The binding in neutral transition metal-water complexes

Volume

126, number

3,4

CHEMICAL

PHYSICS

LETTERS

THE BINDING IN NEUTRAL TRANSITION METAL-WATER

Margareta R.A. BLOMBERG, Ulf B. BRANDEMARK Institute

9 May 1986

COMPLEXES

and Per E.M. SIEGBAHN

of Theoretical Physics, University of Stockholm, Vanadisviigen 9, S-113 46 Stockholm, Sweden

Received

5 February

1986; in final form 28 February

1986

SCF and MC SCF calculations have been performed on neutral transition metal-water complexes with the main purpose to explain the large differences in binding energy between recent calculations on these systems and the results from matrix-isolation studies. A variety of different basis sets ranging from standard double-zeta sets to large polarized sets were used on the singlet state for the nickel-water system. A secondary purpose of the calculations has been to understand the measured water bending frequency shifts. For this reason the bending frequency shift was calculated for the copper-water complex and compared to experiments. Calculations were also done on the triplet states of nickel-water. An attempt to understand the trend in the experimental frequency shifts obtained for water complexes with iron, cobalt, nickel and copper was made by calculating the metal polarizabilities.

1. Introduction During recent years there has been an experimental effort to produce accurate results on small transitionmetal containing systems. The results from these measurements can be directly compared to quantum chemical calculations. By the use of ion beam techniques, dissociation energies have, for example, been obtained for simple ions like NiH+ , NiO+ and NiCHi [l-3]. Fragmenting molecules by photon or electron impact has led to the determination of the dissociation energies for Ni(C0); [4] and Ni(CO),’ [5]. By the use of the latter values and a determination of the electron affinities, dissociation energies for the neutral Ni(CO), systems have also been obtained [6]. In a series of papers we will present results from calculations on all these systems and make detailed comparisons to experiments. Such comparisons are needed to establish the accuracy of both the calculations and the experiments. Another area, which will be discussed in this paper, where interesting experiments are being performed on simple transition-metal compounds is the area of matrix-isolation spectroscopy. Since the experimental information mainly comes from vibrational frequencies, a direct quantitative comparison between theory and experiment is not as straightforward as in the com0 009-2614/86/$0350 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

parison between measured and calculated relative energies. Some general qualitative comparisons between matrix-isolation results and calculations can, however, sometimes be made. A particularly intriguing example is the recent finding of Kauffman et al. [7] that the Ni atom is the only atom among the first-row transition metals which does not bind to H20. Even considering large matrix effects, the Ni-H20 system should be at most very weakly bound. This result may seem quite surprising since a recently published standard CI calculation gave a binding energy of 24 kcal/mol (CAS SCF 19 kcallmol) for the singlet state [8]. In another recent paper Bauschlicher obtained a binding energy of 9 kcal/mol both for the triplet and singlet states [9]. Already the discrepancy between the two theoretical results showed that there are some problems in the calculations, and an investigation of the origin of this problem was underway when the experimental result appeared. This investigation showed that there are some quite unusual problems in the choice of the basis sets for the metal-H20 systems, which we discuss in this paper. The binding between water and transition metals is of general interest in understanding the standard Dewar-Chatt-Duncanson mechanism for transition metal-ligand binding [ 10,111. Since there is no IIbonding (T backdonation) to water it should be a good 317

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model for a neutral pure u-donor, and water has been used in such contexts, see for example ref. [ 121. No other simple neutral pure u-donor seems to exist. In light of the finding that there is practically no binding between water and nickel, one might well ask if u interaction in general is at all attractive, or if all the binding between transition metals and ligands is due to 7rbonding, or simple ionic effects. Proposals in this direction have been made by Bauschlicher and Bagus et al. [ 13,141. An analysis of the mechanism of the binding between transition metals and water is therefore also presented in this paper. The present investigation should be regarded as only a qualitative study of the interaction between transition metals and water. The effect of van der Waals interaction is neglected, even though its contribution to the binding energy may not be negligible. It is deemed that an accurate treatment of the van der Waals interaction is too difficult at present for this type of system. Our main purpose with the present study has been to clarify some of the aspects of the electrostatic interaction between transition metals and water, and in particular to understand the origin of the large discrepancies between experiments and recent calculations .

2. Computational

details

There have been two recent CI calculations on the nickel-water complex. As mentioned in section 1 the computed binding energies in these two studies differ markedly. In order to clarify the origin of these differences several different basis sets were used, which will be described in this section and in table 1. The methods used are either the simple one-configuration SCF method or the CAS SCF method [ 151 with a very small active space. The dynamical correlation effects have been neglected in all cases, as discussed in section 3.1. In our previous study [8] on the nickel-water complex we used our standard basis set, which is essentially of double-zeta quality. This is the SDZC set (1) of Tatewaki and Huzinaga [ 161 for nickel with the 3d and 4s shells split into two functions and a diffuse d function added in an even-tempered manner. Two functions are added to represent the 4p shell. The core orbitals (including 3s and 3p) are minimal basis con318

9 May 1986

tracted and frozen in their atomic shapes. For oxygen the MIDI-3 basis of Tatewaki et al. [ 171 was used and for hydrogen the 4s basis of Huzinaga [ 181 contracted to three functions. This is basis A in table 1. As it turned out the major deficiency of this basis set is on water. The first improvement of basis A is therefore a MIDI-4 rather than a MIDI-3 basis set on oxygen. This basis has one more uncontracted p function but the same number of contracted functions. On hydrogen a 5s set was used instead of the 4s set. These changes led to basis B in table 1. In basis C a larger p basis is used for oxygen, where the outermost p function is expanded into two functions [ 191 leading to a contracted 3s,3p set. Basis D adds the normal 2p polarization function on hydrogen with exponent 0.8. In basis E a more diffuse 2p function with exponent 0.4 is used instead. In basis F a d function with exponent 1 .O is added on oxygen. Basis G uses the Wachters basis set on nickel [20] with 13s, 8p, 5d contracted to 8s, 6p, 3d. On oxygen the van Duijneveldt 1 Is, 7p set [21] contracted to 4s, 3p is used with two sets of d polarization functions (exponents 1 .O and 0.15). For hydrogen a 6s set [21] contracted to 3s and a p polarization function with exponent 0.4 is used. This is a basis set for water recommended by Clementi and Habitz [22], which reproduces both the Hartree-Fock limit dipole moment (0.78 au) and polarizability (8.14 au). The basis set G has then been used in all subsequent calculations on the other states of nickel and on copper, iron and cobalt. The final entry in table 1 refers to the calculation by Bauschlicher [9]. The geometry of water has been kept fmed, unless otherwise stated, at the experimental geometry with r(O-H) = 1.78 au and bond angle 104.5”. A planar geometry for the metal-water systems has also been used in all cases to simplify the calculations even though the optimal geometry for these systems are most probably non-planar. Curtiss and Pople [ 23 ] have, however, shown that the energy differences between planar and non-planar forms of these systems are extremely small and not of a qualitative importance for describing the binding.

3. Results and discussion The calculations on the metal-water systems started with the singlet state of nickel-water, for which a

9 May 1986

CHEMICAL PHYSICS LETTERS

Volume 126, number 3,4

Table 1 Basis sets used for the nickel-water system. The dipole moment 01) is for the isolated water fragment. The Ni-0 and dissociation energy De are from CAS SCF calculations on the ‘Al state Uncontracted basis

basis A

basis B

basis C

basis D

basis E

basis F

basis G

ref. [9]

Ni 12,8,5 0

7,3

H

4

Ni 12,8,5

Contracted basis

bond distance

Hz0 p (au)

R (Ni-0)

(au)

De (kcal/mol)

5,4,3[161 3,2[171 3[181

0.93

3.79

18.9

0.93

3.95

13.5

10.9

0

7,4

H

5

5,4,3 3,2 3

Ni 12,8,5 0 7,s H 5

5,4,3 393 3

0.93

3.99

Ni 12,8,5 0 I,5 H 5, l(O.8)

5,4,3 393 331

0.89

4.00 a)

5.5

Ni l&S, 5 0 I,5 H 5, l(O.4)

5,493 393 331

0.79

4.30

3.8

Ni 12,8,5 0 7,5,1 H 5, l(O.4)

5,4,3 3,331 391

0.75

4.40

2.7

Ni14,11,6 0 11,7,2 H 6,1(0.4)

8,6,3[201 4,3,2[211 391 1211

0.78

4.07

4.6

Ni 14,11,6 0 9,s H 6, l(1.0)

8,6,4[201 4,3[211 4,1[211

0.94

4.07

8.8

a) Not optimized.

large discrepancy has been obtained between two recent CIcalculations [8,9]. As is turned out the more accurate calculations rule out the possibility that a singlet state is the ground state of this system. Different triplet states were therefore investigated and compared to the matrix-isolation experiments [7], which did not find a bound nickel-water complex. Calculations werealso performed for copper-water, for which

an experimental water bending frequency shift has been obtained. A comparison between the calculated and experimental shift will thus give an estimate of the obtained accuracy of the calculations. The electrostatic interaction between water and a metal atom is dominated by the dipole-induced-dipole interaction. It therefore seems reasonable that the measured bending frequency shift might be correlated with the metal ’ 319

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atom polarizability and the metal atom radius. In section 3.4 calculated polarizabilities are presented for a series of transition metals: nickel, copper, iron and cobalt. 3.1. The singlet state of nickel-water The results from the CAS SCF calculations on the singlet state of nickel-water using different basis sets are given in table 1. The CAS SCF active space has two electrons in the nickel 3d, and 4s orbitals, which allows for the important sd hybridization effect discussed in ref. [8]. Our previous calculation, basis A in table 1, gave a large binding energy of 18.9 kcal/mol and a bond distance of 3.79 au, which does not entirely rule out the possibility for a chemical u bond. The population analysis further gave a charge transfer of 0.13 electron in the u system, indicative of a weak u bond. The occupation of (sd)_ (4s-3d,) was 1.27 and of (sd), 0.73. Not even this calculation, which gave such a large binding energy and short bond distance, showed any trace of n-bonding, however. The dominating contribution to the binding was instead claimed to be due to electrostatic effects, mainly of dipole-induced-dipole type. The magnitudes of these interactions can be extremely sensitive to the basis sets used, as shown in the table. This is also our recent experience in a study of the Na+(H,O),, system [24]. The major problem with basis A is the basis set on water, which leads to superposition errors and too large a dipole moment for water. Using a larger uncontracted basis (B) reduces the binding energy to 13.5 kcal/mol and increases the bond distance to 3.95 au. Increasing also the p basis set on oxygen as in basis C takes away most of the remaining superposition error. The binding energy is now 10.9 kcal/mol and the bond distance 3.99 au, in reasonable agreement with Bauschlicher’s corresponding values of 8.8 kcal/mol and 4.07 au. It should be added that going from basis A to basis C does not change the dipole moment of water. The large qualitative error due to superposition using a standard doublezeta basis on oxygen is remarkable and not of common knowledge. The second sequence of improvements in the basis sets concerns the description of the water dipole moment. Bases A-C give too large a dipole moment of 0.93 au, compared to the Hartree-Fock limit value of 0.78 au and the experimental value 0.72 au. To obtain

320

9 May 1986

smaller dipole moments polarization functions on hydrogen and oxygen are needed. Adding a p polarization function of 0.8, which is close to the energy-optimized value, the dipole moment drops slightly from 0.93 au to 0.89 au. The binding energy decrease from 10.9 kcal/mol, with basis C, to 5.5 kcal/mol, with basis D, at a fixed distance of 4.00 au is larger than expected, particularly in light of Bauschlicher’s result of 8.8 kcal/mol. The reason for this is probably that the optimal bond distance with basis D should be longer. To improve the dipole moment further towards the Hartree-Fock limit value, smaller p exponents are needed for hydrogen. In basis E a p exponent of 0.4 has been used, which is the value recommended in ref. [22]. This leads to a substantial decrease in dipole moment down to 0.79 au and a decrease in the binding energy to 3.8 kcal/mol. The optical bond distance is now as long as 4.30 au. Adding also a d function on oxygen, basis F, continues the same trend. The dipole moment drops to 0.75 au, the bond distance increases to 4.40 au and the binding energy is as low as 2.7 kcal/ mol. At this stage it is clear that the singlet state cannot be the ground state of the nickel-water system, since the atomic splitting between the triplet and the singlet states is 9.7 kcal/mol [25]. Before we go on to study other states of this system we go over to a more standard basis set. This is a Wachters basis set for nickel and the Clementi-Habitz basis set for water, basis G in table 1. This basis set gives the Hartree-Fock limit value for the water dipole moment and consequently a slightly larger binding energy than basis F, and also a shorter bond distance. Basis G is used in all the following calculations. It is likely that the correct result should be somewhere in the neighbourhood of the CAS SCF results for bases F and G. Since there is no trace of chemical bonding, the absolute size of the dynamical correlation effects, which have not been calculated here, are expected to be small. There are mainly two effects of dynamical correlation. The first effect is the attractive van der Waals interaction. The second effect is a reduction of the dipole-induced-dipole attraction, through both the dipole moment of water and the polarizability of nickel. The two effects due to dynamical correlation should therefore tend to cancel each other. 3.2. The triplet states of nickel-water Since the atomic splitting between the lowest triplet

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state (3F) and the lowest singlet state (‘D) of nickel is 9.7 kcal/mol and the binding energy of singlet nickelwater is probably less than 5 kcal/mol, the ground state of this system should be a triplet. The two lowest triplet states of nickel, 3F (d8s2) and 3D (d9s), are nearly degenerate and are therefore both of interest for formation of the ground state of nickel-water. In the following the experimental splitting between 3F and 3D has been used throughout, since the splitting comes out much too large in this type of calculation 1261. The results from SCF calculations on some of the triplet states of nickel-water are shown in table 2. The 3A, (d9s, di) state was found to be most attractive and the bond distance was therefore optimized for this state. For the other two examined states the energy was only evaluated at R(Ni-0) = 5.00 au and at long distance. The most interesting result obtained is the different behaviour of the d9s and the d8s2 states. The 3AI component of the dgs state, which is the component with the largest polarizability, is bound at the SCF level by 2.8 kcal/mol with an equilibrium bond distance of 4.5 1 au, which can be compared with Bauschlicher’s 8.5 kcal/mol and 4.11 au using a much smaller basis set for water. 2.8 kcal/mol is clearly quite a weak binding, but is nevertheless of the same order of magnitude as the binding energy between copper and water (see below). Experimentally, copper-water is observed as a complex but not nickel-water [7]. The d8s2 state of nickel, on the other hand, is repulsive at 5.00 au by 2.1 kcal/mol. This state is of course bound at longer distances, but probably by a very small amount. A possible explanation for the fact that nickel-water is not observed is therefore obtained if only the d8s2 state of nickel is present in the argon

Table 2 Results from SCF calculations on the triplet states for nickelwater State

Configuration

Bond distance (au)

Binding energy (kcal/mol)

3A1 3A2

d9s (d’) s d9s (d&I d’s2

4.51 5 .oo a)

2.8 -0.3

5 .oo a)

-2.1

3A1

a) Not optimized.

9 May 1986

matrix. This does not seem to be the case, however. Vala et al. [27] have studied nickel atoms in an argon matrix and found that both d8s2 and d9s states are present. Some other explanation must therefore be found for the fact that nickel-water was not observed in the matrix experiment. 3.3. The copper-water complex Unlike the nickel-water complex, the copperwater complex was observed in the matrix experiment. A frequency shift for the water bending mode of 20.5 cm-l was observed upon the addition of one copper atom, whereas no freqency shift was observed when nickel was added. It should be pointed out that the appearance of a bending frequency shift was not the only way complex formation was established, which could have been dangerous since an accidental frequency shift of zero may occur for a complex. A complementary fact was that upon photolysis the metal atom was observed to insert into the O-H bond, only in those cases where a frequency shift had been observed. The insertion thus occurred for copper but not for nickel. To investigate the differences between the nickel-water and copper-water interactions, calculations were also performed for the latter complex. In the first set of calculations on copper-water the metal-oxygen bond distance was optimized in the same way as for nickel, i.e. with a fixed water geometry and a planar complex. The result at the SCF level was a bond distance of 5.08 au and a binding energy of 0.8 kcal/mol, which can be compared to 4.51 au and 2.8 kcal/mol obtained for the triplet nickel complex. Bauschlicher’s results for the copper complex were 4.27 au and 4.6 kcal/mol. The trend in the binding energies between the copper and nickel complexes is consequently the opposite to what was expected from the experimental results. The present calculations therefore do not explain why copper-water is observed and not nickel-water. The bond angle of water was also optimized for copper-water and the harmonic bending frequency evaluated. This led to a bond angle shift from 105.2” for free water to 105.9’ for copper-water. The corresponding frequency shift was a decrease from 1756 cm-l in free water to 1747 cm-l for the complex, i.e. a shift of 9 cm-l compared to the experimental value of 20 cm-l. The calculated shift is consequently of the 321

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correct order of magnitude and in the correct direction, but still contains a substantial error. It seems clear that a quantitative analysis of the matrix experiment is not possible at this level of treatment. To reach higher accuracy, dynamical correlation and probably also matrix effects have to be considered. Nevertheless, the qualitative accuracy reached in the calculations should be high enough to draw some conclusions. For example, it does not seem to be a much larger attraction between copper and water than between nickel and water. On the contrary our calculations indicate that a gas-phase complex between nickel and water should be more stable than a complex between copper and water. It is therefore likely that the origin of the experimental results should be sought in the conditions under which the experiment was performed, for example in matrix effects. If the interaction between the dgs state of nickel and water is prevented in some way, the experimental result would be explained, since the d8s2 state of nickel is almost purely repulsive towards water.

9 May 1986

3.4. The dipole-induced-dipole

attraction

A simple estimate of the electrostatic interactions between water and a metal atom indicates that the leading term is the dipole-induced-dipole attraction. Other terms, such as dipole-quadrupole interaction, have therefore been neglected in the present discussion. The permanent water dipole moment p induces a dipole moment on the metal atom of

(1) where (Y,,is the metal polarizability along the Me-O bond and R is the distance between the metal and the center of the water dipole. The interaction energy between the permanent dipole and the induced dipole is ,ti@,,d-l-c) =

-2a,p2/ft6.

(2)

For this interaction energy there are therefore three critical parameters. In section 3.1 and in table 1 we showed how sensitive the interaction is to the description of the water dipole moment. In this section we discuss the other two parameters, the metal polarizability and the distance R. Since the water dipole factor

Table 3 Atomic polar&abilities in au calculated using basis set G Atom

Atomic state

Occupation

Linear state

~~11 (SCF)

Ni

3F

dss’

3Z3rI

63.9

3A 3Q

3D

d9s

3A

81.9 73.2

eII (CD

58.4

53.6

(Y(NHF) a) 68.8

‘D

d9s

lx+

91.2

Fe

5D

d6s2

sc-

75.8

85.7

co

4F

d’s2

4z-

69.0

76.3

4A

69.8

4Q

70.8

2Fz+

74.3

cu

2S

d”s

a) Numerical Hartree-Fock results from ref. [ 271. 322

3x+

63.6 63.3 63.4

011(MC)

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Table 4 Computed dipole-induced-dipole interaction energies compared to calculated SCF binding energies (in kcal/mol) -E&nd -MC)a) De Ni-Hz0

Cu-Hz0

‘Al (d’s) 3A1 (d’s)

7.2 3.7

4.6 2.8

1.8

0.8

a) Formula (2) is used with q taken from table 3, ti = 0.78 (basis G in table 1) and R = R(Me-0) + 0.55au. is in common for all the metal-water complexes the relative interaction energies should be possible to correlate to the metal polarizability and the metal atomic radius, provided that (2) is the dominant term. In table 3 we list calculated polarizabilities for the atoms Ni, Fe, Co and Cu. In table 4 a direct comparison between energies computed according to formula (2) and calculated SCF binding energies has been made for nickel-water (dgs states) and copper-water. The trend in energies is certainly the same for the two columns. If the water molecule penetrates into the 4s cloud, the effective polarization is less than in table 3, leading to an overestimate of the dipole-induced-dipole contribution. This should be most pronounced for singlet nickel-water where R(Me-0) is shortest. From table 3 it can be seen that the polarjzabilities increase in the order Ni < Co < Cu < Fe. Assuming a correlation between interaction energies and measured water bending frequency shifts, the interaction energies increase as Ni (0.0) < Cu (20.5) < Co (29.0) < Fe (30.5). The values in parentheses are the frequency shifts in cm-l. A rough correspondence between polarizabilities and interaction energies consequently exists, but it is hard to understand why Ni does not form a bound complex at all, even if it has the smallest polarizability. The other atomic parameter which enters expression (2) is the atomic radius, which increases in the order Ni < Co < Fe < Cu. A combination of the polarizabilities and the atomic radii may explain the trend of interaction energies for Cu, Co and Fe but not for Ni. Cu forms a weaker complex than Co and Fe because it has a larger atomic radius. Co and Fe form complexes of equal strengths because Fe has a larger polarizability and a larger atomic radius, parameters which work in

9 May 1986

opposite directions. It should be added that the present explanation of the trend in experimental frequency shifts is clearly oversimplified and should not be regarded as the final answer to this question. One complicating factor is that it may be important how far the water dipole penetrates into the 4s orbital. This effect is difficult to estimate. Other geometrical configurations, with water hydrogen bonded to the metal, as suggested in ref. [ 71, might be important. We should comment briefly on the calculations that led to the polarizabilities in table 3. We first note that the polarizabilities along the bond, CY,, , for the different linear symmetry components of the dns2 configurations are almost equal, which indicates that the contribution to the polarizability from the 3d shell is rather small. A larger sp basis was tested for Cu to see if a reasonable convergence was obtained for the polarizability. When a 4s and a 4p function was added the polarizability increased by only 2% (1.5 au). A reasonable convergence is seen also from the comparison with the numerical Hartree-Fock (NHF) [28 ] results given in table 3. It should be added that the NHF results should not be regarded as the basis set limit results, since the polarizability was computed in an approximate way for the open-shell systems. Results beyond the SCF level were calculated only for the d8s2 (3A) state of nickel but should be representative also for the d”s2 states of cobalt and iron. The MC SCF results given in the table include the s2 to p2 near degeneracy, which, as in the case of beryllium [29], lowers the polarizability. Additional dynamical correlation lowers the polarizability even further. The total effect of dynamical correlation on the dipole-induced-dipole interaction in the metal-water systems should be a decrease in the interaction energy, since both the metal polarizability and the water dipole moment decrease.

4. Summary The transition metal-water interaction has been studied at the SCF and MC SCF levels using a variety of basis sets. The results show a surprisingly high sensitivity to the basis set on water. A standard doublezeta basis set leads to an overestimation of the binding energy by a factor of five for the nickel-water singlet state. The largest contribution to the error comes from 323

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basis set superposition error on the oxygen lone pairs. The remaining error is due to an everestimation of the water dipole moment. In particular, low-exponent p functions are required on hydrogen for obtaining a reasonably accurate dipole moment. There is qualitative agreement between the present calculations and the recent matrix isolation experiments for nickel-water [7] in the sense that the calculated binding energy is found to be very small, in contrast to what was found in other recent calculations [8,9]. The calculations do not, however, provide a consistent explanation for why no bond between nickel and water is observed. A possible hint to an explanation may be found in the fact that the d8s2 state of nickel shows a very weak binding compared to the d9s state. An explanation would then be required for why the d9s state is either not present in the matrix or is in some way prevented from interacting with water. Qualitative agreement between theory and experiment is obtained for the water bending frequency shift in the copper-water system. To reach quantitative accuracy dynamical correlation effects are required. Dynamical correlation will lead to a decrease in the electrostatic binding due to a decrease of both the metal polarizability and the water dipole moment, but gives a positive contribution due to van der Waals interaction. The latter interaction is considered difficult to calculate at present due to the large basis set requirements. Assuming a correspondence between the observed water bending frequency shift and the binding energies, the trend in binding energies, Cu < Co +ZFe, can be understood by considering the electrostatic dipoleinduced-dipole term. Cu has the largest atomic radius and therefore the weakest interaction. Comparing Fe and Co, Fe has the largest polarizability and the largest radius, properties having compensating effects on the binding energy. a

References [l] P.B. Armentrout and J.L. Beauchamp, Chem. Phys. 50 (1980) 37.

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[ 21 P.B. Armentrout, L.F. HaIle and J.L. Beauchamp, J. Chem. Phys. 76 (1982) 2449. [ 31 P.B. Armentrout, L.F. HaIIe and J.L. Beauchamp, J. Am. Chem. Sot. 103 (1981) 6501. [4] G. Distefano, J. Res. Natl. Bur. Std. A74 (1970) 233. [5] R.N. Compton and J.A.D. Stockdale, Intern. J. Mass. Spectrom. Ion Phys. 22 (1976) 47. [6] A.E. Stevens, C.S. Feigerle and W.C. Lineberger, J. Am. Chem. Sot. 104 (1982) 5026. [ 71 J.W. Kauffman, R.N. Hauge and J.L. Margrave, J. Phys. Chem., to be published. [ 81 M.R.A. Blomberg, U. Brandemark, P.E.M. Siegbahn, K. Broth-Mathisen and G. KarlstrGm, J. Phys. Chem. 89 (1985) 2171. [9] C.W. BauschIicher Jr., J. Chem. Phys. 84 (1986) 260. [lo] M.J.S. Dewar, Bull. Sot. Chim.Fr. 18 (1951) C71. [ll] J. Chatt and L.A. Duncanson, J. Chem. Sot. (1953) 2939. [ 121 B. Akermak, M. Ahnemark, J. Ah-&f, J.-E. BickvalI, B. Roos and A. St&&d, J. Am. Chem. Sot. 99 (1977) 4617. [ 131 P.S. Bagus, K. Herman and C.W. Bauschlicher Jr., J. Chem. Phys. 81 (1984) 1966. [ 141 C.W. Bauschlicher Jr. and P.S. Bagus, J. Chem. Phys. 81 (1984) 5889. [ 151 B.O. Roos, P.R. Taylor and P.E.M. Siegbahn, Chem. Phys. 48 (1980) 157. [ 161 H. Tatewaki and S. Huzinaga, J. Chem. Phys. 71 (1979) 4339. [ 171 H. Tatewaki and S. Huzhraga, J. Comput. Chem. 1 (1980) 205. [18] S. Huzinaga, J. Chem. Phys. 42 (1965) 1293. [ 191 R.F. Stewart, J. Chem. Phys. 52 (1970) 431. 1201 A.J.H. Wachters, J. Chem. Phys. 52 (1970) 1033. [21] F.B. van Duijneveldt, IBM Res. Rept. RJ 945 (1971). [22] E. Clementi and P. Habitz, J. Phys. Chem. 87 (1983) 2815. [23] L.A. Curtiss and J.A. Pople, J. Chem. Phys. 82 (1985) 4230. [ 241 M. Arbman, H. Siegbahn, L. Pettersson and P. Siegbahn, Mol. Phys. 54 (1985) 1149. [ 251 C.E. Moore, Atomic energy levels, US Department of Commerce (Natl. Bur. Std., Washington, 1952). [26] M.R.A. Blomberg, P.E.M. Siegbahn and B.O. Roos, Mol. Phys. 47 (1982) 127. [ 271 M. VaIa, M. Eyring, J. Pyka, J.C. Rivoal and C. Grisolia, J. Chem. Phys. 83 (1985) 969. [28] S. Fraga, J. Karwowski and K.M.S. Saxena, Handbook of atomic data (Elsevier, Amsterdam, 1976). [ 291 E.A. Reinsch and W. Meyer, Phys. Rev. Al8 (1978) 1793.