MARKJ. HAZELRIGG, JR., AND PETERPOLITZER
1008 ment.’ Price, Passmore, and Roessler,ll using isoelectronic comparisons, interpolated bond energies for all the first-row hydrides and their singly charged ions; this work gave values sensibly identical with those of JANAFa (Table VII, column 1). This treatment, however, is drastically affected by a number of more recently determined bond energies. In particular, the newly revised values for D(CH-H) and D(CH2-H) of 101 and 108 k c a l / m 0 1 * ~also ~ ~ change ~ the corresponding bond dissociation energies of CH2+and CHa+, the ions that are isoelectronic with BH2 and BH3. These and other new dissociation energies no longer lead to graphs with nearly parallel lines as drawn by Price, et al. The new curves, however, suggest that D(BH2-H) is approximately equal to or greater than D(BH-H). The new interpolation is, therefore, in qualitative agreement with the Jordan and Longuet-Higgins treatment which suggests that D (BH2-H) is larger than D (BH-H) . An sp2 hybridization argument used to explain the successive bond dissociation energies of BF3 (D(BF2-F) = 161 andD(BF-F) = 122kcal/m01)~~
also suggests this ordering. To form BX2, an s electron of BX must be promoted to a p orbital forming an sp2 hybrid, but to form BXa, no promotional energy is needed; this difference results in a larger BX2-X bond energy. For BH2,sp2hybridization is indicated by the bent ground state.’ In view of these arguments D(BH-H)] = and since the sum [D(BH2-H) CA(B-3H) - D(B-H)] is reasonably well known (Table VII, column 13),approximate values for the two bond dissociation energies can be deduced.41
+
Acknowledgments. The authors wish to thank the men of the Chemistry Shop, the Materials Science Shop, and the Chemistry Electronics Shop and especially Mr. Edward Falkenberg, who made special efforts to keep our temperamental experimental set-up running. We would also like to acknowledge helpful discussion with Professor John L. Margrave. (41) NOTEADDEDIN PROOF. New results [E. S. Domalski and G. T. Armstrong, J . Res. Nat. Bur. Stand., 7 2 , 133 (1968)lfor AHr (Bd.z2aC) do not affect the present calculations significantly.
The Electronic Density Distributions in Carbon Monoxide, Carbonyl Sulfide, and Carbon Dioxide
by Mark J. Hazelrigg, Jr., and Peter Politzer Department of Chenidstry, Louisiana State University i n New Orleans, New Orleans, Louisiana 7 0 1 2 2 (Received July 8 , 1 9 6 8 )
Plots of electronic density distributions are presented for CO, SCO, and COz. These are found to vary gradually in the order CO, SCO, C o n ,as expected. The validity of the transferability of bond properties concept is examined for the C-0 bond in SCO and C02, and it is found to be only roughly valid in this case.
The carbon-oxygen bond represents one of the most important and widely found chemical linkages, one which occurs prominently in all branches of chemistry. It would be useful, therefore, to have a better understanding of the electronic structure of this bond and of the manner in which this structure (and hence the properties of the bond) is affected by the presence of various substituents on the carbon atom. At least a start toward the achievement of this kind of understanding is now possible, through the availability of good wave functions for molecules containing the carbon-oxygen bond. The present work has involved the study of three such molecules: carbon monoxide, which has a pure C-0 bond unaffected by the presence of any other atom; carbon dioxide, in which the effect of a second oxygen atom can be seen; and carbonyl sulfide, in which this second oxygen has been The Jouinal of Physical Chemistry
replaced by a sulfur atom, so that the relative effects of oxygen and sulfur atom substituents upon the C-0 bond can be examined-l The molecular wave functions used in this work were the self-consistent-field functions of McLean and Yoshimine.2 They are believed to be close to the Hartree-Fock limit, which means that they should give ( 1 ) Extended-basis-set self-consistent-fleld wave functions, believed
to be good approximations to Hartree-Bock functions, have been calculated for carbon monoxide by R. K. Nesbet, J . Chem. Phys.. 40, 3619 (1964). and W. M. Huo, ibdd., 43, 624 (1965). In both cases, the functions were analyzed in considerable detail, in terms of the expectation values of various molecular properties. An interpretative study of the electrostatic forces within the molecule has also been carried out by P. Politzer, J . Phys. Chem., 69, 2132 (1965). ( 2 ) A. D. McLean and M. Yoshimine, “Tables of Linear Molecule Wave Functions,” International Business Machines Corp., San Jose, Calif., 1967.
ELECTROSIC DENSITYDISTRIBUTIONS IN CO, SCO,
AND
1009
COz
good results, of first-order accuracy, for one-electron properties, such as the electronic density distributions.* For each molecule, the total electronic density and the density difference function were calculated. The tottal density a t any point r is given by
---. ’.
p4
Ni$i*(r)$i(r)
p(r) = 2
where N , is the number of electrons in molecular orbital $i. The density difference function, originally introduced by Roux and coworkers,6*6is defined as A d r ) = P(r)
-
c PAr)
0
C
Figure 4. Density difference function for carbon dioxide. The contours come a t intervals of 0.04, starting from the 0.0 lines; dotted lines correspond to negative values.
j
The second term represents the sum of the electronic densities of the atoms which constitute the molecule, these being placed at the same positions as they occupy in the molecule but assumed t o have undergone no interactions with each other and to have remained undistorted, as in the free state, The density diffelence function is interpreted as indicating the overall rearrangement of charge density which occurs when the atoms come together to form the molecule.
c
S
C
0
Figure 5. Total electronic density distribution in carbonyl sulfide. The contours correspond to the values 10.0, 1.0,0.7,0.4, and 0.15, moving outward from each nucleus.
0
Figure 1. Total electronic density distribution in carbon monoxide. The contours correspond to the values 10.0, 1.0, 0.7, and 0.4, moving outward from each nucleus. Figure 6. Density difference function for carbonyl sulfide. The contours come at intervals of 0.04, starting from the 0.0 lines; dotted lines correspond to negative values.
/
0.0
C
0
Figure 2. Density difference function for carbon monoxide. The contours come at intervals of 0.04, starting from the 0.0 lines; dotted lines correspond to negative values.
C
0
Figure 3. Total electronic density distribution in carbon dioxide. The contours correspond to the values 10.0, 1.0,0.7, and 0.4, moving outward from each nucleus.
The density distributions of the atoms were computed from the self-consistent-field atomic wave functions of Clementi,? which again are close to the Hartree-Fock limit and therefore consistent in accuracy with the molecular functions. In calculating the atomic densities, the p-electron distributions were averaged over all spatial directions. The total electronic density distributions and the density difference functions are presented in Figures 1-6. These diagrams show the distribution of the electrons in each of these molecules and the manner in which this distribution differs from that of the free atoms. A certain amount of caution is necessary in interpreting these diagrams. For example, an initial (3) L. Brillouin, Actualites Sci. I n d . , No. 71 (1933);No. 159 (1934). (4) M. Cohen and A. Dalgarno, Proc. Phys. SOC. (London), 7 7 , 748 (1961). (5) M. Roux, 9. Besnainou, and R. Daudel, J . Chfm. Phys., 5 3 , 218, 939 (1956). (6) M.Roux, ibdd., 55, 754 (1958). (7) E. Clernenti, “Tables of Atomic Wave Functions.” International Business Machines Gorp., San Jose, Calif., 1965. Volume 79,Number 4 April 1989
1010 examination of Figure 1 might suggest that carbon monoxide is made up of a nearly unperturbed carbon atom and a strongly polarized oxygen atom. The density difference plot (Figure 2) shows, however, that the carbon does in fact undergo much rearrangement; there is considerable movement of charge from the regions above and below the nucleus (that is, perpendicular to the bond) to positions along the molecular axis. It turns out that the symmetrical total density contours around the carbon nucleus in Figure 1 are essentially identical with those of the 1s electrons in a free carbon atom; the valence electrons have, for the most part, shifted into the regions to the left or right of the nucleus. Thus the unsymmetrical total density contours around the oxygen nucleus in Figure 1 probably include sizable contributions from the valence electrons of the carbon. The density difference function for carbon monoxide brings out clearly the important features of the molecule: the large buildup of electronic density in the internuclear region, and the localized concentrations of charge near each nucleus (the “lone pairs”). It is in these features that the characteristic properties of carbon monoxide originate-its very strong bond, which has a higher dissociation energy than that in any other diatomic molecule, and its ability to act as an electronpair donor, which involves a sharing of the carbon lone pair (the highest-energy electrons in the molecule) with some acceptor, In examining the electronic structures of carbon dioxide and carbonyl sulfide, it is helpful to view these in terms of the series CO-SCO-C02, which presumably reflects increasing perturbation of the pure carbon-oxygen bond of carbon monoxide. Chemical intuition suggests that a sulfur atom should have a lesser perturbing effect upon the original carbon-oxygen entity than an oxygen, so that the electronic structural change should be less in going from CO to SCO than in going from CO to COz. These expectations are confirmed by the electronic density diagrams, particularly by the density difference plots (Figures 4 and 6 ) . The addition of a sulfur atom has a significant effect upon the charge distribution around the oxygen nucleus of carbon monoxide; there is now a region of negative Ap to the left of the oxygen, instead of the charge buildup which was there previously, and the oxygen lone pair has been very distinctly reduced. In carbon dioxide these trends are carried further; the region of negative Ap has grown, while the lone pair has diminished yet further. I n both of these latter species, the concentration of e1ect;onic density along the C-0 bond is much less than it is in carbon monoxide, which is consistent with experimental data (to be cited) showing the strength of this bond to be considerably less in SCO and COZ than in CO. It is interesting and useful to compare the carbon-oxygen bond in carbonyl sulfide and in carbon dioxide, since such a comparison is very relevant to The Journal of Physical Chemistry
MARKJ. HAZELRIGG, JR.,AND PETERPOLITZER the important question of the transferability of bond properties. The approximation is commonly made that a given type of bond (that is, single, double, or triple) between some two particular atoms will have nearly the same properties in a variety of different molecules in which it is found. Thus there are tables of bond energies, bond moments, and bond lengths, which give supposedly good approximatione to the actual values of these properties in the various molecules in which the given bond occurs. A comparison of the charge distribution in the C-0 bond of SCO and COZ,two different but basically very similar molecules, provides an opportunity to examine the validity of the transferability of bond properties concept, a t least for one particular bond, in a fundamental manner, in terms of the electronic structure of the bond. Qualitatively, the C-0 bonds in COz and SCO are certainly very similar, as can be seen from Figures 4 and 6. There are differences in detail, however, which seem to be fairly significant. The decrease in electronic density to the left of the oxygen nucleus is considerably greater in GOz, while the oxygen lone pair is greatly reduced. It is difficult to estimate the effects of such variatioq8 but it would seem that they are bound to have some influence upon the bond properties, and that these will be only roughly transferable from one molecule to the other. One such property of the C-0 bond in COz and SCO for which an approximate quantitative comparison can be made is the bond energy. The energy required for the process COz --+ C 0 0 is 388 kcal/m01,~which means that a value of 194 kcal/mol can be taken as the strength of each C-0 bond. To break up SCO, SCO-tS C 0, the energy required is 332 kcal/mol,g but here it is not clear how to divide this between the S-C and C-0 bonds. It is possible, however, to make an estimate of these two separate bond energies, in the following manner. For the process CS2 3 C S S, the energy requirement is 256 kcal/mol,10 indicating an energy of 128 kcal/mol for each C-S bond, Thus, if the C-0 and C-S bonds in SCO were the same as in COz and CSZ, the total bond energy would be 128 194 = 322 kcal/mol-which is 10 kcal/mol less than is actually observed. It has already been pointed out, however, that in terms of electronic structure, the C-0 bond in SCO seems to occupy an intermediate position between those in CO and COZ. This suggests that its bond energy should be greater than that of the corresponding bond in C02. By a similar sort of reasoning, the C-S bond would be ex-
+ +
+ +
+ +
+
(8) In fact, they may partially cancel each other as far as affecting the strength of the 0-0 bond is concerned, since the presence of a lone pair, as well as the absence of electrons in the internuclear region, can weaken a bond (see, for example, Politzer, ref 1). (9) Cited in &I. Yoshimine and A. D. McLean, Intern. J . Quantum Chem., S y m p . No. 1 , 313 (1967). (10) T. L. Cottrell, “The Strengths of Chemical Bonds,” 2nd ed, Butterworth and Co. Ltd., London, 1958.
PRIMARY PROCESSES IN THE
101 1.
ACETONEPHOTOCHEMICAL SYSTEM
pected to be weaker in SCO than in CS2, since it would presumably be affected more by a neighboring oxygen than by a sulfur atom. These inferences are supported by the facts that the C-0 bond length is slightly less in SCO than in COz, 1.157 A compared to 1.162 A, while the C-S distance is greater in SCO than in CS2, 1.560 vs. 1.55 A.loJ1 On the basis of these arguments, the value 128 kcal/mol would be an upper bound to the energy of the C-S bond in SCO, and the C-0 bond would therefore have a lower bound of 204 kcal/mol. The actual value for the C-S bond would presumably be somewhat less than 128 kcal/mol, and that for the C-0 correspondingly more than 204 kcal/mol. Thus it would appear that the carbon-oxygen bond in SCO will be stronger than that in C 0 2 by perhaps 15-20 kcal/mol, which is consistent with the conclusion, based on a comparison of electronic structures, that the
properties of the bond in the two cases will be only approximately similar.12 A final point of interest is brought out by the density difference diagram for carbonyl sulfide. Rather surprisingly, Figure 6 shows no localized buildup of charge on the outer side of the sulfur nucleus. The sulfur does not appear to have a lone pair, in contrast to the oxygens in the three molecules studied. The authors are grateful to the Kayser-Roth Foundation for partial support of this work. They also appreciate financial assistance from the L.S.U.N.O. Computer Research Center (NSF Grant NO. GP-2964). Acknowledgments.
(11) Y. Morino and 0. Matsumura, Bull. Chem. SOC. Jap., 40, 1095 (1967). (12) The dissociation energy of the 0-0 bond in carbon monoxide is 256 ltcal/mol (ref 1 0 ) ; as pointed out earlier, it is considerably stronger in C O than in either SCO or COZ.
Primary Processes in the Acetone Photochemical System by H. Edward O’Neall Department of Chemistry, S a n Dieyn Stale College, S a n Diego, California
981 15
and Carl W. Larson Department of Chemistry, University of Washington, Seattle, Washington
(Received August 14, 1068)
-1revised mechanism which quantitatively correlates the data for the principal emission (phosphorescence) and the dissociation primary processes in the acetone photochemical system is presented. Two decomposition processes are proposed, a spontaneous decomposition from upper vibrational levels of hot triplets formed isoergotically after light absorption, and a decomposition of thermalized triplets which is a unimolecular pressure-dependent process. Quite consistent high- and low-pressure Arrhenius parameters for the thermal decomposition are determined from several data sources and place the critical barrier to triplet decomposition at about E , 3r! 10 1 kcal/mol. When treated in accordance with the proposed mechanism, a quantitative correlation of the emission and the decoinposition data in terms of their temperature, pressure, and wavelength dependencies is demonstrated. The zero-point level of the acetone triplet is placed at about 80 kcal/mol above the acetone ground state.
*
Introduction I n a prior communication, we reported the results of the effect of hydrogen bromide on the photolysis of acetone using light in the 3150-A region.2 Decomposition quantum yields (+d) were shown to be strongly quenched by hydrogen bromide, and from studies of 4 d as a function of temperature and hydrogen bromide pressure it was concluded that two kinds of primary decomposition processes were operative. The first involved spontaneousdecomposition from vibrationally excited tripletstate molecules formed isoergotically after absorption;
the decomposition was essentially unaffected by hydrogen bromide. The second involved a pressure-dependent decomposition of triplet-state molecules in thermal equilibrium with their environment; this process could be strongly quenched by hydrogen bromide. The qualitative and quantitative conclusions of the former study with regard to the primary processes in acetone are summarized in the simplified reaction coordinate diagram of Figure 1 and in Mechanism A. (1) Author to whom reprint requests should be sent. (2) C. W. Larson and H. E. O’Neal, J. Phys. Chem., 70, 2476 (1966). Volume 79,Number 4 April 1969
