2 methods

Journal of Electron Spectroscopy and Related Phenomena, 42 (1987) 293-304 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

La,,A’,,MnO,

JUNQING

CATALYSTS

LI, TIANJING

BY MS-Xa AND CNDO/B METHODS

HE, JINA WANG, QIWU WANG

Department of Modern Chemistry, University of Science and Technology (China) YUH-RANG

of China, Hefei, Anhui

PAN*

Department of Chemistry, Boston College, Chestnut Hill, MA 02167 (U.S.A.) (First received

12 September 1986; in final form 24 November

1988)

ABSTRACT This paper presents the orbital energies and the densities of states near the Fermi level of the perovskite type catalysts Lq,&,,MnO (A’ = Sr, Ba, Ca), calculated by the MSXa method. It compares the frontier orbital electronegativities of the catalysts to those of the adsorbed molecules (0, and CO). This work also includes the total energy curves of the catalyst model with the adsorbed molecules calculated by the CNDO/Z method, compares the relative strength of adsorption of both 0, and CO, and discusses the catalytic mechanism of the oxidation of CO. It is promising that the noble-metal catalysts used in the oxidation of CO for purification of automobile exhausts and for other purposes could be replaced by the perovskite type catalysts L%,,&.,MnO, (A’ = Sr, Ba, Ca). The catalysts, which are very active in such an oxidation reaction, have been studied for years by many authors, and considerable headway has been made experimentally. Theoretically, however, interpretation of the catalytic mechanism in terms of molecular interactions has not been available. This paper presents some theoretical results of the adsorption and activity of the catalysts studied by the MS-Xa and CNDO/B methods. INTRODUCTION

Catalysis activity is closely related to the electronic structure of a catalyst, and catalysis usually involves electron transfer between a catalyst and its adsorbed molecules. According to the molecular orbital viewpoint the electrons should transfer between proper orbitals. One can use the electronegativity to measure the ability of an orbital accepting electrons in order to describe the electron transfer quantitatively. The electronegativity X of the ith orbital can be defined as [l-3] K

=

- aE/ani

(1)

where E is the total energy of the system, and n, is the number of the electrons occupying the ith orbital. The relationship between an orbital energy, Q, and the total energy, E, in the MS-Xcr method is [2, 31 *To whom correspondence

0388.2048/87/$03.50

should be addressed.

0 1987 Elsevier Science Publishers

B.V.

294

Comparing eqns. (1) and (2), one can immediately see that the negative of a MS-Xa orbital energy is just the orbital electronegativity. Electron transfer between a catalyst and its adsorbed molecules should occur between the frontier orbitals of both. The frontier orbitals can overlap effectively and electrons can transfer easily if the orbital symmetries match each other and the orbital electronegativities are close to each other, and if the density of the states near the Fermi level of the catalyst is high. Activity of the catalyst, therefore, can be estimated by calculating MS-Xcr orbital energies (or orbital electronegativities) of both catalyst and adsorbed molecules and calculating the density of the states near the Fermi level of the catalyst [l-3]. This paper presents the orbital energies and the densities of the states calculated by the MS-Xa method with the clusters A’MnO, (A’ = Sr, Ba, Ca) taken from the catalysts L%,,A&MnO,; compares the frontier orbital electronegativities of the catalysts to the electronegativities of the adsorbed molecules; and discusses the densities of states of the three clusters. In addition, this work also includes the total energy curves of the clusters MnO,-0, and MnO,-CO calculated by the CND0/2 method in order to obtain some information about the catalysts adsorbing both 0, and CO. In the discussion part of this paper, the mechanism of the catalytic oxidation of CO is studied and the relative activities of the three catalysts are compared in terms of the calculation results.

MODELSANDPARAMETERS The main advantages of the Xa method for calculations on clusters are (a) it is economical, since there is no N4 problem of molecular integrals (it is understood that N is the number of basis junctions in this case), (b) it gives a good description of charge densities, orbital orderings, ionization energies, optical excitation, and other one-electron properties, (c) the method is just as simple to apply to heavy atoms as to light ones. This means that it is uniquely fitted to attack such problems as catalysis produced by a heavy metal; it is particularly appropriate for studying impurity clusters in a solid environment and the effect of surrounding ions in solution can readily be incorporated, and (d) it appears possible to introduce approximate relativistic effects for large molecules. One can use a cluster model with about ten atoms to do the calculation which usually results in energy levels close to the corresponding energy band of the catalyst [2,3]. The La atoms in the catalysts involved in this study hold the other atoms at certain distances apart and usually do not play an important role in the catalysis reaction. In the MS-Xa calculation, therefore, the A’MnOG (A’ = Sr, Ba, Ca) clusters have been taken in order to study the three catalysts. The X-ray diffraction patterns have shown that the three catalysts belong in structure to the perovskite type [4], which contains cubic cells with six facecentered 0 atoms, a body-centered Mn atom, 5.6 La atoms and 2.4A’ atoms on

Fig. 1. Canfarmation of the cluster of both Xocand CNDO/2 ealcuIations.

average at the corners in each cell, In the Xcl calculation such a cubic cell with only one A’ atom left at a corner has been taken as a cluster. The conformation of the cluster is shown in Fig. 1. The length of a side of the cubic cell is ,/ZQ, where a is equal to 4.088,4.186 and 4969~ for the three catalysts with Sr, Ba, Ca, respectively. In the MS-Xolcalculation, the overlapping sphere model [5] has been used, the atomic sphere radii have been chosen according to Norman’s criterion [6] with a certain reduction factor by which the bare Nolan sphere radii {radii containing an atomic number ofele~t~ns~ are to be multipli~ in setting up the Norman staling-potential radii. The maximum t’s of the angular basis on the atoms in the MS-Xcl wavefunctions have been taken as 1 for 0 atoms, 2 for other atoms, and 4 for outer spheres. The 0~‘sinside the atomic spheres have been taken from Schwa&s values [7], and the E’S in the interstitial regions and the regions outside the outer spheres have been taken as the valence-electron weighted average of the a’s for the constituent atoms. The parameters for the MS-Xa calculation are given in Table 1. The threshold for the one-electron energy search in each iteration is 1.0 x W5 Rydberg, and all of the calculations are spin-restricted. TABLE 1 Parameters used in the MS-X@calculationsfor the clustersCaMn~~~Sr%U, Atom

0 Mn Ca Sr Ba Outer sphere

Valenceelectron number 6

7 8 8 10

and BaMnU,

Exchange parameter w.

Maximum af E

Norman reduction factor

0.74447 0.71219 0.71984 0.70604 0.8927

1 2 2 2 2 4

0.88 0.85 0.80 0.80 0.80

296 TABLE 2 Parameters

used in the CNDO/S calculations

Orbital

Orbital exponent

ccw

1.625 1.625 2.275 2.275 1.360 1.360 2.600

C(2P) O(b) O(2P) Mn(4s) Mn(4P) Mn(36)

(eV)

Bonding parameter p(eV)

14.051 5.572 25.396 9.111 3.983 0.975 5.157

-

Electronegativity

21.0 21.0 31.0 31.0 22.0 22.0 25.0

The neutral clusters A’MnO, (A’ = Ca, Sr, Ba) have been used in the calculations. In fact, according to Pauling’s formula [8] WA,

=

1 -

exp [ - (X,

- XB)2/4]

(3)

where WA, is the amount of ionic character, X, and X, are the electronegativities of the bonding atoms A and B, respectively, one can find Wcao =

0.77,

WMnO =

0.59

such that each oxygen atom in the clusters has about 0.68 extra electrons on average. Thus the ionic charge on each cluster should be about 2.72 electrons. All of the calculated orbital energy levels ought to shift upward if each cluster is charged with such extra electrons. In fact, these minus clusters are taken from an infinite crystal, in which the clusters must be surrounded by positively charged circumstances. One could use a Watson sphere [9] with the equivalent plus charge surrounding a minus cluster to simulate the boundary effect, which would make all the energy levels shift downward. In order to compare directly with the photoelectron spectra, one has to calculate the transition-state energies. However, many authors [lo] found, for a given cluster, that the effect of carrying out a transition-state calculation is to give a set of energy levels that differ from the unrelaxed orbital energies by an almost constant shift of all the orbitals to lower energy. The orbital relaxation decreases with increasing cluster size, approaching zero in the limit of the infinite crystal, where the molecular orbitals become Bloch state [ll]. This calculation procedure takes too much computer time to be used in solid state systems, since one has to calculate the transition-state orbital energies one by one. A different procedure has been used in our MS-Xa calculations. Considering that the plus charge on the Watson sphere could not completely balance the influence of the minus charge of the cluster, we used neutral clusters whose MS-Xcl orbital energies must be lower than the energies of the minus clusters surrounded by their Watson spheres. The overall-energy downward shift of the neutral clusters is supposed to compensate for the downward shift of about 3.0eV caused by the transition-state calculations.

297

GYMrlO$

SnMnO6

co

6OMllO6

-

-2.8

2n

s

-5.5 I

-13.6 Fig.

02

--Et

-

-

2. MS-X@ orbital energies.

In the CNDO/Z calculations of the potential curves of MnO,-Oa and MnO,-CO, we used the cluster in Fig. 1 with the number 10 atom and A’ atom left out, and it was assumed that the 0, and CO were both adsorbed along the two arrows marked in Fig, 1. The bond lengths of 0, and CO were taken as 1.207 and 1.150A, respectively throughout the calculations. The other parameters for the CNDOf2 calculations are shown in Table 2. RESULTS

The MS-Xa results of orbital energies are shown in Fig. 2, where only the energies near the Fermi levels (ZQ of the A’MnO, clusters and the energies near the frontier orbitale, of both 0, and CO are shown. In Table 3, we list the energies, occupancies, and charge distributions of the valence orbitals of SrMnO,, BaMnO, and CaMnO, shown in Fig. 2, as determined by the MS-Xor method. The CNDOIZ potential curves of MnO,--O2 and MnO,-CO are shown in Figs. 3 and 4, where Figs. 3(a) and (b) show the potential curves of 0, and CO adsorbed over number 3 0 atom in Fig. 1, respectively, and Figs. 4(a) and (b) are the curves of 0, and CO adsorbed over the vacancy at the number 10 atom in Fig. 1, respectively. The abscissae r(A) indicate the lengths of the adsorbed bond to the number 3 0 atom or to the vacancy. DISCUSSION

Adsorption

of both

0, and CO

0, and CO might both be adsorbed on the surfaces of the catalysts in the catalysis reaction. The frontier orbitals of CO are the occupied 50 orbital and unoccupied 27~orbitals. Adsorbing CO to a catalyst surface is usually a CT--~Z donation-acception process, that is, 5a electrons of CO are donated to the

al aI e

al al e

al al e e

e

al al e

al e

a2 e

a2 e e

0.99 0.99 0.99 0.99

0.95 0.94 0.94 0.91 0.93 0.96 0.96 0.94 0.01

4 2 4 2 2 4 4 2 2 4 4 2 2 4 2 2 4

8.17 8.17 8.24 8.26 8.32 8.47 11.07 11.08 11.14 11.22 11.53 11.53 22.78 22.79 25.79 25.79 26.89 38.28 38.28

1.00 0.96 0.96 1.00

0 0 0 1

8.16 8.16

1.00 1.00

0.02 0.03

0.02 0.04

Q(Mn)

1.00

0.01 0.95 0.98

0.03

Q@r)

e

a1 al al

al aI e e

al e

al al a2 e e

al a2 e e e

e 5.10 5.13 5.24 5.28 5.28 5.49 9.30 9.30 9.34 9.37 19.50 19.52 21.62 21.62 24.00 24.00 31.10 36.37 36.37

2.69 4.79

- E(eV)

Or

Q(0)

n

-E(eV)

Or

0.96 1.00 0.92 0.86 0.90 0.87 0.84 1.00 0.97 0.96 0.96 0.98 0.98

0.99 0.99

0.96

0 0 3 4 4 2 2 2 4 4 2 4 2 2 4 4 2 2 2 4

Q(O)

0

n

1.00 1.00

0.01 0.01 0.02 0.01 0.06

0.01 0.02

Q(Mn)

1.00

1.00 1.00

0.03 0.02

0.01 0.05

Q(Ba)

% e al a, a, e e al al e e a, a, e al a, e

e a2

Or 1.00

0

0 1 4 4 2 2 2 4 4 2 2 4 4 2 2 4 2 2 4

3.89

6.27 8.13 8.13 8.20 8.21 8.45 11.22 11.22 11.27 11.37 13.34 13.34 22.74 22.75 25.92 25.92 30.68 38.66 38.66

0.99 0.98 0.99 0.99

1.00 1.00 0.95 0.95 0.95 0.91 0.96 0.96 0.96 0.94

Q(O)

1.00 1.00

0.02 0.03

0.05

Q(Mn)

1.00

1.00 1.00

Q(Ca)

Q(J) is the inner J atomic

n

-E(eV)

CaMnO,

(8) of the MS-Xa orbitals (Or) of SrMnO,, BaMnO, and CaMnO,.

BaMnO,

(n), and charge distributions

SrMnO,

Energies (E), occupancies sphere charge.

TABLE 3

% m

299 E (eb

-3736.6

-3737.7

E(e\ -3517

-3730.0

-3518 2.4

2.5

2.6

rtm

Fig. 3. (a) the potential curve of MnO,-0,. (b) The potential curve of MnO,-CO. vertically absorbed over the number 3 0 atom in Fig. 1.

0, and CO are both

catalyst while 27~orbitals accept electrons from the catalyst. The CEO bond, therefore, is weakened. The frontier orbitals of O2 are 17cg,to which the electrons of a catalyst could transfer in the process of adsorbing O2 so that the O=O bond is weakened. When 0, and CO are both adsorbed by a catalyst with a certain density of states, the difference in the orbital electronegativity between the catalyst and adsorbed molecules should make a dominant contribution to the adsorption in terms of the viewpoint of electron transfer mentioned in the introduction to this paper. It can be seen from Fig. 2 that the Fermi energies of the three catalysts are all close to the lkp energy of Oz. It should be easy for electron8 to transfer from the catalysts to the 17~~orbital of 02, and 0, can be effectively adsorbed on the catalysts. On the other hand, the Fermi energies of the catalysts are far from the 271energy of CO, so it should be relatively difficult for electrons of the catalysts to transfer to the 2a orbital of CO and for CO to be adsorbed on the catalysts. These facts can qualitatively show that O2 should be more readily adsorbed on the catalysts than CO. By comparing Fig. 3(a) to Fig. 3(b), one can find that the depth of the MnO,-0, potential trap is about 3.0eV, while the depth of the MnO,-CO potential trap is about 1.5 eV. This means that OS is adsorbed more tightly than is CO. This conclusion can also be made by the following argument. We can simulate the potential curves in Figs. 3 and 4 with a power series

$ (3

W9 = $.

5 (3

(r - re)’ + Q re

(r - re)3 + . . .

(4)

‘e

where r, is the adsorbent bond length at the equilibrium position. Each of the derivatives in eqn. 4 can be determined from the E(r) values of the CNDO/B

300 E(eV)

(0)

-3731.9 /

-3733.3

\ . I

.

1.3

E(eV)

1.4

1.5

16

r(H)

(b)

-3518.6 1

Fig. 4. (a) The potential curve of MnO,-O,. (b) The potential curve of MnO,-CO. 0, and CO are both vertically absorbed over the vacancy at the number 1 0 atom in Fig. 1.

calculations. The force constant k of an adsorbent bond can be directly obtained (5) and the vibrational frequency of the adsorbent oscillator is 3 =

1 k 27X J i

-

(6)

where P is the reduced mass. By using the expressions (5) and (6), we have calculated the k’s and it’s of 0, and CO adsorbed, respectively on MnO, at two adsorbent positions. In Fig. 3 where a molecule is adsorbed over the number 3 oxygen atom in Fig. 1, the k’s and S’s are k(0,) k(C0)

= =

3.69 x 10’dyne cm-‘,

i;(O,) = 556cm-’

3.66 x Wdynecm-‘,

i;(CO) = 528cm-’

In Fig. 4 where a molecule is adsorbed over the vacancy at number 1 oxygen atom in Fig. 1, the k’s and f’s are k(0,) k(C0)

= =

0.0 dyne cm-‘,

2.41 x 104dyne cm-‘,

J(0,)

= O.Ocm-’

S(C0) = 148cm-’

The vibrational frequency of metal adsorbing O2 is usually in the region

301

476-580cm-1, and the frequency of metal adsorbing CO is in the region 35@-650cm-’ [12]. So our calculation results of i;‘s should be reasonable. From these data, one can see, first, the gas molecules are adsorbed over the number 3 oxygen atom in Fig. 1 more strongly than over the vacancy at the number 1 oxygen atom, and second, 0, is adsorbed over the number 3 oxygen atom in Fig. 1 more strongly than is CO. Although this conclusion is made by the two adsorbent position CNDO/B calculations (it is also possible that 0, and CO are adsorbed at other positions), the conclusion also agrees with the results of the orbital electronegativities done by the MS-Xa calculations. Therefore, it should be true that 0, is in general adsorbed more tightly than is CO. Recently, M. Huang found experimentally that the catalyst surfaces were covered by 0, over 96% (results to be reported) [13]. It has been verified, both theoretically and experimentally, that most of adsorbed molecules of the catalyst surfaces are 0,. Mechanism

of the oxidation

of CO

The oxidation reaction of CO on the catalyst surfaces might proceed in two ways. First, CO could react with an 0 atom in the catalyst crystal. Second, CO could react with an 0, adsorbed on the catalyst surfaces. Experimental results [14]have shown that the former mechanism did not work at low temperature. From the above discussion, it is clear that the catalysts mostly adsorb 0, so that there is little probability that CO reacts directly with an 0 atom in the catalyst crystal. The dominant reaction should take place between adsorbed 0, molecules and CO molecules in the gas phase, that is, as a CO molecule in the gas phase is close to an adsorbed 0, molecule whose double bond has been weakened, the 0, bond can break and the COz molecule can come into being. From this viewpoint, the experimental results [14] can be interpreted. Density of states and activity of catalysts As mentioned in the introduction of this paper, a high-quality catalyst should have high density of states near its Fermi level. The experimental results of the catalyst activities [4] have shown that among the three catalysts the activity of the Sr-catalyst is the highest, the Ba-catalyst is much lower, and the Ca-catalyst is the lowest. This activity order can be explained in terms of density of the states. In order to make a definite comparison, Gaussian functions can be used to simulate the density of the MS-Xa states of the three catalysts, that is

_ fE -

Ei)z

20’

(7) 1

where N(E) is the density of the states at E, Ei is the energy of the orbital i with di degeneracy, B is taken as 0.136eV. Substituting the 15 upper calculated MS-Xc( orbital energies in Table 3 for the Eis in expression (7), the resulting

302 N(E)1

8.2

6.8

5.4

4.0

2.6

-EfeV)

N(E) 30 I

12.2

10.9

9.5

8.2

6.8

5.4

4.0

2.6 -EfeV)

12.2

10.9

9.5

8.2

6.8

5.4

4.0

2.6 -E(eV)

N(E) 301

Fig. 5. The electronic densities of states for SrMnO,, BaMnO, and CaMnO, clusters based on the Gaussian broadened MS-Xcr energy levels shown in Table 3.

density-of-states profiles are shown in Fig, 5, where E,‘s indicate the Fermi levels. It can be seen that the density of states near the Fermi level of SrMnO, is the highest, and that of CaMnO, is the lowest. The order of the densities of states near the Fermi level of the three catalyst crystals should be the same as that calculated with the cluster models, and so the order of the catalyst activities should be according to the previous discussion. This is qualitatively in agreement with experiment [14]. Interactions

of orbitals between catalysts and adsorbed molecules

From Table 3, one can see that the frontier orbitals of the clusters of the three catalysts are mostly the combinations of the atomic orbitals of oxygen atoms (i.e., the surface orbitals [ll], the n-type orbitals (2p, and 2p,) and the o-type orbitals (2p, and 2s) shown in Fig. 6(a). The a-type orbitals of the clusters cannot match the n-type frontier orbitals of the adsorbed oxygen molecules (because most of the adsorbed molecules are oxygen molecules), so we can consider the n-type orbitals of the clusters only. Using the symmetries associated with the frontier orbitals (az and e) and according to the group theory and the coordinate system in Fig. 6(a), the components of the x-type frontier orbitals of the clusters are

303

(P,2+ Px3 - PE5 + Py2 - Py3 - Pyd a2= -!&

I

_L (2P,2+ Py3 f P,s>

e

=

fi

where px and py are 2px and 2p,atomic orbitals of an oxygen atom, respectively. Figures 6(b) and (c) show the profiles of a2 and e orbitals, respectively. The e orbital with oblique lines is the orbital (l/J@ (2px2+ pr3 + pr5).If an oxygen molecule is adsorbed vertically over the number 5 oxygen atom in Fig. 6, both the a2orbitals and the e orbitals can in symmetry match the la, frontier orbital of the oxygen molecule; but if an oxygen molecule is adsorbed perpendicularly to the joint line of the (001) face and the (iO0) face in Fig. 6, the a2 orbital matches in symmetry the In, orbital of the oxygen molecule, while each of the e orbitals does not. In this case, an e orbital of a catalyst cannot overlap with the In, orbital of an 0,, and so the adsorption cannot occur. The selectivity of e orbitals makes a catalyst with e-type frontier orbitals unfavorable to the adsorption.

-+

+

-

+t

+$!

Fig. 6. (a) Coordinate system of atomic orbitals of 0 atoms. (b) Profile of a2 orbital in a cluster. (c) Profile ofe degenerate orbitals in a cluster, the orbital with oblique lines is l/S (ZP,, + P,3 f PA.

304

The density of states in the vicinity of the Fermi level of the BaMnO, cluster is close to the one of the SrMnO, cluster, and the HOMO of the BaMnO, is very near to but a little higher than In, level of the oxygen molecule (see Fig. 2), all of which are favorable to the electron transfer from the Ba-catalyst to an 0, and, in turn, favorable to the adsorption. In fact, the activity of the Ba-catalyst is much lower than the activity of the Sr-catalyst, and close to (i.e., a little higher than) the activity of the Ca-catalyst. The reason might be that the three upper occupied orbitals of the BaMnO, cluster are all e orbitals (see Table 3) which are unfavorable to the adsorption. CONCLUSIONS

(i) The Fermi levels of the three clusters are all close to the lx, frontier orbital of an oxygen molecule, and the adsorbent bond of MnOS-O2 is stronger than that of MnO,-CO, so that oxygen molecules could be easily adsorbed on the surfaces of the catalysts. (ii) The orbital components in the vicinity of the Fermi levels of the clusters are mostly oxygen atomic orbitals, and the adsorbent potential curve over an oxygen atom of MnO, has an obvious trap, but the potential curve over the vacancy of the oxygen atom does not. This indicates that an oxygen atom on surfaces of the perovskite type catalysts is the center of the catalysis activity. (iii) The density of states near the Fermi level of the Sr-catalyst is the highest, and the symmetry of its frontier orbital a, is favorable to the adsorption to oxygen molecules. These should be the reasons why the Sr-catalyst is the best one. ACKNOWLEDGEMENTS

We are very grateful to Dr. M. Cook and Prof. M. Karplus who offered us the MS-Xa program used in this work. REFERENCES

2 3

9

10 11 12 13 14

K.H. Johnson, Int. J. Quantum Chem. Symp., 11 (1977) 39. A. Tang, Z. Yang and Q. Li, Quantum Chemistry, Science Press, Beijing, 1982, p. 357. J. Li, Xa Method in Quantum Chemistry and its Applications, Anhui Publishing House of Science and Technology, Hefei, 1964. Q. Wang, J. Rong, P. Lin and S. Shan, Kexue Tongbao, 25 (1960) 967. N. Rosch, W.G. Klemperer and K.H. Johnson, Chem. Phys. Lett., 23 (1973) 149. J.C. Norman, Jr., Mol. Phys., 31 (1976) 1191. K. Schwarz, Phys. Rev. B, 5 (1972) 2466. L. Pauling, The Nature of the Chemical Bond, 3rd edn., Cornell University, New York, 1966, p. 96. R.E. Watson, Phys. Rev., 111 (1958) 1108. D. Li, J.K. Zhu, J. Li and Y.K. Pan, J. Electron Spectrosc. Relat. Phenom., 33 (1964) 1. R.P. Messmer, SK. Knudson, K.H. Johnson, J.B. Diamond and C.Y. Yang, Phys. Rev. B, 13 (1976) 1396. N. Sheppard, in R.F. Willis (Ed.), Vibrational Spectroscopy 1960, p. 165. M. Huang, private communication. P. Lin, Y. Fu and S. Yu, J. Catal., 2 (1981) 166.

of Adsorbates,

Springer, Berlin,