1146
J . Phys. Chem. 1984, 88, 1146-1 148
Relativistic Quantum Calculations of Low-Lylng States of Lead Hydride. Comparison with Experimental Spectra K. Balasubramanian and Kenneth S. Pitzer* Department of Chemistry and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (Received: June 29, 1983)
Relativistic quantum calculations including configuration interaction (CI) and spin-orbit interaction are described for five low-lying states of PbH. Two of these states have not been observed experimentally. Spectroscopic properties are calculated and discussed in comparison with experimental spectra. The calculated dissociation energy of 1.64 eV agrees well with experiment (1.59 eV). From the nature of the CI wave function it is shown that the low-lying electronic states are heavily mixed by spin-orbit interaction and cannot be assigned to any A-S state uniquely.
1. Introduction
TABLE I: Basis Set Employed in This Calculationa
Relativistic quantum calculations of molecules containing very heavy atoms are of considerable because of the large spin-orbit interaction in those systems which alters their electronic and spectroscopic properties to a substantial extent. Our calcul a t i o n ~on~ TlH were very successful in explaining several interesting experimental observations. Hence, it seemed to be of interest to look at the next hydride, PbH. The early interpretations of the experimental spectra for PbH were confused by lack of recognition of the large spin-orbit effect. In their recent summary, however, Huber and Herzberg6 give a tentative interpretation which is substantially the same as is indicated by our results. The very extensive and complex bands in the red and near-infrared were measured by Watson' and by Watson and Simon.* Their parameters for the ground state, a 1/2 state, are accepted, although the state is now regardedg as 2111/2 rather than 221/2. The zIIs state is at much higher energy and has not been found. Geroib reinterpreted the highly perturbed excited states, A and B, for these bands as two 22, states, but states it seems much more likely that they are the 4Z1/< instead." A higher energy band has been reported* but not analyzed. Our objective is to determine the energies and wave functions for several low-energy states for PbH. In section 2 we describe our method of calculations and in section 3 comparisons are made with experimental spectroscopic properties. In the last section we discuss the nature of C I wave function and the properties of a few low-lying electronic states of PbH.
(1) K. Balasubramanian and K. S.Pitzer, J. Chem. Phys., 78,321 (1983). (2) K. S.Pitzer and K. Balasubramanian,J. Phys. Chem., 86,3068 (1982). (3) K. Balasubramanian and K. S. Pitzer, Chem. Phys. Lett., 100, 273 (1983). (4) K. Balasubramanianand K. S.Pitzer, J. Phys. Chem., 87,4857 (1983). (5) P. A. Christiansen, K. Balasubramanian, and K. S.Pitzer, J . Chem. Phys., 76, 5087 (1982). (6) K. P. Huber and G. Herzberg, 'Spectroscopic Constants of Diatomic Molecules", Van Nostrand, New York, 1979. (7) W. W. Watson, Phys. Reu., 54, 1068 (1938). (8) W. W. Watson and R. Simon, Phys. Reu., 57, 708 (1940). (9) H. G. Howell, Proc. Phys. Soc., London, 57, 37 (1945). (10) L. Ger6, Z . Phys., 116, 379 (1940). (11) B. Kleman, Ph.D. Thesis, Stockholm, 1953. (12) K. S. Pitzer, Int. J . Quantum Chem., 25, 131 (1984).
H atom
1.9021 (4) {0.8482(4)
11.1264 1.4108 (1)
(1)
{3.5804 ( 4 j 1.6047 (4)
Numbers in parentheses are principal quantum numbers. TABLE XI: A Few MO Configurations and the Resulting A-S and w-w Statesa
MO
configuration
A-S state
w-w
state
u271
00'71
a
2. Method of Calculations The methodology of relativistic, effective potential calculations of molecules containing heavy atoms is discussed by Christiansen et al.,5 and in a review paper by Pitzer.l2 Relativistic effective potentials were obtained from relativistic numerical Dirac-Fock solutions of the lead atom. For our S C F calculations we included the outer d10s2p2electrons on the lead atom and the 1s electron
Pb atom
The MO's resulting from s and d orbitals on Pb are not shown.
TABLE 111: A Few Low-Lying W-w States and Their Dissociation Limits w-w
state
dissociation limit
energy,
cm -'
of the hydrogen atom. The relativistic effective potentials were averaged with respect to spin at the SCF stage of our calculations for the sake of computational convenience. Thus, all other relativistic effects except the spin-orbit effect were included at the S C F state. The one-electron spin-orbit operator was obtained by differencing the relativistic effective potentials with respect to spin and was introduced for the configuration interaction calculations. We employed a double-{ basis for the Pb atom which was optimized to the 3Pstate of the lead atom. For hydrogen we adopted the basis set used by Code and Huo13 for a SiH calcu-
0022-365418412088-1146%01.50/0Q 1984 American Chemical Societv
The Journal of Physical Chemistry, Vol. 88, No. 6, 1984 1147
Low-Lying States of Lead Hydride TABLE 1V: Spectroscopic Properties of a Few Low-Lying Bound States of PbH Re, state
theory
'/z(I)
1.95 1.92 2.68 2.44
3 ~ 1 )
'/z(II) %(II)
w e , cm-'
T e , cm-'
expt 1.84 2.36 2.60
theory
expt
0.0
6846 17213 20341
0.0
17590 18030
theory 1418 1457 391 442
expt 1564 500 419
TABLE V: Potential Energya Curves of PbH Rb 2.5 3.0 3.2 3.4 3.6 4.0 4.5 5.0 6.0 9.0 a
1/20
0.0601 -0.0330 -0.0484 -0.0568 -0.0599 -0.0568 -0.0446 -0.0307 -0.0108 0.0
In hartrees.
'I2 0.0857 -0.0044 -0.0190 -0.0265 -0.0289 -0.0245 -0.0114 +0.0026 0.0200 0.0284
%(W 0.1284 0.0482 0.0356 0.0283 0.0244 0.0209 0.0191 0.0183 0.0213 0.0284
3/2(11)
=I2
0.05 88 0.0464 0.0396 0.0362 0.0339 0.0334 0.0331 0.0400 0.0415
0.1932 0.1111 0.0962 0.0860 0.0788 0.0686 0.0594 0.0530 0.0470 0.0466
In bohrs.
40
30
I
I
1
50
6.0
70
R / bohr
lation. These basis sets are shown in Table I. We now discuss the symmetry properties and dissociation relationships of a few low-lying states of PbH. Table I1 shows a few MO configurations, the A-S states and the corresponding (3-w states resulting from them. In Table I11 we show the dissociation limits of some of these low-lying states. Next we discuss the selection of configurations for our C I calculations. While the 1/2(1) ground state is primarily 2111/2, various states from the ua2, u2d,and uda configurations can mix by correlation and spin-orbit interaction. Consequently, our configuration interaction calculations should include at least these states as reference configurations. Our S C F and CI programs are based on Cartesian Slater orbitals and thus the MO's must state expands to u2 (ax be expanded in Cartesians. The zlI+1/2 ia )p in terms of Cartesian MOs. This results in the reference condgurations u2ax/3and u2ayp. Similarly the azuconfiguration results in a2ua, a,2ua, nxaayPua,~ ~ p a ~ a and u a ,axaayaup configurations for the state. The + 1 / 2 configurations arising from the a3configuration are a2ag and .,"a#. We also included &a as a reference configuration for the state. This results in 10 reference configurations from which all possible single and double excitations were allowed. In all this yields 1731 configurations for the 1 / 2 state. This includes excitations from the s but not the d orbitals on the lead atom. The MO's which were primarily d orbitals on Pb were frozen at the CI stage of the calculation. The 3/2 state calculations included two Cartesian reference configurations (u2axa,."aya) from the 2113/2 state, four reference configurations (a2up, a;u& axaay(?up,axPayau@)arising from the 2A3/2, axaaYauareference configurations from the 4&/2-, a2aya,a;axa references from the a3,and uau'aax/3, uau'aayp references from the uu'a configuration. Single and double excitations from these reference configurations result in 1723 configurations. Our calculations of the 5/2 state included four reference configurations (a,2ua, a,2ua, axaa#ua, axpayaua)arising from the *A512 and uadaaxa,uadaaya references from the 4115,2 configuration. Single and double excitations from these six reference configurations give rise to 1044 configurations.
+
3. Results and Comparisons with Experiments The calculated spectroscopicproperties of a few low-lying b u n d states of PbH and the corresponding experimental values are shown in Table IV. The full array of calculated energy values are given in Table V and the potential curves shown in Figure 1. Some of the excited states of PbH are repulsive. The ground-state 1/2(1) is dominantly 211112,which confirms Howell's (13) P. Code and W. Huo, J . Chem. Phys., 47,649 (1967)
Figure 1. Potential energy curves for PbH. The calculated energies of separated atoms are indicated on the right.
TABLE VI: Fractional Populations of Various A-S Configurationsfor a Few Low-LyingStates of PbH state
'"(I) 3/2(1)
'h(ll) 3iz(11)
distancea
{::: {: {::: {:::
i:::
s'z
a
u2n(lII)
u ~ ' ( ~ C )u ~ ' ( ~ A ) u u ' r
0.884 0.502 0.842 0.063 0.026 0.211 0.047 0.267
0.022 0.213 0.057 0.327 0.743 0.419 0.815 0.0
0.0
0.0 0.0
0.0
0.009 0.055
0.0 0.0
0.0 0.0
0.023
0.103 0.0 0.0
0.0 0.0 0.0
0.0 0.0 0.0
0.0
0.230 0.785 0.384
0.0
0.096 0.001 0.331 0.015 0.157 0.054 0.298 0.047 0.387
In bohrs.
reinterpretations of Watson's spectra. The 4 Z 1 /and ~ 221jz states make only a small contribution (2% and 1%, respectively) to the ground state. Our calculated Reand we values of the ground state (1.958, and 1418 cm-') are in reasonable agreement with the experimental values of 1.84 8, and 1564 cm-', respectively. The 3/2(1) state state makes a is dominantly a 2113/2 state. However, the 423/2significant contribution (6%). A few other states such as 2A3/2 make small but nonnegligible contributions. Our T, value for this state is 6846 cm-I, which is slightly lower than the 3P0-3P1splitting of the Pb atom. The Re and we values of 3/2(1) state are quite close to the corresponding values of the 1/2(1) state. The 1/2(11) and 3/2(11) states are the upper states for the observed bands in the red and infrared. These states are primarily 481/2and 4Z32- but are substantially mixed with other A-S states. The potentia[ curves are quite flat from 4 to 5.5 bohr, yielding low vibration frequencies in approximate agreement with experiment. Since the 3/2(11) state dissociates to a higher energy Pb atom (3P2)than the 1/2(11) state, our results giving a shorter Re value for the 3/2(11) state seem reasonable. The reported rotational constants,6,I0however, associate a larger Revalue with the higher energy state which is presumably the 3 / 2 state. Also the reported energy difference between these two states is much smaller than we calculate. The experimental spectra show complex perturbations and the interpretation of GeroI0 was based on two 22states rather than 4Z1/2-and 423/2-. Thus, a reexamination of these spectral data seems desirable. It should also be realized that our calculations may not be accurate with respect to small details, although we are confident that they are correct with respect to the major featnres.
1148
J . Phys. Chem. 1984, 88, 1148-1 151
The difference in calculated energy at 9 bohr from that at the minimum yields a De value for the ground state of 1.64 eV. This value is in excellent agreement with the experimental De value of 1.59 eV based on mass-spectrometric experiments.
with other A-S states accounting for the rest of the population at 4.0 bohr. At long distances the other A-S states such as 211 and the ones arising from UU'T configurations have significant coefficients. The 3/2(11)and 5/2 states exhibit interesting avoided at 4.0 bohr while crossings. The 3/2(11) state is dominantly 423/2it becomes a mixture of 'II312, 2A3/2, and other A-S states arising making practically no contribution at all from UU'T with 42212at 6.0 bohr. The /z state is dominantly 2A5/2 at 4.0 bohr. At 6.0 bohr this state is an almost equal mixture of 2A5j2and 4115/2, indicating the crossing of 2A and 411 A-S states at 6.0 bohr.
4. Nature of the Wave Functions Table VI shows fractional populations of various A-S configurations for the five low-lying states at 4.0 and 6.0 bohr. The ground state is dominantly 2111/2at 4.0 bohr. At long distances (6.0 bohr) it is a mixture of 2111/2and 42,/;with other A-S states making a small contribution. Although the spin-orbit interaction lowers the state at both 4.0 and 6.0 bohr, it mixes 211and 42Acknowledgment. This work was supported by the Director, states to a greater extent at 6.0 bohr. The 3/2(1) state also behaves Office Of Energy Research, Office of Basic Energy Sciences, in a similar manner except that at 6.0 bohr U ' T ( ~ I makes I ~ / ~ only ) Chemical Sciences Division of the U S . Department of Energy, a small contribution with dominant contributions from U T ~ ( ~ Z ) under Contract No. DE-AC03-76SF00098. and UU'T configurations indicating an avoided crossing in this region. The 1/2(11)state is a mixture of 42-(74%) and 22-(10%) Registry No. PbH, 14452-81-4.
Polarization Effects upon Adsorptive and Catalytic Properties. 1, CO Oxidation over Pd Deposited on LiNbO, Ferroelectrics Yasunobu Inoue,* Isao Yoshioka, and Kazunori Sat0 Analysis Center, Technological University of Nagaoka, Nagaoka, Niigata 949-54, Japan (Received: June 15. 1983)
In relation to metal-support interactions, polarization effects upon catalysis were studied by using poled single crystals of LiNb03 ferroelectrics as the support. Palladium metal was deposited on either the positive or negative polar LiNb03 surface in the thickness range 0.02-20 nm and was examined for CO oxidation in the temperature range 493-673 K up to a pressure of 4 kPa. The kinetic behavior was found to differ depending on the polar direction of the support. The activation energy, E,, over the Pd on the positive polar surface (Pd/(+)) changed from 126 kJ mol-' above a Pd film thickness of 0.2 nm to 96 kJ mol-I at 0.02 nm, whereas the Pd on the negative polar surface (Pd/(-)) gave rise to almost constant E,, 128 kJ mol-', over a whole range of Pd deposition. The reaction order with respect to the oxygen pressure was nearly unity independent of polar direction, whereas the CO pressure dependence varied from -1.0 for 0.02-nm Pd/(-) to -0.6 for 0.02-nm Pd/(+) catalyst. It was concluded that the positive polar effect was prominent for small Pd particles and can work so as to weaken the CO adsorption bond. A model of the polarization effect is presented by taking into account the depolarization of the substrate surface due to charge transfer.
The adsorptive and catalytic properties of metals often characteristically vary when metals are dispersed on supports as fine particles. In an effort to understand the effects of dispersion, the role of the supports has been recently emphasized, since it has been suggested that an interaction between the metal particles and substrates evidently gives rise to the alternation of the adsorptive capability as well as the catalytic activity of the dispersed metals.'S2 In view of the possible improvement of metal catalysis, the support effects are important and are expected to be more clearly exerted when materials with physically or chemically specific properties are used as supports. In this regard, ferroelectrics have drawn considerable attention, since their surfaces generate spontaneous polarization which is due to the positively and negatively charged domains. One interesting point is the effect related to a phase transition between ferro- and paraelectricity, and the other is the effect associated with the direction of polarization. In the present work, the latter effect was studied in detail, because it is of particular interest to see how the adsorptive and catalytic properties of the metals deposited vary depending on the polar direction of the support. These studies have scarcely been done before and un(1) S. J. Tauster, S. C. Fung, and R. L. Garten, J . Am. Chem. SOC.,100, 170 (1978). (2) B. Imelik, C. Naccache, G. Coudurier, H. Praliaud, P. Meriaudeau, P. Gallezot, G. A. Martin, and J. C. Vedrine, Eds., "Metal-Support and Metal-Additive Effects in Catalysis", Elsevier, Amsterdam, 1982, Stud. SurJ Sci. Catal. Vol. 11.
0022-3654/84/2088-1148%01.50/0
doubtedly provide precise information on the polarization effects. It is also to be noted that the former phase-transition effect can be well elucidated on the basis of a better understanding of these polarization effects. Ferroelectric polycrystallines are usually composed of almost equivalent amounts of oppositely polarized domains and, for the present purpose, it is required to differentiate the positive and negative polar surfaces. This can be done by poling the ferroelectric single crystal under an external electric field, which permits the exclusive exposure of a single domain characterized by one kind of polar surface. In the present study, poled single crystals of lithium niobate (LiNbOJ were employed as support, because it possesses spontaneous polarization as high as 71 pC cm-2 at room temperat~re,~ and its ferroelectric phase is stable up to a high temperature of 1483 K. Palladium was chosen as the deposited metal because of its high catalytic activity for oxidation. In the first work of this series on the polarization effects, the kinetic behavior of the C O oxidation was investigated.
Experimental Section Two kinds of LiNb03 single crystals which had been poled by applying an electric field were employed in the form of polished wafers 0.5 mm in thickness and 30-50 mm in diameter. One (3) S. H. Wemple, M. DiDomenico, Jr., and I. Camlibel, Appl. Phys. Left., 12, 209 (1968).
0 1984 American Chemical Society
