Conference given by Dr. Jordi Poater at the ACS National Meeting in Boston, Division of Organic Chemistry. 22-26th August 2010.

2. J.
Poater,
F.
Feixas,
E.
Ma,to,
M.
Solà
Ins$tute
of
Computa$onal
Chemistry
Universitat
de
Girona
(Catalonia,
Spain)

3. I. INTRODUCTION
TO
AROMATICITY
II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES
III. PATTERNS
OF
π-­‐ELECTRONIC
DELOCALIZATION
IV. CONCLUSIONS

4. I. INTRODUCTION
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!

5. I. INTRODUCTION
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…)

6. I. INTRODUCTION
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.

7. I. INTRODUCTION
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?

8. I. INTRODUCTION
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

9. II. 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.

10. II. 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

11. II. 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

12. II. 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

13. II. 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

14. II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES
F. Feixas, E. Matito, M. Solà, J. Poater, J. Comput. Chem. 2008, 29, 1543

15. III. 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

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

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

18. III. PATTERNS
OF
π-­‐ELECTRONIC
DELOCALIZATION
B3LYP/6-­‐31G(d)

19. III. 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

20. III. 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

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

22. III. 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)
↓
F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126

23. III. 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)
↑
F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126

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

25. III. 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-­‐
F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126

26. III. 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)
↑
F. Feixas, E. Matito, M. Solà, J. Poater, Phys. Chem. Chem. Phys. 2010, 12, 7126

27. III. 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

28. III. 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