, 12, 1156 – 1161

FULL PAPER
be neglected, the most favorable situation occurs when the
reactants have equal softness. This is the DFT formula-
tion[14,19] of Pearsonꢀs hard–soft acid–base (HSAB) princi-
ple.[20]
are open subsystems freely exchanging energy and elec-
trons) of the system. The contribution to DW due to the in-
teraction between atom i in molecule P and atom k in mole-
cule Q is
Clearly, a local (atomic) reactivity index is needed to
study regioselectivity. The best suited for this purpose is
local softness s(r)=(@1(r)/@m)n(r), which represents the sensi-
tivity of the molecular electron density 1 at point r to a
change in m. The physical significance of s(r) can be made
clearer by writing s(r)=[(@1(r)/@N)(@N/@m)]n(r) =f(r)S.[13] The
derivative with respect to N is the Fukui function f(r) de-
fined by Parr and Yang[21] and represents how the electron
density 1(r) rearranges as a consequence of a change in the
number of molecular electrons, irrespective of what causes
such change. The other derivative is the global softness rep-
resenting the charge transfer due to a change in m, which in
our case is brought about by the collision between the reac-
tants. Therefore, s(r) describes both the charge transfer be-
tween the reactants and how charge is redistributed within
the reactants themselves. A local HSAB principle[22] can
then be devised as follows: a regioisomer is favored when
the new bonds form between atoms with equal softness. The
local HSAB principle has provided many reliable qualitative
predictions of regioselectivity for 1,3-dipolar cycloadditions
(1,3-DC),[23–29] as recently discussed in detail.[11]
The modern theory of regioselectivity just outlined under
the name of “local HSAB principle” does not stand against
FMO theory, rather it improves the latter in several respects
by abandoning the wavefunction approach and the related
concept of orbital. FMO theory can be regarded as a special
case of the more general theory of chemical reactivity pro-
vided by DFT. For instance, the electron chemical potential
m is usually computed in the finite-difference approximation
as mffiÀ(I+A)/2, for which I and A are the vertical ionization
potential and electron affinity, respectively. Similarly, Sffi
(IÀA)À1. If one neglects the relaxation of the electron densi-
ty upon ionization, then one can write mffi(eHOMO+eLUMO)/2
and Sffi(eHOMOÀeLUMO)À1, so that a clear parallel between the
two theories appears. The accuracy loss due to the neglect
of electron relaxation is, however, significant when chemical
accuracy is the target. Furthermore, the HOMO and
LUMO can be regarded as an approximation to the finite-
difference expression of the Fukui function, for example, for
the case of electrophilic attack fÀ(r)ffiHOMO. However, the
FMOs are a poor approximation of the Fukui function.[13,30]
Finally, the DFT-based theory should not be considered as a
mere refining of the FMO theory as it relies on a quite dif-
ferent theoretical basis and, as we will soon discuss, it is
amenable to a quantitative formulation of regioselectivity.
It is assumed that when two reactants approach each
other the interaction occurs between pairs of atoms located
in different molecules. Charge is transferred within such
pairs in the very first step of the bond-forming interaction
between the specific atoms. Such transfer equalizes the elec-
tron chemical potential and induces a variation DW of the
grand potential (i.e., the natural thermodynamic quantity
used to describe the behavior of the reactants’ atoms, which
1
2
sPisQk
sPi þ sQk
Pi
Qk
2
ð1Þ
DW ¼ À ðmPÀmQÞ
For the case of concerted 1,3-DCs, we can obtain DW for
each regioisomer as the sum of two bond-forming interac-
tions and their difference dDW describes the relative stabili-
zation of the two regioisomeric promoted complexes. Given
that in 1,3-DCs the relative energy of transition states is par-
alleled by the relative energy of the weakly interacting com-
plexes forming in the early stage of the reaction,[10] the ne-
glect of the charge reshuffling term is reasonable.[31,32] More-
over, the many successful qualitative predictions of regiose-
lectivity found in the literature suggest that the interaction
energy between the reactants forming the activated complex
should be closely related to the transition-state energy. For
the above reasons, DW is expected to be proportional to the
transition-state energy and to provide a quantitative predic-
tion of regioselectivity without the need to locate the transi-
tion state. On these grounds, a generalization of the local
HSAB principle has been introduced,[33] which enables one
to compute the relative stabilization of the two regioisomer-
ic transition states from m and s of the reactants only. This
method has been successfully applied by us to the 1,3-DC
between nitrilimines and alkynyl or alkenyl dipolaro-
philes,[34–36] and between arylazides and methyl propiolate.[37]
Some qualitative predictions of the regiochemistry of the
1,3-DCs of nitrile oxides to electron-deficient acetylenes,
based on DFT calculations, have been reported.[38] In order
to have a clearer and more systematic picture of the sub-
stituent effect on the regioselectivity of the 1,3-DC of nitrile
oxides to methyl propiolate, we present here a quantitative
study of the regioselectivity observed in the cycloadditions
between (4-substituted)benzonitrile oxides and methyl pro-
piolate (see Scheme 1). The present study is based upon the
DFT theory and the HSAB principle, and does not involve
the location of the transition structure and the calculation of
the activation energy. The latter point is important as the
calculation of the activation barrier for the 1,3-DC of nitrile
oxides is very sensitive to the treatment of electron correla-
tion, both for alkynyl[39] and alkenyl[40] dipolarophiles.
Results and Discussion
It has been known for a long time that the 1,3-DCs between
(4-substituted)benzonitrile oxides 2 and methyl propiolate 3
give mixtures of regioisomeric 4-methoxycarbonyl-3-(4-sub-
stituted)phenylisoxazoles 4 and 5-methoxycarbonyl-3-(4-sub-
stituted)phenylisoxazoles 5.[41]
The regioselectivity and total yield presently observed for
the 1,3-DCs of 2a–e and 3 (Scheme 1) in refluxing CCl4 are
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1157

A. Ponti and G. Molteni
and therefore a predominance
of 4a–d is expected. Converse-
ly, the 1,3-DC between 2e and
3 is subject to major LUMO-
dipole control and 5e is expect-
ed to be the major product.
Comparison with the experi-
mental data in Table 1 shows
that FMO prediction is correct
only for 2e+3, as regioisomer
5
predominates in any case.
Hence, to better understand the
regioselectivity of the cycload-
Scheme 1.
dition between 2 and 3, we
turned our attention to the local HSAB principle, as formu-
lated within DFT. The main results of our DFT calculations
at the B3LYP/6-311+G(d,p) level are reported in Table 3.
The electron chemical potential difference between 2 and
3 determines the direction of the overall charge flow upon
the interaction of the reactants, as electrons flow towards re-
Table 1. Experimental yield ratios for 4:5 and total yields for the cyclo-
addition reactions between benzonitrile oxides 2 and methyl propiolate 3
in CCl4 at 778C.
R
Yield ratio[a]
Yield [%]
4:5
4+5
a
b
c
d
e
H
29:71
32:68
40:60
28:72
30:70
>95
90
88
95
83
Me
MeO
Cl
Table 3. Results of B3LYP/6-311+G(d,p) calculations: electron chemical
potential difference between benzonitrile oxides 2 and methyl propiolate
3, along with the dDW difference[a] and predicted yield ratios of 4:5 for
their mutual cycloaddition.
NO2
[a] Determined by NMR spectroscopic analysis of the crude reaction
mixture.
R
m(2)Àm(3) [eV]
dDW [kJmolÀ1
]
Predicted ratio of 4:5[b]
reported in Table 1. The yield ratio was obtained from
NMR spectroscopic analysis of crude reaction mixtures.
This regioselective outcome cannot be fully rationalized
on the basis of the electronic demand of the reactants.
When the substituents are ordered by the yield ratio of 4:5,
one obtains MeO<Cl<Me<NO2 <H. Even if the most
electron-donating group, MeO is at one end, and at the
other end one finds the “null” substituent H. Linear regres-
sion of the yield ratio versus Hammett sp values[42] results in
a scattered plot with a very low correlation coefficient, 1=
0.47. As for FMO theory, the FMO energies at the B3LYP/
6-311+G(d,p) level are reported in Table 2. For 2a–d the
HOMO-dipole–LUMO-dipolarophile difference (ranging
from 4.5 to 5.1 eV) is 1–2eV smaller than the LUMO-
dipole–HOMO-dipolarophile difference (ranging from 6.1
to 6.7 eV), whereas the latter difference (4.6 eV) is 1.1 eV
smaller than the former (5.7 eV) for nitro-substituted 2e.
Both FMO interactions can thus be effective, and one can
only predict that a regioisomeric mixture will result. Pushing
FMO theory a little further, major HOMO-dipole control
can be associated with the 1,3-DCs between 2a–d and 3,
H
0.70
0.87
1.15
0.57
À1.63
À1.89
À5.01
À0.73
À1.71
30:70
31:69
40:60
28:72
30:70
Me
MeO
Cl
NO2
À0.49
[a] Difference in grand potential variation for the pathways leading to
isoxazoles 4 and 5. [b] From computed dDW and Equation (4); uncertain-
ty Æ1%.
gions at low electron chemical potential m. Charge flows
from the substituted benzonitrile oxide to methyl propiolate
in the reaction of 3 with 2a–d and vice versa in the reaction
of 3 with 2e, that is, 2a–d act as nucleophiles, whereas 2e
acts as electrophile. Note also that 2a–b and 2e show very
similar regioselectivity, although the very different electron-
demand properties of the substituents make the m(2)Àm(3)
difference largely unequal and opposite in sign. As it de-
pends only on global indices, the direction of the overall
charge flow is the same irrespective of regiochemistry.
The local charge transfer, that is, the transfer of electrons
between interacting atoms can be computed as[22]
À1
DNðC1 ! C20 Þ ¼ ½mð3ÞÀmð2ފ sðC1Þ sðC20 Þ ½sðC1Þ þ sðC20 ފ
Table 2. Frontier MO energies of dipole benzonitrile oxides 2 and dipo-
larophile methyl propiolate 3 at the B3LYP/6-311+G(d,p) level.
ð2Þ
Entry
R
HOMO energy [eV]
LUMO energy [eV]
À1
DNðO3 ! C10 Þ ¼ ½mð3ÞÀmð2ފ sðO3Þ sðC10 Þ ½sðO3Þ þ sðC10 ފ
2a
2b
2c
2d
2e
3
H
À6.7
À6.5
À6.3
À6.8
À7.4
À8.1
À1.8
À1.6
À1.4
À2.0
À3.5
À1.7
Me
MeO
Cl
in which DN is the degree of electron population transferred
from the dipole atom to the dipolarophile atom and the
atoms are numbered as illustrated in Scheme 1 (these equa-
tions are easily generalized so that they can be transferred
NO2
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Chem. Eur. J. 2006, 12, 1156 – 1161

Cycloadditions
FULL PAPER
to other interacting atom pairs). The actual direction of
local electron flow to alkynes in the 1,3-DC of HCNO has
recently been debated.[18,43–46] Our calculations show that at
the beginning of the reaction, the oxygen atom behaves as a
donor and the nitrile oxidic carbon atom as an acceptor, the
only exception being 2e+3!4e, for which the reverse be-
havior is observed. Our results are thus in agreement with
spin-coupled valence-bond calculations,[45,47] but they also
imply that the amount and direction of both global and
local electron transfer depends on the substituent present in
the reactants.[44]
We now turn to regioselectivity and, as selectivity criteri-
on, use the grand potential change due to two bond-forming
interactions between 2 and 3,[33] because of the general
agreement about the concertedness of 1,3-DC reactions. The
grand potential change for the pathway leading to 4-methoxy-
carbonyl-3-(4-substituted)phenylisoxazole 4 is
Figure 1. Linear relationship between the computed difference dDW in
grand potential variation for the pathways leading to cycloadducts 4 and
5, and the correspondent difference in activation energy dDE°, computed
from the experimental yield ratio of 4:5. The error bars illustrate the un-
certainty in dDE° due to the error in the yield ratio, estimated at 1%.
DWð4Þ ¼ ð1=2Þ ½mð3ÞÀmð2ފ ½DNðC1 ! C20 Þ þ DNðO3 ! C10 ފ
ð3Þ
The negative intercept in the equation above implies that
there is a preference towards the 5-methoxycarbonylisoxa-
zoles 5, as dDE° =<0 when dDW=0. Such a preference is
independent of the specific electronic interaction between
the reactants and the individual reacting sites. It might be
tentatively attributed to steric hindrance between the aryl
and the carbomethoxy moieties that become close to each
other when approaching to form regioisomer 4. The slope in
Equation (4) is significantly larger than 1. This means that
the difference in transition-state energy is about one third of
the computed energy difference between the promoted com-
plexes. Given that in our previous studies of arylnitrili-
mines[34] and arylazides[37] the regression slope was always
ꢀ1, we checked whether the neglected constant electron
potential term DWm (charge reshuffling) could counter-bal-
ance the constant external potential term DW of Equa-
tion (3) and reduce the slope. To this end, we computed the
grand-potential contribution of the step at constant electron
chemical potential as
DN for this equation is defined in Equation (2). DW(5) can
be obtained by exchanging C1’ and C2’. Each new bond con-
tributes to the stabilization of the promoted complex by a
term consisting of the amount of electrons transferred be-
tween the relevant atoms multiplied by the electron chemi-
cal potential difference. The stabilization difference dDW=
DW(5)ÀDW(4) is reported in Table 3. The negative sign of
dDW shows that cycloadduct 5 is the major one, in line with
experimental results.
The regioselective similarity of the 2e+3 cycloaddition to
that of the 1,3-DCs involving 2a and 2b is now clearly ex-
plained by our DFT-HSAB approach, as the relevant pro-
moted-complexes have similar computed stabilization. This
is the result of two opposite effects: the large difference in
the amount of charge transferred upon the formation of the
two possible regioisomeric complexes for 2e+3 (compara-
ble to that observed in 2c+3) is counterbalanced by the
smaller (in absolute value) difference m(2e)Àm(3), which
makes the charge transfer less effective in producing ener-
getic stabilization.
À1
À1
DWmð4Þ ¼ Àð1=2Þ lf½sðC1Þ þ sðC20 ފ þ ½sðO3Þ þ sðC10 ފ
g
ð5Þ
We now proceed one step further by demonstrating that
dDW is a quantitative regioselectivity index for the present
1,3-DC reactions. The difference in activation energy, dDE°
of the two reaction paths can be obtained as dDE° =ÀRT
log(Y) in which T is the reaction temperature (350 K) and Y
is the experimental ratio of 4:5. Estimating the error in Y at
Æ1%, weighted least-squares linear regression results in
in which DWm(5) can be obtained by exchanging s(C1’) and
s(C2’) and l is a positive parameter related to an effective
number of valence electrons.[25] As the value of l is not pre-
cisely set by theory, we carried out a bilinear regression of
dDE° with dDW and dDWm for which l was considered a pa-
rameter to be optimized. Such regression does not repro-
duce the experimental data better than the linear one in
Equation (4); the slope related to dDW and the intercept are
very close to that previously obtained, and the optimized
factor, l=À1.4”10À4 is clearly not significant. This confirms
that in 1,3-DCs the relative transition-state energy depends
on the relative energy of the promoted complex formed by
charge transfer in the chemical-potential equalization step
dDW ¼ ð2:7 Æ 0:3Þ dDE°Àð8:1 Æ 0:9Þ kJ molÀ1, 1 ¼ 0:99
ð4Þ
in which 1 is the linear correlation coefficient (Figure 1).
The predicted ratio of 4:5 (Table 3), obtained from the com-
puted dDW by using Equation (4), is in very good agreement
with the experimental values (Table 1).
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A. Ponti and G. Molteni
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step. As for possible structural peculiarities in the benzoni-
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Experimental Section
Cycloadditions between nitrile oxides 2 and methyl propiolate 3: Com-
pounds 4a–e and 5a–e are known in the literature.[36]
General procedure: A solution of 2 (5.0 mmol) and 3 (0.43 g, 5.0 mmol)
in dry carbon tetrachloride (25 mL) was refluxed for 20 h. Evaporation
of the solvent in vacuo gave a residue, which was separated by chroma-
tography on a silica-gel column with EtOAc/hexane 3:7. The major prod-
uct, 4-methoxycarbonylisoxazole
4 was eluted first, followed by the
minor product, 5-methoxycarbonylisoxazole 5. Crystallization from diiso-
propyl ether gave analytically pure 4 and 5.
Computational methods: DFT calculations were performed with the
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basis set. The in-vacuo geometry of 2a–e and 3 was fully optimized and
characterized with vibrational analysis at the same level of theory. The
anion and cation of 2a–e and 3 were treated at the UB3LYP level by
using the geometry of the neutral systems. Atomic electron populations
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atom-centered dipoles), which has already proved to be
a reliable
method.[50] Reactivity indices were computed within the finite difference
approximation:[12] m=À(I+A)/2and S=(IÀA)À1 in which I and A are the
(vertical) ionization potential and electron affinity, respectively. The local
softness s (condensed to each individual atom[51]) was computed as s+
=
S[p(N0+1)Àp(N0)] for electrophiles, and as sÀ =S[p(N0)Àp(N0À1)] for
nucleophiles in which p(N), N=N0À1, N0, and N0 +1 represent the
atomic electron population of the cationic, neutral, and anionic system,
respectively.
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Chem. Eur. J. 2006, 12, 1156 – 1161

Cycloadditions
FULL PAPER
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Received: June 28, 2005
Published online: October 31, 2005
Chem. Eur. J. 2006, 12, 1156 – 1161
ꢁ 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemeurj.org
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