Journal of Molecular Catalysis, 39 (1987) 21 - 41 21

MOLECULAR ORBITAL STUDY OF COBALT-OXYGEN INTERACTION

ANTONIO HERNANDEZ

Departamento de Quimica, Universidad Sim6n Bolivar, Apartado 80659, Caracas (Venezuela)

FERNANDO RUETTE and EDUARDO V. LUDE%A

Centro de Quimica, Znstituto Venezolano de Znvestigaciones Cientificas, ZVZC, Apartado 182 7, Caracas 101 O-A (Venezuela)

(Received February 4, 1986; accepted August 6, 1986)

Summary

A modified CNDO-UHF procedure is used to discuss cobalt-oxygen interactions in Co0 and [COO~]~ (q = -1, 0, +l, +2, +3). The cobalt orbitals that contribute most to the bonding in these systems are the 4s and 3d orbitals with relatively little contribution from the 4p orbitals. The ground state of Co0 is calculated to be a *x with a 7~ hole localized in the 3d orbit&. The dioxygen activation in the Coo29 systems is described in terms of the local electron configuration of the O*(R) antibonding orbitals together with the charge, Mulliken bond order and bond length of coordinated 02. The distortion properties are described in terms of the thermodynamic stability difference and the energy barrier for the peroxo to superoxo transformation. The Coo2 systems studied were classified into two groups depending on the degree of dioxygen activation and distortion properties. The lowest activa- tion energy calculated to break the O-O bond corresponded to 69 kcal mol-‘, suggesting that dissociative chemisorption of O2 on a single Co atom is not a likely process.

Introduction

Because of its biochemical interest and importance both for homoge- neous and heterogeneous catalysis [l - 61, the dioxygen interaction with transition metals has been the subject of numerous investigations. Several qualitative and quantitative quantum mechanical methods have been applied to the study of these complexes in an attempt to understand their electronic and binding properties. Among these methods, which have been reviewed recently by BoEa [ 71, the CNDO-UHF method is of particular importance in the sense that it has led to correct interpretations of experimental data on a large series of metal-O2 complexes. This method has also been applied with some success to surface chemistry, where one usually deals with large clusters and where the aim is to obtain theoretical insight into the chemical

0304-5102/87/$3.50 @ Elsevier Sequoia/Printed in The Netherlands

22

bonding and reactivity of systems such as adsorbates on transition metals anchored to metal oxides [8 - 121 and metallic surfaces [ 13 - 161.

In the present work, we report CNDO-UHF calculations for dioxygen bound to a cobalt atom in the range of geometrical possibilities going from the peroxo symmetrically bonded coordination to the superoxo bent structure [l]. Although this system, due to its small size, is amenable to a more accurate ab initio treatment, we have considered it worthwhile to carry out the present calculations using the CNDO-UHF method for the following reasons:

The treatment of this simple system may be considered as a preliminary step in the calculation of the properties of CoOZ on oxidic supports such as zeolites. For these very large systems the use of ab initio methods becomes cumbersome due to the large computational time required.

Semi-empirical methods have not been used to their full capabilities in the sense that the state of minimum energy for a given configuration is not maintained when the molecule undergoes a structural change and reaches a new geometrical arrangement. One of the main aspects of the present work is to show that one may accurately study the behavior of a given electronic state along the distortion and dissociation paths using semi-empirical methods, and that this description provides an adequate framework for the explanation of experimental data. This preservation of electronic states is achieved by means of the incorporation of a selective molecular orbital occupancy scheme [ 171 which allows us to choose and maintain [ 121 a given electronic state along the deformation and dissociation reaction coordinates.

It is also important to remark that the poor CNDO estimates of binding energies may be considerably improved by an adequate parametrization which yields at the same time reasonable bond lengths and energy values. The usual choice of CNDO parameters has relied on spectroscopic fitting of ab initio data for small transition metal complexes [ 18,191. More realistic estimates of these parameters for the description of metal complexes and metallic surfaces have been obtained, however, through the incorporation of thermodynamic data [ 20, 211. This thermodynamic fitting has been recently discussed by Blyholder et al. with regard to the applications of MIND0/3 to transition metals [ 221.

In real systems of catalytic interest, transition metal atoms interact with different kinds of surroundings, which either donate or withdraw electrons and which in consequence lead to a net charge formation both on the metal atom and on its adsorbed molecule. For this reason we have studied the effect of a net charge Q on the stabilization of electronic states for the system [CoOJ9, where we have spanned the values of q = -1, 0, 1, 2, 3.

In the next section, we describe some relevant details of the CNDO- UHF method used. Later, we discuss the general features of the most stable states of [COO]~, and of [CoOJq as functions of the net charge q and of the distortion and dissociation angle. Finally, we select as two representative situations those of q = 0 and q = 2, and discuss in detail the electronic and

bonding factors which are responsible for the relative superoxo structures and for the dioxygen activation.

Method of calculation and parametrization

23

stability of peroxo and

A modified QCPE-290 algorithm, based on the extended CNDO-UHF formalism described by Rinaldi [23], was used to perform the present calculations. The modifications include symmetry and selective molecular orbit& occupancy (Head et al. [17]) and the generation of all singly- and double-excited configurations out of the lowestenergy Huckel configuration used to obtain an initial density matrix in the SCF cycle. We have introduced this last feature in order to perform a search for the most stable electronic states at any given molecular geometry. This state is maintained along the deformation and dissociation reaction coordinates using the calculated Fock matrix at any given point as the initial guess for the next point [12, 241. All the calculations were done without symmetry restrictions [ 171. These non- symmetric solutions lead to a lowering of the total energy relative to the symmetric ones [25], and have been used before in SCF calculations [26].

The selected Slater coefficients .$ and bonding parameters @ (p = s, p, d) are listed in Table 1. They were chosen to reproduce the experimental bond energies and equilibrium bond lengths of Co0 and Oz. This parametrization scheme has been used successfully in MINDO/SR applications [22, 24, 29, 301. The .$$ and /3: parameters of Co are linearly correlated to the electro- negativity factor l/2 (Ip + A,) given in Table 1, in agreement with the work of Freund and Hohlneicher [ 191. Nevertheless, following Kai and Nishimoto [21], our /3&, is taken to be smaller than the p&. The Co(4s’, 3d*) configura- tion corresponds to the ground state calculated with the parameters listed in

TABLE 1

Parameters for cobalt and oxygen

Orbital p -l/2& + Ap) (ev)

co

4s 4P 3d

4.17a 1.71 13.9 1.16a 0.90 7.5 5.84* 1.90 17.9

0

2s 2P

aReference 27. bReference 28.

25.39017b 2.275b 23.0 9.11b 2.275b 22.3

24

Table 1. It corresponds to the valence Co configuration in COO, as obtained in a previous CNDO calculation [ 311.

General properties of cobalt-oxygen interaction

Bonding in Co0 The result of the calculations for a variety of configurations of Co0 are

shown in Table 2. The most stable configuration corresponds to a *YT state with a hole in a T orbital localized on Co(3d,,). A 4E state lies about 2 kcal mol-l above in energy. Currently, neither experimental nor theoretical information exists concerning the ground state of COO, and there are rather few calculations concerning diatomic oxides of the late transition metals. GVB ab initio calculations predicted that the ground state in NiO [32] corre- sponds to a X3x- state with a hole in a Ni(3d) orbital. Recent ab initio calculations found *T as the ground state in CuO with a hole localized on a Cu(3d,) orbital at the SCF level [ 331. These results, and the fact that a variation of the parameters over a 20% range does not change the relative order of the lowest calculated electronic states (see Table 2), indicate that the calculated CoO( *n) ground state is a reasonable result. The expectation value of S* wsls 0.81, showing that there is a slight mixture with states of greater multiplicity since a pure doublet has (S*> = 0.75. The calculated bonding properties of the ground states of Co0 and O2 are presented in

TABLE 2

Co0 calculated properties

Binding energy (kcal mol-’ )

Bond length (A)

Charge on Co (e)

a - au7r26*na *7r -133.2 1.90 +0.25 p - oa7rW.r

(Y - ou?r%27r2 2 -128.2 1.97 +0.30 p - uon%u

0! - uun%%ru 2 -111.1 1.93 +0.27 2 - u(m2lr2u

01 - uo+62n% 4(2)x c -131.3 1.94 +0.29 8 - ua7rW

(II - uulr%=n~u 4 -114.3 1.98 +0.26 p - uunWu

(Y - uu7r%%r2uu 6 -62.1 2.11 +0.02 p- 0m261

aSee ref. 22 for notation. bSpectroscopic designation for the two lowest states are included. c4C and 2X are degenerate states in CNDO.

25

TABLE 3

Co0 and 02 calculated properties

Molecule Orbital occupancies Mulliken Bond lengthb Binding energyb

S P d s P bond order (A) (kcal mol-‘)

sp-sp sp-d

co 0

CoO(%T) 1.20 0.11 7.44 1.86 4.39 0.62 0.45 1.90 (1.80jc -133.2 (-103 * 6)d

0

02(3w)a 1.88 4.12 - 1.31 - 1.205 (1.207)e -118.6 (-118.1)f

a3Z and ‘I: are degenerate states in CNDO. bValues in parentheses represent experimental values. CRef. 34. dRef. 35. eRef. 29. f Ref. 36.

Table 3. The experimental values shown in this table for Co0 are estimated from thermochemical data on Co(OH), [34, 351. The calculated Co0 bond length of 1.90 A is closer to the value of 1.86 A which is observed in Co complexes [ 71.

The C00(~n) molecular orbital diagram is shown in Fig. 1. The 2s orbital of oxygen is rather low in energy, and participates only slightly in the bonding. The main u bonding is represented in Fig. 1 by the 20 level, formed from the 0( 2p,) and Co( 3dZl + 4s) atomic orbitals. The main ?T inter- action is represented by the bonding and antibonding In level, formed from the 0(2p,) and Co(Sd,) orbitals. The unoccupied Co(4p) orbitals are unstable and are not shown in Fig. 1. Their relatively low orbital occupancy (of 0.11 according to Table 3) and the fact that their orbital mixing is never larger than 2% indicates their small contribution to the bonding in COO, in agreement with recent ab initio results [32, 331. Since the size of the 4s orbital is about 1.5 times larger than that of the 3d orbit&, the higher overlap favors the Co(4s)-0( 2p) bonding over the Co( 3d)-O( 2p) interaction. This is corroborated by the value of. 0.62 for the sp-sp and 0.45 for the sp-d Mulliken (overlap-weighted) bond orders shown in Table 3. The non- interacting Co(3ds) orbit& show lower energy in Co0 as compared to Co. This is due to the net electron density transfer from Co to oxygen in Co0 (of 0.25 according to Table 2) which reduces the electron-electron repulsion between these orbitals [ 371.

Distortion properties of [COO~]~ A search for the most stable electronic states in different geometric

arrangements, ranging from the side-bonded to the linear-bonded Co-O2

26

-0.2

-0.4

r 0 -0.Z

z [L

: w

-0.0

-1.2

- 1.4

2.2/10 0 coo CO

Fig. 1. Orbital energy diagram for the 2~ ground state of COO. The cx and fl labels refer to the two spin sets in the calculation. l : Co character of orbit&; 0: oxygen character of orbitals (in 10% units).

1 a

‘-5632.

” 2’A,

2

5

5 2 -5634- 3A2

& b

O\TO / O/O

z Y

/ \ co k- X

-5636- PEROXOW/ SUPEROXO (Co)

/

p /’ I’A, -’

-5638 J

60 100 140 180

Co-O-0 ANGLE

Fig. 2. Energy of [ Co02]* as a function of the Co-O-O bond angle for the states listed in Table 4; distortion curves for (a) q = -1, (b) q = 0, (c) q = +l, (d) q = +2 and (e) q = +3.

27

*A, _/’ P

60 100 140 If Co-U-O ANGLE

- 56.99 ‘Al 60 100 140 II

Fig. 2. (continued) Co -0-O ANGLE

adduct, were carried out. For the states selected, a minimum-energy distor- tion path was calculated, i.e. for each Co-O-O angle, the bond lengths were varied until an energy minimum was reached. The distortion energy curves for the lowest electronic state of both the peroxo and the superoxo structures of [COO~]~ (q = 1, 0, 1, 2, 3) are shown in Figs. 2a to 2e. When the ground states of the peroxo and of the superoxo species are in different spin states, we have also included those states with energies closest to the crossing-point energies which preserve the spin symmetry of the transition (see Figs. 2a, 2c and 2e). In Figs. 2b and 2d other states are also shown in order to discuss in

28

-55.19

-55.25

E

Co-O-O ANGLE

- 54.00.

-54.04-

7

.z

z

5 - 54.00 -

l?i

+

-54.12- 3A” s

-54.16 60

Fig. 2. (continued}

100 140 180

Co-O-O ANGLE

detail the bonding and electronic factors responsible for the relative stability of the peroxo and superoxo structures for other representative situations. The crossing between states of different symmetry in Figs. 2a to 2e occurs due to the absence of coupling terms in the Born-Oppenheimer Hamiltonian used in this work (this is also valid for the orbit& in the Walsh diagrams represented in Figs. 6 and 7). The corresponding bond lengths, total energies and charge on O2 calculated at the minimum of their distortion energy curves are given in Table 4. The peroxo to superoxo transformation may be

29

TABLE 4

Distortion states of [ CoOs]a

Statea Configuration Bond length (A) 1 Total energy Charge on 02

co-o o-o (a.u.) (e)

[coo*]-’ llAl

3A,,

2lA’

4Afr

12A’

6A’

[coos]+’ ‘Al

3B2

1(3)A"b

[coo2]+2

2B2

2A’

4A2

6A’

[coo2]+3 3A"

3(1)&b

‘A’

(11- 5a12b12bz2az p - 5a12b12b22aa cx - 8a’4a” /I - 7a’3a” cx - 8a’3a” /I - 8a’3a”

01- 5a12b12b22az fl- 4a12b12b22as 01- 5a12b12b22a2 fl- 5a12bllbs2a2 (Y - 8a’4a” fl- 6a’3a” CY - 8a’3a” 0 - 7a’3a” (Y - 9a’4a” fl- 6a’2a”

CY - 4a12b12b22a2 fl- 4a12b12b22a2 (Y - 5a12b12b22a2 fl- 4a12bllb22az c~ - 8a’2a” p - 7a’3a”

(Y- 4a12b12b22as fl- 4a12bIlb22aa (Y - 7a’3a” p - 6a’3a” LY - 5a12b12bs2a2 fl- 3a12b12bslas CY - 8a’4a” fi - 5a’2a”

(Y - 7a’3a” fl- 6a’2a” (Y - 4a12b12ba2as fl- 4a12bllb2las 01 - 7a’2a” @ - 7a’2a”

2.01 1.34 -56.3702 -0.65

2.04 1.30 -56.3425 -0.53

2.03 1.30 -56.3284 -0.49

2.02 1.31 -56.3515 -0.35

2.03 1.30 -56.3402 -0.30

2.05 1.29 -56.3146 -0.36

2.01 1.29 -56.3082 -0.32

2.i2 1.26 -56.2421 -0.30

2.02 1.29 -55.9848 -0.02

2.04 1.26 -55.9691 -0.01

2.07 1.27 -55.9330 +0.07

2.03 1.27 -55.2452 +0.32

2.08 1.25 -55.2322 +0.36

2.12 1.24 -55.2184 +0.33

2.14 1.24 -45.1925 +0.28

1.99 1.26 -54.1196 +0.67

2.12 1.25 -54.1135 +0.66

2.01 1.26 -54.1132 +0.66

aC2v designation is used for the peroxo states and C, for the superoxo states. blA” and 3A” (3B1 and ‘B1) are degenerate states in CNDO.

0 +1 +2 4

TOTAL CHARGE q(e) Fig. 3. Stability difference (A) and energy barrier (E,) for the peroxo -+ superoxo trans- formation of [CoO# as a function of g.

characterized by the thermodynamic stability difference A = E, - E, and the energy barrier E, = E, - E,. Here, E, and E, correspond to the energy at the points S and P in Fig. 2, represent~g the minima disto~ion-ener~ points of both the superoxo and peroxo ground states, respectively, and E, represents the energy of the crossing point between these two states (point C in Fig. 2). The calculated values of A and E, for the peroxo to superoxo transfo~ation in the [CoO# (q = -1, 0, 1,2,3) systems are plotted in Fig. 3. They allow us to classify the studied systems into two groups:

Group I Peroxo stable systems characterized by a large value of A and E,. This

group is represented by the species with q = -1, 0 and +l, whose A (or E,) values range from -20 kcal mol-r for q = -1, to -30 kcal mol-’ for q = +l. For q = -1, the most stable peroxo and superoxo states have different multiplicities, and the closest crossing point preserving the spin symmetry occurs 5 kcal mol-’ above C (point C’ in Fig. 2a). These results seem to indicate that the peroxo geometry is the most stable for O2 in [CoO# (4 = -1, 0, +I). This group is also characterized by bent high-lying superoxo states with optimum deformation angles increasing from around 80”for q = 1, to about 100”for q = +l.

Group If Peroxo or superoxo stable systems characterized by moderately low

values of A and E,, which are represented by the adducts with q = +2 and

31

i3. The distortion energy curve for the q = +2 system shown in Fig. 2d indicates a peroxo 2B2 ground state with a 2A’ superoxo state -8 kcal mole1 above in energy. The energy barrier for this transformation is of 12 kcal mol-i. As indicated in Fig. 2e, this relative peroxo to superoxo stability is reversed in the q = +3 systems. Here, the superoxo 3A” state corresponds to the ground state, with a peroxo ‘Bi state lying 4 kcal mol-i above in energy, and with an energy barrier around 14 kcal mol-’ for the superoxo to peroxo transformation. This group is also characterized by bent low-lying superoxo states with optimum deformation angles increasing from around 110” for q = +2 to about 120” for q = +3. The moderately low value of E, in this group seems to indicate that the presence of ligands may become important for the relative peroxo.to superoxo stability.

Dioxygen activation properties of [COO~]~ The X(x) index introduced by BoEa [7,39,40] to describe the dioxygen

activation, together with the charge q(02), Mulliken bond order MB0(02) and the bond length r(02) of coordinated O2 for the most stable deforma- tion state of [COO~]~ (q = +3, +2, +l, 0, -l), are collected in Table 5. These properties show unambiguously that the degree of O2 activation decreases when q increases from -1 to +3, as indicated by the decrease of the electron density to O2 and by the lowering of the r(02) bond length. In terms of BoEa’s formulation [7], indicated by the last column of Table 5, the activa- tion of O2 decreases when the oxidation state of cobalt increases from Co(O) to Co(III), in agreement with previous findings [ 33 - 411.

The calculated dioxygen activation properties given in Table 5 allow us to classify the studied systems into two groups:

Group I Dioxygen activated systems characterized by an approximate n*3 con-

figuration, which represents an increment of one electron with respect to

TABLE 5

O2 activation properties of the most stable deformation state of [ CoOslq

Systema Os(n*) electron Charge Mulliken Bond populationb a(O2) bond orderb lengthb X(T) (e) MBC(C2) r(O2)

(8)

BoEa’s formulation

11A1[Co02]-r 2 + 1.37 -0.65 0.76 1.34 2A1 [ Co0210 2 + 0.97 -0.35 0.87 1.31 ‘AI 2B2 [Coo21:: [Co021

2 + 0.63 -0.02 0.92 1.29 2 + 0.26 +0.32 1.07 1.27 [ Co”‘( 02 )-I I+2

3A”[ Coo2 ]+3 2 - 0.24 +0.67 1.11 1.26 [coI”(o2)0]+3

aC2v designation is used for the peroxo and C, for the superoxo states (see Fig. 2). bFor free 02: MBO(02)= 1.31, r(02)= 1.205 A and the population of the 02(x*) molecular orbital is 2.

32

the A*’ orbital occupation in free OZ. This activation is evidenced in Table 5 by a subst~ti~ increase in the calculated r(0,) bond length from 1.21 a to 1.34 - 1.29 A when going from free O2 to [CoO$ (91 = -1, 0, +l). They are also characterized by distortion-energy curves with large values of A and E,, i.e., they belong to the peroxo stable systems discussed in the previous section.

Group II Systems with slightly or non-activated dioxygen, characterized by an

electron con~~uration close to z** as in free 02, and represented by the = +2 and +3 species. Although according to BoEa’s criterium these species

Gould have different dioxygen activation properties ([ Com( 0,)-i] +* us. [CO~“(O,)~]~~), they have similar calculated values of MBO(&) and r(Oz), present a net electron density transfer away from the coordinate 02, and belong to the distortion-energy group II mentioned above. These similarities are discussed in more detail in the last section.

Dissociatiun properties of coordinated U2 The calculations for the group I systems illustrate the dioxygen activa-

tion in terms of the O-O bond softening under coordination with cobalt in its lowest oxidation states. This activated ‘molecular’ state is often assumed to be a precursor for the dissociation of 0, into individual coordinated oxygen atoms (or ‘dissociated’ state) by metals at low temperature [ 61. The process of dissociation of O2 through interactions with Co(0, I) in terms of the opening of the O-Co-O bond angle is examined below.

The calculated minimum-energy dissociation curves for the most stable molecular and dissociated states of multiplicity 2 and 4 in [COO~]~, and 1 and 3 in [COO,]-‘, are shown in Figs. 4a and 4b, respectively. Their corre- sponding equilibrium bond distances, total energies, and charge on the oxygen atoms at the minimum of their dissociation coordinates are shown in Table 6.

The dissociation curves depicted in Fig. 4a for the neutral species indicate that the ‘A1 and 4A2 molecular states are lower in energy than the 4B1 and *Bz dissociated states. They also indicate a stability difference (A) among these states of 62 kcal mol-’ with a thermal dissociation barrier (E,) of about 91 kcal mol-i (points M, D and C in Fig. 4a). The dissociation curves in Fig. 4b, for the q = -1 system are qu~itatively similar, but the values of A and E, are substantially reduced to 37 and 69 kcal mol-‘, respectively, with respect to the neutral species. Nevertheless, this barrier is still very high, although in agreement with previous MINDO/SR calcula- tions for the Fe-O, interaction [ 421, suggesting that O2 dissociation on a simple metal atom is not a likely process. Recent calculations of the Hz dissociation by a Ni cluster, clearly indicated the collective nature of the metallic interaction leading to the hydrogen chemisorption [ 241, The nature of this cooperative interaction in the dissociative chemisorption of dioxygen on transition metal surfaces remains to be investigated.

33

-56.301 L/ ;

- 56.40 1 20 60 100 140 180

(4 O-Co-O ANGLE

(b) O-Co-O ANGLE

Fig. 4. Energy of [Co02]Q as a function of the O-Co-0 bond angle for the states listed in Table 6; dissociation curves for (a) q = 0 and (b) q = -1.

Electronic and bonding properties of the Co-O* interaction

In this section we discuss the electronic and bonding factors which are responsible for the relative stability of peroxo and superoxo structures and the activation of coordinated dioxygen in [CoOJs. For this purpose we have selected as the representative situations of groups I and II, those correspond- ing to q = 0 and q = 2, respectively.

34

TABLE 6

Dissociation energy states of [ Co02’J” and [ CoOzlpl

Statea Configurationa Equilibrium distance (A)

co-o o-o

Total energy (a.u.)

Charge on oxygen atoms

(e)

[C0021° 2A1 CY - 5ar2b12bs2a*

fl- 4a12b12b22a2

4A2 cr - 5a13b12bz2az fl- 4a12bIlbs2az

4BI (II - 5a13b12bs2az fl- 4a13bIlbzlaz

2B2 cr - 5a13b12bzlaz /3 - 5a13bI lbslas

[coo2]-r llA, CY - 5a12b12b22a2

p - 5ar2b12b22az

3As a! - 5a13b12bz2az fl-- 5a12bIlb22a2

3B1 01- 5a13b12a22b2 0 - 5ar3brlazlbs

21A1 (Y - 4a13b12b22az /1- 4a13b12b22a2

2.02 1.31 -56.3515 -0.35

2.10 1.29 - 56.3109 -0.38

1.94 2.97 -56.2535 -0.52

1.95 3.38 -56.2431 -0.52

2.01 1.34 -56.3702 -0.65

2.10 1.30 -56.3412 -0.57

1.98 3.43 -56.3117 -0.86

1.96 3.00 -56.2730 -0.82

Vee Fig. 4 and ref. 37 for notation,

[Co021° The calculated distortion curves shown in Fig. 2b for the most stable

electronic states of the neutral species give a peroxo ‘A, ground state with a hole in an al orbital localized on Co(3d,* + 4s). A 2Bz peroxo state with a b, hole localized on Co(3d,,) lies about 7 kcal mol-l above in energy. The lowest quadruplet state, which lies 23 kcal mol-’ above the ground state, is bent and corresponds to the 4A” term (see Table 4). The most stable sextet state corresponds to a superoxo structure and lies at 69 kcal mol-’ above the ground state. We have also included the bent 12A’ state corresponding to the most stable linear state.

The molecular orbital diagram for the peroxo 2Al ground state is shown in Fig. 5, where the subscripts ‘s’ and ‘a’ are used to indicate the symmetric or antisymmetric character with respect to the XOZ plane of symmetry, respectively, and the asterisk is used to indicate the Co-O2 antibonding character of the level. We have indicated the main Co and O2 components of each molecular orbital following its group-symmetry CzV designation, in order of importance according to the relative value of their mixing coeffi- cients. The Co(4p) orbital mixing amounts to less than 2% in the most favorable case and it is neglected in this diagram. The lowest levels correspond to the a, (20) and bI (2u*) orbit& of 02, and they are excluded from Fig. 5.

35

00 c 2b;hr,n:) -

-0.5

-0 6

-0.7

3+2- 4s.30) + 0

Ib;(yz,n,) +t o

lo;(xY,il;) # 0

40,(x2-Y2) ft-

C0(xz) - 02(x;) 2b, (xz,n;) + 00

2b, C&z) + 00

l92(di,XY) # l

+

Fig. 5. Orbital energy diagram of the ZAl ground state of [Co02]“. l : Co character of orbitals, 0: oxygen character of orbitals (in 10% units).

The stable side-bonded geometry of this state follows from the dominant role of the valence completely-occupied lb,*(3d,, n,) orbital. This Co-O2 antibonding orbital is continuously destabilized along the distortion coordinate and it is correlated to the more antibonding ?r*(3dyZ, n,) level in the linear structure [43]. The valence semi-occupied 3a,( 3dZl - 4s, 30) orbital remains essentially localized on Co along the distortion coordinate, and makes a relatively smaller contribution to properties of [CoOJo. In the 2B2 state the occupation of these two orbitals is inverted, resulting also in a stable peroxo state. The geometry of all the other states depicted in Fig. 2b follows from the occupation of the 2bT( 3d,,, ?rz) LUMO level in Fig. 5, which pushes the system toward the bent superoxo geometry. The orbital distortion- energy diagram shown in Fig. 6, constructed from the lb** and 3a1* levels of the 2A, state and the 2b1* level of the 4A2 state, corroborates the above assertions. In Table 7, we list the valence electronic configuration of the ground states of both the peroxo and superoxo geometries for all the group I systems (q = -1, 0, +l). The following features are important:

36

n7xzp:) ‘\ _.H.

‘\ _./d. , n*cyz,nI$ ‘\ 4’

_.H’

‘\ /’ /

3a:c 2?4s

‘1 ._._,_._.___.-.~._.-.~. / ,361 /

c&2- 4S,3U)

__-- _---

*_____-_---

I b, Cyz,nJ

-0451 I I

60 100 140 160

0 10

‘co Co-O- 0 ANGLE

Fig. 6. Orbital distortion-energy curve of [CoOJo, constructed from lb** and 3ar* levels of the 2Ar state and 2br* level of the 4A2 state.

TABLE 7

Valence configuration of the most stable state for both peroxo and superoxo structures of [coo2]c

System [Co02 lq

State= Valence orbitals occupationb Group Stable geometryC ( C2v designa- tion) la2* lbz* 3a1* 2br*

-1 -1

0 0

+1 +1 +2 +2 +3 +3

2 z 2 0 2 1 2 1 2 z 1 0 2 1 1 1 2 z 0 0 2 1 0 1 2 1 0 0 2 0 1 0 1 1 0 0 1 0 1 0 -

I P I S I P I S I P I S II P II S II P II S

aSee Fig. 2. bThe underlined orbital is responsible for the deformation properties of the state. cP = Peroxo and S = Superoxo.

(a) The peroxo (A,) ground states correspond to the ( lb*,)2(3aI*)” (n = 2, 1, 0) valence configurations. Based on Fig. 6, one may explain the stability of these states upon deformation mainly in terms of the lower energy of the lb2* orbital.

(b) The most stable superoxo state arises from a one-electron lb2* + 2bI* vertical excitation in (a), resulting in the (lb2*)‘(3al*)“(2bl*)r valence

37

configuration. Here, the distortion behavior of the 2br* level in Fig. 6 determines the bent geometry of these states.

(c) The large energy separation among the lb2* and 2b1* levels is mainly responsible for the large value of A calculated for all members of this group. In the [COO~]+~ system, there is the possibility of occupying either the 3a1* or the nearby lb2* orbital Thus, close-lying peroxo and superoxo states are to be expected. It is important to remark at this point that all the conclusions regarding the distortion properties of the 2b,*, 3a1* and 2b1* levels are in agreement with the qualitative Huckel-Walsh diagrams discussed by Hoffman et al. [ 431 for the coordination modes of diatomic molecules on transition metal centers.

The molecular orbital diagram in Fig. 5 also describes the bonding and dioxygen activation properties of the peroxo ground state of the neutral species, in terms of the main interactions between the Co(4s’3d8) and O2 subsystems. It shows the following features: (a) in the lower energy region of the spectrum, the main bonding interaction corresponds to the 3a1(xs, 3dzl + 4s) orbital. It represents the major electronic mechanism for the donation of 0.62 electrons from O2 to Co; (b) in the upper energy region the 2b,(n,*, 3d.J and 2bi (3d,., xs*) spin orbitals represent the main a back-bonding interaction responsible for the donation of 0.97 electrons from Co to 02. Since the u donation drives away electron density from a bonding 02(7r) orbital and the K back-bonding increases the 02(7r*) popula- tion, they are both responsible for the observed activation of dioxygen. This is evidenced by the substantial increase in the calculated r(02) bond length from 1.21 A to 1.31 A (see Table 5), on going from free O2 to [ Co02]’ in its peroxo ground state.

These results are in agreement with the CNDO calculations of Sakaki et al. [44] for a number of peroxo complexes of Rh, Ni, Pd and Pt, although they seem to completely neglect the participation of 3d orbit& in the (3 donation interaction. The main u donation and R back-donation interactions for the peroxo ground state of group I systems, and for both the peroxo and superoxo ground states of the group II system, are shown in Table 8. This table indicates that the above interactions are qualitatively the same for all the peroxo states of the group I systems. Quantitatively, the 3ai donation remains relatively constant while the 2bi x back-donation decreases from 1.37 to 0.63 electrons (see Table 5) when q increases from -1 to +l. Thus, the 7~ back-bonding measured by BoEa’s X(n) index [7], is in fact a good measure of the dioxygen activation properties for all the members of this group.

[COO21 +2 The calculated distortion energy curves in Fig. 2d for the charged +2

system give a peroxo 2B2 ground state and a bent 2A’ state 8 kcal mol-’ above in energy. The geometry of these states may be understood in terms of the distortion properties of the lb2*(3d,, x,) and 3a1*(3d,l- 4s, 30) orbit& depicted in Fig. 7, and their valence electronic configurations shown

38

TABLE 8

Main u donation and IT back-donation interactions

[Co0214 Statea u donation 02(7r) --f co (e)

n back-donation co -+ 02(7r*) (e)

-1 0

+l +2 +3

+2 +3

peroxo 1’Ar 2AI ‘AI 2B2

3B1

superoxo 2 A' 3A”

3al b 2blb 0.72 1.37 0.62 0.97 0.61 0.63 0.58 0.26 0.40 -0.27’

3a’ + 4a’ a 0.42 0.42

2a ” a

0.06 -0.24’

aSee Fig. 2. bMain bonding interactions depicted in Figs. 5 and 8. CThe minus sign indicates a 02(n*) --f Co donation.

-1.07

-1.17 I 60 I00 I40 160

o-o ? 2

‘CD’ 0 Y

Lo tL x

Co- O-O ANGLE

Fig. 7. Orbital distortion-energy curve of [COO~]+~, constructed from lbz* level of the 2B2 state and 3aI* level of the 2A1 state.

in Table 7. The side-bonded geometry of the 2B, state follows from the distortion behavior of the lbz* level. In the ‘Ai state this orbital is emptied in favor of the 3a1* level, which pushes the system toward the bent geometry. In the 4A2 state, internal electrons are promoted and both lb2* and 3al* orbit& become occupied. The peroxo geometry follows from the dominant role of the lb** level. As found in connection with the bent states of the neutral system, the stable bent geometry of the 6A1 state follows from the

39

occupation of the 2b1* level. Table 7 indicates the following characteristics of the group II systems: (a) the peroxo states correspond to the (la?*)“( lbz*)’ (n = 2, 1) valence configuration. The peroxo stability of these states follows from the dominant role of the lb2* level. (b) The most stable superoxo state arises from the lbz* * 3ai* vertical excitation in (a), resulting in the (1az*)n(3a1*)1 valence configuration. Here, the distortion behavior of the 3a1* level determines the bent geometry of this state. (c) The small energy separation between the lbz* and the 3a,* levels is responsible for the close- lying peroxo and superoxo states in this group.

The relative stability of these structures (A > 0 or A < 0) depends on the relative importance of the u and 7~ back-bonding interactions. A detailed orbital-by-orbital analysis of the energetic factors determining the stability of a number of peroxo complexes of Rh, Ni, Pd and Pt has been given by Sakaki et al. using the CNDO method [44]. As before, the bonding and dioxygen activation properties of the q = +2 system may be described in

0.u

- I.10 i-

5o'(n;,z') +j- "

40'(3U,xzf iiF’

3a’(n,,z2+4slQ-.

Fig. 8. Orbital energy diagram for the peroxo 2Bz and superoxo =A’ lowest states of [co02]*2. l : Co character of orbit&; 0: oxygen character of orbit& (in 10% units, 4 or @ represents 5%).

40

terms of the main bonding interactions shown in Table 8 and depicted in the orbital diagrams shown in Figs. 8(a) and 8(b) for both the peroxo and superoxo lowest states, respectively. This Table indicates that the main u and x back-bonding interactions of the peroxo state of all systems studied here present qualitatively the same characteristics, i.e. they are represented by the 3ai and 2bi levels (see Figs. 5 and 8(a) for the neutral and the g = +2 charged systems, respectively). Quantitatively, the magnitude of the 3ai donation remains relatively constant, but the 2bi a back-donation is drastically reduced when the total charge Q increases from -1 to +3. This reduction in the w back-donation explains why the u donation becomes the main factor in the dioxygen activation of the group II systems in their lowest peroxo state. This is also the case for the lowest superoxo state of all members of this group. Here, the u donation represented by the 3a’ and 4a’ levels (see Fig. 8(b)) is more important than the R back-bonding interaction represented by the 2a” orbital. Thus, the u donation is the main factor determining the dioxygen activation properties of group II systems. It depends to a lesser degree on the K back-bonding, which in turn is responsible for the O,(n) population used in the description introduced by BoEa [ 71.

References

1 L. Vaska,Acc. Chem. Res., 9 (1976) 175. 2 R. A. Sheldon and J. K. Kochi, Ada Catal., 25 (1976) 272. 3 H. F. Schaefer III, Act. Chem. Res., 10 (1977) 287. 4 I. B. Afanas’ev, Russ. Che. Rev., 48 (1980) 527. 5 R. G. Graselli and J. D. Burrington, Adu. Catal., 30 (1981) 133. 6 G. K. Boreskov, Catalysis Science and Technology, Vol. 3, SpringerVerlag, New

York, 1982, Chapt. 2. 7 R. BoEa, Coord. Chem. Rev., 50 (1983) 1. 8 S. Beran, J. Phys. Chem., 87 (1983) 55. 9 J. Sauer and D. Deininger, Zeolites, 2 (1982) 114.

10 S. Beran,J. Phys. Chem., 86 (1982) 111. 11 S. Beran, P. Jiru and B. Wichterlova, J. Phys. Chem., 85 (1981) 1951. 12 F. Ruette and E. V. Ludeiia, J. CataZ., 67 (1981) 266. 13 H. Kobayashi, H. Kato, K. Tararna and K. Fukui, J. Catal., 49 (1977) 294. 14 G. Blyholder, J. Chem. Phys., 62 (1975) 3193. 15 M. B. Kuzminskii, A. Bagaturyants, G. Zhidomirou and V. Kazanskii, Kinet. Katal.,

22 (1981) 151. 16 R. Dovesi, C. Pisani and C. Roetti, Surf. Sci., 103 (1981) 482. 17 J. D. Head, G. Blyholder and F. Ruette, J. Comp. Phys., 45 (1982) 255. 18 J. A. Pople, D. P. Santry and G. A. Segai, J. Chem. Phys., 43 (1965) S130. 19 H. J. Freund and G. Hohlneicher, Theor. Chim. Acta (Rerlinj, 51 (1979) 145. 20 G.‘Blyholder, J. Res. Znst. Catalysts, Hokkaido Univ., 21 (1973) 95. 21 E. Kai and K. Nishimoto, Znt. J. Quantum Chem., 181 (1980) 403. 22 G. Blyholder, J. Head and F. Ruette, Theor. Chim. Acta, 60 (1982) 429. 23 C. Rinaldi, Comput. Chem., 1 (1976) 109. 24 F. Ruette, A. Hern&ndez and E. V. Ludefia, Surf. Sci., 151 (1985) 103. 25 J. I. Musher, Chem. Phys. Lett., 7 (1970) 397. 26 P. S. Bagus and H. F. Schaeffer III, J. Chem. Phys., 56 (1972) 224. 27 D. W. Clack, N. S. Hush and J. R. Yandle, J. Chem. Phys., 57 (1972) 3503.

41

28 J. A. Pople and D. Beveridge, Approximate Molecular Orbital Theory, McGraw-Hill, New York, 1970.

29 F. Ruette, A. Hernandez and E. V. Ludena, Znt J. Quantum Chem., 29 (1986) 1351. 30 G. Blyholder, J. Head and F. Ruette, Surf. Sci., 131 (1983) 403. 31 T. Anno and H. Teruya, J. Chem. Phys., 52 (1970) 2840. 32 S. P. Walch and W. A. Goddard III, J. Am. Chem. Sot., 100 (1978) 1338. 33 (a) J. Schamps, B. Pinchemel, Y. Lefebvre and G. Raseev, J. Mol. Spectrosc., 101

(1983) 344;(b) P. V. Madhavan and M. D. Newton, J. Chem. Phys., 83 (1985) 2337. 34 G. Belton and A. Jordan, J. Phys. Chem., 71 (1967) 4114. 35 D. Jensen and G. Jones, J. Chem. Sot., Faraday Trans. I, 72 (1976) 2618. 36 A. G. Gaydon, Dissociation Energy and Spectra of Diatomic Molecules, Chapman and

Hall, London, 1968, Chapt. 20. 37 F. Ruette, G. Blyholder and J. Head, J. Chem. Phys., 80 (1984) 2042. 38 R. BoEa,J. Mol. Catal., 10 (1981) 187. 39 R. BoEa,J. Mol. Catal., 14 (1982) 313. 40 R. BoEa, J. Mol. Catal., 18 (1983) 41. 41 R. BoEa, J. Mol. Struct., 65 (1980) 173. 42 G. Blyholder, J. Head and F. Ruette, Znorg. Chem., 21 (1982) 1539. 43 R. Hoffmann, M. M. L. Chen and D. L. Thorn, Znorg. Chem., 16 (1977) 503. 44 S. Sakaki, K. Hori and A. Ohyoshi, Znorg. Chem., 17 (1978) 3183.