J . Phys. Chem. 1990, 94, 6996-7001
6996
Theoretical Structures of Aluminum-Boron Hydrides Gilbert J. Mains,* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078
Charles W. Bock, Department of Chemistry, Philadelphia College of Textiles & Sciences, Philadelphia, Pennsylvania I91 44, and American Research Institute, Marcus Hook, Pennsylvania I9061
Mendel Trachtman, Joe Finley, Kevin McNamara, Maryann Fisher, and Lori Wociki Department of Chemistry, Philadelphia College of Textiles & Sciences, Philadelphia, Pennsyluania I9144 (Received: February I , 1990; In Final Form: April 13, 1990)
The ab initio structures of AIBH,, n = 1 to 6, have been investigated at the HF/6-31G*//HF/6-31G* level. The effects of correlation using Mdler-Plesset perturbation theory at the MP4SDTQ//HF/6-3 IG* level have been included. For all the hydrides, the structures are determined primarily by the fact that B-H bonds are significantly stronger than AI-H bonds. I n the case of AIBH3, the lowest energy isomer is a Lewis adduct between an AI atom and BH3 molecule, suggesting the application of BH3 as an atom trap. For AIBH,, the lowest energy confomer is an ionic structure, AI+BH4-. The double H-bridged radical, H2AI(H2)BH,is more stable than the single H-bridge radical, H2AI(H)BH2,contrary to that found for the diboryl radical. Similarly, H2AI(H2)AIHis more stable than H2AI(H)AIH2. This reversal in isomer stability is discussed in terms of a Lewis acid/base interaction between XH2 radicals and XH3, where X = B, AI. The hexahydrides, dialane(6) and aluminoborane, AIBH,, have structures similar to that of diborane.
Introduction The chemistry of group IIIA elements presents another opportunity to compare the properties of elements of the first row in the periodic table with those in subsequent rows.] In some respects, the challenge is more interesting than for the group IVA elements; however, opportunities to compare theoretical predictions with experiment occur less frequently. The first indication of the unique and rich chemistry of group llIA elements was the discovery of the double H-bridged structure for diborane, which can be thought of as the Lewis adduct between the acidic region of BH,, the low-lying empty p orbital of boron, and the basic region of BH3, Le., the relatively "electron rich" B-H bonds. Similarly, this ansatz explains the formation of the B2H, radical as the Lewis adduct between BH2 and BH,. Thus, the preferred H2B(H)BH2 structure reflects the fact that the unpaired electron in the sp2 hybrid orbital of BH2 is more basic than the electron pair in the B-H of BH,. The ab initio prediction' of the ordering of the B2H5 isomers has been experimentally verified,, and the theoretical predictions have been extended for neutral boron hydrides4 as well as the cationic boron hydride^.^,^ This interpretation should make it possible to better understand the structure and stability of many other group lllA hydrides. In this regard mixed boron-aluminum hydrides are especially interesting since they should reflect the relative acidities of the empty p orbitals on these elements and the relative basicities of the B-H and AI-H bonds. We report here a study of mixed boranes and alanes, a logical extension of our recent studies of boron-silicon
Vax I 1/780 or Cray XMP/48 computers. The energy surfaces were explored by using the 6-31G*(6D)'IJ2 basis set. Electron correlation using Merller-Plesset perturbation theoryI3 at the MP2, MP3, MP4SDQ, and MP4SDTQ/6-3 lG*(6D)//HF/6-3IG*(6D)(frozen core) levels was included. Vibrational frequencies were obtained from analytical second derivative^'^ calculated at the HF/6-31G*//HF/6-3 1* level to assess the character of all stationary points. Restricted H F calculations were used for closed shell molecules and analogous U H F procedures were used for the higher multiplicity calculations. Although the spin contamination was usually small, values before and after spin annihilation are reported. The figures were prepared with a Macintosh microcomputer by typing the optimized GAUSSIANE~ output into Molecular Editor15 and then cutting and pasting the resultant structure into MacDrawI6 so that the atoms could be identified and electron spins labeled.
Results and Discussion AlBH. The energies and structures for the aluminum-boron monohydrides are given in Table I and shown in Figure 1. The
GAUSSIANM program
All molecular orbital calculations were performed with the developed by Pople and his colleaguesI0 on
structure that results in the formation of B-H and B-AI covalent bonds, Figure la, is over 40 kcal/mol more stable than the other isomers. Since the B-H bond energy is greater than the AI-H bond energy, this observation is not surprising, although the difference is somewhat larger than might be expected on the basis of simple bond strengths, ca. 10-20 kcal/mol. One possible explanation is a strong interaction between the empty p orbital on B and the electron lone pair on AI. The AI-B-H bond angle, 174.5', is only slightly less than that expected on the basis of linear sp hybrid orbitals and is probably a consequence of the interaction of the empty p orbital on AI with the H. The effect is much less
( I ) Scuseria, G . E.; Geertsen, J; Oddershed J. J . Chem. Phys. 1989, 90, 2338. (2) Trachtman. M.; Bock, C. W.; Niki, H.; Mains, G . J. Struct. Chem. 1990, 1, 171. (3) Ruscic, B.; Schwarz, M.; Berkowitz, J. J , Chem. Phys. 1989, 91,4183. (4) Curtiss, L. A.; Pople, J. A. J . Chem. Phys. 1989, 91, 4189. ( 5 ) Curtiss, L. A.; Pople, J. A. J . Chem. Phys. 1989, 90,4314. (6) Curtiss, L. A.; Pople, J. A. J . Chem. Phys. 1988, 89, 4875. (7) Bock, C. W.; Trachtman, M.; Mains, G.J. J . Phys. Chem. 1986, 90, 51. (8) Bock, C. W.; Trachtman, M.; Mains, G . J. J. Phys. Chem. 1988, 92, 294, (9) Bock, C. W.; Trachtman, M.; Mains, G.J. J . Phys. Chem. 1989, 93, 1745.
(10) GAUSSIAN86, Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, R.; Martin, R. L.; Stewart, J. J. P.; Rohlfing, C. M.;Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A., Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA; 1984. ( I I ) Hariharan, P. C.; Pople, J. A. Theoref. Chim. Acfa 1973, 28, 213. (12) Francl, M. M.; Pietoro, W. J.; Hehre, W. J.; Binkley, J. S.Gordon, M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654. (13) Maller, C.; Plesset, M. S. Phys. Reo. 1934, 46, 678. (14) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. In!. J. Quantum Chem., Quantum Chem. Symp. 1979, 13, 225. ( I 5) Wargo, R.; McFerren, D.; Smith, A., Drexel Univeristy, Philadelphia, PA, 1986. (16) Cutter, M. Apple Computer, Inc., Cupertino, CA, 1985.
Computational Methods
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The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 6997
Aluminum-Boron Hydrides TABLE I: Total Energies for Aluminum-Boron Monohydrides
level
state freq = Anal. rel. energy (kcal/mol)
AlBH -267.050 376 -267.05 1 467 -267.142 535 -267.163484 -267.169 387 -267.171 320 ?.A,! all 0.0
Figure
la
UHF/6-3 1G*//UHF/6-3 I G* UHF/6-3 1G**//UHF/6-3 1G*
UMP2/6-31G8*//UHF/6-3IG*
U MP3/6-3 1G **/ /UHF/6-3 1G* U MP4(SDQ)/6-3 1G* * / / U H F/6-3 1G* U MP4( SDTQ)/6-3 1G * *//UHF/6-3 1G *
AlHB .-266.975 448 -266.97641 8 -266.066 708 -267.092 508 -267.101 125 -267.102 073 2n
+
TABLE 11: Total Energies for Aluminum-Boron DihvdridesO level AIBH2 HF/6-31G*//HF6-3IG8
-267.665010
HF/6-31G8*//RHF6-31G* MP2/6-31G8*//RHF6-31G* MP3/6-3 1G * *//R H F6-3 1G * MP4(SDQ)'// R H F6-3 1G * M P4(SDTQ)'/ /RH F6-3 1G*
-267.666901 -267.798 900 -267.815 613 -267.821 580 -267.823 882
state freq = Anal. rel. energy (kcal/mol) Figure
all + 0.0 2a
'A,
HAIBH/t -267.632 81 8 -267.634 -261.749 -267.771 -267.775 -267.778 3Atr all 28.3 1 2b
+
8 11 68 I 076 558 766
HAlB -266.971 861 -266.972 758 -267.064 001 -267.084457 -267.090 41 4 -267.093 274
all
2z+
+
all
48.45
43.45 Ib
AIBH, -267.564 897 -267.567 -267.123 -267.745 -267.752 -267.760 'A,
all
826 481 646 138 740
IC
HAIBH/s -267.587 127 (-267.600 92)" -267.589 278 -267.7 17 740 -267.741 618 -267.747 099 -267.751 094
singlet
[A,
all 45.67 2d
39.62 2c
-267.502 593 -267.624948 -267.652 128 -267.660003 -267.663 530
all +
+
+
H2AIB -267.500750
100.62
2e
'Spin state designated after formula as / s for singlet, / t for triplet. bComplex orbitals. 'Using 6-31G**. than that observed for the interaction of empty p orbitals with B-H bonds. A high energy, doubly bonded Al=B-H was also found at the U H F level but proved to be unstable." Reversing the positions of the H and B atoms in Figure l a produces an interesting result. The H-B moiety backed away from the AI atom and found a potential minimum at 3.6477 A. The Mulliken population analysis finds a small (0.003) contribution between the H and the AI. The dissociation energy into AI (2P) and B-H ('E+)is only 0.56 kcal/mol (at the MP4SDTQ level), confirming that this is a van der Waal's minimum, Le., the H-B is best described as hydrogen bonded and nor hydrogen bridge bonded to the AI atom. A similar structure should exist where AI-H is hydrogen bonded to the B atom, but no specific search was employed since such are expected to be high energy structures (vide infra). Figure I C is the isomer that places the H on the aluminum atom. level, at which all energy At the MP4SDTQ/6-3lG**//HF/6-31* comparisons will be made, it is 48.5 kcal/mol higher in energy than the structure in Figure l a , again reflecting the difference in dissociation energy between the AI-H and the B-H bonds as well as a difference between the interaction of the empty p orbital on AI with the lone pair on B. As shall be seen, this difference in bond energy is the single most important factor in determining AI BH, structures. AIBH2. The energies for the dihydrides are given in Table I1 and the structures are in Figure 2. As expected from relative bond energies, the lowest energy structure involves two B-H bonds, as shown in Figure 2a. The boron atom is clearly using sp2 hybrid orbitals. Surprisingly, the triplet state shown in Figure 2b is only 28.3 kcal/mol higher in energy. The energy difference expected, based on the energies of conformers l a and IC, is about 48 kcal/mol. However, the short AI-B distance, 1.91 12 A, and the large overlap population, 0.653, suggest that both the unpaired electrons are in bonding orbitals, effectively constituting the equivalent of a double bond. The structure shown in Figure 2c is 39.2 kcal/mol higher in energy than the lowest energy conformer 2a. In the conformer 2c the boron atom has moved toward an sp3 configuration, reflected by the promotion of one of the lone-pair electrons on the AI atom and the closing of the H-B-H bond angle. Since the symmetry of this state is the same as that of the ground state,
*
t@tt
H Ib
z IC
Figure 1. HF/6-31G8//HF/6-3IG* structures for AlBH isomers. Electron-pair bonds are shown as heavy black lines. Approximate atomic localization of other electrons are shown by vertical heavy arrows. Arrow pointing up is (Y spin; arrow pointing down is 0 spin. (a) 2A" bond lengths: AI-B = 2.1049 A, 9-H = 1.1843 A. Bond angle: AI-9-H = 174.52O. before annihilation = 1.2627, after = 0.8056. (b) bond lengths: AI-B = 3.6477 A, 9-H = 1.2286 A. Bond angle: linear. (e) 22bond lengths: AI-B = 1.9107 A, AI-H = 1.5666 A. Bond angle: linear. before annihilation = 1.7776, after = 0.8432.
2n
Figure 2a, the U H F procedure may not be reliable here. Hence, some caution is warranted. Spin coupling the electrons of the triplet state in Figure 2b raised the energy about 17 kcal/mol and produced the classic doublebond structure, Figure 2d. The overlap is 0.713 and the bond length is 1.9179 A, consistent with the double-bond assignment. The final dihydride structure places both hydrogen atoms on the AI in an sp2 configuration. It is, as expected, very high in energy, about 100 kcal/mol above the structure in Figure 2a. AlBH3. The energies of the trihydrides are given in Table 111; the structures are shown in Figure 3. The lowest energy conformer has three B-H bonds, Figure 3a, and a first glance appears to have a B-H-AI bridge bond. However, electron density is actually removed from the H,-AI region, so this molecule is simply a Lewis adduct between borane, BH3, and the lone pair of the
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Mains et al.
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990
TABLE Ill: Total Energies for Aluminum-Boron Trihvdrides
level
AI(H)BH2
UHF/6-31G1//UHF6-3IG* UHF/6-31G**//UHF6-31G* MP2/6-31G1*//UHF6-31G* MP3/6-31G**//UHF6-31G* MP4(SDQ)/6-3 1 G**//UHF6-3 lG* MP4(SDTQ)/6-3 1G**//UHF6-3 1 G *
-268.267 537 -268.270943 -268.412 117 -268.437 956 -268.443 807 -268.447084
HAIBH, -268.251 304 -268.254 161 -268.381 427 -268.405 8 13 -268.41 1050 -268.413 515
state
*AI all 0.0 3a
all + 2 I .06 3b
freq = Anal. rel. energy (kcal/mol)
Figure
HBAIH2 -268.231 028 -268.233 860 -268.354992 -268.379946 -268.385 447 -268.387 443
2A’
+
*BI all + 37.43 3c
3a
d
3b
ZC
Figure 2. HF/6-31G*//HF/6-31G*(6D) structures for AIBH, isomers. Electron-pair bonds are shown as heavy black lines. Approximate atomic locales of other electrons are shown by vertical heavy arrows. Arrow pointing up is 01 spin; arrow pointing down is fl spin. (a) !Al bond lengths: AI-B = 2.2521 A, B-H = 1.1993 A. Bond angles: H-B-AI = 123.23’. (b) 3A” bond lengths: AI-B = 1.9072 A, B-H = 1.1773 A, AI-H = 1.5679. Bond angles: HS-B-AI = 167.79’, B-AI-H, = 166.32’, planar. before annihilation = 2.0190, after = 2.0001. (c) ‘Al bond lengths: AI-B - 2.0730 A, B-H = 1 . I 723 A. Bond angle: H-B-AI = 98.35. (d) Singlet bond lengths: AI-B = 1.9103 A, B-H = 1.1744 A, AI-H = 1.5631 A. Bond angles: HS-B-AI = 180.0’, B-AI-H, = 180.0’. (e) !A, bond lengths: AI-B = 2.0010 A, AI-H = 1.5696. Bond angles: Hs-AI-B = H6-AI-B = I 1 1.68’.
AI atom. The electron density donated to the BH, is distributed to the H atoms and the tilted structure may be due to the empty p orbital on AI interacting with the B-H bond, which is lengthened about 0.04 A. Attempts to find a triple H-bridged system by starting the three H atoms in a plane between the boron and aluminum atoms led to the conformer in Figure 3a, as did starting trihydride structures that attempted to generate a double Hbridged structure. A structure with C,, symmetry was found in which the BH3 plane was nearly perpendicular to the B-AI axis (angle HBAl = 98.4O), but this had two negative eigenvectors and was only about 0.7 kcal/mol higher in energy than the next most stable conformer at our highest level of computation. Thus, the BH3 adduct is probably quite floppy. The fact that conformer 3a is the lowest energy trihydride supports our earlier assertion9 that BH, might be useful as an atom trap. The next stable structure, shown in Figure 3b, moves a H atom from boron to aluminum. This structure, in which both AI and B appear to exhibit sp2 hybridization, is only 21.1 kcal/mol higher in energy, consistent with the relative B-H and AI-H bond strengths. Placing two H atoms on AI, Figure 3c, raised the energy another 17 kcal, again reflecting the relative bond strengths. It is interesting that no Lewis adduct of the type AIH3-,B was found at the R H F level: every attempt resulting in the dissociation to
3c
Figure 3. HF/6-3 lG*//HF/6-3IG*(6D) structures for A1BH3isomers.
Electron-pair bonds are shown as heavy black lines. Approximate atomic locales of other electrons are shown by vertical heavy arrows. Arrow pointing up is a spin; arrow pointing down is fl spin. (a) 2A‘ bond lengths: AI-B = 2.2048 A, B-HS = 1.2362 A, B-H6 = B-H, = 1.1953 A. Bond angles: HS-B2-H, = HS-B2H, = 115.32’, AI-B2-H, = 110.49’, AlB2-HS = 70.39’. before annihilation = 0.8199, after = 0.7506. (b) ’A’ bond lengths: AI-B = 2.13 16 A, B-Hs = B-H6 = 1.1934 A, AI-H, = 1.5958 A. Bond angles: H,-AI-B = 126.20’, H,-B-AI = 121.63’. before annihilation = 0.7527, after = 0.7500. (c) 2Afbond lengths: AI-B = 2.221 1 A, AI2-H7 = I .5838 A, AI2-H3 = 1.7570 A, AI2-Hd = 1.7569 A, Bs-H8 = BS-H9 = 1.1914 A, BS-H3 = 1.2914 A, B5-H4 = 1.2915 A. Bond angles: H3-AI2-H6 = H4-AI2-H6 = 108.76', H8-BS-H7 = 120.64', H3-Bs-H8 = 107.46'. before annihilation = 0.7531, after = 0.7500. (d) 2Af bond lengths: AI-B = 2.1837 A, A12-H6 = AI2-H7 = 1.5751 A, Al2-H4 = 1.8309 A, BS-Hs = BS-H9 = 1.1866 A. Bond angles: H4-AI2-H7 = H4-A12-H6 = 1 10.31', H4-BS-H8 = H4-B5-H9 = 1 13.60'. before annihilation = 0.7554, after = 0.7500.
contradicting the present result. A better understanding of the single and double H-bridged radicals can be found by considering these X2H5 radiclas to be formed by a Lewis acid/base interaction between H2X radicals and H3X, where X = B, AI. Then, the
AlBH,. Electron-pair bonds are shown as heavy black lines. Approximate atomic lacale of other electrons are shown by vertical heavy arrows. Arrows pointing up is a spin; arrow pointing down is p spin. (a) 'A, bond lengths: AI-AI = 2.6386 A, Al2-H6 = AI2-H7 = AIs-H~ = AIs-H9 = 1.5746 A, AI2-H3 = AIS-H3 = AI2-H, = AIS-H4 = 1.7475 A. Bond angles: H3-A12-H7 = H4-A12-H6 = H3-AIS-H8 = 109.43', H6-AI2-H7 = 127.72'. (b) 'A' bond lengths: AI-B = 2.2010 A, AI2-H7 = A12-H6 = 1.5713 A, A12-H3 = A12-H4 = 1.7461 A, Bs-H~ = BS-H9 = 1.1 899 A, BS-H3 = Bs-H, = 1.2925 A. Bond angles: H3-A12-H7 = H4-A12-H7 = 1 1 1.13', Hg-Bs-H, = 120.93', H3-BS-Hs = 107.48'.
stability of the isomers must be explained in terms of the relative basicities of the X-H bond and the unpaired electron in the H2X radical. If we suggest that the latter is more basic for the case of boron, whereas the former is more basic (hydridic) for AI, all the observed structures are consistent. The structures found for the mixed hydride, AIBH5, Figure 5c and Figure 5d, are understandable in terms of the interaction of BH3 with an AIH2 radical. The empty p orbital on the BH3 would be more likely to interact with the more hydridic AI-H bond than with the unpaired electron on AIH2 This is also reflected in Table V, where the energy for the classical conformer is 13.2 kcal/mol lower than the nonclassical structure. One anticipates that the classic, i.e., double H-bridged, radical will be more stable for gallium as well. This reasoning would further predict that the double H-bridged structures of AIGaH, and BGaH, will be lower in energy than the single H-bridged structures as well, and we
J . Phys. Chem. 1990, 94, 7001-7007
look forward to future calculations to confirm these predictions. It is important to note that the mixed structure which places the unpaired electron on the boron atom was unstable, reverting to the structure in Figure Sc. A/BH6 and A12H6. Although the structures for dialane(6)I9 and aluminoborane20 have been reported, we include them here for completeness in Table VI and Figure 6. The U H F energy of aluminoborane is in agreement with that reported by Barone and Minichino,20 who employed 6-21G*, triple {as well as more extensive basis sets. Included in the table are computed energy changes for the dissociation of the hexahydrides into the appropriate trihydrides. The structures are presented in Figure 6. These structures are, of course, analogous to the diborane structures. In terms of the Lewis acid/base properties of the group I11 trihydrides, they are a consequence of the interaction of the empty p orbital on XH, with the X-H bond on another XH, molecule, resulting in the well-established three-center H-bridge bonds. We must anticipate the formation of such bonds any time molecules with low lying empty orbitals (Lewis acids) interact with molecules containing no electron-rich (Lewis base) region. Since AIH, is less acidic, it is not surprising that the decomposition AlzH6 2A1H3 requires less energy than the decomposition A1BH6 AIH3 BH,. Although not shown, the decomposition B2H6 2BH3 at the highest level on the table is endothermic by 40.4 kcal/mol, using the same basis set. Thus, as observed previously,20because
--
+
-+
(19) Baird, N. C. Can. J . Chem. 1985, 63, 71. (20) Barone, V.; Minichino, C. Theorer. Chim. Acta 1989, 76, 53.
700 1
the AI-H bonds are more hydridic than B-H bonds, the mixed hexahydride (aluminoborane) is more tightly bonded than diborane itself.
Conclusions The structures of AIBH, ( n = 1 to 6) are understandable in terms of ( I ) the relative strengths of the B-H and AI-H bonds, (2) the relative acidities of the empty orbitals of the boron and aluminum hydrides, and (3) the relative basicity of the AI-H, B-H, and half-filled sp2 orbitals of boron and aluminum. These group I11 hydride structures are a consequence of the fact that sp3 hybrid structures are more stable than sp2 hybrid structures. Thus, when possible, BH4 structures are energetically preferred over A1H4 structures. The reversal of conformer stability in going from B2Hs to BAlH5 and to A12H5is further striking evidence that the first row of the periodic table is unique and, hence, not always a good model for predicting the chemistry of subsequent rows. Acknowledgment. C.W.B. and M.T. thank the donors of the Petroleum Research Fund, administered by the America1 Chemical Society, for their support of this research. This work was partially supported by NCSA Grant CHE890003N (to G.J.M.) and utilized the Cray XMP/48 system at the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign and partially by NCSA Grant CHE890006P (to C.W.B.) and utilized the Cray YMP/832 system at the Pittsburgh Supercomputer Center.
Structures of C,H,+ Brian Weiner,* Charles J. Williams, Donald Heaney, Department of Physics, Penn State University, DuBois, Pennsylvania 15801
and Michael C. Zerner* Quantum Theory Project, University of Florida, Gainesuille, Florida 3261 1 (Received: February 5, 1990; In Final Form: April 6, 1990)
C5H3+isomeric structures are identified and characterized according to their vibrational and electronic spectra for possible identification in sooting flame environments and in model FT-ICR experiments. By using quantum chemical means, it is found that the cyclopropenylium cation is the most stable species (MP2/6-3lG*//6-3lG*), more stable than the others investigated by at least 20 kcal/mol. An estimate of 375 kcal/mol of the heat of formation of ethynylcyclopropenylium cation is made. The production of CSH3+in flames from the decomposition of CSHs+into C5H3+and H2is examined, and this reaction is found to be unlikely, even at the high temperatures reached in sooting flames.
Introduction Two mechanisms of soot formation have been proposed. One of these involves the reactions of small radicals in the particle inception step; the other involves small ions.I4 We continue to examine the aspects of the latter mechanism here. Mechanisms involving small ions are suggested based on the observation that fuel-rich flames have an abundance of carbocations such as C3H3+,CSH3+,and CsHs+.l-ll The principal precursor is postulated to be the most abundant of these small species, C3H3+,and nucleation then involves reactions of this ion with neutrals such as acetylene, C2H2,diacetylene, C4HZ,and, perhaps, C2H in rapid condensation and condensation-elimination *Corresponding authors.
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reactions, forming successively larger ions and eventually yielding soot particles. ( I ) Gaydon, A. G.; Wolfhard, H. G. Flames, Their Structure, Radiation and Temperature; Wiley: New York, 1979. (2) Muller, W. J . 14th Symposium on Combustion, The Combustion Institute, 1973. (3) Olson, D. B.; Calcote, H. F. In Particulate Carbon: Formation During Combustion; Siegla, D. C . , Smith, G. W., Eds.; Plenum Press: New York, 1981; p 177. (4) Calcote, H. F. Mechanisms of Soot Nucleation in Flames-A Critical Review. Combust. Flame 1981, 42. 215. (5) Calcote, H. F.; Kurzius, S. C.; Miller, W. J. Tenth Symposium on Combustion, The Combustion Institute, 1965. (6) Miller, W. J. Oxidn. Combust. Reo. 1968, 3, 98. (7) Tse, R. S.; Michaud, P.; Delfau, J. L. Noture 1978, 153. ( 8 ) Hayhurst, A. N.; Kittelson, D. B. Combust. Name 1978, 31, 37.
0 1990 American Chemical Society
