J. phys. Chem. 1983, 8 7 , 4857-4881
to red shift in the presence of 1.0 M DEA. From the IR data, photolysis of the non-hydrogenbonded ketones should produce solvent-separated ion pairs, A,, = 770 nm. Photolysis of the hydrogen-bonded ketones could produce either contact ion pairs or the hydrogen-bonded 4-phenylbenzophenone radical anion. If the hydrogen bond is not broken in the excited state, contact ion pair formation will be precluded; the thermodynamically more stable hydrogen-bonded anion will be formed immediately following the electron transfer. Deconvolution of the absorption band given in Figure 2 suggests that the absorbance arises from both hydrogen= 719 nm,12and the solvent-separated bonded anion, A, ion pair, in agreement with predictions based on the infrared analysis. Examining the time evolution of the transient absorption spectrum, we fiid that the component at 770 nm undergoes a hypsochromic shift with a half-life of 77 ps to 719 nm, indicating complete formation of the hydrogen-bonded 4-phenylbenzophenone ketyl. The rate of hydrogen-bond formation revealed by the shift in absorption maximum from 770 to 719 nm is approximately twice that observed for the benzophenone-DEA contact ion-pair separation in ethanol. The photoreduction of benzophenone by DEA in ethanol proceeds through initial contact ion-pair formation in less than 25 ps." In addition to transient spectral data, the presence of the contact ion pair was confirmed by infrared studies which revealed a ground-state interaction between both hydrogen-bonded and non-hydrogen-bonded ketones and DEA in ethanol." However, no initial hydrogenbonded anion is formed in the benzophenoneDEA system, (12) The radical anion absorption at 719 nm in neat ethanol cannot be due to an amine-ketone ion pair but must arise from the hydrogenbonded species. This conclusion is supported by both the observations previously reported for benzophenone" and spectral shifts observed for the photoreduction of 4-phenylbenzophenone by amines in acetonitrile (CIP at 750 nm). Furthermore,in a solvent which is capable of solvatin cations, a red shift, not a blue, shift is expected for the contact ion pair,'% see, for example: Smid J. In 'Ions and Ion Pairs in Organic Reactions"; Szwarc, M. Ed.; Wiley: New York, 1972; Vol. 1.
4857
in direct contrast to that observed for 4-phenylbenzophenone. This result can be attributed to the difference in the electronic configurations of 3n7r* and 3ir7r* states. Relative to the ground state, there is a decrease in charge density on the oxygen in the 3n7r* state of benzophenone. This is manifested by significant weakening, if not breaking, of the hydrogen bond that existed in the ground state. Upon electron transfer to the excited ketone, the complex immediately collapses to a contact ion pair; no hydrogen-bonded anion is formed. The contact ion pair subsequently undergoes solvent separation and hydrogen bond formation with a half-life of 150 ps. In the case of 4-phenylbenzophenone, excitation to the 37r7r* state results in an increase in electron density on the carbonyl oxygen. This is manifested by a strengthening in the hydrogen bond. Our results indicate that this ketone remains hydrogen bonded in the excited state. Thus upon electron transfer, the radical anion is instantaneously hydrogen bonded; contact ion-pair formation would not be observed.
Summary In conclusion, we have examined the dynamics of hydrogen-bond formation to radical anion of aromatic ketones formed by electron transfer to 3n7r* and 37r7r* excited states. We find that contact ion-pair formation preceeds hydrogen bonding for state. However, in the 37r7r* state, a substantial percentage of the ketones is hydrogen bonded, yielding hydrogen-bonded anions subsequent to electron transfer.
Acknowledgment. This work is supported by a grant from the National Science Foundation, CHE-8117519. K.S.P. acknowledges support from the Henry and Camille Dreyfus Foundation for a teacher-scholar grant and the Alfred P. Sloan Foundation. Registry No. Benzophenone, 119-61-9;4-phenylbenzophenone, 2128-93-0; benzophenone radical anion, 16592-08-8; 4-phenylbenzophenone radical anion, 74741-79-0; N,N-diethylaniline, 91-66-7.
Relativistic Configuration Interaction Calculations for Several Low-Lying States of PbO: Comparison with Chemiluminescent Spectra K. Balasubramanian and Kenneth S. Plizer' Department of Chemlstty and Lawrence Berkeley Laboratory, University of Callfornia, Berkeley, California 94720 (Received: May 2, 1983; In Final Form: August 22, 1983)
Relativistic quantum calculations including configuration interaction and spin-orbit interaction are described for 11 low-lying states of PbO. Comparison calculations are presented for eight A-S states obtained in the absence of spin-orbit interaction. These calculations were carried out by using relativistic effective core potentials. Spectroscopicproperties of these low-lying states of PbO are computed and compared with the spectra resulting from chemiluminescent reactions of Pb with 03,NzO, etc. Possible assignments of the experimentally observed bands are suggested. Spectroscopic properties are predicted for several low-lying electronic states that have not yet been observed experimentally. The effect of spin-orbit interaction and the nature of CI wave functions are discussed and comparisons made with SnO.
I. Introduction The lead oxide molecule is of considerable experimental interest because of the chemiluminescence of the reaction of P b with 03.The electronic of PbO reveals (1) Barrow, R. F.; Deutsch, E. M.; Travis, D. N. Nature (London)1964, 191, 374.
0022-365418312087-4857$0 1.5010
the existence of several emission systems in the visible and ultraviolet region. One of the important bands is the in(2) Nair, K. P. R.; Singh, R. B.; Rai, D. K. J. Chem. Phys. 1965, 43, 3570. (3) Oldenborg, R. C.; Dickson, C. R.; Zare, R. N. J . Mol. Spectrosc. 1975, 58, 283.
0 1983 American Chemical Society
4858
The Journal of Physical Chemistty, Vol. 87, No. 24, 1883
TABLE I: A Few MO Configurations of PbO and t h e Terms Arising from Them in A-S and w--w Coupling Schemes configuration
A - s state
Balasubramanian and Pitzer
TABLE 111: Number o f Reference and Total Configurations Included in CI Calculations for t h e Lowest-Energy State of Each Symmetry
w - w state
RCa
state
total
~~~
U2R4 UT4T*
u2n 3n*
'z
3z
'z: +(O+) '(1)
0'
+
3n 'n
19 2480 8 1492 'I: '(o-) 12 2137 "(2) 12 2137 RC stands for t h e number of reference configurations,
O', 0 - , 1, 2
3z
1 0-, 1 1, 2, 3
+
3A
3z'z:
,'O
1
0' 2
+
'A
'z -
TABLE IV: Orbital Exponents in Slater Type Basis Functions Optimized for t h e 3P Oxygen and Lead Atomsa
0-
TABLE 11: Molecular States of PbO Related to Atoms
molecular states
O', 1, 2 0-, 1 0' 0', 0-( 2), 1( 3), 2( 2), 3 0 + ( 2 ) ,0 - , 1(2), 2 0-, 1
dissociation limit O/Pb
atomic energies in c m - ' Pb + 0
'P, + 3P, 3P1 + 3P0 3P0 i.'Po 3P, + 'P, 'P, + 3P1 'Po + 3P1
0.0 158.5 385 7819.4 7978 8204
-
tense band attributable to the allowed A(O+) X(O+) transition, where X(O+) is the ground state and A(O+) is an excited state of same symmetry as the ground state in the double group symmetry of the molecule. Several other less intense systems such as a X(O+),b X(O+) etc. have been observed. One of the objectives of this theoretical investigation is to compute the spectroscopic properties of several low-lying electronic states with the intent of assigning the emission systems observed experimentally to the appropriate electronic states. The calculations presented here were carried out with the method formulated by Christiansen, Balasubramanian, and Pitzers for diatomics containing very heavy atoms. This method was found to be quite successful for the computation of the spectroscopic properties of several low-lying electronic states of the molecules such as TlH: Pb2,*10 Sn2,loand Sn0.l' In section 2 the method of our calculations is described. In section 3 we compare the calculated spectroscopic properties of several electronic states with available experimental spectra. In the last section the nature of CI wave functions for several states is discussed and compared with those of the tin oxide (SnO) molecule.
-
-
2. Method of Calculations The lead oxide molecule has a closed-shell ground state u2ir4(considering only p electrons and ignoring the s and d electrons of the lead and oxygen atoms). Promotion of a *-electron to the **-antibonding orbital generates six A-S states which are split into ten w--0 states by spin-orbit interaction. The promotion of the a-electron to a **-orbital generates 311 and lII A-S states which are split into five w-w states. Table I summarizes these low-lying electronic states. In Table I1 we show the dissociation (4) Kurylo, M. J.; Braun, W.; Abramowitz, S.; Krauss, M. J. Res. Natl. Bur. Stand., Sect. A 1976, 80,167. (5)Linton, C.;Broida, H. P. J. Mol. Spectrosc. 1976, 62, 396. (6)Brom, J. M.; Beattie, W. H. J. Mol. Spectrosc. 1980, 81, 445. (7)Huber, K.P.; Henberg, G. "Spectroscopic Constants of Diatomic
Molecules"; Van Nostrand New York, 1979. (8)Christiansen, P.A.; Balasubramanian, K.; Pitzer, K. S. J. Chem. Phys. 1982, 76, 5087. (9)Pitzer, K.S.;Balasubramanian, K. J.Phys. Chem. 1982,86,3068. (10) Balasubramanian, K.; Pitzer, K. S. J.Chem. Phys. 1983, 78, 321. (11)Balasubramanian, K.;Pitzer, K. S. Chem. Phys. Lett., in press.
S
Pb
0
1.9021 ( 4 )
9.6982 (1) 6.9562 (1) 2.6786 ( 2 ) 1.6927 ( 2 )
0.8482 ( 4 ) P
1.5189 ( 4 ) 0.8599 (4)
d
3.5804 ( 4 ) 1.6047 ( 4 )
3.7183 ( 2 ) 1.6671 ( 2 )
a The principal quantum numbers are shown in parentheses.
limits of these electronic states. The atomic states of the lead atom have been described in both L-S and j-j coupling schemes in our earlier paperlo on Pb2 and Sn2. As reported there, our calculations for the atoms reproduce the atomic energy levels quite satisfactorily. We will now consider the selection of configurations for our relativistic CI calculations. All A-S states that give rise to states of same w-w symmetry mix in the presence of spin-orbit interaction. Thus the ground state is a mixture of lZ+, 3n(O+), %(O+), 'Z+(II)(O+),etc. Similarly the l(1)state is a linear combination of 5+(1), %(l), 3A(l), 311(1), and lII(1). The coefficients in the linear combination are determined variationally. The lowest 0' state included u2r4,u2x3r*,and ur4r* as reference configurations. Further, for the sake of electron correlation and to represent the molecule properly near the dissociation limits we included the u27r2a*2,u ~ K K * ~ , ~ ~ 7 r *uu*a37r* ~ , configurations were added. An extensive array of single and double excitations from these configurations were allowed. To compute the properties of the lowest 1state we included the 2$a*, u7r47r* configurations with spin and angular momentum chosen appropriately to yield the 1 state. Single and double excitations were allowed. The lowest 0- and 2 states were also represented in a like manner. Our calculations were carried out with a molecular program that uses Cartesian Slater type orbitals in & symmetry. The above configurations were expanded to the Cartesian basis. Table I11 summarizes the number of reference configurations and the to;al number of configurations included in our CI calculation. Our SCF calculations were carried out by using relativistic effective potentials for the lead atom obtained from relativistic numerical Dirac-Fock calculations of the atom. Fourteen electrons of the lead atom (dlos2p2)and all eight electrons of oxygen were included in our SCF calculations. The relativistic effective potentials were averaged with respect to spin a t the SCF stage. We employed a double {basis set of Slater functions. The Slater exponents were optimized for the 3P lead and oxygen atoms. The optimized exponents are shown in Table IV. The 1s orbital of the oxygen and all of the primarily d orbitals of the lead atom were frozen after the SCF stage to limit the number of configurations. Our final CI calculations included 6 u
The Journal of Physical Chemisfty, Vol. 87, No. 24, 1983
CI Calculation of Low-Lying States of PbO
TABLE V: Spectroscopic Properties of PbO Re, a state calcd exptl
O+(II);A 1( 111), B 3z- O+(III),c l ( I V ) , C' 'n (1(V)), D lx+(II)(O+(IV)), E
3 2
+
-
'z3n In I
1.92 2.12
2.09 2.07
2.14
2.05 2.18
L: +(11)
3. Results and Interpretation of Experimental Spectra of PbO Our calculated spectroscopic properties of ten low-lying w-w states and the corresponding eight A-S states (in the absence of spin-orbit interaction are shown in Table V. Several authors' have observed the A(O+) X(O+)emission system of PbO at about 19 863 cm-'. Our calculated value for the A(O+) X(O+) separation is 18890 cm-l which is in good agreement with these experimental observations. This A(O+) state is a mixture of the 311(0+)and
-
cm-l
exptl
calcd
exptl
0 14 461 1 4 551 15 205 1 5 360 1 6 035 18 758 18 890
0 1 6 454? 1 6 025 1 6 454?
715
721 441? 482 441?
27 215
487 540 472 451 576 528
1 9 863 22 285 23 820 24 947 30 1 9 9 34 454
612 521
682 1 6 610 18 267 20 292 20 477 22 469 24 7 7 1 39 202
orbitals and 4a, and 4aYorbitals. Separate SCF calculations were carried out for the three configurations $a4, ~ P P and * , an+*. The CI calculations were based on the most appropriate set of SCF orbitals. While the O+(I),1(I),O-(I), O-(II), 2(1), and 2(II) states have been calculated by the above scheme, the higher roota of these symmetries have been calculated somewhat less accurately. Since our calculations were based on Cartesian orbitals in Czusymmetry, different C,, symmetries involve the same Cartesian orbitals but with different sign relationships among the coefficients. While our CI program, in principle, maintains the symmetry as determined by our input, any asymmetry from the SCF orbitals or round-off errors can cause a collapse from a high energy root of the desired symmetry to a lower root of another symmetry. For example, a 2 state has the same set of configurations as an 0- state but with different sign relationship. Thus a 2 state could collapse to an 0- state. In some cases this collapse could be avoided by calculations with fewer configurations, but the results are now much less accurate. The O+(II)state had all of the 311(0+),'Z+(O+), and 'E+(11)(O+) reference configurations with single and double excitations. The O+(III)state included only the 'E+,32-, and '2+(11) configurations with single and double excitations. The 1(I) and 1(II) states included 3Z+(l),3A(l), 3Z-(1), 311(1),and "(1) state reference configurations. We allowed single and double excitations from these reference configurations. The l(I1I) and 1(IV) states are mixtures of 311, 3Z-, and 'II and were not calculated accurately enough to be reported. The upper root of a calculation involving 311and lII configurations appears to be a reasonable estimate for l(V)('n) and is reported. Thus the spectroscopic properties of some of the highly excited states such as O-(III),O+(III),l(V), etc., are only estimates and should not be regarded as accurate calculations.
-
w,,
calcd
20 747
2.23
2.02 2.21 2.24 2.23 2.22 2.13 2.15 2.22
+
31: 'A
2.02 2.23 2.23 2.23 2.24 2.24 2.14 2.13
T,,cm-'
4859
444 498 532 4 94 530 454
706 503 485 600 594 514 505 703
lZ+states. Linton and Broida5 and Oldenborg et al.3have observed several new bands in the a(1)-X(O+) and A(0')-X(O)+ emission systems which enabled calculation of we values of these states. In Table 111we show the we and T, values calculated by these authors based on these new bands. Our calculated T, and we values for the a(1) state which is our 1(I) state are in reasonable agreement with the values obtained in ref 3 and 5. The a(1) state is assigned to 3Z+(l)by several authors. Our calculations confirm this assignment. The two components of the 32+term are very substantially mixed by spin-orbit interaction. The 0- state is about 3/4 3Z+(O-) and 1/4 '8-while the 1 state is about 3/4 32+(1)and 1/4 3Z-(l). The mixing of 3A(l), 311(0+),and 311(1)is small. Our calculations give 32+(1)a littler higher than 3Z+(O-) whereas most other investigators3s4have come to the opposite conclusion. The theoretical argument of Kurylo et aL4appears to be valid for small mixing, but higher-order effects might arise for such large mixing as we find. Experimentally, the weak and presumably "forbidden" transition at 16 454 cm-I might arise from 3A(2)as well as from 3Z+(O-). The approximations in our calculations are such that we cannot draw a definite conclusion, but we believe that the alternate assignment of the b state at 16454 cm-' to 3A(2) should be considered as a possibility. An emission system B X(O+) has been observed. The B state was assigned to 311(1)state with a T, value 22 285 cm-' by several investigators. As noted above, we could not calculate with accuracy the l(1II) state, but we know that its T, value is lower than the T, value of the 311state obtained without spin-orbit operator. Thus the assignment of the B state to 311(1)seems to be appropriate, although this state is certainly a mixture of 3 ~ ( 1*II(l), ), and 3Z-(l) with 311(1)making a dominant contribution. The experimental T, value of the C state is 23 820 cm-'. This state should be 3Z-(O+) and our calculated T, is somewhat lower. The calculated o,value (613 cm-') is in good agreement with the experimental value. The D X(O+)and E X(O+) emissions have also been observed experimentally. The experimental T, values of these states are 30 199 and 34 454 cm-'. The D and E states correspond to our 1(V) and O+(IV) states. These states are dominantly 'II(1) and 'V(11) states. The experimental T,value for the C'(l(1V)) state is shown in Table V, but we could not calculate the spectroscopic properties of this state with sufficient accuracy. The experimental T,and we values
-
-
-
4860
The Journal of Physical Chemistry, Vol. 87, No. 24, 1983
Balasubramanlan and Pitzer
TABLE VI: Potential Energy Curves o f PbO
O+(I)
R
'E+
3.0 3.25 3.5 3.65 3.75 3.85 4.0 4.1 4.2 4.5 8.0
o-(I) 3 2
+
1(I)
2(I)
'Z
'A
+
0.0944 0.1994 0.2065 -0.0151 0.0744 0.0795 -0.0915 0.0086 0.0195 -0.1053 -0.0093 -0.1095 -0.0207 -0.1099 -0.0323 -0.0319 -0.1066 -0.0407 -0.0405 -0.0433 -0.0430 -0.0442 -0.0438 -0.0713 -0.0404 -0.0394 0.0
VII: R
TABLE
3.0 3.25 3.5 3.65 3.75 3.85 4.0 4.1 4'2 4.5
2(II)
l(I1) 'A
0.1267 0.0161
0.2345 0.0819 0.0244
-0.0180 -0.0286 -0.0371 -0.0400 -0.0372 -0.0349
-0.0264 -0.0357 -0.0387 -0.0400 -0.0368
IA
0.0325
o-(II)
'n
O'(I1)
l(II1)
'n
3n
0.2061 0.0792 0.0135
0.2428 0.0823 0.0169
-0.0157 -0.0019 -0.0228 -0.0207 -0.0211 -0.0115 -0.0325 -0.0244 -0.0240 -0.0184 - 0.0357 -0.0244 -0.0236 -0.0195
l(1V) O+(IV) O'(II1) 3 2 'n 'Z'(I1) 0.3034 0.1413 0.1163 0.2136 0.0518 0.0511 0.1361 -0.0067 -0.0037 -0.0121 -0.0149
0.0222 0.0171 0.0140 0.0142
0.0929 0.0827 0.0732 0.0696
-0.0348 -0.0078 -0.0054 -0.0040 -0.0050 0.0308 0.0835
Potential Energy Curves o f PbO Calculated without the Spin-Orbit Effect
'c
+
0.1026 -0.0123 - 0.1024 -0.1064 -0.1068 -0.1034
-0.0679
3C
+
IC 0.3042 0.1421 0.0523
'n
'n
0.3037 0.1415 0.0516
0.2163 0.0923 0.0283
0.2373 0.1087 0.0421
0.2186 0.1361
0.0061 -0.0046 -0.0133 -0.0165
0.0068 -0.0039 -0.0127 -0.0158
0.0001 -0.0050 -0.0077 -0.0073
0.0121 0.0066 0.0030 0.0029
0.0929 0.0827 0.0732 0.0696
-0.0089
-0.0082
0.0102
0.0188
0.0835
'A
0.1324 0.0287
0.1455 0.0403
-0.0235 -0.0317 -0.0339 - 0.0344 -0.0289
-0.0139 -0.0227 -0.0256 -0.0268 -0.0230
'C -
of this state are close to those of C(O+(III)). Our T,values of the excited states are somewhat lower than the experimental values. We believe that this is attributable to a poor *+-antibonding orbital for the ground state which was optimized only for the excited states. This could have led to imbalance in the amount of correlation in the ground state and excited states. Our calculated dissociation energy of 3.0 eV for the PbO molecule is based on the molecular calculation at 8.0 bohr. This is in reasonable agreement with the experimental value of 3.83 eV. Our calculated Re and we values for the ground state are in good agreement with the experimental values and the values obtained by Basch, Stevens, and Krauss using a MCSCF calculation.12 The calculated we and Re values for the excited states are also in good agreement with the available experimental results. As one can see from Table V spin-orbit interaction is quite large and important for the lead oxide molecule. The original calculated energy values for the several low-lying electronic states mentioned above are shown in Tables VI and VII. A few potential energy curves are also shown in Figure 1. 4. The Nature of CI Wave Functions and Comparison with SnO Spin-orbit interaction not only changes the Te values of several w-w states in comparison to the T,values of the corresponding A-S states but also mixes several A-S states that have the same w-w symmetry. This effect is larger for PbO than SnO. This difference can be explained on the basis of the properties of the atomic states of P b and Sn. While the 3P0-3Pseparation for the tin atom is only 13 mhartrees, the corresponding value for Pb is 43 mhartrees. In general the lower root of a given w-w symmetry is stabilized by spin-orbit interaction but this lowering is smaller for the molecule in comparison to the atom. We next discuss in some detail the nature of the CI wave function for some electronic states. The ground state O+ at the equilibrium bond length 3.75 bohr is populated 84% by 'Z+(I), 0.8% by 311, and 3.0% by 3Z-.The rest of the (12)Basch, H.; Stevens, W. J.; Krauss, M. J. Chern. Phys. 1981, 74, 2416.
3.0
5 .O
4.0
I
2 +(11)
6 .O
R/Bohr
Flgure 1. Potential energy curves of three low-lying states of PbO.
population is attributable to single and double excitations from the ground state. Thus this is dominantly a lZ+A-S state with considerable correlation. One can thus explain relatively small lowering of this state by spin-orbit interaction. At equilibrium bond distances the l(1) state is a mixture of about 314 3Z1+and 114 3Z- with a little 3A. The contribution of 311and 1 ' 1 states to this state is very small. The O-(I) state is 74% 32+and 20% 'Z-. The contribution of 311 at equilibrium bond distances is negligible. The O+(II) and O+(III) states are primarily 311 and 3Z-, respectively, but have nonnegligible coefficients for the l P ( 1 ) and 'Z+(II) states. The 0-(11) state is 90% 311 and 5.5% 3Z+with an only small contribution from the lZ-. There are two striking differences in the CI wave function and electronic properties of PbO and SnO. First, the tin oxide molecule can be described reasonably well within A-S coupling scheme. When the spin-orbit interaction was included the mixing of A-S states that have different A-S symmetry but the same w-w symmetry has a negligible effect on the energy (but may be important for transition probabilities). This mixing is much larger for PbO as discussed above. Secondly, there is a significant lowering of the T,values of the excited states in com-
J. Phys. Chem. 1083,87,4861-4867
parison to the T, values of the corresponding A-S states. This can be explained on the basis of the nature of the a*-antibonding orbital. While the a-bonding orbital is mainly on the oxygen atom with only a small contribution from the heavier atom, the a*-orbital is mainly on the heavier atom. Thus promotion of a u- or ?r-electron to the antibonding a*-orbital picks up the large spin-orbit interaction on the heavy atom. Of course, as discussed above, this effect is noticeably large for the lead atom in comparison to the tin atom. Consequently, spin-orbit interaction stabilizes most of the excited states which arise from the promotion of an electron to the a*-orbital. However, the mixing of 311(1)and 'II(1) lowers the T,value of 311(1) and increases the T, value of lII(1). Thus our l(V) state has a higher T, value in comparison to the T, value of the I l l A-S state. The w e values of the various electronic states of PbO (and SnO) me very sensitive to the basis sets although the T , and Re values do not change appreciably in different basis sets. If we employ a single { basis for the oxygen 1s and 2s and a double {basis for the oxygen 2p orbital (the basis set for the heavy atom being the same as in Table 111), the ground state we values for PbO and SnO are 900 and lo00 cm-l, respectively. The we values of the excited states are in the region of 650-950 cm-l for PbO and the corresponding range for SnO is 700-1000 cm-'. Thus a
4861
smaller basis set tends to increase the we value. This dependence of w, value on the basis sets was also noted by Datta, Van Wazer, and John13for the ground state of PbO molecule. There is an avoided crossing of the states arising from 2 a * configuration of a given symmetry with a compatible 311 state of the same w-w symmetry. For example, the 10) state is dominantly 311at shorter distances and it becomes dominantly 3Z+at equilibrium bond distances. This avoided crossing is also observed for the O-(I) and O+(II) states in the repulsive regions. This crossing occurs at 3.5 bohr for PbO and 3.25 b o k for SnO. The crossing in SnO is sudden because of the small mixing of 311 and 3Z+states. However, there is significant 311and 3Z+ interaction in the l(1)and O-(I) states of PbO in this region since spin-orbit effects are quite large for the lead atom. Acknowledgment. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the US.Department of Energy under Contract No. DE-AC03-76SF00098. Registry No. PbO, 1317-36-8;Pb, 7439-92-1; Os,10028-15-6; NzO, 10024-97-2. ~~
(13)Datta, S.;Van Wazer, C. S.;John, R. Chen. Phys. Lett. 1978,57, 83.
Effect of the Solvent on the Entropy of Formation of the Mercury/Solution Interface W. R. Fawcett' belph-Waterloo Centre for cireduate Work In Chemistry (Guelph Campus), Department of Chemistry, Unlvershy of Guelph, Guelph, Ontarlo, Canada N1G 2 W l
and 2. Borkowska InstirUte of Physical Chemlstry, Polish Academy of Sclences, 01-224 Warsaw, Poland (Recelved: June 29, 1982; In Final Form: February 14, 1983)
The temperature dependence of the dielectric properties of a monolayer of solvent dipoles at a polarizable interface, including the entropy of monolayer formation, are examined within the context of a multistate model in which the solvent molecules are represented as hard, polarizable spheres having a dipole moment which can take up specified orientations with respect to the field at the interface. Data are presented for the entropy of formation of the mescury/nonaqueous solution interface with methanol (MeOH),N-methylformamide (NMF), NJV-dimethylformamide(DMF), and propylene carbonate (PC) as solvents. When these results are considered within the context of the multistate model and the previously presented three-state model, it is clear that the simpler model is not able to account for the experimental results obtained with aprotic solvents. The experimental data are also discussed with respect to the classification of the interfacial solvent behavior proposed by Parsons.
Introduction Solvent effects on the differential capacity, interfacial tension, and other thermodynamic properties of the mercury/solution interface have been well documented in the literature.14 The dependence of differential capacity on electrode charge density in the absence of specific adsorption has been attributed to a change in the dielectric properties of the solvent at the interface. In this regard, inner-layer-capacity curves have been analyzed on the basis of simple molecular models which assume that the solvent (1) Payne, R. Adu. Electrochem. Electrochem. Eng. 1970, 7, 1. (2) Parsons, R. Electrochim. Acta 1976, 21, 681. (3) Fawcett, W. R. Isr. J. Chem. 1979, 18, 3. (4) Damaskin, B. B.; Ivanova, R. V. Uspekhi Khim. 1979, 68, 1747.
dipoles are present in a monolayer in which they can take up a finite number of orientations with respect to the electrode's field.3p5*e Far fewer experimental data are available regarding the temperature dependence of interfacial dielectric properties for nonaqueous solvents. The temperature dependence of the inner-layer capacity of the Hg/solution interface has been determined with dimethylformamide (DMF),' propylene carbonate (PC),* (5) Parsons, R. Trans. SOC.Adu. Electrochem. Sei. Technol. 1978,13, 239.
(6)Rangarajan, S. K . "Specialist Periodical Reports: Electrochemistry";Chemical Society: London, 1980;Vol. 7, p 203. (7) Fawcett, W. R.; Ikeda, B. M.; Sellan, J. B. Can. J. Chem. 1979,57, 2268. ~~.~
(8)Nguyen Huu Cuong; Jenard, A.; Hurwitz, H. D. J . Electroanal. Chern. 1979,103, 399.
0022-3654/83/2087-486 l$O 1.50/0 @ 1983 American Chemical Society
