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Comment on “About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error” [J. Chem. Phys. 123, 164110 (2005)] 1 2 3 4 4 5C. Adamo , V. Barone , A. Bencini , R. Broer , M. Filatov , N.M. Harrison , 6 7 6 F. Illas , J.P. Malrieu and I. de P.R. Moreira 1) Ecole Nationale Supérieure de Chimie de Paris, UMR CNRS-ENSCP n° 7575, 11 rue P. et M. Curie, F-75231 Paris Cedex 05, France 2) Dipartimento di Chimica, Universita' Federico II Complesso Universitario Monte S. Angelo, via cintia, I-80126 Napoli, Italy 3) Dipartimento di Chimica, Polo Scientifico dell'Università di Firenze, via della Lastruccia 3, I-50019 Sesto Fiorentino (FI), Italy 4) Theoretical Chemistry, Materials Science Centre, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands 5) Department of Chemistry, Imperial College London, SW7 2AY, and CCLRC, Daresbury Laboratory, Daresbury, Warrington, WA4 4AD, U K 6) Departament de Química Física, Universitat de Barcelona, C/Martí i Franquès 1, E-08028 Barcelona, Spain 7) IRSAMC, Laboratoire de Physique Quantique, Université Paul Sabatier, 118 Route Narbonne, F-31062 Toulouse-Cedex, France 1 The energy differences between states of different spin multiplicity play a central role in the interpretation of magnetic properties of organic diradicals, magnetic molecular complexes and magnetic solids, since these energy differences can be related to the ...

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Publié par
Nombre de lectures 24
Langue English

Exrait

1
Comm
ent
on “
About the cal
cu
lat
ion
of ex
ch
ange
coupl
ing con
st
ants
us
ing
d
ensit
y-
funct
ional th
eory:
The
role
of the self-interact
ion er
ror”
[J. Ch
em. Phys. 123, 164110 (200
5)]
C. Adamo
1
, V. Bar
one
2
, A. Benci
n
i
3
, R. Br
oer
4
, M. Fila
t
o
v
4
, N.M. Harris
o
n
5
,
F. Illas
6
, J.P. Mal
rieu
7
and I. de P.R. Moreira
6
1) Ecole Nationale Supérieure de Chimie de Paris, UMR CNRS-ENSCP n° 7575,
11 rue P. et M. Curie, F-75231 Paris Cedex 05, France
2) Dipartimento di Chimica, Universita' Federico II
Complesso Universitario Monte S. Angelo, via cintia, I-80126 Napoli, Italy
3)
Dipartimento di Chimica, Polo Scienti
fico dell'Università di Firenze,
via della Lastruccia 3, I-50019 Sesto Fiorentino (FI), Italy
4) Theoretical Chemistry, Materials Science Centre, University of Groningen, Nijenborgh 4,
9747 AG Groningen, The Netherlands
5) Department o
f Chemistry, Imperial College London, SW7 2AY, and CCLRC, Daresbury
Laboratory, Daresbury, Warrington, WA4 4AD, U K
6) Departament de Química Física, Universitat de Barcelona,
C/Martí i Franquès 1, E-08028 Barcelona, Spain
7) IRSAMC, Laboratoire de Physique Quantique, Université Paul Sabatier,
118 Route Narbonne, F-31062 Toulouse-Cedex, France
2
The
ener
gy
differences
be
tween
s
ta
tes
of
differen
t
s
pin
m
ul
ti
plici
ty
play
a
cen
tral
r
ole
in
t
he
in
terpre
ta
ti
on
of
ma
gne
tic
pr
oper
ties
of
organic
dira
dicals,
ma
gne
tic
m
olec
ular
c
om
plexes
an
d
ma
gne
tic
s
olids,
since
these
ener
gy
differences
can
be
rela
ted
t
o
the
ener
gy
spec
trum
of
a
m
o
d
el
s
pin
Hamil
t
onian
and
theref
ore
pr
ovide
es
tima
tes
of
the
parame
ters
(ma
gne
tic
c
oupling
c
ons
tan
ts)
defi
ning
these
m
odel
Hamil
t
onians.
1
In
m
olec
ular
sys
tems
these
ener
gy
differences
can
be
direc
tly
c
ompu
ted
using
accura
te
ab
initio
me
th
ods,
such
as
c
onfigura
ti
on
in
terac
ti
on
(CI)
yiel
ding
wave
f
unc
ti
ons
in
which
the
relevan
t
s
pin
symme
tries
(defined
by
the
sq
uare
of
the
to
tal
s
pin
and
i
ts
z-
c
omp
onen
t,
S
2
and
S
z
)
are
pr
operly
imp
osed.
2-4
In
the
case
of
s
olid
s
ta
te
sys
tems
a
differen
t
pr
ocedure
is
ap
plie
d
beca
use
alm
os
t
universally
ban
d
s
truc
ture
calc
ula
ti
ons
rely
on
the
use
of
an
effec
tive
one-par
ticle
pic
ture
in
which
s
pin
symme
try
cann
ot,
in
general,
be
imp
osed.
In
the
la
t
ter
cases,
a
map
ping
pr
ocedure
can
be
used
by
em
pl
oying
the
ener
gy
differences
be
tween
the
ferr
oma
gne
tic
and
br
oken
symme
t
ry
an
tiferroma
gne
tic
s
olu
ti
ons
ob
tained
in
the
appr
opria
te
supercell.
5-7
These
ener
gy
differences
are
rela
ted
to
the
ener
gy
spec
trum
of
the
appr
opria
te
m
odel
s
pin
Hamil
t
onian
which,
in
this
case,
is
the
Isi
ng
m
odel
beca
use
only
S
z
is
defined.
The
br
oken
symme
t
ry (BS)
s
olu
ti
ons can
be
ob
tained
usin
g ei
ther
s
pin-
Unres
tric
ted Har
tree-F
ock (UHF)
or a
ny
of
the
exchan
ge-c
orrela
ti
on
po
ten
tials
wi
thin
the
s
pin-
Unres
tric
ted
K
ohn-
Sham
appr
oach
(UKS)
to
Densi
ty
F
unc
ti
onal
The
o
ry
(DFT).
In
this
way,
UKS-DFT
can
be
used
to
ex
trac
t
ma
gne
tic
c
ou
plin
g
c
ons
tan
ts
ei
ther
in
m
olec
ules
or
s
olids
bu
t
i
t
is
imp
or
tan
t
t
o
realize
tha
t,
since
s
pin
symme
t
ry
is
br
oken,
a
s
ui
table
pr
ocedure
is
needed
to
rela
te
c
ompu
ted
ener
gy
differences
t
o
ma
gne
tic
c
ou
plin
g
c
ons
tan
ts.
The
map
ping
pr
ocedure
t
o
the
appr
opria
te
s
pin
Hamil
t
onian
ou
tlined
ab
ove
f
ulfills
this
req
uiremen
t
and
is
c
onsis
ten
t
wi
th
the
me
th
ods
pr
op
osed
earlier
t
o
s
tudy
a
t
omic
and
m
olec
ula
r
m
ul
ti
ple
t
s
8,9
and
ma
gne
tic
c
ou
pling
c
ons
tan
ts.
10,11
Essen
tially,
all
these
pr
ocedures
are
based
on
the
fac
t
that
the
br
oken
symme
t
ry
s
olu
ti
on
is
a
mix
ture
of
tw
o
(
or
m
ore)
spin
s
ta
tes
and
the
desire
d
ener
gy s
pli
t
tin
gs are
ob
tained
by s
pin pr
ojec
ti
on
or by
the s
um r
ule.
9
In
a
recen
t
paper,
Ruiz
e
t
al.
12
c
ompare
n
ume
rical
res
ul
ts
f
or
the
ma
gne
tic
c
ouplin
g
c
ons
tan
ts
ob
taine
d
f
or
H-He-H
an
d
rela
ted
m
odel
sys
tems
and
inves
tiga
te
the
effec
t
of
the
se
lf
in
terac
ti
on
err
or
(SIE).
These
au
th
ors
find
tha
t
the
F
ull
CI
(FCI)
value
f
or
the
ma
gne
tic
c
ou
pli
n
g
c
ons
tan
t
is
repr
oduced,
ei
ther
by
the
ener
gy
difference
be
tween
the
hi
gh-s
pin
an
d
the
br
oken
symme
t
ry
s
ta
tes
wi
th
ou
t
spin
pr
ojec
ti
on
pr
ovided
that
the
SIE
is
n
ot
rem
oved,
or
by
the
ener
gy
difference
wi
th
appr
opria
te s
pin pr
ojec
ti
on
if
the
SIE
is rem
oved.
Their ex
plana
ti
on
of
this res
ul
t
is
tha
t
in
the
pr
ojec
ted
br
oken
symme
t
ry
DFT
calc
ula
ti
on
wi
th
ou
t
SIE
correc
ti
ons,
the
n
on-
dynamic
al
elec
tr
on
correla
ti
on
is
taken
in
t
o
acc
oun
t
twice:
once
via
the
map
ping
on
to
the
pure
s
pin
symme
t
ry
s
ta
te
and
once
via
the
exchange
par
t
of
the
densi
ty
f
unc
ti
onal
.
H
owever,
this
s
ta
temen
t
lac
ks
a
fi
rm
3
the
ore
tical
basis.
Indeed,
as
i
t
has
been
f
o
und
by
P
ol
o
e
t
al.
13
and
Cremer
e
t
al.,
14
the
SIE
of
the
exchange
f
unc
ti
onal
sim
ula
tes
n
on-
dynamic
elec
tr
on
c
orrela
ti
on
pr
ovided
tha
t
sin
gle
de
terminan
t
s
pin-Res
tric
ted
Densi
ty
F
unc
ti
onal
The
o
ry
(RKS
-DFT)
calc
ula
ti
on
is
car
ried
out.
H
owever,
in
the
case
of
a
br
oken
symme
t
ry
s
pin
unres
t
ric
ted
calc
ula
ti
on,
the
SIE
c
orrec
ti
on
sim
ula
tes
pred
ominan
tly
the
effec
t
of
dynamic
elec
tr
on
correla
ti
on,
especially
in
case
of
wea
kly
c
ou
ple
d
ma
gne
tic cen
ters.
14
The
res
ul
ts
by
R
uiz
e
t
al.
12
d
o
pr
ovide
evidence
tha
t
in
br
oken
symme
t
ry
DFT
calc
ula
ti
o
ns
the
s
pin
pr
ojec
ti
on
has
a
c
onsiderable
effec
t
on
the
ener
gy
and
thus
they
pr
ovide
in
direc
t
evidence
tha
t
spin
pr
ojec
ti
on
is
unav
oidable
or,
in
o
ther
w
ords,
tha
t
the
br
oken
symme
t
ry
s
olu
ti
on
is
a
mix
ture
of
differen
t
s
pin
s
ta
tes
as
argued
in
seve
ral
papers.
5-10
H
owever,
Ruiz
e
t
al.
sugges
t
takin
g
the
ener
gy
of
the
br
oken
symme
t
ry
s
olu
ti
ons
as
tha
t
of
the
open
shell
sin
gle
t.
They
obse
rve
tha
t
a
“pr
ocedure
tha
t
gives
excellen
t
c
ompu
ta
ti
onal
res
ul
ts
is
t
o
c
onsider
tha
t
the
ener
gy
of
the
br
oken-
symme
t
ry
s
olu
ti
on
al
rea
dy
c
on
tains
the
n
on
dyn
amical
c
orrela
ti
on
c
on
t
ribu
ti
ons
in
tr
oduced
by
the
SIE
correc
ti
on
and
theref
ore
em
pl
oy
the
n
onpr
ojec
ted
appr
oach.”
As
discussed
ab
ove,
this
c
onjec
ture
lac
ks
a
fi
rm
the
ore
tical
basis.
M
oreover,
i
t
is
als
o
inc
orrec
t
fr
om
a
purely
n
ume
ric
al
p
oin
t
of view,
beca
use,
f
or all
sys
tems s
tu
died
by
R
uiz
e
t al.,
12
the
bes
t perf
o
rmer
in
the
unpr
ojec
te
d
case
is
the B
3LYP
f
unc
ti
onal,
where
the effec
t
of the SIE has
alrea
dy
been reduced (c
ompared
t
o i
ts
pure
densi
ty
f
unc
ti
onal
anal
og
BLYP)
due
t
o
the
mix
ture
wi
th
HF
exchange.
This
means
tha
t
an
im
plici
t
fine
tuning
of
the SIE c
orrec
ti
on
is al
rea
dy presen
t in
their
n
ume
rical pr
ocedure.
Since
c
orrec
ting
f
or
the
SIE
in
real
sys
tems
is
ex
tremely
diffic
ul
t,
the
pr
ocedure
sugges
te
d
by
R
uiz
e
t
al.
may
p
o
ten
tially
lead
t
o
a
c
onvenien
t
n
ume
rical
recipe
which
reduces
the
s
tr
ong
depen
dence
of
the
calc
ula
ted
ma
gne
tic
c
ou
pling
c
ons
tan
ts
on
the
ch
oice
of
exchan
ge-c
orrela
ti
on
f
unc
ti
onal and
may
be usef
ul
t
o unravel
ma
gne
t
ostruc
tural c
orrela
ti
ons. H
owever, al
th
ough SIE-free
po
ten
tials
are
bec
oming
available,
15
the
SIE
is
inheren
t
t
o
all
appr
oxima
te
exchange
c
orrela
ti
on
po
ten
tials
curren
tly
used
in
s
tandard
KS-DFT
calc
ula
ti
ons.
Hence,
i
t
affec
ts
res
ul
ts
ob
tained
usi
n
g
the
s
pin
p
ola
rized
im
plemen
ta
ti
on
of
the
K
ohn-Sham
(KS)
pr
ocedure
as
well
as
th
ose
ob
taine
d
using
KS
im
plemen
ta
ti
ons
in
which
s
pin
symme
try
is
pr
operly
imp
osed.
These
pr
ocedures
are
alrea
dy available
16
and
have
been recen
tly ap
plied t
o c
ompu
te ma
gne
tic c
ou
pling c
ons
tan
ts.
17
In
the
la
t
ter
case,
there
is
n
o
reas
on
t
o
carry
ou
t
the
s
pin
pr
ojec
ti
on
sim
ply
beca
use
the
reference
sys
t
em
has
a
defined
value
f
or
b
o
th
S
2
an
d
S
z
and
s
till
the
res
ul
ts
are
affec
ted
by
the
SIE.
Theref
ore,
one
p
oin
t
of
the
R
uiz
e
t
al.
line
of
reas
oning
is
n
o
t
c
orrect
and
the
s
ource
of
mis
unders
tan
ding
c
omes
fr
om
impr
ope
rly
mi
xing
the c
oncep
t
of SIE wi
th
tha
t
of s
pin symme
try.
The
unde
rlying
pr
oblem
ar
ound
this
discussi
on
is
whe
ther
curren
t
im
plemen
ta
ti
ons
of
DF
T
based
on
the
KS
appr
oach
d
o
or
d
o
no
t
requi
re
the
imp
osi
ti
on
of
s
pin
symme
t
ry.
This
is
an