J. Phys. Chem. 1988, 92, 959-962 clusion. On the other hand, application of Creighton’sl* selection rules to pyridazine suggests that the A2 modes should be the least enhanced ones for edge on adsorption. Actually, our sol spectrum does not show bands belonging to this species while enhancement occurs for normal modes which classify into the remaining representations and present nonvanishing intensity in the 1 M aqueous solution.
Conclusions Raman spectra of 1,4-, and 1,3- and 1,2-diazine adsorbed on Ag sols show characteristic scattering enhancement very similar to that observed in corresponding experiments on silver electrode. Differences between the results obtained with the two techniques were found only for pyrazine and are probably due to adsorption of reaction products. Chemisorption plays a role in the adsorption of diazines since evidence of Ag-N bond formation was found
959
in the low-frequency region of the SER spectra of all three diazines. The assignment of broad bands in the 200-230-cm-’ region to Ag-N stretching, well distinguished from Ag-Cl modes at about the same frequency, clearly supports an edge on adsorption on the Ag substrate in agreement with observed relative enhancement ratios which correspond to Creighton’sl* surface selection rules. Two Ag-N bands are observed for pyridazine and this implies an adsorption through both nitrogen atoms with a relevant contribution of chemisorption to the total enhancement. This is consistent with an enhancement for the latter molecule 2 orders of magnitude larger than that observed for the other two diazines.
Acknowledgment. This work was supported by the Italian Consiglio Nazionale delle Ricerche. Registry No. Ag, 7440-22-4; pyrazine, 290-37-9; pyrimidine, 28995-2; pyridazine, 289-80-5.
Geometrical Structure and Vibrational Frequencies for the Oxygen Analogue of Hexasulfur Charles P. Biahous I11 and Henry F. Schaefer III* Department of Chemistry, University of California, Berkeley, California 94720 (Received: June 5, 1987)
Self-consistent field (SCF)methods with minimum (STO-3G), double { (DZ), and double {plus polarization (DZP) basis sets predict the O6ring to assume chair, twist, and boat conformationsanalogous to similar forms for cyclohexane. All predicted vibrational frequencies for the chair and twist forms are real. Six symmetrically equivalent oxygen atoms are predicted to comprise the lowest energy chair form, with 0-0 bond distances of 1.364 A and bond angles of 104.7O at the DZP SCF level of theory. The boat form is not found to be an energy minimum but rather exhibits one imaginary vibrational frequency which when followed tends toward assumption of the twist form. Energy differences at the DZP SCF level are computed to be 15.9 kcal between the chair and twist forms and 17.5 kcal between the chair and boat. We interpret these results by analogy with cyclohexane and assign the larger energetic discrepanciesto shorter bond distances and inherently greater eclipsing effects for adjacent lone electron pairs than those attributed to bonding electron pairs. Homodesmotic and hyperhomodesmotic reactions devised to predict the decomposition exothermicity of the ring give rather different results, namely, 130 (homodesmotic) and -75 (hyperhomodesmotic) for the heat for formation of 06.
-
Introduction
D3d symmetry and exhibits the electron configuration
The idea that oxygen rings may in principle be stable molecules takes root in the observation that sulfur, oxygen’s lower neighbor on the periodic table, exists naturally in ringed systems.’ The analogy cannot be too rigidly extended, however, because of the vastly differing character of oxygen-oxygen and sulfur-sulfur bonds. For example, a 2n-membered sulfur ring with a standard sulfur-sulfur bond strength near 54 kcalZlies at an energy level comparable to that of n diatomic sulfur molecules (bond strength 100 kcal/mo13), whereas the relatively weak nature of oxygenoxygen single bonds (35 kcalZ in peroxides) implies that a 2nmembered oxygen ring would lie in energy far above n diatomic oxygen molecules (bond dissociation energy = 118 kca13). One infers, therefore, that oxygen rings, if sufficiently stable, are molecular systems wherein large quantities of energy might be effectively stored (crudely estimatedl8 to be 144 kcal in a sixmembered ring, or 48 kcal per O2molecule). The work described here is an attempt to locate theoretical energy minima which correspond to conformations of such ringed systems comprised of six oxygen atoms.
1afgle: 1e: 1af,2afg2e:2e:2af,3a:,
1a:,3e:3a:,3e:4e:4e:4a~~
which, in the lower CZhsymmetry employed in the present geometry optimizations, corresponds to l a i l a i l bi2ai1bi2bi3ai2aZ3bi4ai2bi4b~5a~3a~6ai3bi5bi4ai6b~ 5ai7bZ7al4bi8ai The next lowest in energy, the “twist” form, displays D2 symmetry and has the orbital occupation scheme
1b: 1a:1 bf 1b:2a:2b33a:2b:3b:4a:2b:4b$3b:3b:5a:5b$4b:6af5b: 6b:4b:7a:Sbf6b: A C, “boat” structure was optimized as well with the electron configuration: 1b: 1af 1bf2af 1a$2b$3a:3b:2bf2a$4af4b$3bf5af6af5b:4bf3a$5bf 6bf7a:8a:4af7b:
Theoretical Approach Conducting our geometry optimizations from a variety of starting points led us to focus our study on the three optimized conformations of greatest importance. The lowest energy of these, hereafter referred to as the “chair” conformation, optimizes to ‘Author to whom correspondence should be addressed.
0022-3654/88/2092-0959$01 SO/O
(1) (a) Schaefer, H. F.,to be published. (b) For background on cyclic sulfur structures see Meyer, B. Sulfur, Energy and Enuironment; Elsevier: Amsterdam, 1977. (2) Pine, S . H.; Hendrikson, J. B.;Cram, D. J.; Hammond, C. I. Organic Chemistry, 4th ed.; McGraw-Hill: New York, 1980; p 85. (3) Huber, K.; Herzberg, G. Consrants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979.
0 1988 American Chemical Society
Blahous and Schaefer
960 The Journal of Physical Chemistry, Vol. 92, No. 4, 1988
Figure 2. Figure 1.
Using the standard Pople minimum basis set" STO-3G, as well as Dunning's double { (DZ) and D Z p o l a r i ~ a t i o n(DZP) ~ ~ basis sets, the aforementioned conformations were optimized via S C F gradient t e c h n i q ~ e s . ~With , ~ the exception of the ground state structure, the optimizations were carried out with symmetry restrictions (respectively D2 and C20)equal to those of the actual conformation. Although the chair form assumed a D3dstructure, it was in fact optimized with only a C2,constraint. Subsequent to initial optimization, relaxation of these symmetry constraints and reoptimization confirmed the reported symmetry characteristics of these three species. Analytic S C F second-derivative techniques? were employed to determine the harmonic vibrational frequencies reported here. As these results were produced by single-configuration S C F theory, we found it appropriate to introduce isodesmic, homodesmotic, and hyperhomodesmotic reactions"" to compensate for errors in correlation energy that would arise from directly comparing the Hartree-Fock energies of O6 and O2and thus better estimate the heat of formation of the chair form. The aforementioned theoretical methods were applied with identical basis sets to H 2 0 , H 2 0 2 , H203, and HzO4 for this purpose. The structures of H2O3 and HzO4 were fully optimized for the for HzO4. We will 'open-chain" isomers, e.g., H-0-0-0-0-H not attempt here to detail the theory and procedures associated with these methods other than to say that the strain inherent in the lowest energy conformation of O6was estimated by comparison of the Hartree-Fock energies calculated for the participants in the reactions
+
isodesmic
O6 + 6 H 2 0 homodesmotic 0 6
+ 6H2O2
O6
+ 6H2O3
-
6H202
(1)
6H2O3
(2)
6H204
(3)
hyperhomodesmotic +
The evaluation of the heat of formation of O6 from the above homodesmotic and hyperhomodesmotic reaction heats is not s' .aightforward, since the heats of formation of H 2 0 3and H204 2 not known from e x eriment. Benson estimated AHf(H203) = -13.5 kcal and AHf, = 5.5 kcal in the 1968 edition of his well-known book.I2 'ore recently, Benson has estimated the heat of formation of H: to be -15.7 kcal.I3 A second estimate may be from Jackels ai Phillips14 ab initio prediction that De(4) (a) Hehre, W. T.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51,2657. (b) Dunning, T. H., Jr.; Hay, P. J. Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York, 1977; Vol. 3, pp 1-27. The d function orbital exponent used in this research was a d ( 0 )= 0.8. ( 5 ) Pulay, P. Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York, 1977; Vol. 4, pp 53-183. (6) Dupuis, M.; King, H. F. J . Chem. Phys. 1978, 68, 3998. (7) Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1982, 77, 5647. (8) Haddon, R. C. Pure Appl. Chem. 1982, 54, 1129. (9) George,P.; Trachtman, M.; Brock, C. W.; Brett, A. M. J . Chem. SOC., Perkin Trans. 2 1976, 1222. (10) George, P.; Trachtman, M.; Brock, C. W.; Brett, A. M. Terrahedron 1976, 32, 317. (11) Hess, B. A.; Schaad, L. J. J . Am. Chem. SOC.1983, 105, 7500. (12) Benson, S. W. Thermochemical Kinetics; Wiley: New York, 1968. (13) Nangia, P. S.; Benson, S. W. J. Phys. Chem. 1979, 83, 1138.
Figure 3.
TABLE I: Summary of Self-consistent Field Theoretical Predictions for the 0,Ring (See Figures 1-3 for Definitions of Geometrical Parameters) chair E (hartrees) a (4 a (ded twist E a b a boat
E a
b a
STO-3G
DZ
DZP
-442.853 56 1.405 103.3
-448.495 98 1.427 104.8
-448.695 91 1.364 104.7
-442.833 46 1.417 1.393 105.O
-448.476 95 1.446 1.410 106.1
-448.670 58 1.386 1.344 106.1
-442.83070 1.396 1.436 105.9
-448.475 21 1.415 1.476 106.4
-448.668 07 1.350 1.421 106.4
(HO-OOH) = 26.4 kcal/mol. Combination with the 0 K heats of formation of OHISa(9.2 f 0.3 kcal) and HO2lSb(3.5 f 2.0 kcal) radicals yields AHf(O K) = -13.7 f 2.3 kcal for HZO3. In this work we use the value -14 kcal for the heat of formation of H 2 0 3and attach an uncertainty of about 5 kcal. For Hz04,the 1979 Benson estimate for the heat of formation is 1.1 kcal/mol. The best estimate of the heat of formation probably comes from the theoretical predictionI6of the dissociation energy De(HO2-O2H), namely, 11 kcal/mol. Combined with the experimental heat of formation of H 0 2 (3.5 f 2.0 kcal), one obtains a AHdO K) of -4.0 kcal. We estimate the true heat of formation of H204to be -4 f 5 kcal. The figure -4 is used hereafter in the present report. Note finally that the value of the heat of formation of H20z(0K) (for the homodesmotic reaction) used here is -31.0 kcal, taken from the JANAF tables.l5
Theoretical Predictions for Chair, Twist, and Boat Conformations The three conformations of O6are shown below in Figures 1, 2 , and 3 (chair, twist, and boat, respectively). The energies of these conformations and the parameters designated in the figures are tabulated in Table I. At the DZP level of theory, the twist and boat conformations lie considerably higher in energy than the chair, 15.9 and 17.5 kcal respectively (1 hartree = 627.5 kcal). This contrasts with experimental differences for other known six-membered rings such as cyclohexane, for which these chair-twist and chair-boat differences are 5.5 and 7.0.17 As is the case with cyclohexane, only the chair and twist forms represent energy minima, as indicated (14) Jackels, C. F.; Phillips, D. H. J . Chem. Phys. 1986, 84, 5013. (15) (a) Chase, M. W.; Davies, C. A,; Downey, .I. R.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd Ed.; American Institute of Physics: New York, 1986. (b) Benson, S. W. J. Phys. Chem. 1983, 87, 3479. (16) Fitzgerald, G.; Lee, T. J.; Schaefer, H. F.; Bartlett, R. J . Chem. Phys. 1985, 83, 6275. (17) Kemp, D. S.; Vellaccio, F. Organic Chemistry; Worth: New York, 1980; p 488
The Journal of Physical Chemistry, Vol. 92, No. 4, 1988 961
Oxygen Analogue of Hexasulfur TABLE II: Self-Consistent Field Vibrational Frequencies for Three Conformations of the 0, Ring
freq, cm-’
sym
TABLE III: Homodesmotic and Hyperhomodesmotic Reactions for O6
DZ
DZP
STO-3G
1026 1002 960 999 890 604 577 378 1063 1059 1040 986 980 944 818 614 589 435 380 127 1057 1056 1033 1028 928 914 84 1 610 587 473 404 llli
1142 1127 1097 1093 1016 714 656 450 1139 1183 1151 1118 1106 1053 927 693 676 518 449 156 1190 1190 1180 1123 1018 1013 960 700 657 565 495 136i
Homodesmotic
~
E(O6) E(H202) E(H203)
O6 strain (eq 2), kcal AHf(06)
DZ
-442.853 56 -448.495 98 -148.765 00 -150.756 71 -222.58051 -225.51460 24.8 32.2 126.8 134.2
DZP -448.695 91 -150.819 80 -225.60957 26.8 128.8
Hyperhomodesmotic E(H204) O6 strain (eq 3) AHf(06)
-296.392 20 10.4 70.4
I
H
-300.268 11 -300.396 07 15.7 14.5 75.7 74.5
H
Figure 4.
motic-based O6 heats of formation are significantly lower. It is not of inherent concern that our values for the strain energy vary with the choice of method, as the definition of strain changes as well with the type of reaction used. The two types of reactions should in principle, however, lead back to the same value of AHHf. While this discrepancy could theoretically arise from unreliable values for the experimental AHf of H203or H204,we expect that our single configuration results for this system may be inadequate for a reliable prediction of AHf for 06.This problem may be exacerbated by the unconventional bonding in HzOs, H204,and 06.Future studies with highly correlated wave functions are clearly in order.
by the harmonic vibrational frequencies tabulated in Table 11. Displacement of the atoms in the boat conformation along the vibrational mode of imaginary frequency tends toward assumption of the twist form. We will comment further on these structures under Discussion and note here only that, apart from the larger energy differences between conformations, these oxygen ring structures strongly resemble their cyclohexane analogues. As is the case with the carbon ring, all six positions in the chair conformation are symmetrically equivalent (the symmetry of this conformation is perhaps more easily appreciated if visualized as a Star of David rather than a chair). However, where cyclohexane maintains this universal bond length equivalence in its twist and boat forms,18 the central oxygen-oxygen bonds of these two oxygen ring structures are distorted. The 0-0 bond (at the D Z P level) lengthens from the 1.364-A value in the chair to 1.421 in the boat and is compressed to 1.344 in the twist structure. The opposite effect is observed in the four symmetrically equivalent bonds which attach the “end” oxygens, this bond shortening to 1.350 A in the boat and lengthening to 1.386 in the twist. The overall effect of these bond length distortions is to decrease the total nuclear repulsion energy in moving from the chair to the twist form and again in moving from the twist to the boat. As is sometimes the case with cyclic hydrocarbons,” the devised isodesmic reactions yielded unsatisfactory results for AHf, in fact indicating that our oxygen ring systems might in an energetic sense be aromatic. The results of our homodesmotic and hyperhomodesmotic reactions are shown in Table 111. These total energies are consistent with previous results reported and by Fitzgerald16 by Pople19 (in the cases of H202and H203) (for H204). While the predicted homodesmotic heats of formation are in the general area of our initial guesses made on the basis of standard oxygen-oxygen bond strengths, the hyperhomodes-
These results are most easily interpreted through comparison with explanations for the conformational preferences of cyclohexane. Molecular mechanics calculations18*20 have repeatedly attributed cyclohexane’s preference for the chair form to the increased torsional strain in moving to the twist and boat forms. In the cyclohexane boat, the hydrogens on the floor carbons are exactly eclipsed, as in Figure 4. Additional strain results from the proximity of the flagpolq hydrogens, although this is considered by molecular mechanics to have a smaller effect. In the cyclohexane chair, the hydrogens on adjacent carbons are optimally staggered and, in addition, strain in the bond lengths and bond angles is largely absent. This means that, apart from its very small van der Waals repulsion terms, cyclohexane is considered a virtually strainless system. Naively, 1 kcal of strain assessed for every pair of eclipsed hydrogens in the boat (from the 3.0 kcal/mol rotational barrier for ethane2’) would lead to the conclusion that is should be something near 8 kcal higher in energy than the chair form, which is within approximately 1 kcal of the experimental value. If we extend this principle to our oxygen systems, we expect that the strain introduced from eclipsing the lone pairs of adjacent oxygens in the boat form should similarly raise the energy higher than that of a chair. The large energy differences we have obtained for the two forms could result from the shorter bond lengths of the oxygen system relative to cyclohexane in combination with an inherently larger eclipsing effect for lone electron pairs over those bonded to hydrogen. The idea that this effect should be larger for lone pairs is not trivial to substantiate. The VSEPR model22supports the idea that
( 1 8) Allinger, N. L.;Burkert, U. Molecular Mechanics; American Chemical Society: Washington, DC, 1982. (19) Whiteside, R. A.; Frisch, M. J.; Pople, J. A. Carnegie-Mellon Quontum Chemistry Archive; Camegie-Mellon University: Pittsburgh, PA, 1983.
(20) Hendrickson, J. B. J. Am. Chem. SOC.1961,83, 4537. (21) Lister, D. G.; Macdonald, J. N.; Owen, N. L.Internal Rotation and Inversion; Academic: London, 1978; p 104. (22) Gillespie, R. J. Molecular Geometry; Van Nostrand Reinhold: Princeton, NJ, 1972.
Discussion
962
J . Phys. Chem. 1988, 92, 962-966
lone pairs be very mutually repulsive relative to bonding pairs, but here we have a question not of their absolute repulsion energies but rather the rate of change of these repulsion energies as a function of the degree of eclipsing. This rate of change and consequent effect on molecular geometry has been skillfully examined by Palke and KirtmanVz3 Experimentally, the introduction of oxygens into six-membered rings fails to give unamibiguous support for this idea. For example, Strauss and Pickettz4reported barriers to pseudorotation in trioxane which were actually smaller than those in cyclohexane. This reduction in rotation barriers for the bond pair-lone pair interactions of trioxane relative to the bond pair-bond pair interactions of cyclohexane is consistent with the heirarchy of rotational barriers for ethane, methylamine, and methanol (2.9, 1.9, and 1.1 kcal, respectivelyz5). The larger rotational barrier in cis-hydrogen peroxide (7.0 kcal/moIz6) supports our idea of interactions between Palke, W. E.; Kirtman, B. J . Am. Chem. SOC.1978, 100, 5717. Pickett, H. M.; Strauss, H. L. J . Am. Chem. SOC.1970, 92, 7281. Eliel, E. Conformational Analysis; American Chemical Society: New York, '1965. (26) Hunt, R. H.; Leacock, R. A,; Peters, C. W.; Hecht, K. T. J. Chem. Phys. 1965, 42, 1931.
lone pairs on adjacent oxygens being particularly problematic for rotation to an eclipsed conformation. (Note that this figure corresponds to the eclipsing of two sets of lone pairs. trans-Hydrogen peroxide rotates so as to eclipse two bond pair-lone pair sets and has a smaller 1.1-kcal rotation barrier.) In summary, our theoretical results, though produced in the absence of experimental data on the molecules in question, align relatively intuitively with expectations from analogies with known compounds (cyclohexane, trioxane) whose conformational preferences are well tabulated in the literature. This does not by itself validate our preliminary results produced by single-configuration S C F methods, but we are sufficiently encouraged by this to believe that ascent to higher levels of theory (configuration interaction and coupled cluster) will provide meaningful information regarding structural and energetic predictions for the six-membered oxygen ring. We are currently working on improving our precision in predicting this molecule's energy differences between conformations as well as its exothermicity upon decomposition.
Acknowledgment. This research was supported by the Air Force Office of Scientific Research under Grant AFOSR-87-0182. Registry No. 06,111557-60-9.
Chemical Information from Electron-Energy-Loss Near-Edge Structure. Core Hole Effects in the Beryllium and Boron K-Edges in Rhodizite R. Brydson; D. D. Vvedensky,*W. Engel,# H. Sauer,s B. G. Williams,L E. Zeitler,*g and J. M. Thomas*II Department of Physical Chemistry, University of Cambridge, Lensfeld Road, Cambridge CB2 1 EP, U.K.; The Blackett Laboratory, Imperial College, London SW7 2BZ, U.K.; Fritz-Haber-Institut der Max- Planck- Gesellschaft, Faradayweg 4-6, DlOOO Berlin 33 (Dahlem), Germany: International Centre for Insect Physiology and Ecology (ICIPE), P.O. Box 30772, Nairobi, Kenya; and Davy- Faraday Research Laboratory, The Royal Institution, 21 Albemarle Street, London W1X 4BS, U.K. (Received: June 9, 1987; In Final Form: October 28, 1987)
The prospects of being able to retrieve coordination numbers of light elements ( Z < 10) in solids by analyzing the fine structure of near-edge regions of electron-energy-loss peaks corresponding to excitations from core levels are examined with specific reference to boron and beryllium in the mineral rhodizite, the structure of which is already known. Proof that there are both Beo4and BOptetrahedra in this material is obtained from the correspondence of observed and calculated spectra. Successful modeling using real-space multiple scattering calculations is achieved only if core hole effects are included by use of excited absorbing atom potentials. Various approximations to these potentials are investigated, and we conclude that the best are the ( Z + 1 ) excited-state and ( Z + 2) ion approximations. The importance of core hole effects is discussed for elements of low atomic number; and a comparison is drawn with previous work on beryllium carbide, a new calculation being performed for this solid.
Introduction It has recently been re~ognizedl-~ that information of considerable chemical significance can be extracted from electron-energy-loss spectroscopy (EELS) of solids. Such spectral information is obtainable by using transmission electron microscopes that have attached to them an appropriate electron spectrometer. Chemical composition, oxidation states, and, under favorable circumstances, bond distances and the electronic structure of the solids4 can all be extracted from materials of microscopic dimension, provided they are not ultrasusceptible to electron-beam-induced damage. With the recent advent of so-called parallel d e t e ~ t i o ncoupled ,~ with good energy resolution (ca. 0.5 eV), it has been possible to 'University of Cambridge. 1Imperial College. 5 Fritz-Haber-Institut der Max-Planck-Gesellschaft. International Centre for Insect Physiology and Ecology. l1 The Royal Institution.
0022-3654/88/2092-0962$01.50/0
study, among other things, the electron-energy-loss near-edge structure (ELNES) of inner-shell electron excitations.6-8 Here we concentrate, for heuristic purposes, on the ELNES of the beryllium and boron K-edges in the mineral rhodizite, which has hitherto been the subject of detailed structural studies by X-ray (1) Thomas, J. M.; Williams, B. G.; Sparrow, T. G. Acc. Chem. Res. 1985, 18, 324. (2) Colliex, C. In Aduances in Optical and Electron Microscopy; Barer, R., Coslett, V. E., Eds.; Academic: London, 1984; Vol. 9. (3) Egerton, R. F. Electron Energy-Loss Spectroscopy in the Electron Microscope; Plenum: London, 1986. (4) Thomas, J. M.; Sparrow, T. G.; Uppal, M. K.; Williams, B. G. Philos. Trans. R . SOC.London, A 1986, 318, 259. ( 5 ) Shuman, H. Ultramicroscopy 1981, 6, 163. (6) Lindner, Th.; Sauer, H.; Engel, W.; Kambe, K. Phys. Rev. B Condens. Matter 1986, 33, 22. (7) Vvedensky, D. D.; Pendry, J. B. Phys. Reu. Lett. 1985, 54, 2725. (8) Vvedensky, D. D.; Pendry, J. B. Surf. Sci. 1985, 162, 903.
0 1988 American Chemical Society
