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Treating I
−
anion as a zero-electron system : the LiI
−
and CsI
−
alkali halides anions.
Vincent Robert, Fernand Spiegelman, Marie-Bernadette Lepetit
To cite this version:
Vincent Robert, Fernand Spiegelman, Marie-Bernadette Lepetit. Treating I
−
anion as a zero-electron
system : the LiI
−
and CsI
−
alkali halides anions.. Chemical Physics, Elsevier, 2003, 287, pp.217.
�hal-00003049�
Vin ent ROBERT , Fernand SPIEGELMAN, and Marie-Bernadette LEPETIT 1
Laboratoire de Physique Quantique, IRSAMC/UMR5626, Université Paul Sabatier,
118 route de Narbonne, F-31062 Toulouse Cedex 4, FRANCE
2
Permanent address: Institut de Re her hes sur laCatalyse, Laboratoire de Chimie Théorique,
2 av. Albert Einstein, 69626 Villeurbanne Cedex, FRANCE
(Dated: O tober31,2002)
The a ura y of a full ore treatment of I anion based on a zero-ele tron pseudo-potential
(ZEP) in luding ore polarization pseudo-potential (CPP) is examined on referen e ompounds
LiI andCsI onsideredasone-ele tronsystems.Theresultsare omparedtoabinitioCASPT2
al ulations involving 8a tive ele tronson iodine and 3(respe tively 9) onlithium (respe tively
esium). An original s heme is proposed to build a pseudo-potential des ribing the short-range
ele tron-I intera tion beyond the point hargeapproximation. The importan e of the ZEP in
one-ele tron al ulationsisestimatedforthementionedanions.
I. INTRODUCTION
The quantum me hani aldetermination of ele troni
propertiesoflargemole ulesandsophisti atedmaterials
has be ome one of the major hallenges in the ab
ini-tio ommunityoftheoreti al hemists. However,theuse
of quantum hemi al approa hes has longbeen limited
to small systems due, in parti ular, to the number of
ele tronswhi haretobetakeninto a ount. Therefore,
mu heortwasdevotedto redu ethenumberofa tive
ele trons in the al ulations. It is known that
hemi- al bonding as well as most hemi al properties
essen-tially depend on the valen e ele trons. Su h
observa-tionhasleadtheoreti ianseithertofreezetheinner
ele -trons as in their mean- eld des ription or to elaborate
so- alled Model Potentials (MP), ee tive ore
poten-tials(ECP) orpseudo-potentials(PP)theories. These
ideas date ba k to early pioneering works
14
and have
been extensively developed in atomi physi s and
ele -troni ollisions
511
, quantum hemistry
1216
and solid
statephysi s al ulations
1720
. It isnoti eable that the
nowadays derivations of ECP's and PP's allow oneto
rea h quantitative a ura y for many systems in their
groundandex itedstates. ExtensionsofthePP theory
hasmadeavailablethein orporationofs alarrelativisti
ee ts leading to an a urate and still tra table
treat-ment of mole ules in luding heavy atoms
16,21,22
. F
ur-thermore, overpassing the stri tly frozen s heme,
te h-niques havealso been proposed to restore the ore
po-larizationand ore-valen e orrelation in an operatorial
form 23
.
Beyond these standard and now routine
determina-tionand useofvalen e ECP's, dierentstrategieshave
beendevelopedtoentirelyrepla einertatoms andions,
and evenmorere ently fun tionalgroups
24
, by
pseudo-potentials. The former approa h orresponds to
zero-ele tronpseudo-potentials(ZEP), withtwomain elds
of appli ations. The rst one involves thetreatment of
rare-gas atoms in mole ules, lusters and even
embed-ding matri es. Rare-gas omplexes are indeed of
inter-textof ollisionalorspe tros opi studies,manyauthors
haveput mu h eort to derivemodel potentials (MP)
or pseudo-potentials for rare-gas atoms in alkali
rare-gas mole ules. The early studies suggested empiri al
or l-independent MP's
5,8,10
. More re ent versions
in- ludethe l-dependen y ofthe PP's and were extra ted
by tting ele tron rare-gaselasti dierential ross
se -tions 9,27
. Re ent works have demonstrated the power
of these PP treatments sin e quasi-spe tros opi
a u-ra yhas beenrea hed onalkali rare-gasand rare-earth
rare-gasdiatomi s
25,26
. These ond lassofappli ations
foratomi ZEP involveshalogennegativeions
(isoele -troni torare-gasatoms),metinessentiallyioni
materi-als.Thesesystemsin lude ondensedmatter ompounds
aswell asioni lusters for whi h lo al spe tros opy is
widely investigated
29
. The des ription of inert ions in
periodi systems hasattra tedsometheoreti al interest
in the ab initio ommunity. Indeed, ab initio
spe tro-s opi te hniques are limited to nite systems.
There-fore,embedded fragmentmodels must be onsidered in
order to simultaneously restri t the quantum hemi al
al ulationtoasmallnumberofatomsandproperly
de-s ribethe fragmentspe tros opy in its rystalline
envi-ronment. Few groupshave tried to address the
impor-tantissueofsurroundingee tsmodeling
28
. Spe i PP
te hniques havebeendevelopedto a ountforthe
in u-en e of the rest of the rystal on the fragment under
onsideration 29
. One main a hievement is the so- alled
AbInitioModelPotential(AIMP)methodsuggestedby
SeijoandBarandiáraninwhi hmaterialspe i PP are
derivedfrom periodi Hartree-Fo k al ulations
30
. This
s hemeisparti ularlyinterestingsin eitallowsthe
treat-mentofbothanionsand ationsonthesamefootingwith
equaleort. However,themaindrawba kisthattheuse
ofthePP is onstrainedto thestru tural onditionsin
whi h it has been extra ted. Hen e, appli ations in a
dynami al ontext or in situations for whi h the
geom-etryis apriori unknown, seemto belimited. Similarly,
su h approa h is not adapted to the study of surfa es,
nor lusters in whi h the lo al geometry may strongly
dier from the bulk situation. In the investigation of
lus-ters withex essele trons 31 (namelyM n X p , Malkali,X
halogen),theX ionswereusually onsideredassimple
point harges
32,33
. Su h approximationsmightbe
ques-tionableforheavyhalogenatoms. Indeed,onemaythink
thatanextrapseudo-potentialisrequiredtoa ountfor
theele tron-X short-rangeadditionalrepulsion. Ab
ini-tio al ulationsusingtheperturbedionmodel with
or-relations ontributions have been re ently presented on
similarsystems
34
. However,this typeof approa hhasa
veryhigh omputational ost.
The s ope of the present work is to investigate the
reliability of a zero-ele tron treatment of the I ion.
As ben hmark al ulations, we onsider the smallest
mole ules whi h an be des ribed as one-ele tron
sys-tems for whi h ab initio referen e al ulations anstill
bea hieved, namelythe diatomi alkali halogenanions.
Wehave hosenthe LiI andCsI diatomi s,as
exam-plesoflight-heavyandheavy-heavy ompounds. Wewill
hereafterexaminethereliabilityofone-ele tron
al ula-tions a hieved within both the point- harge, and point
harge+extra short-range pseudo-potential
approxima-tions. For the latter, a zero-ele tron pseudo-potential
(ZEP)extra tions hemeissuggestedfortheI ion.
While system-independent zero-ele tron ations
pseudo-potentials(ZEP) aneasilybedeterminedusing
similar methods as those derived for standard ECP's,
the situation is mu h less favorablefor anions. Indeed,
the referen e system in luding one extra ele tron does
not usually exist. One ould think of using dierential
ele tron-anion rossse tionsfor this purpose. However,
thosearemostofthetimenotavailable assu h,neither
experimentally nor theoreti ally, in ontrast with the
situation for rare-gas atoms. In the s ope of
theoret-i ally understanding the hemistry of silver-bromide
surfa es 35
, Flad et al. derived a pseudo-potential for
the Br anion. In order to stabilize the Br
2
spe ies,
theyembeddedtheanionin agaussian-shapedauxiliary
potential.
Followingasimilarinspiration,weproposetostabilize
oftheextraele tronviaapositively hargedsurrounding.
InadditiontotherepulsivePP, orepolarizationee ts
will be in luded using the s heme developed by Müller
et al
23
. Se tion II isdevotedto the PP extra tion
pro- edure andinternal he ksof itstransferability. Se tion
IIIdetails thetest al ulationsonalkali-iodinediatomi
neutralsandanions. Thepotentialenergy urvesof
neu-tralsareindeedrequiredas ore- ore ontributionsinthe
one-ele trontreatmentofanions.
II. METHOD
The I zero-ele tron pseudo-potential will be
on-stru teda ordingtothel-dependentsemi-lo al
expres-sionofBarthelatandDurand
12 ^ W = 1 r + X W l ^ P l (1) with W l = X i C li e lir 2 r nli (2) and ^ P l = m=l X m= l jlm><lmj (3) ^ P l
istheproje torontheusualspheri alharmoni sjlmi.
Itshould beremindedthat inthepresentstudy,the
lo- al part is repulsive. The PP operator is expe ted to
mimi theintera tionofextraele tronswiththeI ion.
Therefore,a referen esystemin luding at leastone
ex-tra ele tron has to be onsidered. Quantum hemi al
standardpro eduresforPP extra tionsarebasedonthe
existen eofatomi boundstatesofthereferen esystem,
from whi h orbital energies, pseudo-orbitals and nally
pseudo-potentials anbedetermined. Here,themain
is-suestemsfromtheunstable hara terofI
2
spe ies. We
thereforeimposed an arti ial onstraint onthe system
in order to stabilize the extra ele tron. This goal was
a hievedbyembeddingtheI
2
anionwithinapositively
harged ageofsodium ations. The hoi eofthe ageis
obviouslypartlyarbitrary. However,several riteriahave
guidedour hoi e. First,thewavefun tion oftheextra
ele tronmustkeepanon-vanishingdensity losetotheI
ore. Se ond,thesymmetry ofthe agehas beentaken
o tahedral so that it preservesthe degenera y of the p
orbitals, whi h orrespond to thehighest l omponents
of thePP onsidered in thepresent work. One should
note that the dorbitals of iodine split in su h an
o ta-hedralenvironment. A age of highersymmetry should
beusedtoevaluatethepseudo-potentialsd omponents.
The iodine-sodium distan e R
I Na
was set to 6:0a
0 as
ompared to the equilibrium distan e 5:2a
0
in the NaI
diatomi s 36
. Aslongastheinformation fromthe
wave-fun tion is transferable, this parti ular distan e should
notbea riti alparameter. This importantissueis
dis- ussedlaterin thetext. Thus, ourpro edure onsistsin
onstru tingaPP fromanHartree-Fo k al ulationfor
anextraele tronin the eld ofI (Na
+ )
6
. Usualvalen e
relativisti PP's were used to des ribe both the iodine
anion 37
(8 a tiveele trons) andsodium ations
38
(1
a -tiveele tron per sodium)in orderto avoid the ollapse
oftheextraele trononthesurroundingions.
Thereferen e al ulationof thissystem wasa hieved
asfollows. First,weperformedanHartree-Fo k
al ula-tion on I . The resulting orbitals were left frozen, I
being the referen e ore system. This pro edure
pre-ventsthe oreele tronsfrom beingpolarizedor
delo al-izedwith thein lusion ofthe age inthefollowingstep.
Then, the al ulation of the full I
2 (Na + ) 6 systemwas
performedandtheresultingorbitalsandorbitalenergies
weretakenasreferen es. Third,forea hl-manifold,the
standard methodology was used : i) determination of
the nodeless, normalized and shape- onsistent
pseudo-orbitals, ii) inversion of the one-ele tron S hrödinger
Sin ethepotentialgeneratedbythesixNa +
ationsdoes
not havea spheri alsymmetry, wewere lead to use an
adaptedleast-squareminimizationpro edurein orderto
extra t thePP. Within ea h symmetry, the al ulated
normL
l
intheleast-squarepro edurereads
L l = ^ F+ ^ W l ^ ' l " l ^ ' l (4) where'^ l
isthereferen epseudo-orbitalinea hsymmetry
l. A rather large un ontra ted basis set of
Gaussian-type orbitals (9s and 9p un ontra ted primitives) was
used. The L
l
minimization with respe t to
^ W l leadsto L l 10 2
a:u: Thepseudo-potentialparametersin
semi-lo alrepresentationarelistedinTable I.
l li Cli nli
0 0 :19022 0 :15536 1
11 :92021 11 :18667 1
1 0 :13759 0 :28112 1
TABLEI:Zero-ele tronpseudo-potentialparametrizationfor
I . li ,C li andn li
arede nedinEq.2.
Inordertoroughlyevaluatethezero-ele tron
pseudo-potential transferability, one an look into the
La-grangian L =
P l
L l
variations under distortions of the
(Na
+ )
6
age. The deviation from the referen e value
L ref
= 7:9 10
2
enables to validate this important
riterion. Two types of deformations hara terized by
themodi ationoftheR
I Na
distan eswere onsidered,
either a ordingto an homotheti expansion preserving
the O
h
symmetry, or to an axial D
4h
distortion. The
resultsarepresentedinTableII. FortheD
4h
distortion
thefour equatorialI Nadistan es areset equalto the
originalvalue6:0a
0
. Oneimmediatelyseesthatthe
vari-ations ofL areless than20%of itsnominal value,that
is an order of magnitude lessthan the errorin thePP
extra tion. RI Na (a:u:) 10 2 L (a:u:) Oh D4h 5 :0 10 8 :2 5 :5 9:2 7 :9 6 :5 8:3 7 :8 7 :0 10 8 :3
TABLEII:Variations ofthe LagrangianunderO
h
andD
4h
deformations of the age (Na
+
)6 . The referen e value is
Lref=7:910
2 .
The I ion beingquite polarizable,it is ne essaryto
introdu eaCPPoperatorinordertore overthe ore
po-larizationand ore-valen e orrelationee ts. Itshould
beemphasizedthatthepreviouslymentionedfreezingof
theI orbitalsavoidsthedouble ountingofthese
ontri-butions. FollowingMülleretal.
23
, the orepolarization
potential ^ V CPP (CPP)isin orporatedas: ^ V CPP = 1 2 I f I f I (5) where I
standsfortheI polarizabilityandf
I
isthe
ele tri eldprodu edbythesinglevalen eele tronand
allother oresa ting onI . Theele tri eld integrals
utoradius,
, hasbeentakenasastepfun tion,
a - ordinglytotheworkofFou raultetal.
39 .
The dipole polarizability has been previously
al- ulated to be 69a
3 0
from time-dependent se ond-order
Möller-Plesset perturbation theory
40
. Based on
ele -troni ex itations experimentsof salt lusters
32
, the
po-larizationtermshave been estimated to a rather
dier-entvalue,40a
3 0
. Inourstudy,theabinitiopolarizability
value has been assumed. The uto radius
was
de-terminedtomake onta tbetweentheionizationenergy
oftheembeddedI
2
spe iesandtheone-ele tronenergy
omputed from the ombined ZEP +CPP approa h.
Therefore,we rst performedreferen e CASPT2
al u-lationsonI andI 2 in the( Na + ) 6 environment. Then,
aone-ele tron al ulationin ludingdynami al
polariza-tion ee ts by means of the CPP was adjusted to the
CASPT2energiesdieren e. TheCPPparametrization
andtheenergeti ontributionoftheCPP orre tionon
theionization energyof embedded I
2
are given in
Ta-bleIII.
Energeti ontribution IE(a.u.) forI
2 Parametrization PP ontribution .5886 8s;8p CPP ontribution .0011 I =69 =3:50
TABLEIII:CPP parametersandenergeti ontributionsto
theembeddedI
2
ionizationenergy(IE).Allvaluesaregiven
inatomi units.
III. CALCULATIONS WITHINA ZEP
TREATMENT
Sin e transferability is a main on ern in our study,
inthisse tionweinvestigatethepotentialenergy urves
of two model systems, namely LiI and CsI . Let us
remindthattheZEP wasextra tedinano tahedral
en-vironment. Within the C
1v
symmetry, the degenera y
of thep orbitals is obviouslylifted. Thus, both the
lo- alsymmetryandthe hemi alenvironmentaredierent
fromthepseudo-potentialextra tion onditions.
Based on our ZEP + CPP parametrization, the
energy urves of LiI and CsI were omputed and
ompared to referen e ab initio al ulations. In the
ZEP + CPP s hemethe(MI) systemis represented
byaoneele tronhamiltonian
^ h = 1 2 ^ 1 r + + ^ W M ++ ^ W CPP M + (6)
+ 1 r I + ^ W I + ^ W CPP I + ^ V M + I (R )
where R is the M I distan e, r
M + and r I are the ele tron-nu lei distan es, ^ W M + and ^ W I the
mean- eld ZEP, and
^ W CPP M + and ^ W CPP I
the orepolarization
pseudo-potentialsofM + andI ,respe tively. ^ V M + I (R )
is a lassi al potential representing the ore- ore
rigid-ionintera tionbetweentheM
+ andI ions. ^ V M + I (R )
modelstheintera tion ofthezero-ele tron(M
+
,I )
sys-tem, ex luding the ions polarization already a ounted
for in theCPP operator. The MIsystems, from whi h
the ore- oreV
M +
I
(R ) potentials were extra ted, and
the referen eanions MI were omputedusing a
Com-pleteA tiveSpa eSelfConsistentFieldplusse ondorder
perturbationtheory(CASPT2,MOLCASVersion5
41 ).
ThetypeofCI methodwasmotivatedbythe
multi on- gurational hara ter of the wave-fun tion in ludingat
least the ion pair and the ovalent on gurations. For
thesakeof onsisten y, thesameCI treatmentwas
ap-pliedtothemole ularanions. The al ulationswere
per-formed using a 11s5p3d, 7s6p4d3f and 5s5p4d3f basis
sets for Li, Cs and I, respe tively. The iodine and
e-sium oreele tronsweretreatedviarelativisti ee tive
ore potentialwith 7valen e ele tronsfor iodine and 9
for esium
42
. Conversely,the1sele tronsoflithiumwere
expli itly onsideredinthe al ulations. Thea tivespa e
onsisted of 8and 9ele trons in 8orbitals for the
neu-tralandioni ompounds, respe tively. Thus, thea tive
spa ein ludesthemole ularorbitals(MO)derivedfrom
the 5s and 5p atomi orbitals (AO's) of iodine, those
orrelatedwiththe6s(or2s)AOof esium(orlithium)
andthefour nexthighervirtualMO's. TheinnerMO's
(5s, 5p for esium, 1s for lithium) were left ina tive in
thea tivespa e,butwere onsideredintheperturbative
pro edure.
Letusnote thatamajorpartofthe ore-valen e
or-relation ee ts (last inner shell, valen e) is treated at
the perturbativelevel. Under these onditions, the
al- ulated ionizationpotentials(IP's)of LiandCsare5.31
and3.66eV, tobe omparedwith theexperimental
val-ues 5.39 eV and 3.89 eV
43
. The ele tron a nity (EA)
of I is al ulated to be 3.15 eV, slightly
overestimat-ing the experimental value of 3.06 eV
46
. Figure 1
dis-playstheCASPT2potentialenergy urvesof LiI, LiI
(Fig.1a)andCsI,CsI (Fig.1b). Thespe tros opi
on-stants of theneutrals potentialenergy urves are given
inTableIV. Theyareinfairlygoodagreementwiththe
experimentaldata(seeTableIV).
The equilibrium distan es absolute errorsare smaller
than 0:05a
0
, whereas the disso iation energies,
deter-mined relatively to the ions pairs M
+
+I are
under-estimatedby-1700and-2100 m
1
forLiIandCsI,
respe tively. One should point out that the adiabati
disso iationyieldstotheneutralfragmentsM+X. The
spe tros opi onstants!
e
arealsovery loseto the
ex-perimentaldata(490versus498 m
1
forLiI,115versus
119 m
1
for CsI). CCSD(T) al ulationson LiI have
47
systems sour e Re(a0) De( m
1 ) !e( m 1 ) EA(eV) LiI expt. 4.52 a 48390 a 498 a 0.75 CASPT2 4.56 46620 490 0.65 Coul omb 0.82 ZEP 0.76 CsI expt. 6.25 b 35490 b 119 b 0.62 CASPT2 6.30 33360 115 0.55 Coul omb 0.54 ZEP 0.58 LiI CASPT2 4.84 10100 370 Coul omb 4.95 10450 367 ZEP 4.91 9950 361 expt. 10960 CsI CASPT2 6.77 7380 86.3 Coul omb 6.89 6870 79.3 ZEP 6.91 6700 78.2 expt. 9110
TABLE IV: Spe tros opi analysis of LiI, LiI , CsI and
CsI . a Ref.43. b Ref.44. Ref.47. tan eR e =4.57a 0
almostidenti altoourCASPT2value.
Those potential energy urves have been tted using
anexpressionin ludingtheBorn-Mayerrepulsion
(expo-nential form), the ele trostati and polarization
ontri-butions E CASPT2 M + I = V M + I (R ) I + M + 2R 4 = Aexp( aR ) 1 R I + M + 2R 4 (7)
3
5
7
9
R (a
0
)
−6.5
−5.5
−4.5
−3.5
−2.5
energy (eV)
(a)
4
6
8
10
12
14
R (a
0
)
−5
−4
−3
−2
−1
energy (eV)
(b)
FIG.1: Potentialenergy urvesofa)LiIandLiI ;b)CsIand
CsI . Thezero energy orresponds to the disso iated pairs
M +
where V M
+ I
(R ) is the rigid-ion energy de ned above,
whereastheCASPT2obviouslyin ludesthepolarization
ee tsonea hion,duetothepresen eoftheotherone.
The Born-Mayer parameters in atomi units are given
in Table V. Sin e the disso iation energies of the ions
pairsareunderestimatedwithrespe ttoexperiment(see
above), we have also determined experimental
Born-Mayer parametersin order to avoidthe propagation of
su herrorin the ore- ore ontributionof theMX
an-ionsintheZEP approa h.
LiI CsI
A=91:526=89:714 A=140:450=134:047
a=1:5994=1:5788 a=1:3292=1:3126
TABLEV:Born-Mayerparametersinatomi units. The rst
data refer to the t of the CASPT2 values, the se ond to
experimentaldisso iationenergies
44,45
(Eq.7).
The CASPT2 potential energy urvesfor the anions
are also displayedin Fig. 1and the al ulated
spe tro-s opi onstants given in Table IV. Partial
experimen-tal data an be extra ted from the above MX
experi-mental spe tros opi data,themole ular ele tron
a ni-ties 48
(0.62eV forLiI,0.75eV for CsI), and the
ioniza-tion potential of M. Estimatedexperimental values are
D e
= 10960 and 9110 m
1
for LiI and CsI ,
respe -tively. The CASPT2 D
e
valuesare found to be10100
and7380 m
1
. Thedis repan ywithexperimentseems
to be mu h larger for the CsI anion ( -1600 m
1 )
thanforLiI (-800 m
1 ).
We now turn to the single ele tron des ription using
the ombined ZEP + CPP + ore ore s heme.
TheanionsLiI ,CsI potentialenergy urvesare
read-ilydeterminedbythediagonalizationoftheone-ele tron
hamiltonian, omplementedbytheBorn-Mayerterm
(us-ingtheexperimental parametersin TableV).
E (MI) = V M + I (R )+" (8)
where"isthesingle-ele tronenergyofMI .
Inthisone-ele tronpi ture,weusedratherlargebasis
sets, namely 6s4p3d, 5s5p4d and 8s8p7d for Li, Cs and
I,respe tively. Figure2reportsthereferen e CASPT2
potential energy urves, the ZEP +CPP al ulations
and those assuming MI being a one-ele tron systems
without the
^ W I
pseudo-potential. In this parti ular
approa h, theele tron-I repulsion isonlydes ribedby
the1=r
I
term. The al ulatedspe tros opi onstants
are summarized in Table IV. In both systems, the
in- rease of the equilibrium distan es with respe t to the
MXsystemsexhibitedbytheCASPT2results,is fairly
reprodu ed in the one-ele tron approa hes. In the ase
of LiI , the disso iation energies with and without the
short rangePP operator( oulombi repulsiononly)are
9950 and 10450 m
1
, respe tively. Both values are
3
4
5
6
7
8
9
R (a
0
)
−1.35
−1.15
−0.95
−0.75
−0.55
−0.35
energy (eV)
(b)
5
6
7
8
9
10
11
12
13
R (a
0
)
−1.0
−0.8
−0.6
−0.4
−0.2
0.0
energy (eV)
(a)
FIG.2: Potentialenergy urvesofa)LiI ;b)CsI . Solidlines
aretheCASPT2referen e;dashedlinesthepurely oulombi
al ulations, and dotted lines the ZEP +CPP. The zero
energy orrespondstothedisso iatedpairsM+I .
or10960 m
1
). However, the totalZEP result o urs
to be in good agreement with the CASPT2 referen e
value. Theee t of theshort-rangepseudo-potentialis
to redu e D
e
by 500 m
1
. On the other hand, the
resultsare slightly less a urate for CsI , sin e the
en-ergies with and without short range PP are 6700 and
6870 m
1
, respe tively. Theee t ofthePP issmaller
thaninLiI sin etheequilibriumdistan eissigni antly
larger,redu ingtheroleoftheI - enteredPP. An
over-all600-800 m
1
underestimationofD
e
with respe tto
theCASPT2resultisobserved. However,thethree
the-oreti al al ulationsprovidesmallerdisso iationenergies
thanthe experimental estimation. This dis repan y
re-mainstobe lari ed. Finally,letusnotethatinCsI,the
PP orre tion is smaller than the residual errors in all
al ulations.
IV. CONCLUSION
Inthis paper,wehavedevelopedan originalstrategy
to parametrize a zero-ele tronpseudo-potential (ZEP)
for ananioni spe ies. As long as ore-valen e
orrela-tion (CPP) and ore- ore intera tion ee ts are
intro-du ed, a very satisfa tory level of a ura y is rea hed
within this ZEP formalism for LiI . The ee t of the
shortrangePP istode reasethedisso iationenergyby
500 m
1
withrespe ttoapure oulombi treatment
ofthehalogen. Theee t isonly 200 m
1
forCsI .
one-withrespe ttotheab initioCASPT2referen e
al ula-tion. Obviously,monitoringthe ut-o radius toadjust
theCASPT2result ouldbedone. However,su h
pro e-durewouldhindertheabinitioextra tionphilosophyand
would require tranferability ontrols on larger systems.
The CASPT2 disso iation energy value might be
im-provedbyin reasingthealreadylargebasisset and
per-forming CI al ulations. Nevertheless, the one-ele tron
resultson both systemsturn outto befairly onsistent
with the ab initio CASPT2 referen es. The
omputa-tional ost in ZEP al ulations is obviously mu h
re-du ed withrespe t to astandardapproa hrelyingona
seven-ele trondes ription ofiodine. Sin e the hemi al
environmentsofthediatomi systemswe onsidered are
verydierent from the extra tion situation, we believe
thattransferability,amajor on ern,isa hieved.
There-fore, su h a formalismmightbe extremelyuseful to
re-du ethenumberofa tiveele tronswithoutany
tremen-dous lost of a ura y. In this respe t, the limiton the
number ofele tronsin largesystemssu h asioni
lus-tersissigni antlymoved. Itmightalso beworth
om-paringthepresentPP extra tionstrategywithprevious
parametrizationofele tron-Arpseudo-potentialsrelying
ons attering properties
27
. A verysimilar approa h is
nowbeing arriedonfor ounter-ionsCl andBr whi h
arefrequentlymetin rystalstru turesofsolidstate
om-pounds. Finally,oneshouldmentionthatsimilarZEP's
ould be extra ted within the DFT framework
exten-sivelyusedto investigatelargesystems. Theire ien y
should howeverbe he ked onsistently withthe ability
of various fun tionals. Besides, the implementation of
CPP'sforseveralvalen eele tronswithindensity-based
formalismremainstobedevelopped.
Ele troni address: vrobertirsam .ups-tlse.fr,f ax:
(+33)561556065 1
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