J. Phys. Chem. 1984,88, 5759-5763 zeolite composition (for unperturbed hydroxyls, the stretching frequency varies between 3600 and 3600 cm-' for an average electronegativity calculated from the unit-cell composition (Sanderson's scale49)varying between 4.2 and 3.9, respectively). The framework composition dependency is therefore consistent with the high sensitivity of the intrinsic properties of these hydroxyls. A similar influence for the terminal hydroxyls was not detected. The nonlinearity of the frequency shift of the terminal O H bonds upon adsorption of acetone" is also in agreement with the increased sensitivity with increasing average electronegativity. The experiments reported by JacobsIz are probably in a too narrow range ( A S in the Sanderson scale 0.3 vs. 1.4 for the experiments with terminal OH) to detect a deviation from linearity.
General Conclusion An understanding of the interaction of small molecules with surface hydroxyls is possible in terms of an electron donor-electron acceptor mechanism by applying Gutmann's rules, as evidenced by an ab initio, extended Huckel and CNDO quantum-chemical study. These apply to the large majority of EA-ED interactions (inter- or intramolecular interactions involving a change in coordination) and are in agreement with the experimental observations. A quantitative prediction of the bond strength variation is possible by using Gutmann's experimentally determined donor numbers, but care should be taken for those molecules for which the donor number was derived by indirect methods. An exception
5759
to Gutmann's first bond length variation rule (adjacent bonds) was found for C O in the absence of back-donation, but the bond strengthening (also in agreement with the observations) conforms with the second rule (electron shift from a more to a less electronegative atom). An exception to the first and second rules is the hydrogen-bond formation with nitriles.50 Individual bonds of a given complex will be more susceptible to perturbations (e.g., adsorption of molecules or change in composition) if the coordination number increases (or if these bonds are initially weaker).
Acknowledgment. P.G. thanks Dr. M. Peterson and Dr. G. De Mar6 (UniversitB Libre de Bruxelles) for a copy of the MONSTERGAUSS program, and Dr. J. Sauer for providing the ab initio equilibrium geometries of some of the model systems used here. W.J.M. is grateful to the "Belgian National Fund for Scientific Research" (NFWO) for a permanent research position as senior research associate (Onderzoeksleider). Registry No. Silica, 7631-86-9; alumina, 1344-28-1. ~~
(50) In the H-bond complexes with nitriles where an electron flow from C to N occurs upon interaction and despite the higher electronegativity of N, a CN bond stren th increase is found, by both experimental and theoretical investigations.s1*5 4 (51) White, S. C.; Thompson, H. W. Proc. R. SOC.London, Ser. A . 1966, 291. 460. (52) Figeys, H. P.; Geerlings, P.; Berckmans, D.; Van Alsenoy, C. J. Chem. SOC.,Faraday Trans. 2 1981, 77, 721.
Relativistlc Configuration Interaction Calculations of Low-Lying States of SnO', PbO', PbS', and PbSe'. Comparison with the Photoelectron Spectra of SnO K. Balasubramanian* Chemistry Department, Arizona State University, Tempe, Arizona 85287 (Received: January 3, 1984;
In Final Form: May 14, 1984)
Relativistic configuration interaction (CI) calculations including spin-orbit interaction are calculated for the low-lying states (2111/2,3/2, 22?1/2) of PbO+ and SnO+. Comparison calculations are also carried out for the 'I'I1/2:3/2 states of PbS' and the ionization energies of PbSe+. Spectroscopicproperties (Te,Re,and we) and the dissociation energies are computed for these states. The vertical ionization potentials corresponding to the ionization of the ' P o + state to the 2111,2,3,2 and zZ+1,2states are computed and compared with available experimental results.
1. Introduction The group 4 monoxides are of considerable experimental inN20, t e r e ~ t l -since ~ many of the group 4 atoms react with 03, etc., with very high photon yields. The chemiluminescence of these reactions provides significant information on several low-lying states of group 4 monoxides. Recently the vacuum-UV photoelectron spectra of several group 4 monoxides have been recorded.6-9 Further, theoretical investigations of the ionization potentials of especially lighter group 4 monoxides have also provided very interesting information.'JO Dyke et aL9 have recently recorded the He I photoelectron spectrum of SnO(XIB+)state. This spectrum reveals the existence of low-lying states of SnOCwhich were assigned to 211 and 2Z+. Further, these authors have also computed the vibrational frequency (we) of the 211 state of SnO+. These authors considered Dirac-Fock and SCF-Xa calculations with the intent of predicting the order of 2X+ and 211states of SnO+ so that the observed bands of the photoelectron spectrum of SnO could be assigned. While Koopman's theorem predicts the correct ordering for the 21'1 and 2B+ states of lighter group 4 monoxides, 'Alfred P. Sloan Foundation Fellow.
0022-3654/84/2088-5759$01.50/0
it does not predict the right ordering for heavier oxides. Also, the relativistic effects such as spin-orbit interaction would be significant for heavier group 4 oxide ions. Balasubramanian and Pitzer"JZ have carried out relativistic configuration interaction calculations of the low-lying states of PbO and SnO. For these two molecules correlation and relativistic ( 1 ) Deutsch, E. M.; Barrow, R. F. Nature (London) 1964, 201, 815. (2) Capelle, G. A.; Linton, C. J . Chem. Phys. 1976, 65, 5361.
(3) Barrow, R. F.; Deutsch, E. M.; Taravis, D. N. Nature (London) 1964,
191, 374.
(4) Oldenborg, R. C.; Dickson, C. R.; Zare, R. N. J . Mol. Spectrosc. 1975, 58, 283. (5) Linton, C.; Broida, H. P. J . Mol. Spectrosc. 1976, 62, 396. (6) Colbourn, E. A,; Dyke, J. M.; Fackerell, A,; Morris, A.; Tricale, I. R. J . Chem. SOC.,Faraday Trans. 2 1977, 73, 2278. (7) Colborn, E. A.; Dyke, J. M.; Lee, E. P. F.; Morris, A.; Trickle, I. R. Mol. Phys. 1978, 35, 873. (8) White, M. G.; Rosenberg, R. A.; Lee, S. T.; Shirley, D. A. J . ElecZron Spectrosc. Relat. Phenom. 1979, 17, 323. (9) Dyke, J. M.; Morris, A,; Ridha, A. M. A.; Snijders, J. G. Chem. Phys. 1982, 67, 245. (10) Wood, C . ; Hiller, I. H. Mol. Phys. 1979, 37, 1329. (1 1) Balasurbramanian, K.;Pitzer, K. S. Chem. Phys. Lett. 1983,100,273. (12) Balasubramanian, K.; Pitzer, K. S. J . Phys. Chem. 1984, 88, 1146.
0 1984 American Chemical Society
Balasubramanian
5760 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 TABLE I: A Few Low-Lying States of MO+ in Both A-S and w--w Couding Schemes"
electronic confiauration
A-S state
w-w
TABLE 11: Dissociation Relationship of Some of the Low-Lying States of MO+
dissociation limit M++ 0
state
" M is a group 4 atom.
effects were found to be significant. Thus, in view of current theoretical and experimental interests on these systems it was decided to carry out relativistic configuration interaction calculations of the low-lying states of SnO+ and PbO+ with the intent of exploring relativistic and correlation effects in these systems and calculatiqg the ionization energies and spectroscopicproperties of these systems. Although the attempts by Dyke and co-workers to record the photoelectron spectrum of PbO did not prove succ e s ~ f u lthe , ~ present calculations on PbO+ would be of interest in comparisgps with SnO+and with any possible spectra that could be recorded in the future. We employ here the method of relativistic configuration interaction developed by Christiansen, Balasubramanian, and Pitzer.13 In this method one averages the relativistic effective potentials (obtained from numerical Dirac-Fock solution of the atom) at the S C F stage. The spin-orbit operator is obtained by differencing the relativistic effective potentials with respect to spin. The spin-orbit integrals thus obtained are introduced at the configuration interaction stage. This method was found to be successful for molecules such as TlH,13Pb2, Sn2,14*15 Pb0,12 SnO," PbH,16 SnH,17 etc. In section 2 we describe the method of relativistic configuration interaction calculations applied to SnO+, PbO+, and PbS+. In section 3 the properties of the low-lying states of SnO+, PbO+, and PbS+ are computed and compared with experiments. For the PbSe+ system only the ionization energies are calculated. In the last section we discuss the nature of these states and C I wave functions.
2. The Methodology of Calculations of Low-Lying States of SnO+, PbO+, PbS+ and PbSe+ The group 4 chalconides have the closed-shell ground state X'e+(O+) arising from the configuration u2a4(ignoring the rest of the electrons). The ionization of one of the a electrons leads to u 2 d configuration which generates zIIl/2and 2113/2 states. On the other hand, the ionization of the u electron leads to the 2Z+1 state. Since the orbital energies of u and a orbitals of PbO, Pbd, and SnO are not substantially different, the separation of 211 and 2Z+ (A-S) states ought to be small. Table I shows a few low-lying states of group 4 chalconide ions both in A-S and w-w coupling schemes. As one can see from this table, there is a number of l/zand 3 / 2 states resulting from several low-lying configurations. Table I1 shows the dissociation relationship of some of these low-lying states. Since the first ionization potential of oxygen and sulfur is much larger than that of Sn or Pb, the low-lying electronic (131 Christiansen. P. A.: Balasubramanian. K.: Pitzer. K. S.J. Chem. Phis. 1982,76, 5087. (14)Balasubramanlan, K.; Pitzer, K. s. J . Chem. PhYs. 1981,78,321. (15) Pitzer, K. S.; Balasubramanian, K. J . Phys. Chem. 1982,86,3068. (161 Balasubramanian. K.: Pitzer. K. S.J . Phvs. Chem. 1983.87.4857. (17j Balasubramanian,'K.; Pitzer, k.S.J . Mol:Spectrosc. 1984,103,105.
molecular state
TABLE III: Orbital Exponents in Slater Type Basis Functions" Pb Sn 0 S Se s 1.9021 (4) 2.6829 (5) 9.6982 (1) 15.7137 (1) 4.2573 (3) 0.8482 (4) 1.6074 (5) 6.9562 (1) 5.322 (2) 1.882 (3) 2.6786 (2) 2.3513 (3) 1.6927 (2) 1.911 (3) p 1.5189 (4) 2.3775 (5) 3.7183 (2) 6.282 (2) 2.4915 (4) 0.8599 (4) 1.3523 (5) 1.6671 (2) 3.7379 (4) 1.4963 (4) d 3.5804 (4) 3.9532 (4) 1.9512 (4) 1.6047 (4) 1.5175 (4)
"The numbers in parentheses are the principal quantum numbers. states of PbO+, SnO+, and PbS+ are assumed to dissociate into Pb+ 0, Sn+ 0, and Pb+ S, respectively. The selection of configuration for the relativistic CI calculations merits some discussion. In general, all A-S states of the same w-w symmetry would mix in the relativistic configuration interaction. For example, the ll2(I) state would be a mixture of states arising from 2111,2(u a3),ZZl/z+(uaf),zIIl,2(u2aza*),etc. The amount of mixing of these states is determined by the magnitudes of both spin-orbit interaction and correlation. Our SCF (self-consistent field) calculations of SnO+ and PbO+ (which did not include spin-orbit interaction) indicate that the a orbital is dominantly on the oxygen atom while the u orbital is a mixture of oxygen and metal orbitals. (This aspect is discussed further in the Discussion section.) Thus, the spin-orbit splitting arising from u2a3is expected to be dominantly from the oxygen which is rather small. Thus, the zII state arising from u2a3of SnO+ can be represented quite accurately within the A-S coupling scheme. Nevertheless, we include here all low-lying w-w states of a given symmetry in the CI calculations so that some of the excited states can be treated with sufficient accuracy. Our trial calculations indicate that only the 2111/2state arising from u2a3and the 2Zl,2+ state arising from ua4are important for the first two l/zstates, and the rest of the 1/2 states in Table I do not make a significant contribution to the first two 1 / 2 states. Thus, to calculate the properties of the two low-lying 1 / 2 states, we included single and double excitations from the configurations u2axfla;, u 2 x ~ a y f l , and ua,2a? We also included 12 configurations without excitations resulting from the $a2a* configuration expressed in terms of Cartesian orbitals. Since our program is designed for real Cartesian orbitals, the configurations have to be expressed in terms of Cartesian orbitals. This amounts to 1941 configurations for the 1/2 state. We calculate here only the lowest root of the 3 / 2 state. This was dominantly 2113/2with practically no mixing from any upper state. This is a consequence of the fact that the a orbital does not have any appreciable contribution from the heavier metal atom. Thus, our 3 / 2 calculations included single We also and double excitations from a2a,ot?ry2and u2aXZaya. included 10 configurations arising from $a2a*without excitations. The new configurations among these that were not generated as single excitations from (u2a3)3/2did not have practically any mixing with the 3/2(1) state. The S C F calculations used relativistic effective potentials for the Pb and Sn atoms. All eight electrons of oxygen were included at the S C F stage. For the PbS+ system all the electrons of S were included. However, for the PbSe+ ion we used a relativistic effective potential for se.The d electrons of the lead and tin atoms were included in the SCF stage but frozen at the c1stage in Order to limit the number of configurations. Also, excitations from the
+
+
+
Low-Lying States of SnO+, PbO+, PbS+, and PbSe+
The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 5761
TABLE I V Spectroscopic Properties of Low-Lying States of SnO', PbO+, and PbS+ Re, Te, cm-I we, cm-l state theorv exut theorv exut theorv exot
sno+ zn PbO+
PbSt
z2t
2.05 1.96
3/2(1) '/z(I) '/z(II)
2.18 2.16 2.09
46 4979
3/z
2.56 2.56
506
'I2
2.00
0.0 3616
0.0
0.0
0
695 708
TABLE VI: Potential Energies" for SnOt at Several Internuclear Distances ( R ) b R zn 22+ 3.0 3.25 3.5 3.6 3.7 3.8 3.9 4.5 8.0
700
590 610 712 363 335
"In hartrees. TABLE V Ionization Energies of (IE) of SnO and PbO molecule method state IE, eV zn 6.73 SnO SCF" CIb 2n 8.44 SnO CI 2z+ 8.76 SnO SnO KTc 2n 10.15 2zt
PbO PbO
PbS PbS PbSe PbSe
2n
SCF CI CI
2z+ljz
KT
2 n
CI
2n3/2
KT
2 n
CI
*ns/2
KT
2n3/2,1/2
zz+ zz+
2n
2z+
9.79 6.23 8.10 8.52 9.82 9.31 7.87 8.77 8.98 7.48 7.63 8.36
"The ionization energy is the difference in the S C F energy of and zII states at 3.75 bohrs for SnO and 3.85 bohrs for PbO. bThe value is the difference in the CI energy of the lZt state and the 211 or zZt state at 3.75 bohrs for SnO, 3.85 bohrs for PbO, 4.5 bohrs for PbS, and 5.4 bohrs for PbSe. 'Koopman's theorem.
M O which is dominantly Pb or Sn s were not allowed at the C I stage. The basis sets employed in these calculations are shown in Table 111.
3. Properties of Low-Lying States of SnO+, PbO', and PbS+ and Comparison with Experiments Table IV shows the spectroscopic properties of the low-lying states of SnO+, PbO+, and PbS+, respectively, calculated from the relativistic quantum calculations. For SnO+the experimental results for the 211state obtained from the photoelectron spectrum of SnO(XIZ+)are also included. As one can see from that table, the calculated Re and we values of the 211 state are in excellent agreement with the experimental results. We also obtain the correct ordering for the 211 and 2Z+ states. The separation of 211-22+ is around 3616 cm-'. Our dissociation energies for the 211 and ?Z+ states of SnO+ are 2.95 and 2.50 eV, respectively. These values are in reasonable agreement with the corresponding experimental values of 3.23 and 2.71 eV reported by Dyke et ale9 Our calculated De values are somewhat lower as a consequence of the small number of configurations which was adequate but not complete and the fact that our C I was based on a singleconfiguration S C F as opposed to a multiconfiguration S C F (MCSCF). This discrepancy was much more for SnO" since the ground state is a closed-shell l 2 + state while the dissociated atoms are nonclosed-shell 3Patoms. The De values of the 3/2, and 1/2(11) states of PbO+ are 2.28, 2.26, and 1.66 eV, respectively. The dissociation energies for the 3/2 and states arising from the 211A-S state of PbS+ are 1.52 and 1.47 eV, respectively. The 211 state is below the ?Y+ state for PbS+ in the near-equilibrium regions. We also calculated the energies for ionizing the 'Z+(O+) to zII and 22+states. These results are summarized in Table V. For the PbSe+ comparison values are included for ionizing the *Z+(O+) to 2113/2 states. The experimental ionization energiesgfor ionizing the l2+state of SnO to 211 and 2Z+ states are 9.98 and 10.12 eV, respectively. Our calculated CI values are the best, and they are
0.0843 -0.0274 -0.0841 -0.0960 -0.1038 -0.1063 -0,108 3 -0.0856
0.0294 -0.0539 -0.0855 -0.0901 -0.0919 -0.0893 -0.0874 -0.0494
0.oc
bohrs. cThe zero of energy is that for zII at 8.0
bohrs.
TABLE VI1 Potential Energies" for PbO+ at Several Internuclear Distances ( R ) b
R
3/2(1)
l/z(I)
l/z(w
2n
%+
3.0 3.25
0.2148 0.0577 -0.0261 -0.0604 -0.0729 -0.0826 -0.0838 -0.0832 -0.0717
0.1244 0.0084 -0.0471 -0.0667 -0.0734 -0.0829 -0.0830 -0.0824 -0.0710
0.2271 0.0650 -0.0203 -0.0532 -0.0581 -0.0609 -0.0579 -0.0544 -0.0432
0.2187 0.0608 0.0235 -0.0581 -0.0708 -0.0807 -0.0819 -0.0815 -0.0703
0.1280 0.0122 -0.0431 -0.0608 -0.0593
3.5
3.7 3.8 4.0 4.1 4.2 4.5 8.0
-0.0575 -0.0540 -0.0427
O.OC
"In hartrees.
bohrs. 'The zero of energy is that of
at 8.0
bohrs.
off from the experimental values. This calculation was based on the CI energy calculated by Balasubramanian and Pitzer for the SnO('2') state." As noted by these authors, their calculated De for SnO (3.70 eV) is considerably smaller than the experimental value of 5.49 eV. This was attributed to the inadequacies in that CI calculation which was quite extensive but not complete. Thus, the present calculated ionization potentials are low in comparison to the experimental values. The SCF ionization potentials do not take into account correlation and spin-orbit effects. Koopman's theorem applied to the S C F results of SnO and PbO predicts incorrect ordering of the 211and z2+states of the corresponding ions. This was also noted by Dyke et al.9 We believe that our calculated CI ionization energies for PbO are closer to experimental values than for SnO since the calculated Devalue for PbO'O (3.0 eV) is in better agreement with the experimental value of 3.83 eV than the corresponding values for SnO. Thus, the vertical 2111/2,3/2 (8.10 eV) and 0' ionization energies of PbO for 0' 22ij2+ (8.52 eV) are expected to be reasonably close to experimental values. The vertical CI ionization energies of PbS for the O+ 2113 state is 7.87 eV, and the corresponding value for the PbSe moiecule is 7.48 eV. It is interesting to note that Koopman's theorem predicts the correct ordering of the 211 and 22+states for PbS and PbSe molecules (see Table V).
-
-+
-
4. The Properties of the CI Wave Function, Potential Energy Curves, and SCF Orbitals Tables VI and VI1 show the potential energies of several lowlying states of SnO+ and PbO+, respectively, as a function of internuclear distances. For the 22+and 211 states of SnO+ the spin-orbit effects were quite small. Thus, we show the energies without spin-orbit splitting for SnO+. For the PbO+ ion we show the energies both with and without spin-orbit interaction. Figures 1, 2, and 3 show the potential energy curves of these low-lying states of SnO+, PbO+, and PbS+, respectively. For PbO+, PbS+, and PbSe+ near-equilibrium bond distances there is significant mixing of the 2111/zand 2212+ states. At 3.8 bohrs the state of PbO+ is 74.8% and 15.7% 221/2+. The rest of the population is attributed to the single and double excitations from these reference configurations. The other interesting feature is the crossing of *Z+ and zII states which leads to an avoided crossing in the potential energy curve. This crossing occurs at ap-
Balasubramanian
5762 The Journal of Physical Chemistry, Vol. 88, No. 23, 1984 ,050 -
.14-
13-
12
-
-
,040
,110-
-
1-
30
5
4
R-
0
7
75
(Bohr)
Figure 1. Potential energy curves of SnO+.
R-(Bohr) Figure 3. Potential energy curves of PbS+.
TABLE VIII: orbital U
?T
orbital U
R -(Bohr)
Figure 2. Potential energy curves of PbO+.
proximately 3.55bohrs for SnO+ and at 3.73 bohrs for PbO+. This results in a shoulder in the 1/2(1) potential energy curve of PbO' in this region. Thus, the l/z(I)state of PbO+ is dominantly 221/2: in the repulsive region (3-3.5); it is a significant mixture of 2Z,lz and 2111/2in the near-equilibrium distances, and it becomes dominantly zII1/zat longer distances.
?r
Orbitals of SnO. SnOt. PbSe. and PbSe+ coefficient basis function SnO SnO+ STO exponent 0.227 0.412 Sn 5s 2.6828 0.227 Sn 5s 1.6074 0.234 -0.369 -0.317 Sn 5p 2.3775 -0.207 -0.124 Sn 5p 1.3523 0.096 0.110 Sn4d 3.9532 -0.046 -0.059 Sn 4d 1.5175 -0.016 -0.013 0 1s 6.9562 -0.005 -0.001 0 IS 9.6982 0.039 0 2s 2.6786 0.035 0.148 0.070 0 2s 1.6927 0.205 0 2p 3.7183 0.209 0.542 0 2p 1.6671 0.533 0.172 0.093 Sn 5p 2.3775 0.194 Sn 5p 1.3523 0.066 -0.097 -0.073 Sn 4d 3.9532 0.097 Sn 4d 1.5175 0.067 0.248 0 2p 3.7183 0.292 0.677 0 213 1.6671 0.729
u and ?r
coefficient PbSe PbSe' 0.195 0.02 -0.479 -0.049 0.053 -0.018 0.203 0.004 0.391 0.380 0.258 0.097 -0.050 0.04 0.455 0.490
0.150 0.004 -0.402 -0.008 0.056 -0.0495 0.211 0.002 0.492 0.364 0.250 0.035 -0.055 0.048 0.510 0.470
STO
basis function exponent
Pb 4s Pb 4s Pb 4p Pb 4p Pb 4d Pb4d Se 3s Se 3s Se 4p Se4p Pb4p Pb4p Pb 4d Pd 4d Se 4p Se4p
1.9021 0.8482 1.5189 0.8599 3.5804 1.6047 1.882 4.2573 2.49 15 1.4963 1.5189 0.8599 3.5804 1.6047 2.4915 1.4963
Koopman's theorem predicts incorrect ordering of the '2' and zII states for SnO+ and PbO' but predicts the correct ordering for the heavier chalconides, namely PbS' and PbSe'. This can
J. Phys. Chem. 1984,88, 5763-5764 be explained by comparing the highest u and a orbitals of the chalconides and the corresponding ions. Table VI11 shows the coefficients of the highest occupied u and a orbitals of SnO, SnO+ and PbSe, PbSe+ pairs. As one can see from that table, the orbital relaxation effects are much greater for SnO than PbSe. There is a significant increase in the s poplation of Sn (in the u orbital) accompanied by a decrease in the p population of Sn as well as 0. The a orbitals of both SnO and SnO+ are mainly on oxygen and are thus nonbonding. In the case of PbSe there is more a
5763
bonding. The breakdown of Koopman's theorem is thus explained on the basis of more relaxation of the orbitals of SnO than PbSe. At shorter distances the a orbitals are more localized on the chalconide atom, thus stabilizing the ua4configuration. Consequently, reverse ordering of and zllstates is observed at short distances for SnO+, PbO+, and PbSe+. Registry No. SnOt, 92456-21-8; PbO+, 92456-20-7; PbS+, 9245622-9; PbSe+, 92456-23-0; SnO, 21651-19-4; PbO, 1317-36-8; PbS, 1314-87-0; PbSe, 12069-00-0.
COMMENTS Surface Structure of Iron Catalysts for Ammonia Synthesis Sir: Ammonia synthesis catalysts consist of metallic iron with small amounts of unreduced oxides. A typical commercial catalyst, called KMI, made by Topsere A I S contains 3 wt % of AlzO3, 3 wt % of CaO, and 0.75 wt % of KzO. These so-called promoters represent 0.96 or 0.93 mole fraction of the surface as determined by Auger electron spectroscopy' or selective chemisorption,2 respectively. The rest of the surface is metallic iron. The purpose of this Comment is to point out that the structure of the iron seems to be that of the (1 11) face. The evidence is offered by data of Spencer et aL3 who report turnover rates on the three low index faces of iron single crystals with the result that the (1 11) face is much more active than the other two. Turnover rates ut at 748 K were measured at 10 atm and at four different partial pressures at 20 atmS3We note that these very low conversion data fit the rate equation of Temkin et aL4 which was shown to fit low conversion data on iron:
vt/s-' = 12.8 e ~ p ( - 9 7 7 0 / T ) ( f " ~ P ~ ~ ) ~ / ~ where Tis in kelvin, the value 9770 K corresponds to the activation energy reported by Spencer et al., and the partial pressures are in Pa. Our expression for ut assumes that each active site consists not of C4 atoms as assumed in ref 3 but consists of a pair of C7 atoms, as suggested earlier on the basis of Mossbauer effect data.s Surface atoms C7 with a coordination number of 7 are characteristic of (1 11) planes on bcc iron. With eq 1, we can extrapolate the data of Spencer et al. to the conditions of Topsere et namely, atmospheric pressure, reactants stoichiometric ratio, 673 K, and a conversion 15% of equilibrium. Because of this very low conversion the data of Topsoe et al. need not be corrected for inhibition of the rate by ammonia. Under these conditions, the value of ut from eq 1 is 0.3 s-'. This must be compared to a value of ut = 0.5 s-' reported by Topsere et aL6 for the KMI commercial catalyst discussed above. This value of ut was obtained by Topsere et al. by means of the classical titration of surface iron atoms by chemisorption of CO at 195 K, but with the assumption that each CO molecule adsorbed cor(1) D. C. Silverman and M. Boudart, J. Cutal., 77, 108 (1982). (2) A. Nielsen and H. Bohlbro, J . Am. Chem. SOC.,74, 953 (1952). (3) N. D. Spencer, R. C. Schoonmaker, and G.A. Somorjai, J . Catal., 74, 129 (1982). (4) M. I. Temkin, N. M. Morozov, and E. M. Shapatina, Kinet. Cutal., 4, 260 (1963). (5) J. A. Dumesic, H. Topsae, K. S. Khammouma, and M. Boudart, J . Catal., 37, 503 (1975). (6) H. Topsm, N. Topsae, H. Bohlbro, and J. A. Dumesic, "Proceedings of the Seventh International Congress on Catalysis", Part A, T. Seiyama and K. Tanabe, Eds., Kcdansha, Tokyo, 1981 p 247.
responds to two Fe atoms as may be the case on (1 1 1 ) planes.' Considering the bold extrapolation of the data of Spencer et aL3 to the conditions of Topsere et a1.,6 the close correspondence of the values of ut for (1 11) single crystals and the commercial catalyst suggests that the surface of the latter exhibits predominantly (1 11) faces, since the value of v, for the commercial catalyst was obtained by CO chemisorption that counts iron atoms as may be the case on (1 11) planes. Besides, the commercial catalyst possesses the same turnover rate as found on a clean single crystal, almost irrespective of the very large amount of surface promoters. Surely these tentative conclusions are of theoretical and practical significance. At any rate, as has happened many times in the past ten years, work on single crystals provides the standards by which work on commercial catalysts can be a ~ s e s s e d . ~ Acknowledgment. This work was supported by NSF Grant CPE 8219066. D.G.L., on leave from the University of Mar del Plata, thanks CONICET of Argentina. Registry No. Iron, 7439-89-6; ammonia, 7664-41-7. (7) M. Boudart and G. DjEga-Mariadassou, "Kinetics of Heterogeneous Catalytic Reactions", Princeton University Press, Princeton, NJ, 1984, p 157.
Department of Chemical Engineering Stanford University Stanford, California 94305
M. Boudart* D. G. Loffler
Received: June 1 , 1984
Comment on "Equilibrium and Rate Constants for Ion Association in Liquid Ammonla" Sir: Stevenson et al.' calculate a value of 3.1 X for the association constant of the nitrobenzene anion radical with sodium cations. This value is surprisingly low and the paper tries to explain why ionic association is so low in liquid ammonia. Equilibrium constants for ionic association of many 1-1 salts in liquid ammonia at -33.5 "C have been calculated from conductance data (see Table 118, p 174, in ref 2); their values fall between lo2 and lo3. The same order of magnitude (1.3 X loz) is found for the association of solvated electrons, which are anion radicals, with sodium cation^.^ (1) Stevenson, G. R.; Reiter, R. C.; Ross, D. G.; Frye, D. G.J. Phys. Chem. 1984, 88, 1854-7. (2) Jander, J. "Anorganische und allgemeine Chemie in fliissigen Ammoniak"; Interscience: New York, 1966. (3) Evers, E. C.; Frank, P. W. J . Chem. Phys. 1959, 30, 61.
0022-365418412088-5763$01.50/0 0 1984 American Chemical Society
