Aromaticity and Electronic Delocalization in All-Metal Clusters with Single, Double, and Triple Aromatic character

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

Ins$tute
of
Computa$onal
Chemistry

Universitat
de
Girona
(Catalonia,
Spain)

I. INTRODUCTION
TO
AROMATICITY

II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC

AROMATIC
MOLECULES

III. INDICES
OF
AROMATICITY
IN
INORGANIC
AROMATIC

MOLECULES

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

V. CONCLUSIONS

I. INTRODUCTION
TO
AROMATICITY

The
concept
of
“aroma,city”
is
oMen
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!

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…)

I. INTRODUCTION
TO
AROMATICITY

It
is
your
favorite
index
of
aroma,city

beèr
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.

I. INTRODUCTION
TO
AROMATICITY

It
is
your
favorite
index
of
aroma,city

beèr
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?

I. INTRODUCTION
TO
AROMATICITY

It
is
your
favorite
index
of
aroma,city

beèr
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

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.

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

shiM)
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

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

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

II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

15
PROPOSED
TESTS

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

II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

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

II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

 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. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

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

II. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

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. INDICES
OF
AROMATICITY
IN
CLASSICAL
ORGANIC
AROMATIC
MOLECULES

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

III. INDICES
OF
AROMATICITY
IN
INORGANIC
AROMATIC
MOLECULES

F. Feixas, J. O. C. Jiménez-Halla, E. Matito, J. Poater and M. Solà
J. Chem. Theory Comput. 2010, 6, 1118

III. INDICES
OF
AROMATICITY
IN
INORGANIC
AROMATIC
MOLECULES

 The
examples
analyzed
show
that
there
is
not
yet
a
single
indicator
of

aroma,city
that
works
properly
for
all
cases.
It
is
important
in
this
context
to

inves,gate
the
strong
and
weak
points
of
the
diﬀerent
indexes.

 According
to
our
results,
the
best
indicators
of
aroma,city
are
the
electronic

indices
based
on
the
calcula,on
of
mul,center
delocaliza,on
indices.

F. Feixas, J. O. C. Jiménez-Halla, E. Matito, J. Poater and M. Solà
J. Chem. Theory Comput. 2010, 6, 1118

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

Al42-‐,
the
all-‐metal
aroma,c
cluster

• Al42-‐
is
the
quitessen,al
all-‐metal
aroma,c
cluster.

• 1
pair
of
delocalized
π-‐e
and
2
pairs
of
σ-‐e
(MOs
with

orthogonal
radial
and
tangen,al
direc,ons).

• Conﬁrmed
aroma,city.

F. Feixas, E. Matito, M. Duran, J. Poater and M. Solà
Theor. Chem. Acc. 2011, 128, 419

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

Al42-‐,
the
all-‐metal
aroma,c
cluster

• π
delocaliza,on
slightly
larger
than
σ.

• Al44-: antiaromatic 4π-e system.
• Al4: aromaticity depending on the orbital.
• MCI does not provide information about antiaromaticity.
• δα1,3 is computationally much cheaper.
Theor. Chem. Acc. 2011, 128, 419

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

C4v
Al42-‐
+
ca,on

• Aroma,city:
Al42-‐
>
LiAl4-‐
>
NaAl4-‐
>
CuAl4-‐

• Reduc,on
more
important
for
π
than
σ
component
due
to

par,al
transfer
of
the
2π-‐e
from
Al42-‐
to
the
ca,on.

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

Al4
+
ca,ons

• From
Al44-‐
to
Li2Al42-‐
there
is
an
important
decrease
of
the

an,aroma,c
π-‐character:
par,al
transfer
from
Al4
to
Li+.

• Aroma,city:
Li2Al42-‐
>
Li3Al4-‐
=
Li4Al4

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

Symmetry
distor,on
of
Al42-‐

• Expected
trend:
Al42-‐
>
Al3Ge-‐
≥
Al2Ge2
≤
AlGe3+
>
Ge42+

(reduc,on
of
symmetry
and
subs,tu,on
by
more

electronega,ve
Ge).

Theor. Chem. Acc. 2011, 128, 419

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

Symmetry
distor,on
of
Al42-‐

Theor. Chem. Acc. 2011, 128, 419

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

Transi,on-‐metal
rings

• Cu3+
is
σ-‐aroma,c.

• CunHn
cannot
be
considered
as
aroma,c.

• Y3-‐
and
La3-‐
are
ﬁrst
reported
transi,on-‐metal
systems
with

double
σ-‐
and
π-‐aroma,city.

Theor. Chem. Acc. 2011, 128, 419

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

δ-‐aroma,city

Theor. Chem. Acc. 2011, 128, 419

IV. SINGLE,
DOUBLE
AND
TRIPLE
AROMATIC
CHARACTER

δ-‐aroma,city

• 5Ta3-‐:
strong
overlap
between
σ
2e’
and
δ
3a1’.

• 3Hf3:
Single
occupa,on
of
e’’
orbitals.

Theor. Chem. Acc. 2011, 128, 419

V. CONCLUSIONS

Conclusions

• The
quan,ta,ve
evalua,on
of
aroma,city
in
inorganic
clusters

is
cumbersome
due
to
the
lack
of
aroma,c
inorganic
systems

that
can
be
used
as
a
reference.

• The
aroma,city
of
these
species
can
only
be
assessed
by
the

use
of
the
simple
Hückel’s
4n
+
2
rule
and
the
calcula,on
of

the
NICS
and
MCI
descriptors.

• MCI
of
planar
(or
pseudo-‐planar)
species
can
be
separated

into
the
σ-‐,
π-‐,
and
δ-‐components.
These
MCIα
(α
=
σ,
π,
and

δ)
indices
provide
quan,ta,ve
valuable
informa,on
about
the

type
of
aroma,city
that
a
certain
aroma,c
inorganic
cluster

has.

Theor. Chem. Acc. 2011, 128, 419

V. CONCLUSIONS

Conclusions

• The
crossed
term
corresponding
to
the
two
farthest
atoms
in

the
ring
(i.e.,
δπ1,3
in
4-‐MRs)
decreases
also
in
aroma,c

inorganic
species
when
two
electrons
are
added
or
removed

and
that
this
crossed
term
is
higher
for
the
most
aroma,c

molecule
in
a
series
of
same-‐membered
rings.

• Consequently,
this
crossed
term,
which
is
less
computa,onally

demanding
than
MCI,
is
also
a
good
descriptor
of
aroma,city

in
all-‐metal
and
semimetal
clusters.

Theor. Chem. Acc. 2011, 128, 419

Aromaticity and Electronic Delocalization in All-Metal Clusters with Single, Double, and Triple Aromatic character

Aromaticity and Electronic Delocalization in All-Metal Clusters with Single, Double, and Triple Aromatic character

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