J. Phys. Chem. 1982, 86, 3121-3126
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Role of Electron Correlation and Polarization Functlons in the Energy Difference between cls- and frans-1,P-Dlfluoroethylene Suketu R. Qandhl,“ Mark A. Benzel,la Cllfford E. Dykstra,*’asb School of Chemical Sciences, Unhersity of Illlnols, Urbana, Illlnois 6 180 1
and Tadamlchl Fukunaga
‘’
Cenfral Research and Development Department, Id Experimntal Stetbn, E. I. du Pont & “ o u r s Wllmlngton, Delaware I9898 (Recelved: Merch 5, 1982)
and Company,
Extensive ab initio calculations have been performed on the cis- and trans-1,2-difluoroethyleneisomers with large, extended basis sets. Energies were evaluated at the self-consistentfield (SCF) molecular orbital level and with perturbational and variational treatment of electron correlation effects. Geometrical parameters were optimized at correlated and uncorrelated levels, and correlation and basis set effects were examined through density difference plots. The results indicate that electron correlation effects are indispensable in determining true geometrical molecular structures, and that using basis sets which include polarization functions is crucial in accounting for the small experimentally determined cis-trans energy difference (1.08 f 0.12 kcal).
Introduction A large body of experimental data2~3 concerning the relative stability of isomeric (and rotameric) fluorocarbons, their reactivities, and their acidities is full of puzzles that point to a lack of a basic understanding of fluorine effects. Many differing qualitative concepts and models have been advanced including the I-?r effect, negative hyperconjugation, stabilizing or destabilizing lone pair interactions, electrostatic dipole models, and electronegativity effects to alter hybridization. Attempts at quantitative theoretical calculations of fluoro compounds have been equally unsuccessful because they have not always attained the necessary accuracy to provide a meaningful understanding.2 The greater stability of cis-1,2-dfluoroethylene over the trans isomer is well established by experimental studies: even though steric factors as well as electrostatic dipole repulsion would seem to favor the trans structure. This anomaly also occurs with ethylenes substituted vicinally with electronegative atoms and has been termed the “cis effect”. From studying the thermodynamic functions of 1,2-dichloroethylenes, Pitzer and Hollenberg5 suggested a resonance stabilization that would be greater for the cis isomer than for the trans isomer. A comprehensive picture of attractive nonbonded interactions has been developed by Epiotis? It predicts an attractive interaction of lone pairs on nearby centers by way of mixing with an unfilled antisymmetric orbital. Still another view is that of Bingha” who argued that effects associated with electron (1) (a) University of Illinois. (b) Alfred P. Sloan Research Fellow, 1979-81. (c) E. I. du Pont de Nemours & Co. (d) Contribution No. 2956. (2)(a) R. E. Banks, ‘Fluorocarbons and Their Derivatives”,Macdonald, London, 1970; (b) R. D. Chambers, ’Fluorine in Organic Chemistry”,Wiley, New York, 1973; (c) W. A. Sheppard and C. M. Sharts, ‘Organic Fluorine Chemistry”,W. A. Benjamin, New York, 1969; (d) ‘Fluorocarbon and Related Chemistry”,Specialist Periodical Report, Senior Reporters R. E. Banks and M. G. Barlow, Chemical Society, 1971, Vol. 1; 1974,Vol. 2; 1976,Vol. 3. (3)B. E. Smart, ‘The Chemistry of Functional Groups”,Supplement D, “The Chemistry of Halides, Pseudohalidesand Azides”,S. Patai, Ed., ‘Fluorocarbons” in press. (4)(a) N. C. Craig and E. A. Entemann, J.Am. Chem. SOC.,83,3047 (1961); (b) N. C. Craig and J. Overend, J. Chem. Phys., 51,1127(1969); (c) N. C. Craig, L. G. Piper, and V. L. Wheeler, J.Phys. Chem., 76,1453 11971\. ,- - . -,. (5)K.S. Pitzer and J. L. Hollenberg, J. Am. Chem. SOC.,76, 1493 (1964). (6)N. D.Epiotis, J. Am. Chem. Soc., 96,3087 (1973). 0022-3054/82/2086-3121$01.25/0
delocalization dominate. He contended that delocalization will favor a trans conformation only when no antibonding orbitals are occupied, and that in 1,2-difluoroethylene, which can be viewed as a four-center six-electron system, the cis form is less destabilized by delocalization than the trans form. Implicit in these arguments is that calculations at the Hartree-Fock limit would correctly describe the system. Several ab initio studies of the cis-trans energy difference in 1,2-difluoroethylene have been reporteda8-12 In most of these calculations, a treatment using various standard basis sets at the uncorrelated SCF level gives an energy difference of about 1 or 2 kcal but with the trans rather than the cis structure being the more stable. With a measured value of 1.08 kca1,24 the net error is a small but obviously important 2-3 kcal. Some of the most exhaustive calculations8 are capable of predicting that the cis form is more stable than the trans form by 0.26 kcal, and that part of the stabilization is due to a greater correlation energy in the cis form. The recent calculations of CremerI2using a polarized basis set and a second-order treatment of correlation appear to have given a much more satisfactory energy difference of 0.9 kcal. That fluorine plays a potentially unique role in the molecular electronic structure is suggested by the fact that the fluorine molecule is unbound at the SCF 1e~el.l~ Of course, when correlation is included, a binding energy close to the experimental value is obtained.14 The small atomic radius of F (0.57 A) coupled with the relatively large van der Waals radius (1.35 A) must be the genesis of the sizable correlation effect that may need to be reckoned with in the anomalies in fluorocarbon chemistry. Another subtle but potentially important basis set effect can be gleaned from the SCF calculations of difluoroethylene. As the quality of basis set improves,ll the C=C and C-H bond lengths become shorter and deviate more (7) R. C. Bingham, J. Am. Chem. SOC.,98,535 (1976). (8)J. S. Binkley and J. A. Pople, Chem. Phys. Lett., 45,197 (1977). (9)F. Bernardi, A. Bottoni, N. D. Epiotis, and M. Guerra, J. Am. Chem. Soc., 100,6018 (1978). (IO) A. Skancke and J. E. Boggs, J.Am. Chem. SOC.,101,4063(1979). (11) C. W. Bock, P. George, G. J. Mains, and M. Trachtman, J. Chem. Soc., Perkin 2,814 (1979). (12) D. Cremer, J. Am. Chem. Soc., 103,3633 (1981);Chem. Phys. Lett., 81,481 (1981). (13)A. C. Wahl and G. Das, Adu. Quantum Chem., 5,26 (1970). (14)T.L.Gilbert and A. C. Wahl, J. Chem. Phys., 55, 5247 (1971).
0 1982 American Chemical Society
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The Journal of phvsical Chemistry, Vol. 86, No. 16, 1982
TABLE I: Basis Set Descriptions and Designations no. of basis set functions DZ
44
DZ'
52
DZ"
*
62
DZ+P
74
TZ
66
TZtP TZ+++P
96 114
Gandhi et at.
TABLE 11: Experimental Structures of cis- and trans-Difluoroethylene
description Dunning17a(9s5p/4s2p) contraction o n C and F and (4s/2s) contraction o n H of Huzinaga primative bases" DZ basis plus diffuse functions o n fluorine [ a s = 0.11 and cup = 0.081 DZ' basis plus diffuse functions o n carbon [a,= 0.05 and ( u p = 0.041 and o n hydrogen [CY,= 0.05 J polarized DZ basis [ a d ( c ) = 0.75; and CY (H) = 1.01 C Y ~ (=F 0.9; ) Dunning''b ( 1 O s 6 p / ~ s 3 pcontraction ) on C and F and ( 5 4 3 s ) contraction o n H of Huzinaga primitive bases polarized TZ basis T Z + P basis supplemented with the diffuse functions as in the DZ" basis
from the experimental values; the predicted C-F bond length tends to be overelongated and in greater error throughout. A similar basis set effect on bond-length contraction has been reported in a detailed study of diimide.15 However, it was found that inclusion of correlation effects rectifies the overcontraction essentially by removing electron densities from the bonding regions thereby elongating bonds. Since electron correlation can be significant in the regions of high electron densities, contribution of correlation effects may be large in the description of some anionic16 and polyfluorinated species. At the outset of this study we anticipated that inclusion of electron correlation effects beyond the Hartree-Fock limit would (1)rectify the overcontraction of C=C and C-H bond lengths, (2) contract the C-F bond by relieving antibonding lone pair electron repulsion between the atoms, and (3) contribute to the cis-trans energy difference.
Theoretical and Calculational Approach In the course of our study we selected a number of different basis sets of atomic orbitals in the form of standard, contracted Gaussian functions. To fully identify all the calculations performed, we provide a list of the basis sets and designations in Table I. All sets are of at least double-l (DZ) quality, and the most important distinction among the sets is that some include polarization functions, designated by "+P", while the rest do not. The polarized basis sets all included a complete set of polarization functions, i.e., 3d functions on carbon and fluorine and 2p functions on hydrogen. The molecular wave functions and energies were obtained at four levels, the first being the uncorrelated SCF or molecular orbital level. Correlation effects were treated in some calculations by using second-orderMoeller-Plesset perturbation theorylg (MP2), by using variational selfconsistent electron pair (SCEP) theory,20,21 or by using the approximate double-substitution coupled clusters approach22(ACCD). In MP2 and SCEP all doubly substi(15) C. A. Parsons and C. E. Dykstra, J. Chem. Phys., 71,3025 (1979). (16) C. E. Dykstra, A. J. Arduengo, and T. Fukunaga, J. Am. Chem. SOC.,100, 6007 (1978). (17) (a) T. H. Dunning, J. Chem. Phys. 53,2823 (1970); (b) ibid.,55, 716 (1971). (18) S. Huzinaga, J. Chem. Phys., 42, 1293 (1965). (19) J. A. Pode, J. S. Binklev, and R. Seeger, Int. J. Quanfum Chem., S G p . 10, 1 (1976). (20) W. Meyer, J . Chem. Phys., 64, 2901 (1976). (21) C. E. Dykstra, H. F. Schaefer, and W. Meyer, J. Chem. Phys., 65, 2740 (1976). (22) R. A. Chiles and C. E. Dykstra, Chem. Phys. Lett., 80,69 (1981); S. M. Bachrach, R. A. Chiles, and C. E. Dykstra, J. Chem. Phys., 75,2270 (1981).
electron diffraction ref 29
ref 3 0
microwave31
Cis 1.311 1.332 1.100 122.5 127
1.331 1.335 1.084 123.72 121.56
1.324 1.335 1.089 122.1 124.0
Trans 1.320 1.338 1.088 119.8 125
1.329 1.344
1.080 119.33 129.25
tuted electron configurations were included in the wave function, and with SCEP all singly substituted configurations were also included. Higher order correlation effects are included with ACCD. Not included in any correlation calculation were configurations which would arise from substitution of the four lowest energy molecular orbitals. These four frozen orbitals are the carbon and fluorine atomis 1s orbitals. Equivalent or localized orbitals were constructed from the symmetry-adapted molecular orbitals prior to performing SCEP and ACCD calculations. By using the equivalent orbitals, we reduced the number of correlated electron pairs that need be treated explicitly from 144 to only 78 using the symmetry scheme of the s C E P ~ Ocomputer ~~ program. The first set of MP2 calculations were performed with an approximate natural orbital program" modified to evaluate second-order energies, and the remainder were performed with SCEP80.
Determination of Equilibrium Structures A key aspect of our study of the cis effect in 1,2-difluoroethylene is to answer the challenge of reproducing the experimentally measured cis-trans energy difference. Critical stability studies usually require attention to three factors: the adequacy of the atomic basis set or sets, the effects of electron correlation, and the selection of the molecular structures at which one evaluates total electronic energies. Complicating the situation is the fact that these factors are necessarily Thus,a change in the basis set size will affect the total correlation energy and both may also affect the location of potential surface minima (i.e., equilibrium structural parameters). In the calculations of Binkley and Pople? for example, an assumed, standard geometry was used for the 1,Bdifluoroethylene isomers, though a 4-31G/SCF optimization of the structural parameters was also performed. Their optimization and the similar calculation by Skancke and BoggslO gave structural parameters differing from the standard structures by up to 0.03 A. This affected the cis-trans relative energy by about 0.25 kcal, or almost as much as the correlation stabilization that Binkley and Pople found. (23) C. E. Dykstra, R. A. Chiles, and M. D. Garrett, J. Comput. Chem.,
2, 266 (1981).
(24) C. E. Dykstra, QCPE,11, 388 (1980). (25) H. F. Schaefer, 'Critical Evaluation of Chemical and Physical Structure Information", D. R. Lide and M. A. Paul, Ed., National Academy of Science, Washington, DC, 1974, p 591; Annu. Reu. Phys. Chem., 27, 261 (1976). (26) S. Bell, J. Chem. Phys., 68, 3014 (1978). (27) C. E. Dykstra, Annu. Reu. Phys. Chem., 32, 25 (1981). (28) D. J. DeFrees. B. A. Levi. S. K. Pollack, W. J. Hehre, J. S. Binkley, and J. A. Pople, J. Am. Chem. SOC., 101, 4085 (1979).
-
-
Energy Difference between cis and trans 1,P-Difluoroethylene
TABLE 111: Optimized Structural Parameters of cis- and trans- Difluoroethylene
SCF
DZtP/ MP2
Cis 1.317 1.368 1.068 122.7 123.6
1.314 1.323 1.072 122.4 123.0
1.340 1.349 1.082 122.1 122.9
Trans 1.316 1.376 1.067 119.4 126.7
1.312 1.327 1.073 120.5 124.9
1.339 1.356 1.081 119.4 125.5
DZI
SCF
Rcc, RCF,
a
a
RCH,
LFCC, de!? LHCC, deg R c c , '4
RCF, a RCH, LFCC, deg LHCC, deg
a
DZtPI
A level of calculation that is of insufficient quality to yield reasonable equilibrium structures may have its energetic deficiencies either masked or exaggerated because of the net distortion of the shapes of the potential surfaces, a distortion that causes the poor quality structural predictions. Use of experimental geometries, when available, will be most reliable only when the level of calculation becomes sufficient for properly locating the true potential surface minima. Two important factors for attaining such sufficiency in structure predictions are polarization function effects and electron correlation effe~ts.~' Thus, part of our study was the complete pointwise geometry optimizations of the isomers with a polarized double- basis, designated DZ+P, and with correlation effects accounted for a t the MP2 level. Energies were evaluated at these predicted structures and also at experimentallydetermined structures. A problem with experimental structural value^^*^^ for 1,2-difluoroethylene is that there are differences of as much as 0.02 A and 5.4O (see Table 11). To distinguish on the basis of systematic trends the most reliable experimental structures, one can compare the three geometry optimizations performed, the first at the DZ/SCF level, the second at the DZ+P/SCF level, and the third at the DZ+P/MF'2 level. The results are given in Table 111. The error at the DZ/SCF level is sizable relative to predictions on non-halogen-containing organic molecules.27 Inclusion of polarization functions does not improve the predictions since it results in overcontracted bonds. The DZ+P/MP2 treatment properly lengthens the C=C bond and shortens the C-F bond relative to DZ/SCF. The much more complete DZ+P/MPB treatment does not change the DZ/SCF bond angle predictions very much and, thus, the bond angles are being well predicted even at this low level. The comparison of the optimized cis and trans structures reve& that the FCC bond angle is about 3 O less in the trans isomer while the HCC angle is about 3O greater. Also, the C-H and C=C bond lengths are about the same in both isomers. While there will be differences between theoretical parameters and experimental values because of vibrational averaging, the electron diffraction results of Carlos et al.30seem to be in better agreement with these trends than the results of Shaick et al.29 Because of this we considered the structures given by Carlos and coworkers to be the most appropriate for this study. This was also the geometry used by Cremer.12 However, it has been
c
(29)E.J. M.Van Schaick, F. C. Mijlhoff, G. Renes, and H. J. Geise, J. Mol. Struct., 21,17 (1974). (30)J. L. Carlos, R. R. Karl,and S. H. Bauer, J. Chem. SOC.,Faraday
Trans. 2,177 (1974). (31)V. W. Laurie and D. T. Pence, J. Chem. Phys., 38, 2693 (1963); V. W.Laurie, ibid., 34,291 (1961).
The Journal of Physical Chemistty, Voi. 86, No. 16, 1982 3123
suggested32that the HCC angle of the trans isomer obtained by Carlos et aL30 may be in error. Comparing cis and trans L ~ C Cangles in Tables I1 and I11 does make their trans LHCC angle appear to be 3-4' too large. Thus, we have also carried out calculations on the trans isomer with this geometry adjusted so that LHCC= 125'. The two sets of results along with the relative energies of the DZ+P/ MP2 optimized structures give an indication of the extent of a lingering geometry effect in our final relative energies. The DZ+P/MP2 geometries themselves are reasonable, though the C-F and C-C bonds seem overelongated by -0.01 A. A more complete treatment of electron correlation effects may be required to produce more accurate structures.
cis -trans -Difluoroethylene Energy Difference Our attempt to understand the detailed nature of the greater stability of the cis isomer is an attempt to determine the electronic structure factors that are required to produce the correct cis-trans energy difference, taking an experimental value for that difference. The experimental value is 1.08 f 0.12 kcal and has been determined from enthalpy measurements for the iodide-catalyzed cis to trans isomerization reaction followed by extraction of the pure electronic equilibrium energy difference with spectroscopic data! To some extent our analysis relies on the validity of this result, though our calculations independently show convergence to about this value. A summary of the relative energy predictions at the various levels of treatment is given in Table N. A feature of these results is that polarization functions (e.g., functions that have the topological forms of 3d atomic orbitals on carbon and fluorine and atomic 2p orbitals on hydrogen, but that are less diffuse) favor the cis structure by as much as 1 kcal. This was identified but as a lesser effect by Binkley and Pople? Their use of standard geometries may have modified some effects relative to our results. Another factor which contributes more to the stability of the cis isomer is extra flexibility in the atomic s,p basis sets. All "TZ" AE's are lower than the corresponding "DZ" values. Correlation effects seem to be of nonnegligible importance when comparing the DZ+P/SCF and DZ+P/MP2 results. This is consistent with what Binkley and Poplea determined. However, Moeller-Plesset perturbation theory energies are evaluated knowing only the wave function at the next lower order, which in the case of MP2 energy is just first order. At first order, correlating configurations are mixed into the wave function independent of each other. Thus, there may be the possibility of exaggerating or underestimating the correlation effect of individual configurations since their importance in the wave function is not relaxed to account for the other correlating configurations. At the SCEP level, all configurations are variationally relaxed with respect to each other, and the correlation contribution with the DZ+P basis is reduced from the MP2 value of -0.24 kcal to only -0.08 kcal. About the same shift toward the trans structure is seen for all three relative energies with the DZ basis when comparing MP2 and SCEP. Higher order correlation effects either estimated by the modified Davidson formula,33or an exponential or obtained from a size-consistent ACCDZ2wave function continue to undo the MP2-predicted correlation effect. In the end, it seems that the (32)D. Cremer, private communication. (33) E. R. Davidson, "The World of Quantum Chemistry", R. Daudel and B. Pullman, Ed., Reidel, Drodrecht, 1974;P. E. M. Siegbahn, Chem. Phys. Lett., 55,386 (1978);R.J. Bartlett and I. Shavitt, Int. J. Quantum Chem., Symp. No. 11, 165 (1977). (34)C. E. Dykstra, Chem. Phys. Lett., submitted for publication.
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The Journal of phvsical Chemistry, Vol. 86, No. 16, 1982
TABLE IV : Energies of cis- and trans-l,2-Difluoroethylene DZ+ PIMP2 optimized geometries, A E , kcal
exptl geometry30 calculational level DZ/SCF DZ+/SCF DZ++/SCF
E,,, au - 275.698 94 -275.703 33 -275.704 71 -276.091 44 -276.063 71 -276.106 60 -276.109 25 -276.104 75
trans, au
AE ,
A E ‘ , kcal
kcal
-275.700 08 -275.704 10 -275.705 29
0.71 0.48 0.36
1.39 1.09 0.92
1.17 0.81 0.66
-276.092 -276.064 -276.107 -276.110 -276.105
23 73 73 39 87
0.50 0.64 0.71 0.72 0.70
1.37 1.46 1.55 1.56 1.55
1.28 1.33 1.45 1.48 1.45
-275.795 -276.386 -276.333 -276.405 -276.410
84 72 16 13 20
- 0.86
- 0.23 - 0.28
- 0.27 -0.30
DZ+ P/SCEP+ A& DZ+ P/SCEP+ ~b
-275.797 20 -276.388 48 - 276.334 66 -276.406 49 - 276.41 1 55
DZ+++P/SCF T Z + P/SCF TZ+++P/SCF
-275.802 09 -275.832 58 -275.834 21
-275.800 20 -275.830 90 -275.822 27
-1.19 -1.05 -1.21
-0.65 -0.53 - 0.69
-0.72 -0.65 -0.80
DZ/MP2 DZ/SCEP DZ/SCEP+A~ DZ/SCEP+B~ DZ/ACCD DZ+P/SCF DZ+P/MP2 DZ+P/SCEP
expt4
-1.10 -0.94 - 0.86 -0.85
-1.08
* 0.12
The “A” correction to the energy is the modified Davidson a AE’ is based on the trans HCC angle being set to 125”. correction33where the correlation contribution of the double substitutions, ED, is simply scaled by the correlated wave function normalization ($ l\cI ) where (@ I$ ) = 1 and @ is the SCF wave function. The “B” correction” is similar, but scales ED by exp(($I\cI) - (@ I@)), and has been found to give estimates very close to full CCD results. n
F
F
Figure 2. This is a qualitative representatinn of the result of combining’ a p (T)carbon atomic orbital with a d carbon orbiil. The two possible results are 4 which is bonding and 4 which has lobes pointing between atomic centers.
e -
Figure 1. Electron density difference plots. The six plots are of contours35for the density difference between a DZ+P/SCF and a DZ/SCF wave function. The solid lines correspond to regions where electron density increases due to including polarization functions and the dashed lines correspond to regions where the density decreases. The contour levels are 0.0391, 0.0156, 0.0063, 0.0025, and 0.0010 electrons/au? The plots are of the cis (a) and trans (b) isomers in the molecular plane, the cis (c) and trans (d) isomers in the plane perpendicular to the molecular plane that includes the carbons, and (e) the cis in the perpendicular plane that includes the two fluorines.
difference in correlation energies of the isomers is negl’igible. This contradicts the conclusions of Cremer12from studies only at the MP2 level. It is unlikely that the correlation energy contribution to the cis-trans energy difference will change substantially
for larger than DZ+P bases. Thus, the energy differences obtained at the SCF level with the 114-function TZ+++P basis represent the most complete treatment. These values are -0.7, -0.8, and -1.2 kcal with the differences reflecting geometry effects. They cover a range that includes the experimentalvalue; clearly, more attention to the geometry is required to achieve the same accuracy as the experimental value. Nonetheless, the extensive evaluation of energies identifies the electronic factors that are involved in quantitatively determining the cis-trans energy difference. One of the identified electronic structure factors which must be included to stabilize the cis structure relative to the trans isomer $ the molecular orbital readjustments due to availability of polarization functions. Demonstrating the nature of these electronic redistributions are the density difference plots in Figure 1. These plots are contours of the difference in the total electron density between a DZ+P/SCF wave function and a DZ/SCF wave function. The mixing of polarization 3d functions produces a varied pattern of increasingand decreasing electron density changes that are very similar for the cis and trans isomers (35) W. L. Jorgensen, QCPE,10,340 (1977).
The Jorrnel of Pnysical -try,
Vol. 86, No. 16, 1982 91%
TABLE V: Energies of N,F, calculational levela
E& au
DZ/SCF DZIMP2 DZ+P/SCF DZ+P/MPO expt'
-307.533 -308.008 -307.654 -308.326
E-,au 88 15 00 80
-307.53234 -307.999 19 -307.656 88 -308.32347
~E,kcal -0.97 -5.62 1.81 -2.09 - 3.05
Evaluated at experimental g e ~ m e t r y . ~ ' TABLE VI: Dipole Moment of cis-1,2-Difluoroethylenea
DZlSCF DZIMP2 DZ/SCEP DZ++/SCF TZ/SCF
ne*. 3. Electron deMity dmercmce plots.
The four pkts are of contovsforthe"~ betweell correlated Mp2 and UnCaTeklted SCF waw hnctbrw. The oontau kvels are 0.008,0.004, 0.002, O.OOO9, and O.OOO45 ekotrons/eu? pkts (a) and (b) are wlth the DZ baais and (c) and (d) are wlth the DZ+P bask.
(Figure 1, a and b). Figure 2 is a schematic way of picturing this redistxibution. Letting the molecular plane be the r-y plane, pI and py atomic orbitals can be combined to orient an in-plane p orbital any direction, the intuitive choice being along the C-F axis. Likewise, the carbon atom's d, and &a+ polarization functions allow for the choice of any orientation in the plane. Placing one lobe of one polarization function along the C-F axis leads to two linear combinations with the p orbital, $1 and $2, as shown on the right side of Figure 2. participatm in C-C, C-H, and C-F bonding, and the qi2 lobes point between those of I&. Preferential population (through further mixing) of d1over would produce the density changes in Figure 1,a and b. The extent of such mixing is small since the contour levels in the density difference plots correspond to delectron redistributions. The fluorine & polarization functions may be oriented in the molecular plane along the F-C axis. Mixing with a fluorine p orbital similarly oriented (as in p a bond) would diminbh density at the fluorine end of the bond, while between the fluorine and carbon a t o m density would be increased. The density difference contours made in planes perpendicular to the molecular plane (Figure 1, c, d, and e) show the same feature. Because the out-of-plane r orbitals have a node in the molecular plane, it must be that the density readjustments are dominated by changes in the in-plane orbitals. Overall, because the polarization functions enhance the bonding, they diminish the fluorine electrostatic repulsion that otherwise destabilizes the cis isomer. Correlation effects play but an indirect role. Optimization of the geometrical parameters at the DZ+P/SCF level produced structures noticeably different from experimental and DZ+P/MPB structures (Table 111). The DZ+P/SCF and DZ+P/MP2 cis-trans energy differencea evaluated a t those structures are -0.20 and -0.42 kcal, respectively, and are close to the corresponding energies a t the DZ+P/MP2 optimum structures. The importance of the polarization functions is again indicated from the shifts in electron density due to correlation. Plots of the contours of the difference in electron density with correlated MF'2 and uncorrelated SCF wave functions are given in Figure 3, a and b, for the DZ basis and in Figure 3,c and d, for the DZ+P basis. For both sets of plots the
a
dipole moment, D 3.546 3.507 3.248 3.474 3.426
dipole moment, D DZ+P/SCF DZ+P/MP2 DZ+P/SCEP
2.876 2.839 2.648
DZ+++P/SCF TZ+P/SCF TZ+++P/SCF
2.851 2.834 2.818
expP
2.42 i 0.03
Evaluated at experimental geometry.jO
correlation adjustment to the electron density in the cis and trans forms is very similar. However, the correlation redistribution is of roughly opposite form comparing DZ and DZ+P wave functions. With a DZ basis, correlation slightly contracts the charge cloud around the fluorines, while with DZ+P basis the reverse happens. Thus, the absence of polarization functions can completely distort the analysis of correlation effects. The net effect of electron correlation energy on the cis-trans energy difference we find to be small. However, the size of this effect may be misleading. It does not guarantee that correlation can be ignored in considering the cis effect in other systems. The significant effect of correlation on geometrid parameters and the error in SCF level predictions of equilibrium structures are evidence of this. Testing these conclusions are similar but less extensive calculations on the isoelectronic species, N2F2,where the experimental cia-trans energy difference is a more sizable 3.05 kcal.' For cis-N2F2,microwaveSBand electron diffractionm studies are in good agreement for structural parameters, and by using the electron diffraction values for the cis and trans forms, energies were evaluated at the DZ/SCF, DZIMF'2, DZ+P/SCF, and DZ+P/MP2 levels. The results are given in Table V. The DZ/SCF level values are consistent with the previous ab initio calculations.The effects of polarization functions and possibly electron correlation are greater for this system, and the availability of polarization functions actually favors the trans isomer. Again, the effect of electron correlation seems distorted by the absence of polarization functions. Our examination of the cis-trans energy difference in 1,2-difluoroethylene has shown that electron correlation effects for the isomers are similar and do not contribute to the energy difference. This supports the validity of molecular orbital pictures of the cis effectk7 which we believe to now be refined by the understanding of the importance of polarization functions and flexible valence (36)R. L. Kuakoweki and E. B.Wileon, Jr., J. Chem. Phye., 39,1030 (1963). (37)R. K. Bohn and S. H. Bauer, Znorg. Chem., 6, 309 (1967). (38)J. M.Howell and L. J. Kirschenbaum, J. Am. Chem. Soc., 98,877 (1976). (39)K. Straume and A. Sknncke, Chem. Phys. Lett., 73,378(1980). (40)R.P.Blielcennderfer, J. H.5.Wang, and W.H. Flygere,J. C k m . Phye., 51, 3196 (1969).
J. Phys. Chem. 1982, 86, 3126-3130
3126
TABLE VII: Quadrupole Moments of
suited are different levels of calculation to determining different properties. In Table VI, the cis isomer dipole moment values are given and in Table VI1 are the quadrupole moments. As these results show, polarization functions do more than anything else at lowering the value of the dipole moment because of their role in effectively redistributing charge. As is typical, correlation also yields a lowering of the dipole moment value but the amount of lowering is small. On the basis of the results in Table VI, a larger, more complete than TZ+P valence and polarization basis calculation with correlation effects would probably still be 0.1 to 0.2 D too large. However, this difference with experiment is most likely the consequence of vibrational averaging. For quadrupole moments, the experimental error limits are rather large and preclude a detailed analysis. The TZ+P/SCF values do seem in good agreement, as far as it can be judged, affirming the quality of the TZ+P/SCF level description of the electronic structure of 1,2-difluoroethylenes.
cis- 1,P-Difluoroethylene
DZ/SCF DZ/MP2 DZ/SCEP
-2.278 -2.701 -2.533
3.753 3.723 3.506
Q,," -1.025 -1.022 -0.972
DZ++/SCF TZ/SCF
- 2.556 -2.596
3.466 3.558
-0.910 -0.962
DZ+P/SCF DZ+P/MP2 DZ+P/SCEP
-1.711 -1.687 -1.558
3.530 3.502 3.363
-1.820 -1.815 -1.805
DZ"+ P/SCF TZ+P/SCF
- 1.588 -1.702
3.273 3.338
expt40
-1.7 t 0.4
3.0
&ha
Qaa"
* 0.3
-
1.684
- 1.636
-1.3
f
0.5
Quadrupole moment tensor components in the principal axes system. In Buckinghams; evaluated at experimental geometry."
Acknowledgment. We thank Dr. D. Cremer for some interesting and helpful comments and suggestions. This work was supported, in part, by NSF Grant CHE78-15444. Calculations were performed on the University of Illinois, School of Chemical Sciences VAX 11/780 minicomputer, the VAX 11/780 of the Illinois Theoretical Chemistry Minicomputer Laboratory, and on a CYBER 175 with time provided by the University of Illinois Research Board.
basis sets. Establishing the generality of any of the different qualitative models of the cis effect requires comparative study of a number of representative systems, difluoroethylene being only the first.
Molecular Properties An ab initio molecular study at a number of different levels provides an opportunity to understand how well
Photoassisted Water-Gas Shift Reaction on Platinized Titania. The Influence of Preparation Parameters Shiu-Min Fang, Bor-Her Chen, and J. M. White' Lkpartment of Chemistry, The University of Texas, Austln. Texas 78712 (Recelved: March 8, 1982; In Final Form: April 13, 1982)
The variation of the rate of the photoassisted water-gas shift reaction over platinized titania with changes in catalyst preparation has been studied. The following parameters were varied: (1)extent of hydrogen reduction, (2) Pt loading, (3) method of depositing Pt, (4)light intensity and, (5) NaOH loading. The reaction rate does not depend on the method of Pt deposition, is first order in light intensity, is not dependent on the chemical state or the Pt loading above 2 wt % , depends on reduction of the titania, and is strongly dependent on the surface concentration of NaOH. From this work, we conclude that, when NaOH is present, the rate-limiting step in the reaction is the reaction of photoproduced holes with surface OH- ions. 1. Introduction
Photoassisted catalytic reactions are of great current interest1because of their potential for using solar photons as an energy source for driving reactions that have a significant activation energy and are either exothermic or endothermic. In previous reports from this laboratory we have characterized the activity of platinized titania, Pt/ Ti02, for the decomposition of liquid water2 and for the water-gas shift (WGS) reacti~n.~ Coating the catalyst with NaOH improves the performance of Pt/TiOz for both
reaction^.^ In further efforts to characterize such systems, we investigated several experimental parameters which could influence the rate of the water-gas shift reaction, CO + HzO = COz + H2 A summary of the results is presented (1) (a) Zamarev, K. I.; Parmon, V. N. Catal. Rev.-Sci. Eng. 1980,22, 261. (b) Childs, L. P.; Ollis, D. F. J. Catal. 1980, 66, 383. (2) Sato, S.; White J. M. Chem. Phys. Lett. 1980, 72, 83. (3) (a) &to, S.; White J. M . J. Am. Chen. SOC.1980, 102, 7206. (b) Sato, S.; White, J. M. J. CataZ. 1981, 69, 128. 0022-365418212088-3126$01.25/0
in this paper. We chose not to study water decomposition directly because of the complications introduced by the fast back-reaction on Pt-containing catalysts. In earlier work we have noted that the photoassisted decomposition of water molecules is an important part of the water-gas shift me~hanism.~ 2. Experimental Section 2.1. Preparation of Catalysts. Sieved TiOz (MCB, Anatase) with a particle size between 125 and 250 pm was reduced for 6 h in flowing H2 (30 mL/min) at either 700
or 875 "C. X-ray powder diffraction (XRD) indicated no measurable rutile in the starting material. After reduction at 700 "C, no measurable rutile was detected, but, after 875 "C reduction, a significant amount was found. Two methods were used to platinize the titania: photodecomposition and impregnation. In the former, both 2 and 10 wt % Pt/Ti02 samples were prepared from 1.0-g amounts of titania suspended, by bubbling Nz, in an acetic acid-sodium bicarbonate buffer solution (pH 4).4 The 0 1982 American Chemical Society
