A theoretical study of adsorption of CO2 on the (100) face of sodium chloride

\~ohnnc

110. number

CHEMICAL

2

PHYSICS

?I

LETTERS

Septcnlber 1964

A THEORETICAL STUDY OF ADSORPTION OF CO, ON THE (100) FACE OF SODIUM CHLORIDE B. DEPRICK and A. JULG Lcboratoire

Rcccivcd

de Chinlie

2S June

TlGorique.

Uniwrsitr?

de Prownce.

Place Victor Hugo, 133’31 Marseille

3. France

1984

The adsorption energy of a CO? moIecule on various sites of the (100) face of NaCI is determined (i) by considering the n~oleculc in the electrostatic field created by the substrate, and (ii) by treating the cluster (CO2Cl~)‘- in the field created

by the rest of the substrate. The electrostatic The dispersion-repulsion term is successively

and polarization estimated

contributions

by means

arc obtained by

of the hard-sphere

model

IIXXKIS

of the SCF method.

and an adapted

potential

model.

model used. tlic calculated adsorption enegy is in the range 6-10 kcaljmolc; tiiis is in acceptable agreement \viIll e~perimcnr. Ilowever, only the cluster model gives the correct splitting of the v2 frcqucncy of CO=.

\Vhatever

the

I. Introduction The adsorption of organic compounds on the surface of alkali halides has been the subject of numerous previous studies, both esperimental and theoretical. The interaction between a molecule and a solid is directly connected with the heat of adsorption and with the vibrational frequencies of the adsorbate, and is therefore of great interest in catalysis. Since the direct treatment of the supersystem (molecule + crystal) is of course impossible, approximations are necessary. Hiickel tackled this problem in 1925 by means of LennardJones pair potentials [ 1 ] _ Up to the past few years, all the research has been continued in this way (see, for example, ref. [2]). At the present time, due IO the capabilities of electronic calculations, theorists more and mom are turning to much more elaborate treatments which explicitly introduce all the electrons of the system. A first approach consists of treating the molecule within the electric field created by a finite number of point charges, designed to simulate the infinite crystal [3]. A more sophisticated method consists of treating the super-molecule built from the adsorbate itself and a certain number of neighbormg ions of the substrate, all the other ions being replaced by point charges (41 (cluster method). This latter

150

procedure is certainly more satisfying. However, when the sizes of the adsorbed molecule and the crystal ions increase, it leads to calculations which are too lengthy, so that the pair method still remains in favor. In fact, instead of being satisfied with semi-empirical Lennard-

Jones pair potentials, some authors [5] use more sophisticated potentials, determined from self-consistent-field (SCF) calculations, in order to simulate the theoretical scheme of the cluster method. Generally, the methods which use pair potentials lead to satisfactory adsorption energies and to correct sites of adsorption. In contrast, these methods seem to encounter difficulties in predicting the crystal effect on the vibrational spectrum of the adsorbed molecule_ The case of CO? adsorption on NaCl is typical in this connection. A pair potential method, fitted to SCF calculations, predicts the splitting of the v2 vibration of the free molecule [6] with an increase in both resulting frequencies [7], whereas experiment shows a decrease in both these frequencies [8]. The aim of this note is to compare the various possible approaches in the particular case of the adsorption of CO1 on the (100) face of NaCl in order to determine the method best adapted to this kind of problem.

0 009-2614/84/S 03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

2. The method It is well known that adsorption phenomena are governed by the Gibbs energy. Nevertheless, in order to determine the site of adsorption and the main characteristics of the adsorbed molecule at low temperature (a few K), as a first approach, we can consider the adsorption energy only, owing to the fact that, at these temperatures, the entropy terms do not play a detemlining role. Moreover, we assume that the CO, concentration is sufficiently mall to allow us to neglect the intermolecular interactions. First, by means of the ab initio SCF method [9]. we determine the difference +-F between the energy of the molecule (or the cluster) in the isolated state and one within the electric field created by the point charges designed to simulate the substrate. This SCF term includes both the electrostatic interaction between the adsorbed molecule (or the cluster) and the substrate, and the polarization of the adsorbed system by the point charges. The energy of polarization of the ions by the adsorbate is negligible (about ASC,/IOOO). In order to improve the evaluation of the adsorption energy, we introduce a dispersion-repulsion term, ADR_ We use a semi-empirical pair potential that we can write as V,,R = - ,f=, (-4 ‘IN/R6) (i - B/R6) _ M and N are respectively

(1)

an ion of the substmte

and an atom of the adsorbed molecule (or cluster). A 5’S is the asymptotic dispersion coefficient given by London [lO,l I] : A”~N

= f [I&l(I,,

+IN)I

aBI@N 2

(3

where I and cr are respectively the ionization energy and the polarizability of the corresponding atom or ion. Table 1 gives the values we have used [ 12- 153. Within the hard-sphere model, B = ;(R;‘N)6

>

2 1 Septcn&r

CHEMICAL PHYSICS LETTERS

Volume 110. number 2

1964

Table 1 Parameters necessaq in calculating the energy ~DK: ionization energies. I [ I?]. polarizabilities. Q [ 13,14]. and x-an dcr N’aak radii, RQ [ 15 1

c 0 xa+ cl-

ICC\‘)

&i3)

RCA-%)

11.3 13.61 17 3.6

2.10 0.89 0.2 3.0

1.30 1.40-1.60 0.95 1.81

A, which is the same for all MN pairs. In orfler words. we write B as

B = $a#“)6

_

(4)

is weak with respect to &-I.=. this Given that A,, approximation is sufficient. In the hard-sphere model, the mininial approach distance is equal to the sum of the corresponding van der Waals radii of the atoms in conracr. On he other hand, the introduction of X requires the determination

of the position of the molecule by minimization of the total energy. For the cluster model. we assume that the ions of the substrate are not relaxed. only the position of the molecule itself being able to vary with respect to these ions. A minimization calcularion is necessary.

Whatever the model used, the adsorption appears as A=&-,++,,

energy (3

_

Positive values of A correspond to an adsorption on the crystal surface. We have used a version of the GAUSSIAN 70 program, modified to take esterior point charges into account [16], with the STOdG basis set. The substrate

has been sirnulared by 7 X 7 X 4 = 196 point charges equal to +l, located at the sites of the ions in the NaCl crystal. No relaxation = 3.s14a>.

flas been introduced

(cl,_

(3)

Rg’N being the sum of the van der Waals radii of M and N. In this model, ex ression (1) is valid only if rp R > RkfN_ For R < Ri’ , B is equal to infinity. In fact, the atoms or ions are not rigorously impenetrable. In order to take this effect into account, as a first approximation we introduce a coefficient

3. Preferential adsorption

site and corresponding

energy For the free CO, mofccule, we have utilized the following geometrical data [ 151: linear molecule_ (I C-0 = 1.162 A.

151

CIIE~IICAL

IJIIYSICS

21 Scplcmbcr

LfxrIsl
1984

TilblC 2 Total ad.sorpIion cncgics A (lx;~l/~~~olz) in the q,prosi,nalion AI (USC I). The distance z and tlic osygcn radius R(O) arc given in n

R(O) _-----I.4 1 .G

Iiy IL’;ISOII ol’syiiii~ictry, I’oll~~wing

cxics

only:

WC Iiavc

(i) (‘02

10 lllis

slidax

(cast

III cutler 10 dclcrmiiic 11sctl ll,C Ililld-SplWrC I :111il 2 sliow tlcIcr,,,i,ii,,g

111~;dsorl~lioil

Ilic v:,rio,,s

lllc tilcs,l~~sl:1lir:

silts

intcractiotl

1.olcs,

For

sl;iblc IiiiIiiIi1I11n).

2. For

cucrpy

wc Iiavc

lx~silio,~ The

rcstills

(II),

corrcslx~,,ds

;I& :I

;tlignwcnt, IIIC C ;I~OIII lxi11g IOL.IIICC~ II/XJVC 111~CCII~CIo~‘;I Nn,Clq sqttxc (site ?, -- fig. 2). TilblC 3 gives IllC LY~Ircsp‘Ml‘iillg lcsulls. Ni,’ h’;,’

l‘hc

111~1si1iiI1111v3lIiCs

;HL’ 1cspccIivcly lllcv2 ValllCs 111:itc. Ilit casts

5.8

0l~lilillCtl

IlaVC lo l)C coi~sirlcrcil clil’fcrcncc

is suI‘l’icic,~lly

for

antI 10.7 kcal/,nolc. wliicl,

alpars

IilrgC lo alhw

Cuscs

bctwccn

4

0.77 0.68

0.67 0.63

__I~.. __I_I.__LI

____D”

2.63 2.4 I

H.35 1.23

tlcr Wxils for

01’ I

For

A2)

with

iI,sIaIiCd.

iilosl

I*avor-

arc pr3elic3lOl‘ IllC Vi111

R (oxygen) arc

= I.60

S.0 ;IIKI 9.7 kcnl/

II rcspcctivcly.

to iniprovc

li)r tlic prcl’crciili:il (111otlcl

2 is lllc cmxgics

A0 A),111~ KIIIICS

C;,SCS I illld

In ortlcr

silt

by ill1 ill~l>rCCiill~lC VilriiIlioll

r;Itlii.

A (irlstc;itl

al)ovc

tlic adsorption

tlic ;idsorption

ciicrgy

0bt:liiictl

site, wc ilsc lllc al~l~rosi11i3lion

and llir cluster

1ncIl10d

(4)

(13).

I alltl II

Al1l1011gh

ilS Ixing

Silt

Site 3

_.-

IO.73 9.73 __ -_-__

adsorl~tion

III addition,

iiiolc

itt Iahlc ~lx~c

lxirallcl

ly IIllillTCCICtl

lo ;I lo-

lllc iiwxiinui~

lo llic11i0lcc11lc

corrcsponrls

_-.-._

-3.77 -3.52

2.336 2.41 I

able.

play

iltlSOrl~liO1I

arc listctl

1.4 I.6

tlic

As cslx.xIctl. sy~ntnctry

lxxp.MioIrli,r

Ilic lx~~;~llcl uric1~1;11io,,

sorplior,

slutlicil.

5x1 5.75

I

AI ). Figs.

posit ion is tlw OIW ;IIWVC ;I N:I”

I -- I’ig. I ) (this

io,, (silt

site,

1.35 2.55

~._---.._-_.~__-.

IllOlCC\llC

(1110dcl

:IIIJ lllc

Illc

(I I, IIW IIIOS~ I~tvor:hlc

tlic

II).

;1l~l~ro~i1iialio11

Silt _

Total ;Itlsorptiofl cncgics A (k~ill/tll~~l~) in tllc itl>l)roxi,,,i,lion A1 (tax II). The disIilllW z itfltllllc osygcn r;1di,,s R(0) arc Civcn ii, A ____L_LIIIII---_---_ SilC 2 Silt 1 Silt 4 Silt 6 K(O) 2

lxxlxx1~liculnr

(I 00) Sill f;lCC (CiISC I), ;IIlcl (ii) (‘02

I0 IIlC )XllilllCl

c;,lly

co,isidersd

i110lc~ulc

z

Will1iii

approsilhc

us to conclude

two

Ihat

lliis

ol~prosi111ati011.

Ibr various

WC IMVC niiniinizctl

llic cncrgy with

clist:,Iicc

the

2 bctwccn

nuclei ol’ tlw swhce Ily inlcrpolalion,

vidtics

of h.

rcspccr lo lllc

rnolcctrlc and lllc plallc of tllc

ions. Table

4 sl~ows the rcsulls.

lhc consislcncy

bctwccn

z,,

and

1Lblc 4 Toral adsorption cncrgics A (kcal/11101c) in IIW approsirnaIion AZ. for various vslucs <)I’A and correspondir,g dis1ancrs z,,,(n)

h

=m

P

1.1 1.2 1.26 a) 1.3

I .895 2.193 2.336 2.434

11.90 6.49 6.32 6.03

3) Valluc obtained by interpolation A, approximation.

for the distance

z,

of the

IllC Xtllal

nliuituxl approach dist3ncc

sum of tllc van dcr Wxds

given by llic

radii corrcs1x~nds

tiblc

6

to X

= 1.26,

i.c. to z,,, = 2.34 R and A = 6.3 kcal/nwlc. The s3tw proccdurc applied to tlic pcrpcndirular adsorption nbovc site 1 gives practically the saiiic value of h (I .4). This justifies IIK proccdurc, tlw weak difl*crcncc arising very probably ftoni tlic nrlisolropy 01’ tlic oxygen atoms in tlic CO2 iiiolcculc.

III this iiiodcl. wc consider tlic cluster (C02C12P-. built from tlic CO, ~i~olcci~lc and tlic two ncarcstncigiiborilig

atid lhc

Cl‘sur~wc

‘flit

distnncc

is dctcriiiiiictl

ions.

by

CO?

z betwccil niii~i~iiiziitioii

of

llic

value 01’: is equal to 1A9 A, and the corrcsp~~niliiig adsorption cncrgy to --510.3 ciicrgy.

‘i‘lic

calcul;~tcd

kc;ll/lllolc.

‘I‘IICIlCl

Cl13lp!S

Of IIIC iIII)IllS

iii IllC

giwtt itt IillIllJ 5. Wc see. itt particuhr.

cant tr:ii~sf~r froni Cl-

:lustcr ilIT Iltal no sigttifi-

ions towards tlic CO2 11~0lccu1c

occurs. This point is illl]XNtilllt. bccausc it jtistifics tlic point-cktrgc ;Il)prosiiii;ilioi~ usctl for tlic sulxtr:itc. Iii lxissing. wc ilolc tl~i~l, if in ai1 illlClll~~l to iiiiprovc llic

tlcscriptioii

of

tlic

systcin

wc

consiilcrcd

tcr (CO?CI?NiI~)(’ built 1111frortl CO, tlcarcsl-llci~llborilig ions (2 Cl-- atld 2 Ccrtilillly oblain ;I biltl result owing IO C13Na2 ~nolcculc, in the isol:tlcd state.

tlic

cliis-

atId IIIC fout Naf ), WC sl~~ltl

IIIC filC1 tllill tIlC has a strongly disagrccnicnt willi tlic

cov3lcnt chactcr, in coinplctc ionic structure of NaCI. Finally, WC l~avc st udicd the cffcct of a \~crIic;ll 0scillaIion of tlic CO2 ~i~~lcculc itself around its cquilibriunl poshion. The zero-point vibrational cncrgy is ~~~~~~~ to 0.2 kca~/I~lo~~. ~oI~scqllel~tly, th dkt 011 tlic adsorption energy is ncgligiblc.

11.3 15.4 -7.1

Al

A2 II

cxpcrirncnt

IX I

Table 5 Net ~A~rgesQ of

llic crystal field removes the dc-

the iltoms

in IIIC (C02C12)‘-

clusler

U)

Q

-16.7

9. l

-19

9

and conclusion

frequencies

As stated :hovc,

(mc1lmd

10

9 9.’

gcncracy ~CIWCCIItlw two c011il~011c11ts0r tlic v2 vibralion of tl~c free CO, ~~iolcculc. WC ohscrvc tw I’rcquciicics ( trzti and vlb) corresponding rcspccl ivcl> lo vihtions parallel 10 (v,,) mtl pcrpciidiciil;ir to (v,) llic Sllrl~ilCC. wllosc frrqircncics ilK Iowcr Illall Illal of 117. In boll1 nl0dCls A, \vc oblain il splilliiig. bill with il gciicral shift towards high frcqucncics. On Ilic contrilr)‘. Illc~tlcl 1%(clitslcr CO,Clz) giws il correct sliil‘t Ibr hth frcquctrcics (lablc 6). III 41 tlw cdcul~tions. \vCIlilW l;lk~Xl tllc aril~;irnionicity into iICCOIIIlI [ 171. NCVCIIllClCss. tllC frcqucncics II1CIllSCIVcsiIK Systcn~:~tic:~lly ovcrcstimated. For instance. for tlw initi3l I)? frcquciicy. our calculalion gives 601.3 cm- l [O]_ ‘&is is ills0 tlic case for tlic licqumics 011 splilliiig. This result is not surprising. lndced. it is well knowr that only a wry cxtcndcd configuration interaction pcrmits 0llC 10 Ohlilill gOOd Valttcs for IllC force cOnstunts [ I 81. I lowever, our result can bc considcrcd as being correct, owing to the fact tlxtt qunntuni rneclinnics is bcttcr able IO rcproducc variations of a given quantity tllilll I0 predict Ihc acIu;il value 0r this quantity. TIKW calculations IMVCallowed US to verify I Ilat CO2 rcniains practically linear in its equilibrium position (tile ~Ilglllil~ deforniation is less than 0. lo).

5. Discussion 4. Vibrational

-

3.3 G.:!

C

0

Cl

0.508

-0.287

-0.967

Esperimnt sl~ows that CO2 adsorbs in a parallel posit ion with respect to the (100) surface of NaCI and that the adsorption energy is ~5 kc;tl/n~olc [ 191. Our calculations indicate the same adsorption type. However, the values obtained for the adsorption encrgy are systematically larger. The hard-sphere model and the cluster nlodel give practically the same value (~10 kcal/mole). This agreement is certainly accidcntal. The very small approach distance 2 (1239 a) in 153

Volume 110. number Z

the cluster model arises from the fact that the interaction between the two Cl- ionsand the CO, group is tm~ch stronger in the cluster under consideration than in reality.

the Cl-

ions also being linked

with

the other

ions of the crystal. Certainly, the approach distance z is greater t hm I.89 n and, consequently, the adsorption energy is less than 10 kcal/n~ole. Moreover, one can object to our calculation in that it does not iriclude correlation effects. In fact, given that the adsorption energy is obtained as a difference between isoelectropic systems, without electron transfer between one another, even in the cluster model the effects of correlation on the value of the adsorption energy must practicaliy be cancelled out. In contrast. introduction of polarization d orbitals on C and 0 should modify the value of n in an appreciable manner, but without changing the general conclusions. Let us recall that Ileidberg. using pair potentials fitted to SCF calculations, obtained the sanie preferential site and practically the same adsor~~tion energy (6.0- 1 I .5 kcaI!tnole) fs] as us. In contrast, Ire obtained a shift towards higher frequencies for both components of VT 1171. In conclusion,-insofar as the results obtained in the particular exe of CO2 adsorption on N&l are general, the simple model which considers the adsorbed ntolecule within the electric field created by the ions of the substrate, with a dispersion-repulsion pair potential like eq. (4) is sufficient to determine the adsorption site and the order of magnitude of the adsorplion energy. This conclusion is of great interest for treatiug adsorptioil of large molecules fbutadiene, bemenef in view of catalytic applications. iVevcrtheless, our results (methods A, and AZ), and that of Heidberg [7] using a pair-potential method, clearly show thitt, if we Want to obtain information concerning the vibrations, it is necessary to use the cluster mod& even when the cluster under considcration is too small to obtain a good value for the adsorption energy. Acknowledgement The authors thank Dr_ P. Ckverie (University of Paris) for vafuabk and stit~ittlating discussions relared to this work.

154

21 September

CHEMICAL PHYSICS LETTERS

1984

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and B.bJ. Dcnl, Tnns. Faraday Sec. 24 t 1928) 92; E. IIikkel, Adsorption und Kapillorkondensntion (Xkadcmisches Verlaggescllschaft, Leipzig, 1928). 121 A. Lubczkp and $1.Folman, Trans. Faraday Sot. 67

(1971) 3110; P. O’Connor and R. Schoonmaker.

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(1958) 562. 131 A. Julgand Y O&s, J. Chim. Phys. 79 (1982) 31: A. Julg and Il. Deprick, J. Crystal Growth 62 (1963) 587. f4 1 EA. Colbourn and W.C. Mackrodt, Surface Sci. 117

(1982) 571. 151 J. lleidberg. R.D. Singh and C.F. Chcn. 2. I’hysik. Chem. NF 110 (1978) 135. (6 1 C. tlcrzbcrg. Xloleculx specrr~~ and molecular structure, Vol. 2. Infrared and Rarnnn spccrrr! of polyntomic tnolccules Wan Nostrand. Princeton, 1960) p. 274. 171 1. flcidbcq, R.D. Singh and II. Stein, Bcr. Bunscnges. I’hysik. Chrm. 82 (197s) $4. 181 Y. Kozirovski and al. Folman, Trans. Ftlraday Sot. 62,

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qunntum

chemistry.

cds

P.O_ Liitvdin

and B. Pullnxm

(Rcidcl. Dordrecht. 1963) p. 183. 1191 T. Hayakawa, Bull. Chern. Sot. Japan 30 (1937) 124. 236,243,332.