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Patterns of p-Electron Delocalization in Aromatic and Antiaromatic Organic Compounds in the Light of the Hückel’s 4n+2 rule

J.
Poater,
F.
Feixas,
E.
Ma,to,
M.
Solà

Ins$tute
of
Computa$onal
Chemistry

Universitat
de
Girona
(Catalonia,
Spain)

��. INTRODUCTION
TO
AROMATICITY

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC

AROMATIC
MOLECULES

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

IV. CONCLUSIONS

TO
AROMATICITY

The
concept
of
“aroma,city”
is
oLen
invoked
in
organic

chemistry
textbooks
and
research
works
to
explain
a
number

of
chemical
phenomena.

Terms
appearing
as
ar,cle
,tle,
keywords,
or
abstract

ISI
(2000-‐2010)

In
2009,
in
every
2
hours
appeared
a
paper
in
which
benzene

is
in
the
,tle,
keywords
or
the
abstract!

TO
AROMATICITY

How
to
measure
aroma,city?

 Aroma,city
is
not
an
observable,
then
there
is
not

a
unique
and
generally
accepted
measure
of

aroma,city.

 Many
criteria
have
been
used
to
develop
indices
of

aroma,city:

– Energe,c
(ASEs,
REs,…)

– Structural
or
Geometrical
(HOMA,…)

– Magne,c
(NICS,
ring
currents,
1H
NMR…)

– Electronic
(hardness,
ELF,
DIs…)

TO
AROMATICITY

It
is
your
favorite
index
of
aroma,city

beaer
than
mine
?

 Energe,c,
structural,
magne,c,
and
electronic
criteria
are
easily

measurable
but
unfortunately
they
do
not
always
give
consistent

results
among
themselves
→
Mul,dimensional
phenomenon.

 Diﬀerent
indices
aﬀord
divergent
orderings
of
aroma,city
since

one
compound
may
be
more

aroma,c
than
other
in
one
direc,on

and
less
aroma,c
in
another.

 Many
authors
recommend
to
perform
aroma,city
analyses
using

a
set
of
aroma,city
descriptors.

TO
AROMATICITY

It
is
your
favorite
index
of
aroma,city

beaer
than
mine
?

 When
a
new
index
is
defined,
usually
the
results

obtained
in
a

set
of
aroma,c
compounds
are
correlated
with
previously
defined

indices
of
aroma,city.

 The
mul,dimensional
character
of
aroma,city
is

some,mes
used

as
a
generic
excuse
to
consider
any
local
index
of
aroma,city

defined
a
good
descriptor
irrespec,ve
of
the
results
obtained.

 How
can
one
differen,ate
methods
that
provide

essen,ally

spurious
informaIon
from
those
that
simply
do
not
correlate

because
of
the
mul,dimensional
character
of
aroma,city?

TO
AROMATICITY

It
is
your
favorite
index
of
aroma,city

beaer
than
mine
?

 Fortunately,
the
accumulated
experience
provides
several

examples
for
which
most
chemists
would
agree
about
the
expected

aroma,city
trends.
S,ll
most
aroma,city
descriptors
fail
to

reproduce
certain
basic
chemical
situa,ons.

 We
propose
to
build
a
set
of
aroma,city
tests
using
a
series
of

such
examples
to
assess
the
quality
of
the
informaIon
derived

from
the
diﬀerent
indicators.
The
chosen
tests
must
fulﬁll
two

requirements:

 The
size
of
the
systems
involved
should
be
small

 Controversial
cases
must
be
avoided

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

Indices
of
aroma,city
analyzed

Structural
or
Geometric
criteria

 They
are
based
on
bond
length
equaliza,on
between
single

and
double
bonds:

Ropt
=
1.388
Å

α
=
257.7

J.
Kruszewski
and
T.
M.
Krygowski
Tetrahedron
Le>.
1972,
3839.

M.
K.
Cyranski,
B.
T.
Stepien
and
T.
M.
Krygowski
Tetrahedron
2000,
56,
9663.

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

Indices
of
aroma,city
analyzed

MagneIc
criteria

Aroma,c
ring
π-‐electrons
are
induced
to

circulate
in
a
strong
magne,c
field
(Ho)
such
that

the
induced
magne,c
field
is
aligned
with
the

Hind

applied
field
in
the
vicinity
of
the
aryl
protons,
but

opposes
the
applied
field
causing
shielding
(upfield

shiL)
of
protons
above
and
below
the
ring.

MagneIc
shielding
tensor

H

z

0

R av

O

Aroma,c
rings
have
nega,ve
*
N
R0

NICS
values
at
the
center.

R av

P.
v.
R.
Schleyer
et
al.,
J.
Am.
Chem.
Soc.
1996,
118,
6317

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

Indices
of
aroma,city
analyzed

Electronic
criteria

 They
are
based
on
the
calcula,on
of
electronic
delocaliza,on
indices
(DIs)

computed
for
closed-‐shell
HF
or
approximate
DFT
WFs
as:

 The
sums
are
over
occupied
molecular
orbitals.
DIs
measure
the
number
of

electrons
shared
between
atoms
A
and
B.
QTAIM
par,,on
used.

 The
para-‐delocaliza,on
index
(PDI)
is
computed

as
an
average
of
all
possible
DI
between
para-‐
related
carbons
in
a
6-‐MR.

 he
aroma,c
ﬂuctua,on
index
(FLU)
is
constructed
considering
the
amount
of

T
electron
delocaliza,on
and
also
taking
into
account
the
similarity
of
electron

delocaliza,on
in
adjacent
atoms
(symmetry).

Symmetry
Delocaliza,on

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

Indices
of
aroma,city
analyzed

Electronic
criteria

MulIcenter
delocalizaIon
indices

A = {A1, A2, …, AN}


For
monodeterminantal
closed-‐shell
WFs:

M. Giambiagi, M. S. de Giambiagi, C. D. dos Santos and A. P. de Figuereido, Phys.
Chem. Chem. Phys. 2000, 2, 3381

P. Bultinck, R. Ponec and S. van Damme, J. Phys. Org. Chem. 2005, 18, 706

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

15
PROPOSED
TESTS

F. Feixas, E. Matito, M. Solà, J. Poater, J. Comput. Chem. 2008, 29, 1543

I��. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

F. Feixas, E. Matito, M. Solà, J. Poater, J. Comput. Chem. 2008, 29, 1543

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

 The
problem
with
the
calcula,on
of
mul,center
delocaliza,on
indices

is
that
they
are
quite
expensive,
especially
for
large
rings.
It
would
be

convenient
to
have
an
electronic
measure
of
aroma,city
based
on
2c-‐
DIs.
Something
similar
to
PDI
or
FLU
but
more
general
and
eﬀec,ve.

 First
we
looked
at
the
total
and
total
π
electronic
delocaliza,on
taking

into
account
the
4n+2
Hückel’s
rule
we
should
have:

+ 2 e- + 2 e-

+ 2 e- + 2 e-

F. Feixas, E. Matito, M. Solà, J. Poater, J. Phys. Chem. A 2008, 112, 13231

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

B3LYP/6-‐311G(d,p)

C6H62+

C6H6

C6H62-‐

δ(C,C’)
total

14.863
15.618
15.731

δ(C,C’)
π
2.614
3.369
3.482

0.755
0.113

2.614
3.369
3.482


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

B3LYP/6-‐311G(d,p)

Δ1=P(N)-‐P(N-‐2)

Δ2=P(N+2)-‐P(N)
diﬀ=Δ2-‐Δ1


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

B3LYP/6-‐31G(d)

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

 Symmetry
and
signiﬁcant
delocaliza,on


meta
vs
para-‐delocaliza,on

1.828

1.389
1.389
1.008
δ(C,C’)m=0.043

1.008

δ(C,C’)p=0.009

1.389
1.389

0.976
0.976
δ(C,C’)m=0.059

1.389
1.389
δ(C,C’)p=0.014

δ(C,C’)m=0.074
0.978

δ(C,C’)p=0.100

Benzene
Cyclohexene

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

1
δ1-‐2

6
2

δ1-‐3

δ1-‐4

5
3

4

δ1-‐2
δ1-‐2

δ1-‐3

δ1-‐3

δ1-‐5
δ1-‐4

F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

How
do
the
electron
and
geometry
relaxa,on
aﬀect
upon
addi,on/extrac,on
of
2
e-‐?

1)
OPT
Full
geometry
and
MO
relaxa,ons
of
all
N,
N-‐2
and
N+2
species

2)
GEO
Geometry
op,miza,on
only
for
N
species,
N-‐2
and
N+2
keep
the

geometry
of
N,
but
the
MOs
are
fully
relaxed

N-‐2
N
N+2

3)
ONLY
Geometry
op,miza,on
only
for
N
species,
N-‐2
and
N+2
keep
the

geometry
and
the
MOs
of
the
N
system

1.385
1.385
1.400
1.400

geometry
1.539
1.539
1.543
1.543

When
analyzing
the
total
electronic
delocaliza,on
the
eﬀect
of
g1.400

1.385
1.385
1.400
eometry
and

electron
relaxa,on
are
small
enough
to
be
neglected

geometry

C6H62+
D2h
C6H6
D6h
C6H62-‐
D2h

N-‐2
N
N+2

C6H6 N–2 N N+2 Δ Δ2
C6H6 2+

D6h
C6H6
D6h
C6H6 2-‐
1
D6h

OPT δ1-4tot
1.413
0.180
1.413
0.310 0.182 0.130
1.460
1.460
-0.127
1.422
1.422
1.501
1.501

Electronic

0.987
0.987
1.005
1.005

GEO (DI)
tot
Electronic

δ1-41.041
0.185
Structure
1.041
0.310 0.183 1.052
0.125 -0.128
1.052

Structure
(DI)
1.413
1.413
1.460
1.460

ONLY δ1-4tot
1.422

0.187
1.422

0.307 0.193 0.120
1.501
1.501

-0.114
C6H62+
D2h
C6H6
D6h
C6H62-‐
D2h

C6H62+
D2h
C6H6
D6h
C6H62-‐
D2h


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

N-‐2
N
N+2

+2e-‐
+2e-‐

C6H6
Δ1
Δ2

C6H6+2
C6H6
C6H6-‐2

4π-‐e
an,aroma,c
6π-‐e
aroma,c
8π-‐e
an,aroma,c

N-2 N N+2 Δ1 Δ2 diff

δ1-‐2
δ(1-2) 1.270 1.390 1.353 0.120 -0.037 -0.157
δπ(1-2) 0.300 0.425 0.387 0.125 -0.038 -0.163
δ(1-3) 0.148 0.073 0.121 -0.075 0.048 0.123
δ1-‐4
δ1-‐3
δπ(1-3) 0.107 0.036 0.083 -0.071 0.047 0.118
δ(1-4) 0.050 0.103 0.062 0.054 -0.042 -0.095
δπ(1-4) 0.039 0.094 0.052 0.054 -0.041 -0.096
Δ1=[N]
-‐
[N-‐2],
Δ2=[N+2]
–
[N]
diﬀ=Δ2
-‐
Δ1

ANTIAROMATIC
AROMATIC
AROMATIC
ANTIAROMATIC

4N
4N+2
4N+2
4N

δ(1-‐2)
↑
δ(1-‐3)
↓
δ(1-‐4)
↑
δ(1-‐2)
↓
δ(1-‐3)
↑
δ(1-‐4)
↓


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

N-‐2
N
N+2

C8H8
+2e-‐
+2e-‐

Δ1
Δ2

C8H82+
C8H8
C8H82-‐

6π-‐e
aroma,c
8π-‐e
an,aroma,c
10π-‐e
aroma,c

1
δ1-‐2
C 8H 8 N-2 N N+2 Δ1 Δ2 diff
δ(1-2) 1.332 1.401 1.361 0.069 -0.040 -0.109
δπ(1-2) 0.344 0.430 0.409 0.087 -0.022 -0.108
δ1-‐3

δ(1-3) 0.113 0.064 0.094 -0.048 0.030 0.078
δ1-‐5
δ1-‐4

4
δπ(1-3) 0.074 0.029 0.060 -0.046 0.031 0.077
5
δ(1-4) 0.020 0.043 0.026 0.023 -0.017 -0.040
dC-‐C(1-‐5)
>
dC-‐C(1-‐4)
δπ(1-4) 0.016 0.040 0.023 0.023 -0.016 -0.040
δ(1-‐5)
>
δ(1-‐4)
δ(1-5) 0.056 0.008 0.042 -0.048 0.034 0.082
δπ(1-5) 0.054 0.007 0.041 -0.047 0.034 0.082
AROMATIC
ANTIAROMATIC
ANTIAROMATIC
AROMATIC

(N-‐2)

(N)
(N)
(N+2)

δ(1-‐2)
↑
δ(1-‐3)
↓
δ(1-‐4)
↑
δ(1-‐5)
↓
δ(1-‐2)
↓
δ(1-‐3)
↑
δ(1-‐4)
↓
δ(1-‐5)
↑


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

C6H6 C8H8
C8H82+
C8H82-
C6H62+
C6H62-
δ1-2 δ1-3 δ1-4 δ1-2 δ1-3 δ1-4 δ1-5

ANTIAROMATIC AROMATIC AROMATIC ANTIAROMATIC
4N 4N±2 4N±2 4N
4,5-MR 6,7-MR 8,9-MR 4,5-MR 6,7-MR 8,9-MR

δ1-2 Decrease Increase Decrease δ1-2 Increase Decrease Increase

δ1-3 Increase Decrease Increase δ1-3 Decrease Increase Decrease

δ1-4 Increase Decrease δ1-4 Decrease Increase

δ1-5 Increase δ1-5 Decrease


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

6,7-‐MR
C6H6 C 7H 7+ C 7H 7- 8,9-‐MR
C 8H 8 C 9H 9-

1.401 1.382
δ(1-2) 1.390
>
1.371
>
1.366
δ(1-2)
>

0.064 0.070
0.073
δ(1-3)
<

δ(1-3)
<
0.086 <
0.091 δ(1-4) 0.040 >
0.038
δ(1-4) 0.103 >
0.054 >
0.039 δ(1-5) 0.008
<
0.022

C6H6
C8H8

C7H7+
C9H9-‐

C7H7-‐


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

N-2(t) N-2(s) N N+2(s) N+2(t)
δπ 2.543 2.644 3.359 3.466 3.451
δ(1-2) 1.356 1.251 1.397 1.349 1.368
δπ(1-2) 0.401 0.287 0.422 0.382 0.409
δ1-‐2
δ(1-3) 0.082 0.125 0.067 0.119 0.085
δπ(1-3) 0.051 0.088 0.036 0.082 0.056
δ(1-4) 0.109 0.064 0.102 0.062 0.092
δ1-‐4
δ1-‐3
δπ(1-4) 0.099 0.054 0.093 0.052 0.082
FLU 0.009 0.029 0.000 0.024 0.004
SCI 0.162 -0.001 0.078 0.003 0.095

ANTIAROMATIC
AROMATIC

4N
(singlet)
4N
(triplet)

4N+2
(singlet)

δ(1-‐2)
↑
δ(1-‐3)
↓
δ(1-‐4)
↑


II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

D4h
*
Orbital
where
2e-‐
have
been
removed

Al42-‐
N-2(2π e-)
**
Orbital
where
2e-‐
have
been
added

N-2(0π e-) N-2(2π e-) N(2π e-) N+2(4π e-)
CMO-‐
NICS

AIM
Al4 (a1g)* Al4 (a2u)* Al4 (b2g)* Al42- Al44- (eg)**

MCI σ+π 0.197
0.182
0.325
0.359
0.222

LUMO+1(π
virt)

eg
MCI σ 0.010
0.182
0.187
0.172
0.210

MCI π 0.187
0.000
0.187
0.187
0.012

HOMO
(π
occ)

δ1-2

1.050
0.796
0.819
1.071
1.268

a2u
δ1-2 σ

0.800
0.796
0.569
0.821
0.768

-‐17.8

δ1-2 π

0.250
0.000
0.250
0.250
0.500

HOMO-‐1(σ
occ)
δ1-3

0.437
0.551
0.710
0.817
0.629

b2g

+10.8
δ1-3 σ

0.187
0.551
0.460
0.567
0.540

δ1-3 π

0.250
0.000
0.250
0.250
0.089

HOMO-‐2(σ
occ)

a1g
AromaIcity
π σ σ
+
π
σ
+
π σ

-‐3.9

a2u(π)
and
a1g(σ)
orbitals
contribute
posiIvely
to
σ
and
π
aromaIcity
while
b2g(σ)
and
eg(π)
not

F. Feixas, E. Matito, M. Duran, J. Poater, M. Solà Theor. Chem. Acc. 2010, accepted

II��. PATTERNS
OF
π-‐ELECTRONIC
DELOCALIZATION

Al42- Al3Ge- Al2Ge2 AlGe3+ Ge42+

Symmetry D4h C2v C2v C2v D4h
MCI 0.356
0.206
0.165
0.171
0.386

MCI π 0.187
0.114
0.102
0.128
0.187

δ(1-3)

0.818
0.771
0.654
0.771
0.781

δσ(1-3)

0.568
0.546
0.469
0.527
0.531

δπ(1-3)

0.250
0.224
0.184
0.244
0.250

F. Feixas, E. Matito, M. Duran, J. Poater, M. Solà Theor. Chem. Acc. 2010, accepted

�ݺ�ߣ

Patterns of p-Electron Delocalization in Aromatic and Antiaromatic Organic Compounds in the Light of the Hückel’s 4n+2 rule

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Patterns of p-Electron Delocalization in Aromatic and Antiaromatic Organic Compounds in the Light of the Hückel’s 4n+2 rule