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J. Phys. Chem. 1982,86,3068-3070
intensity was shifted from the peak to one of the wings. Such an effect might be observed if the adsorbate assumed a more disordered structure* as the potential was changed. The direct observation of the band at both potential limits by IRRAS is important in that it definitely rules out this
possibility.
Acknowledgment. Support for the facility a t the University of Minnesota was through NSF Grant No. NSF/DMR-8016509.
Properties of Ten Electronic States of Pbp from Relativistic Quantum Calculations Kenneth S. Pltrer' and K. Balasubramanlan hpartment of chemistry and Lawrence serkeley Laboratory, Universtty of Callfornia,Berkeley, California 94720 (Received: May 7, 1982; I n Flnal F m : June 16, 1982)
Relativisticquantum mechanical calculations have been made for ten electronicstates of Pbz as well as comparison calculations excluding the spin-orbit term. A recently developed ab initio method was used in which the spin-orbit effect is introduced at the configurationinteraction step in the calculation. The results allow further interpretation of recent spectral data involving four states of Pb2 and predict six additional states. The present results c o n f i i all of the assumptions in a recent reinterpretation of the mass spectroscopic data for the dissociation energy of Pbz and agree well with that energy. Several recent spectroscopic investigations1i2of diatomic lead have detected the presence of at least seven low-energy electronic states, but the symmetry is clearly established for only three. Electron structure calculations were undertaken to determine the symmetries and other characteristics of these states and the possible existence of other states in the same energy range which have so far escaped experimental detection. The large relativistic effects for Pbz are also of theoretical interest. Adequate theoretical methods have just been developed by Christiansen, Balasubramanian, and Pitzer3 and applied to T1H where excellent agreement was obtained with the experimental spectra. The same calculational program was used for Pb2. Table I gives the molecular states which dissociate to atoms with total energies up to 22000 cm-' above the lowest states 3P0+ 3P,,. Table I1 lists the molecular orbital (MO) configurations expected to be low in energy with the molecular terms first in A-S (type a) coupling and then in w-w (type c) coupling which must be considered for Pbz. It is assumed that the 6s shells are fully occupied; only the MO's derived from 6p orbitals are shown in Table 11. The gg and s, orbitals are bonding; the sgorbitals are moderately antibonding. The uu orbitals are assumed to be so strongly antibonding that they need be considered only for excitations in the CI calculation. Even without including any u, or more than singly occupied sgorbitals, there are in all 23 single electronic states and 36 doubly degenerate terms in w--w coupling. We have limited our calculations to those terms expected to be relatively low in energy (within about 15000 cm-' of the lowest Og+state). In all the energy was calculated for ten type c terms as listed in Table 111; in addition, calculations excluding the spin-orbit (SO) effect were made for three terms (then described as type a). The energy-distance curves are shown in Figure 1 for the g terms and in Figure 2 for the u terms with the lowest Og+ state shown in both.
TABLE I: Molecular States of Pb, Related to Atoms in Several Low-Energy States and Their Energies (in cm-'p dissociation limit molecular states
+ 3P, 3PY 3P, + 3P, 3P, + 3P' JP, 3Pi
t
3P,
t
3P,
0.0 7 819.4 10 650.5 15 638.7 1 8 469.8
3P,
t
3P,
21 300.9
Od
3P, t 'D, 21 457.9 a
In parentheses is the number of states of a given sym.
me try,
TABLE 11: A Few MO Configurations and the Related Terms in both A-S and w-w Coupling o 'n * 'Xi, ' A g , 'Xg Og+, I,, 2,, 0 ; ugn 3nu, 'nu ou+, 0,-, I,, 2,, 1, g4
o+,
TU
'r g+
og2nung
,A,,
ognuzng
5ng,3 @ g >3ng(4),
7iu37rg
3 A U , q x U + r3xu-, 'A,, 'xu+, 'xu-
OU+(2),0,'(2), 1,(3), 2,(2), 3, 0,+(5), 0,(5), 2,(6), 3,(3), 4, 0,+(2), 0,-(2), l d 3 ) , 2,(2), 3,
3Xu+,3 x u - , 'A,, ,xu+,'Xu-
'@
3)
Ing(
TABLE 111: Spectroscopic Parameters for Pb, T,/cm-' R,/A term calcd expt calcd expt calcd xa
A
B
c
0', 1, 2, 1, 2, 0 -,
l,(II) Ogt(II)
0 4 150 6 670 7 570 10 130 12920 1 3 320 13 640 14130 15820
0
12457
103 124 119 119 105 106 100 74 115 123
110 122
2.9, 2.9, 2.7, 2.7, 3.0, 2.7, 3.0, 3.1 2.7, 2.7,
0 ', 15314 129 1,(II) The X, A, B, and C labels are those of Bondybey and
English. ' (1)V.E.Bondybey and J. H. English, J. Chem. Phys., 67,3405 (1977); 76, 2165 (1982). (2)R.A. Teichman, 111, and E. R.Nixon, J. Mol. Spectrosc., 59,299 ( 19-'7-_,. 6) ~ ..
(3) P. A. Christiansen, K. Balasubramanian,and K. S. Pitzer, J. Chem. Phys., in press.
One notes from Figure 1 that the SO effect greatly lowers the Og+ component state of 3Z; (u,2~,2)in the range of the potential minimum. At shorter distances this Og+ state has an avoided crossing with the lZg+ (s:) state (also
0022-3654/82/2086-3068$01.25/00 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, NO. 16, 1982
Letters
-
3P + 3 P
20
2 5
30
3.5
4 0
R (A)
Flgure 1. Calculated potential curves for g states of Pb,. The solid and dashed curves refer to separate calculatlons with and without the spin-orblt effect. I
I
I
I
3P+3P
1
I\
4
3Po+3P2
3069
The calculated spectroscopic properties for the ten terms are given in Table I11 together with experimental values where available. The calculated Re and we values are uncertain by a few hundredths of an angstrom and by about 10 cm-l, respectively. By far the strongest absorption (near 19800 cm-l) is to the second O,+ or F state. This is expected since it is a simple one-electron r, to r, change. An energy curve for this state has been added to Figure 2 at the experimental energy but estimated as to Re. Since this state arises primarily from the configuration u 2r,r it is expected to have a larger Re than that for u,Zr> and this is in agreement with the red shading of the experimental bands.' The transition probability from OB+ to the lower ',0 state is much smaller, in agreement with the nature of these states, and the calculated properties agree reasonably well with those measured, in particular the large anharmonicity and low dissociation energy. Also the calculated Re value for the lowest O,+ is smaller than that for .0, in agreement with the blue shading of the bands.' Bondybey and English' interpret a set of emission bands for Pb2in an inert matrix as arising by internal conversion from the F state to the long-lived B state at 12 457 cm-'. This state is not connected to the ground state by a dipole-allowed transition but does radiate slowly because of matrix distortion or higher-order effects. Our calculations indicate this to be the 0 ; state. Bondybey and English suggested the 2, state, but its energy is much too low from our calculations. Matrix spectra also show emission bands near 13400 cm-' connecting two new states. Since the upper or D state arises by internal conversion from the F state, the lower or A state cannot be more than 6540 cm-' above the ground state. The most probable assignment for the A state is 1, which we calculate at 4150 cm-'. The 2, state cannot be absolutely eliminated since our calculated energy of 6670 cm-' might be in error by several hundred cm-'. The calculated vibration frequency of the 1, term agrees quite well, but again the 2, term cannot be eliminated on that basis. The D state at an energy near 17 500 cm-' (or 19800 cm-' if the A state is 2,) is above the range for which we have reliable calculations. There are a multitude of g states from ugr:rg or u states from u;r,r, or rl3rg some of which can be expected to have appropriate symmetry and to lie in this energy range. The situation is similar for "E-A" emission bands near 14 500 cm-' observed only for a neon matrix by Teichman and Nixon.2 The absence of these bands for argon or other matrices is puzzling. In this case the lower state must be the 1, state. There should be a dipole allowed 1, OB+ transition in the infrared near 7600 cm-'; this region should be investigated. Our present calculations are less accurate for dissociation energy than for energy differences at bond distances. Hence it is probably somewhat accidental that our calculated dissociation energy for the O,+ state of 0.88 eV agrees almost exactly with the value of 0.86 f 0.01 eV from the mass-spectrometric data of Gingerich et a1.,4 as reinterpreted by P i t ~ e r .The ~ published interpretation of these data is further supported by the fact that the Re value of 3.0 A assumed for the partition function of Pbz agrees very closely with our calculated value for the Og+ ground state. Also, none of the other states lie low enough to contribute appreciably to the partition function which confirms that assumption made in the reinterpretation.
i
3P0+3Pl
3 P 0 + 4
0
1 2 .o
I
2.5
3 .O
3.5
4 .O
R (A)
Flgure 2. Calculated potential curves for u states and the ground Og+
state of Pbp. An estimated, dotted curve at the experimental T, Is also given for the upper 0,' state. The solid and dashed curves refer to separate calculatlons with and wlthout the spin-orbit effect.
,)',O
yielding a very peculiar curve with a marked shoulder in the repulsive side. The other component of 3Zg-,the 1 term, is lowered less by the SO effect and has a normal skape of curve. Likewise the 2, term ('4in type a) is quite normal. The 'EF+state (without SO) has a second minimum at longer htances; in this region it is primarily u t r : rather than r,4. The 311uterm (without SO) splits to yield 2,, l,, O,; and O,+ in increasing energy near their minima. But the 2, term dissociates to higher energy atoms than l,, hence the curves cross near 3.3 A. The energy differences in these u terms can be understood best by considering first the r,3 component which yields a lower 2113/2 term if a highenergy ~ 3 1 2spinor is vacant. If a lower energy r l j 2 spinor is vacant, a higher energy 2111/2term results. Then when the spin of the ugelectron is coupled to the r," group, there is a smaller splitting of the 2113/2 to 2,and 1, with 2,lowest in agreement with Hund's third rule. From the 2111jzterm ; and O,+ terms in the energy for ru3there arise the 0 sequence of their dissociation energies and the second 1, term which relates to 'II, in type a coupling. The SO effect causes large changes in dissociation energies. The ground Og+ state is only about half as strongly bound as the 32; state without SO. Among the states arising from 311u on introduction of the SO term, the dissociation energy of 2, is almost unchanged whereas that for 0 ; is greatly reduced.
-
(4) K. A. Gingerich, D.L. Cooke, and F.Miller, J. Chem. Phys., 64, 4027 (1976). ( 5 ) K. S. Pitzer, J. Chem. Phys., 74, 3078 (1981).
J. Phys. Chem. 1982,86,3070-3078
3070
We are making similar calculations for Snz. Our calculated energy values a t various interatomic distances and other details of the calculations for Pbz will be given in a paper together with the corresponding results for Snz.
Calculational Method These calculations follow the same method as those of Christiansen et al.3 for T1H; details and further references can be found in that paper. In brief, fully relativistic effective potentials (REP) are derived from numerical Dirac-Fock calculations for the lead atom. These REP are then averaged with respect to spin (AREP) and differenced to obtain ab initio spin-orbit (SO) operators following Ermler et al.6 and Hafner and S ~ h w a r z . Next ~ a molecular SCF calculation is made in terms of the AREP (Le., without the SO term) for each interatomic distance R for the 32; state. The orbitals from the SCF calculation aFe used for the spin-orbit, configuration-interaction treatment which yields the final results. In these final calculations selected single and double excitations are allowed from appropriate reference wave functions; also the SO terms are introduced. A 14electron atomic valence shell was used for the REP and SCF steps (d'Os2p2). All valence orbitals were freely optimized in the SCF calculation. Thereafter the d orbitals were frozen as fully occupied with excitation of the s and p electrons into the virtual space of d and s as well as p orbitals from the important reference configurations. (6) W. C. Ermler, Y. S. Lee, P. A. Christiansen, and K. S. Pitzer, Chem. Phys. Lett., 81,70 (1981). (7) P. Hafner and W. H. E. Schwarz, Chem. Phys. Lett., 66,537 (1979).
Certain additional configurations important only near dissociation were included but without any excitations allowed. A double t Slater basis was optimized for the 3P atom. The t values were for d orbitals 3.5804 and 1.6047, for s orbitals 1.9021 and 0.8482, and for p orbitals 1.5189 and 0.8599. A multiconfiguration treatment is needed even for the lead atom which is well-approximated neither in LS or j j coupling. Thus the ground state given as 3P0is actually a mixture of about 88% 3P0with 12% lS,,. There is only one state with J = 1, 3P1, but for J = 2 the 3Pzand 'Dz states are mixed. Good agreement is obtained between calculated and experimental energies of these atomic terms. Likewise for Pbz the ground OB+ state involves significant componenh of 0 symmetry from the 32; and l2: terms from u,2~,2and t8e lZg+ term from T,", together with smaller components from the O,+ terms from ug~u"r Some of the excited states are simpler but a multiconfiguration treatment is still essential for accuracy. For the important reference configurations at bond distance an extensive and uniform pattern of excitations was included. Additional references important only near dissociation were added but without excitations. Since judgment is involved in this process, there is a subjective aspect in the final results, but we believe this aspect to be small. +
Acknowledgment. This research was supported by the Director of the Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division, US. Department of Energy through Contract DE-AC0367SF00098.
FEATURE ARTICLE Heterogeneous Catalysis on the Molecular Scale 0. A. SomorJal"and F. Zaera Department of Chemistry, University of Califcfnia, Berkeley. and Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: February 10, 1982; In Final Form: May 10, 1982)
The techniques of modern surface science permit the study of the structure, the composition,and the oxidation states in the topmost surface layer. A new instrument has been developed for the combined determination of the kinetic parameters of catalytic surface reactions at high pressures (atmospheres), and for surface characterization at low pressures (- lo4 torr) by using small area (- 1 cm2) model catalysts. Single-crystal catalyst studies reveal the structure sensitivity of most catalytic reactions. During hydrocarbon conversion, a carbonaceous deposit forms on the catalyst surface whose bonding and stoichiometry influences the surface reactions. A molecular model of the working metal catalysts for hydrocarbon reactions has been proposed. The oxidation states of surface abms also markedly influence the rate and selectivity of catalyzed surface reactions. Using the molecular ingredients of heterogeneous catalysis that have been identified now makes it possible to build new, high-technology catalysts.
Introduction In the k t 15 years the explosive development of surface science has resulted from the introduction of a multitude of techniques that permit the atomic-scale scrutiny of the surface mono1ayer.l The atomic surface structure, the 0022-3654/82/2086-3070$01.25/0
chemical bonding of adsorbates, the composition, and the oxidation states of surface atoms can all be determined (1)G. A. Somorjai, 'Chemistry in Two Dimensions: Surfaces", Comell University Press, Ithaca, NY, 1981.
0 1982 American Chemical Society
