comment-v7-new

Michael Filatov

Description

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 ...

Informations

• Publié par: Nazil
• Nombre de lectures: 24
• Langue: English

Extrait

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