648 least-squares fitted straight lines for each of the solutes. The correlation coefficients indicate a fairly good linear relationship between In DABand 1/ T . Examination of the AE values shows that, for the straight chain phenones, the “activation” energy decreases as the chain length increases. This can conceivably yield the contribution of a CH2 group to the “activation” energy. Figure 7 shows a plot of AE vs. the carbon number of the alkane side chain. The general features of Figure 7 are very similar to those shown in Figure 5, and the discussion made regarding the latter figure might hold true here. To the advocate of the rate approach, the data in Table VI1 and Figure 7 indicate that on the average, each CH2 group contributes initially about 7 3 cal to the “activation” energy, and that the contribution decreases ~~ a linear relaas N increases. Ertl and D ~ l l i e nreported tionship between “activation” energy and the log of the carbon number in the case of self-diffusion of some liquids, provided the carbon number is large enough. Such was not the case in the present study. The similarities between Figures 5 and 7 are noteworthy. Although at this point we cannot offer any explanations, we feel that the resemblance is more than a coincidence. At this point, additional data are needed, especially at low temperatures where the fluidity approach should deviate from the picture given here. In addition, to take full advantage of the more rigorous hard sphere theories, data at a given temperature but at varying pressures should be gathered. This will help in adjusting the model for large nonspherical molecules diffusing in mixtures.
References and Notes (1) A. Einstein, “Investigation on the Theory of the Brownian Movement”, Dover Publication, New York. N.Y., 1956.
(2) S. Glasstone. K. J. Laidler. and H. E. Eyring, “The Theory of Rate Processes”, McGraw-Hill, New York, N.Y., 1941. (3) S. A. Rice and J. G. Kirkwood, J. Chem. Phys., 31,901 (1954). (4) R. K. Ghai, H. Ertl, and F. A. L. Dullien, AlChf J. 19, 881 (1973): 20, 1 (1974). ( 5 ) A. J. Batschinski, Z. Phys. Chem. (Leipzig), 84, 643 (1913). (6) J. H. Hildebrand, Science, 174, 490 (1971). (7) J. H. Hildebrand and R. H. Lamoreaux, Proc. Nat. Acad. Sci. U.S.A., 71, 3321 (1974). (8) H. Ertl and F. A. L. Dullien. J. Phys. Chem., 77, 3007 (1973). (9) E. J. Alder, W. E. Alley, and J. H. Dymond, J. Chem. Phys., 61, 1415 (1974). (IO) D. Chandler, J. Chem. Phys., 62, 1358 (1975). (11) J. H. Dymond, J. Chem. Phys., 60, 969 (1974). (12) J. DeZwaan and J. Jonas, J. Chem. Phys.. 62,4036 (1975). (13) R. B. Bird, W. E. Stewart, and E. N. Lightfoot. “Transport Phenomena”, Wiley, New York, N.Y., 1960. (14) G. I. Taylor, Proc. R. SOC.London, Ser. A, 219, 186 (1953). (15) G. I. Taylor, Proc. R. SOC.London, Ser. A, 225, 473 (1954). (16) A. C. Ouano, lnd. Eng. Chem. Fundam., 11, 268 (1972). (17) K. C. Pratt and W. A. Wakeham, Proc. R. SOC. London, Ser. A, 336, 393 (1974). (18) E. Grushka and E. J. Kikta, Jr., J. Phys. Chem.. 76, 2297 (1974). (19) H. Komiyama and J. M. Smith, J. Chem. Eng. Data, 19, 384 (1974). (20) P. F. Jhaveri, R. N. Trivedi, and K. Vasudera, Diffus. Solutes Solutlon Fiber Syst., Proc. Symp. (1973); Chem. Abstr., 61, 68883 (1974). (21) A. C. Ouano and J. A. Carothers, J. Phys. Chem., submitted for publication. (22) B. J. Alder and J. H. Hiidebrand, lnd. Eng. Chem., Fundam., 12, 387 (1973). (23) H. T. Cullinan. Jr., and G. Kosanovich, AlChf J., 21, 195 (1975). (24) J. C. Shieh and P. A. Lyons, J. Phys. Chem., 73, 3258 (1969). ’ (25) S. Nir and W. A. Stein, J. Chem. Phys., 55, 1598 (1971). (26) H. Y. Lo, J. Chem. Eng. Data, 19, 236 (1974). (27) S. A. Sanni, C. J. D. Fell, and P. Hutchison, J. Chem. fng. Data, 16, 424 (1971). (28) W. F. Calus and M. T. Tyn. J. Chem. Eng. Data, 18, 377 (1973). (29) L. R. Wilke and P. Chang, AlChf J., 1, 264 (1955). (30) A. Couper and R. F. T. Stepto, Trans. Faraday. Soc.. 65, 2486 (1969). (31) R. D. Burkhart and J. C. Merrill, J. Chem. Phys., 46, 4985 (1967). (32) D. V. S. Jain and K. K. Tewari, Chem. Phys. Lett., 10, 487 (1971). (33) J. G. Kirkwood and J. Riseman, J. Chem. Phys., 16, 1565 (1948). (34) C. J. Vadovic and C. P. Colver, AlChf J., 19, 546 (1973). (35) A. L. Van Geet and A. W. Adamson, J. Phys. Chem., 68,238 (1964). (36) H. Ertl and F. A. L. Dullien, AlChEJ., 19, 1215 (1973).
All-Electron Nonempirical Calculations of Potential Surfaces. 111. Dissociation of Ketene into CH2 and CO Phil Pendergast and William H. Fink* Contributionfrom the Department of Chemistry, University of California, Davis, California 9561 6. Received February 13, 1975
Abstract: Ab initio calculations on the lower lying states of ketene have been performed using excited-state S C F and C1 methods. The ground-state and first excited-state surfaces were searched so as to nearly find the optimum theoretical molecular geometry. Dissociations along both linear and bent paths departing from these geometries were then examined. The excited-state assignments of ketene and its controversial photochemistry are discussed in light of the calculated molecular orbital correlation diagrams, the S C F energies, the configuration interaction energies, and the weights of the configurations.
A qualitative and semiquantitative understanding of photochemical processes should be possible by quantum chemical calculations of the potential-energy surfaces involved in these processes. The present work is a state of the art application of quantum chemical methods to the primary photochemical decomposition reactions of ketene (H2C=C=O). While the reliability of SCF methods of calculation for closed-shell, ground-state molecules in the vicinity of the equilibrium internuclear geometry is reasonably well understood, the situation is less clear for open-shell, excited-state molecules or for geometries far from the ground-state equi*Author to whom correspondence should be addressed
Journal of the American Chemical Society
librium. In certain situations, the inadequacy of the valence-shell atomic orbitals to describe low-lying Rydberg levels has become apparent;’ in other situations, the states are simply not adequately described by a single-determinant wave function;2 this latter difficulty often becomes particularly acute at asymptotic values of intermolecular distances where the imposition of a particular occupation precludes the S C F wave function from dissociating to the correct molecular or atomic fragments. The present work includes both an extended basis set and limited configuration interaction calculation in order to be reasonably sure of avoiding these possible deficiencies of a valence-shell SCF calculation. There remains considerable controversy over
/ 98:3 / February 4, 1976
649 Table 1. Experimental Values of Vertical Excitation Energies0 h,,b
370 323 213 170 155
Excitation energyc 3.35e 3.84 5.82 7.295 8.00f
Table 11. Calculated Values of Vertical Excitation Energies0
Assignmentd
Excited configuration
SCFb
Cib
3A,(3Xu3 and 3B,(3Cu+) 'Az('~u3
3A, 'A*
2.96 3.16 7.95 8.15
4.00 4.27 9.42 9.71 12.00
'Bz('Au) 'Bz('Xu+)
3B1 'B,
'B2('%)
Reference 7 except as noted. b Nanometers. CElectron volts. dThe term symbols in parentheses refer to the states of linear CO, with which these states would have correlated. e Reference 5 . f Reference 9. 0
the photochemistry of ketene both with respect to the assignment of its s p e c t r ~ m and ~ - ~with respect to the photolysis.Io An attempt to contribute to the resolution of these controversies and to contribute to the development and testing of quantum chemical methods motivated the calculations reported here. Techniques The calculations were carried out within the framework of performing a limited configuration interaction in an expansion set composed of the molecular orbitals obtained from an SCF calculation of the lowest lying state of a given irreducible representation. The basis set employed was the Gaussian lobe basis."-12 This was augmented by a n approximate oxygen 3s orbital.] The closed-shell SCF calculations were performed in the conventional Hartree-Fock-RoothaanI3 manner as in previous work on formaldehyde photochemical reaction surfaces.2 However, the open-shell SCF calculations were treated differently from the earlier work by employing a variant of the orthogonally constrained method of SegalI4 which had been originally programmed by J. L. Whitten and J. A. Horsley. The routine was revised by the present authors to increase its applicability and to adapt it to the Burroughs B6700 computer. All SCF results reported have been checked to verify that a n inadvertent local minimum in the atomic orbital function space has been avoided. This checking required some care in the regions of the potential surface where changes in electronic configuration were occurring, but did not constitute a major difficulty in the work. Searches for the minimum-energy geometry were carried out on both the ground-state surface and the first excited state. The Rcc and Rco internuclear distances and the OCC angle were systematically varied for both states. The configuration interaction calculations were performed using two separate programs. The four-index transformation program has been reported e l s e ~ h e r e .The '~ output integral list from this program was then interfaced with the configuration interaction program used in the previous work.2 All changes required in this latter program were checked by verifying exact agreement (to within the numerical precision of the B6700 48-bit word) with results obtained from the earlier version. While a complete examination of the potential surface for all degrees of freedom would be desirable, compromises in the interest of economy of both human and machine costs must be made. It was decided to examine two different least motion dissociation paths-a linear C2L.dissociation departing from the lowest energy geometry of the calculated ground-state SCF point and a bent C, dissociation departing from the lowest energy geometry of the calculated first excited state point. Molecular Energies Although it is difficult to establish useful estimates of error limits on calculated energy values, some feeling for the reliability of the generated surfaces may be obtained by comparing calculated quantities with their experimentally
'AI
-
Electron volts. b Results obtained at ground state theoretically optimized geometry. 0
determined equivalents. Further comparisons with other calculations permit a n assessment of the relative reliability of the present work among the hierarchy of available approaches. The available experimental data with which comparison is possible a r e excitation energies of ketene and methylene and thermochemical differences between the heats of formation of ketene and of methylene and carbon monoxide. Table I lists the experimental values of apparent FranckCondon maxima as reported by Rabalais et aL7 along with the tentative assignments made by them to the upper electronic state of these bands. It must be remarked that the maximum reported by them as observed by Dixon and Kirby5 a t 370 nm is regarded as a continuation of the band peaking a t 323 nm by Laufer and Kellers because of the similarities of the vibrational spacings and the apparent smooth dependence of the extinction coefficient on wave length throughout this region. These latter authors deferred assignment of the bands until reliable, detailed molecular orbital calculations were available. The calculated vertical excitation energies obtained with the S C F and C I wave functions are reported in Table I1 along with the nominal or dominant electronic configuration of the calculated state. Ignoring the assignments for the moment, there is reasonable agreement between the experimental and the calculated excitation energy patterns. There a r e two states with excitation energies around 3-4 eV above the ground state and then a n appreciable energy gap (experimentally about 2 eV, theoretically about 5 eV) before the appearance of a cluster of several states. There is essential agreement in the assignment of the lower energy band (bands) to the transition associated with t h e 1.3A2 states of ketene. The assignments of Table I' were based upon correlations with the lower excited states of C02 and upon extended Hiickel calculations of C 0 2 , H 2 C C 0 , and H2CNN. Unfortunately Table I of ref 7 upon which the correlations were based, although correct for the correlation of CO2 from D,h to C2(.by bending the OCO angle (one of the C2 axes perpendicular to the C, axis of D,h becomes the principal C2 axis of C2u), does not apply for ketene and diazomethane (the C, axis of D m h becomes the principal C2 axis of C2,). The important difference in correlation which applies in this latter case is (a,,g bl b2) not ((a, a1 + bl), (7rg a2 b2)J. Consequently the designations of the molecular orbitals and electronic states used for ketene and diazomethane in ref 7 are not the conventional Schoenflies notation and do not correspond with the present results and notation. For the important states of usual nearuv photolysis of ketene then the calculated excitation energies are in reasonable semiquantitative (4 1 eV) agreement with the experimental spectrum. Although no careful optimization of methylene and carbon monoxide geometries was attempted, the asymptotic values of the Calculated potential surfaces may be compared with energies of carbon monoxide and methylene. The results obtained from the bent dissociation path a t Rcc = 10.0 a r e compared with the experimental quantities in Table 111. AEo refers t o the reaction +
Pendergast, Fink
-+
+
-
+
/ Dissociation of Ketene into CH2 and CO
650 Table IV. Geometric Variation of SCF Energies
Table Ill. Experimental and Calculated Energies0 Related to Methylene
A&? 3B, -'B, 'A,-'B. Q
-E
Exptl
CI
8lb
