J. Phys. Chem. 1992,96, 7624-1621
7624
we mention that the current work can be extended to coupled surfaces of polyatomic molecules. Such a generalization would be similar, but not identical, to procedures for multidimensional interpolation of potential surfaces which have been described and applied in the recent past.4648
Acknowledgment. We thank G. Scuseria, J. S. Hutchinson, R. B. Shirts, and G. S.Ezra for valuable assistance, discussions, and references. We also gratefully acknowledge the support of the Fannie and John Hertz Foundation, the National Science Foundation Grants CHE89-10975 and CHE89-09777 (Instrumentation), the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the Robert A. Welch Research Foundation.
References and Notes (1) Dunham, J. L. Phys. Reu. 1932,41,721.
(2)Beckel, C. L.; Engelke, R. J . Chem. Phys. 1968,49,5199. (3) Beckel, C. L.J . Chem. Phys. 1976,65, 4319. (4)Simons, G.; Parr, R. G.; Finlan, J. M. J . Chem. Phys. 1973,59,3229. ( 5 ) Thakkar, A. J. J . Chem. Phys. 1975,62, 1693. 161 Morse. P. M. Phvs. Rev. 1929. 34. 57. (7j Huffaker, J. N. j . Chem. Phys. 1976,50, 4564. Huffaker, J. N. J . Chem. Phys. 1987,86,4715. (8) Hulburt. H. M.; Hirschfelder, J. 0. J. Chem. Phys. 1941,9,61. (9)Murrell, J. N.; Sorbie, K. S. J . Chem. SOC.,Faraday Trans. 2 1974, 70,'1552. (10)Wright, J. S. J . Chem. Phys. 1987,86,4714. (11)Jhung, K. S.; Kim, I. H.; Hahn, K. B.;Oh, K.-H. Phys. Reu. A 1989, 40, 7409. (12) Simons, G. J. Chem. Phys. 1974,61, 369. (13) Carney, G.D.; Sprandel, L. L.; Kern, C. W. Adu. Chem. Phys. 1978, 37,305. (14)Spirko, V.; Jenson, P.; Bunker, P. R.; Cejchan, A. J . Mol. Spectrosc. 1985,112, 183. (15) Gruebele, M. Mol. Phys. 1990, 69,475. (16)Jordan, K. D.; Kinsey, J. L.; Silky, R. J . Chem. Phys. 1974,61,911. (17)Jordan, K. D. J . Mol. Spectrosc. 1975,56,329. (18)Attar, A.-R. H.; Beckel, C. L.; Keepin, W. N.; Sonnleitner, S. A. J. Chem. Phys. 1979,70, 3881.
(19)Attar, A.-R. H.;Beckel, C. L. J . Chem. Phys. 1979,71,4596. (20)Beckel, C. L.;Findley, P. R. J . Chem. Phys. 1980,73, 3517. (21)Beckel, C. L.;Kwong, R. B. J . Chem. Phys. 1980,73,4698. (22)Sonnleitner, S. A,; Beckel, C. L. J . Chem. Phys. 1980, 73, 5404. (23)Sonnleitner, S. A.; Beckel, C. L.; Colucci, A. J.; Scaggs, E. R. J . Chem. Phys. 1981,75,2018. (24)Beckel, C. L.; Kwong, R. B.; Hashemi-Attar, A. R.; Le Roy, R. J. J . Chem. Phys. 1984.81,66. (25)Murrell, J. N.; Varandas, A. J. C.; Brandao, J. J . Theor. Chim. Acta 1987,71,459. (26)Jordan, K. D.Chem. Phys. 1975,9, 199. (27)Jorish, V. S.; Scherbak, N. B. Chem. Phys. Lett. 1979, 67, 160. (28)Baker, G. A., Jr. Essentials of Pad5 Approximants; Academic: New York, 1975. (29)Rydberg, R. Z.Phys. 1931,73,376. (30) Rydberg, R. Z.Phys. 1933,80,514. (31) Klein, 0.Z.Phys. 1932,76,226. (32) Rees, A. L. G. Proc. Phys. SOC.1947,59,998. (33)Chisholm, J. S.R. Math. Comp. 1973,27,841. (34)Jones, R.; Hughes, T.; Makinson, G. J. J. Inst. Math. Appl. 1974,13, 299. (35)Graves-Morris, P. R.; Samwell, C. J. J . Phys. G 1975, I , 805. (36)Johnson, B. R.; Scheibner, K. F.; Farrelly, D. Phys. Reu. Lett. 1983, 51, 2280. (37)Press, W.H.; Flannery, B. P.; Teukolsky, S.A.; Vetterling, W. T. Numerical Recipes, The Art of Scientific Computing; Cambridge: New York, 1986. (38) Dongarra, J. J.; Moler, C. B.; Bunch, J. R.; Stewart, G. M. Linpack Users' Guide; Sam: Philadelphia, PA, 1979. (39)Kahaner, D.; Moler, C.; Nash, S. Numerical Methods and Software; Prentice-Hall: E n g l e w d Cliffs, NJ, 1989. (40)Olson,M. L.; Konowalow, D. D. Chem. Phys. 1977,21, 393. (41)Varandas, A. J. C.; Brandao, J. Molec. Phys. 1982,45. 857. (42)Botschwina, P. J. Chem. SOC.,Faraday Trans. 2 1988, 84, 1263. (43)Smith, A. M.; Jorgensen, U. G.; Lehmann, K. K. J . Chem. Phys. i987,a7,5649. (44)Scuseria, G.E.;Janssen, C. L.; Schaefer, H. F. J . Chem. Phys. 1988, 89,7382. (45)Scuseria, G. E.;Lee, T. J. J . Chem. Phys. 1990, 93,5851. (46)Downing, J. W.;Michl, J.; Cizek, J.; Paldus, J. Chem. Phys. Lett. 1979,67,377. (47)Downing, J. W.;Michl, J. Potential Energy Surfaces and Dynamics Calculations; Plenum: New York, 1981. (48)Yeh, Y. H.; Fink, W. H. J. Comput. Chem. 1986,7,539.
A Theoretical Study of the Spectroscopy and Dissociation Dynamics of HBrCO Y. Zhao and J. S. Francisco**t Department of Chemistry, Wayne State University, Detroit, Michigan 48202 (Received: April 6, 1992; In Final Form: June 5, 1992)
Reaction pathways for the dissociation of HBrCO on the ground state potential energy surface have been studied using ab initio methods. Heats of reactions and barrier heights have been computed by using Maller-Plesset perturbation theory. The most favorable dissociation path is predicted to be the molecular elimination of HBr to yield CO. In addition, frequencies for the fundamental vibrational bands of HBrCO have been calculated and comparisons made with newly reported experimental results.
I. Introduction The formyl bromide molecule (HBrCO) has been identified in many gas-phase reactions involving Br atoms.14 Most recently, Yarwood, Niki, and MakerS used the reaction HCO + Br2 HBrCO + Br (1) to generate HBrCO molecules for kinetic and IR spectroscopic studies. In that work, a loss of HBrCO was encountered and the lifetime for the disappearance of HBrCO was measured to be 100-400 s-'. However, a conclusion could not be reached on the barrier height for the reaction HBrCO HBr + CO (2)
-
-
'National Science Foundation, Presidential Young Investigator, A. P. Sloan Fellow, Camille and Henry Dreyfus Teacher-Scholar.
0022-3654/92/2096-1624$03.00/0
because of the possible heterogeneous decomposition of HBrCO on the cell walls. In this paper, we report ab initio calculations
on the energetics of the dissociation pathways of HBrCO including the barrier height for reaction 2 and discuss the implications for the HBrCO dissociation. In addition, we report calculated frequencies of the fundamental vibrational bands of HBrCO and predict the frequency of the v5 band which was not recorded by Yarwood, Niki, and MakereS 11. Computational Methods
All calculations were performed with the GAUSSIAN 90 package of programs.6 Geometry optimizations were carried out for all structures to better than 0.001 A for bond lengths and 0.lo for angles using Schlegel's method. The basis set used in this work is the 962(d) basis set constructed by Binning and Curtiss' for the Br atom and the standard 6-311G(d,p) basis set8 for other 0 1992 American Chemical Society
Spectroscopy and Dissociation Dynamics of HBrCO
2.614 2.505'
1.097
1.103 1.118'
Figure 1. Transition structure and transition vectors of the molecular dissociation of HBrCO. Parameters with no asterisk are calculated at the HF/(962(d)/6-3 1 lG(d,p)) level of theory; parameters with asterisk are calculated at the MP2/(962(d)/6-31 lG(d,p)) level of theory.
atoms. The combined basis set is denoted as 962(d)/6-31 lG(d,p). Equilibrium and transition state geometries were fully optimized at the Hartree-Fock and second-order Mdler-Plesset (UMP2, restricted wavefunctions for closed shell and unrestricted for open shell) levels with all orbitals active. Single-point energy calculations at higher orders of perturbation were performed using geometries optimized at the UMPZ level, and spin projections were applied to annihilate the highest spin contaminant of the unrestricted wave functions for radicals. The UMP4SDTQ calculation included all single, double, triple, and quadruple excitations using the frozen core approximation. Spin projected energies for radicals are denoted by the term PMP4SDTQ. All harmonic vibrational frequencies were obtained at the UMPZ level of theory.
HI. Results and Discussion A. Geometries and Vibrational Frequencies. The optimized equilibrium geometries for molecular species in the HBrCO system are listed in Table I along with available experimental values for comparison. It can be seen from Table I that calculated ground-state structures at the UMP2 level for HCO, HBr, and CO agree reasonably well with corresponding experimental values. While there are no experimental values available for HBrCO structural parameters to compare with the calculated ones, we believe that the structure of HBrCO is also well described at the MP2/(962(d)/6-31 lG(d,p)) level of theory. The transition structure for 1,l-HBr elimination from HBrCO is shown in
The Journal of Physical Chemistry, Vol. 96, No. 19, 1992 7625 TABLE I: Optimized Crouod-State rod Transition-Sate Gtowtriao species state parameter UHF UMP2 experimentalb ground state HBrCO 'A' r(9r-C) 1.937 1.958 r(H-C) 1.086 1.097 r(C-O) 1.155 1.184 B(BrC0) 123.1 123.7 B(HC0) 126.9 127.4 HCO lA' r(H-C) 1.109 1.123 1.125 r(C-0) 1.152 1.182 1.175 B(HC0) 126.6 123.8 125.0 HBr '2, r(H-Br) 1.409 1.411 1.414 co 'Z, r(C-0) 1.105 1.138 1.128 transition state HBrCO HBr + CO 'A' r(Br-C) 2.614 2.505 r(H-C) 1.103 1.118 r(C-0) 1.097 1.143 r(H-Br) 2.089 1.997 B(BrC0) 126.5 123.2 B(HC0) 183.3 185.9
-
"The basis set used was the 962(d)/6-3llG(d,p). See text for definition. *Sources of the experimental values: HCO (ref 15); all others (ref 16).
Figure 1. It is similar to those for the molecular elimination of H2C0,9HFCO,l0 and HC1CO"J2 in that the transition structure is highly asymmetric and is also of C, symmetry. Attempts were made to locate the transition states for the radical dissociation pathways but no transition state could be found. The vibrational frequencies calculated at the MP2/(962(d)/ 6-31 lG(d,p)) level of theory are listed in Table I1 along with available experimental values. The calculated vibrational vectors for the six fundamentals of HBrCO are presented in Figure 2. The calculated frequencies are in good agreement with their experimentalvalues. The average deviation between theoretical and experimental values for all species is about 4%, well within the established error range.I3 Zero point energies from the frequency calculations are used for the zero-point-energy corrections (AZEP) in the heats of reaction evaluation. Yarwood et al.5 measured the fundamental vibrational frequencies for three isotopes of HBrCO, namely HBrCO, DBrCO, and HBri3C0. The v5 bands were not recorded due to the cutoff of the KBr windows. The frequency for the v5 band of DBrCO was estimated to be 358 cm-l from the difference between v4 (605.2 cm-I) and v4 v5 (963 cm-I). Frequencies for the v5 bands for the other two isotopes can be derived from the experimentally
+
& D3
u4 D5 D6 Figure 2. Vibration vectors for fundamental vibrational modes of HBrCO calculated at the MP2/(962(d)/6-31 lG(d,p)) level of theory.
7626 The Journal of Physical Chemistry, Vol. 96, No. 19, 1992
Zhao and Francisco
TABLE II: Vibrational Frequencies (in em-') and Zero Point Energies (ZPE) (in kcal mol-') species frequency ground state 3109 (2912), 1825 (1789), 1334 (1276), 929 (893), 653 (646), 362 HBrCO HCO 2735 (2483), 1959 (1863), 1133 (1087) HBr 2731 (2649) co 2140 (2170) 2832, 1976, 762, 538, 220, l 2 l l i HBrCO HBr CO transition state
-
+
ZPE 11.74 8.33 3.90 3.06 9.05
" Calculated at the UMP2/(962(d)/6-3 1lG(d,p)) level of theory; experimental values are in parentheses. Source of experimental frequencies: HBrCO (ref 5); HCO (ref 17); all others (ref 16). TABLE III: Total Calculated Energies (in hartree) for Selected Species" sDecies state UHF ground state HBrCO 'A' -2685.51 1 48 -2572.767 88 HBr Br 2P -2572.165 19 HCO 2AI -113.28023 -112.76948 co H 2P -0.499 81 transition state HBrCO HBr CO: 1 A' -2685.455 18 species state spin annihilation for radicals HCO 2A' Br 2P H 2P
UMPZ
UMP4SDTO
~~~
-
-2686.352 84 -2573.249 03 -2572.61 101 -1 13.63060 -1 13.111 42 -0.499 8 1
+
-2686.13526 -2573.049 55 -2572.409 79 -1 13.618 84 -1 13.098 48 -0.499 81
-2686.298 18
-26.86.081 61 PMP4SDTQ -1 13.620 20 -2572.41023 -0.499 8 1
-
"Calculated using the 962(d)/6-3 1lG(d,p) basis set; MP4SDTQ single-point energies were calculated with the geometries optimized at the UMPZ level of theory. TABLE I V Relrtive Energy (in kcal mol-') for the Dissociation Patbwnvs -.- -"- of -- HBrCW species UHF UMPZ PMP4SDTQ PMP4SDTQ + AZPE -8.0 -12.8 -16.2 -4.8 HBr + CO 33.7 31.0 34.3 [HBr-CO]' 35.3 0.0 0.0 0.0 0.0 HBrCO 62.4 69.8 65.8 HCO + Br 41.4 79.5 70.8 48.3 82.0 CO + Br H ~~~~
~
~
H
+ B r + CO
+
Relative energies were calculated using the total energies listed in Table 111; zero-point-energy corrections (AZPE) were calculated at the UMPZ level of theory as listed in Table 11.
estimated frequency for the v5 band of DBrCO and the calculated frequencies for the three isotopic molecules. Table V lists experimental and calculated fundamental frequencies for the three isotopes. It can be seen from Table V that the ratio of the calculated frequencies of each mode for any two isotopes is very close to the ratio of the corresponding experimentalvalues. We call this the ''isotope scaling rule" for convenience. The frequencies of HBrCO and H B r W O derived from the isotope scaling rule are in excellent agreement with their experimental values as can be seen from the last two columns of Table V. Therefore, the derived frequencies, 358.6 and 355.8 cm-', for the v5 bands of HBrCO and HBr"C0, respectively, should have the same accuracy as that of the us band of DBrCO. The isotope scaling rule demonstrated here can be applied to other molecules. The calculated frequencies with isotopic substitutions can be used to predict the frequencies of all isotope molecules provided that the experimental frequencies for one of the isotope molecules are available.
I HBrCO
-12.8
c
HBr + CO
Figure 3. Summary of dissociation pathways of HBrCO calculated at 1lG(d,p)) + AZPE(UMP2) level the PMP4SDTQ//UMP2/(962(d)/6-3 of theory.
B. Heats of Reaction and Barrier Height. The total energies calculated at several levels of theory are listed in Table 111 and the energetics for the dissociation pathways relative to HBrCO are listed in Table IV. Figure 3 is a graphic presentation of the energetics for the dissociation pathways of HBrCO. As can be seen from Table IV, the relative energies for the dissociation pathways of HBrCO obtained at the HartreeFock level are very different from those calculated at correlated levels. Those affected most by the correlation calculations are the bond fission processes. The barrier heights of the transition state for the molecular
TABLE V Calculated and Experimental Frequencies (in cm-') for the Fundamental Vibrations of Formyl Bromide calcd freqs exptl freqs derived' freqs DBrCO HBrCO HBPCO DBrCO HBrCO HBr13C0 HBrCO HBr "CO "I 2321.2 3109.0 3098.3 2205.4 2911.9 2899.9 2953.9 2943.7 "2 1781.4 1824.7 1787.1 1748.3 1789 1753 1790.8 1753.9 y3 1001.1 1333.6 1329.8 969 1276 1272 1290.8 1287.2 y4 612.9 652.6 633.6 605.2 646.3 627.9 644.4 625.6 u5 361.3 361.9 359.1 358 358.6 355.8 y6 774.0 929.1 916.7 746.8 893.4 88 1.6 896.4 883.8 Derived from the "isotope scaling rule"; see discussion in the text.
7627
J. Phys. Chem. 1992,96,7627-7632 elimination calculated at different levels of theory are similar. On the other hand, the changes in the calculated relative energies are less than 4 kcal mol-' from UMP2 to PMP4 calculations, which indicates that convergence has been achieved in the energetic calculations. The quality of the calculations can be Mer assessed from calculated relative energies of s p i e s with known experimental heats of formation. For instance, the energy difference for the two bond fission pathways should be equal to the heat of reaction for the process of HCO H CO, which is 5.62 kcal mol-' as derived from the known experimentalheats of formations. The calculated energy difference at the PMP4SDTQ AZPE level is 8.5 kcal mol-', in reasonable agreement with the experimental value. Furthermore, the calculated heat of reaction for the overall reaction
-
+
+
Br
+ HCO
-
HBr
+ CO
(3)
is 75.1 kcal mol-', which agrees very well with the experimental value of 72.6 kcal mol-'. On the basis of these assessments, we believe that the heats of reactions and barrier heights for the dissociation pathways of HBrCO have been reasonably well estimated at the highest level of calculation in this work. Yarwood et al.s measured the dissociation rate of HBrCO and obtained a lifetime of 100-400 s-I. This lifetime is too short for a homogeneous unimolecular dissociation with a barrier of about 30 kcal mol-I as estimated in this calculation. Consequently, heterogeneous processes were largely responsible for the loss of HBrCO in their experiment as suspected by the authors. Yarwood et aLSalso suggested that, in addition to reaction 1, there existed a second channel for the HCO Br2 reaction, namely HCO + BrZ HBr CO Br, which could account for the appearance of CO in the fmal products. Our calculations suggest that reaction 3 is another important channel for the formation of CO and HBr. The barrier height for the dissociation HBrCO HBr CO is ca. 30 kcal mol-' lower than the exothermicity for the reaction Br + HCO HBrCO, which implies that reaction 3 may proceed rapidly and may compete with the collisional stabilization of the hot HBrCO* intermediate. A similar reaction between F and HCO has been suggested by Sulzle et al.I4 Timonen, Ratajczak, and Gutman4 measured the rate constant for reaction 1 by monitoring the decay rate of HCO. The rate constant obtained therein could be in error since the loss of HCO through reaction 3 had not been taken into account.
-
+
+
+
-
-
+
IV. Conclusion The main conclusions of this work are as follows:
(1) The heats of reaction and barrier height for the dissociation pathways of HBrCO at the PMP4SDTQ//UMP2/(962(d)/63 1lG(d,p)) level of theory agree very well with available experimental values. (2) The calculated barrier height of ca. 30 kcal mol-' for the unimolecular dissociation of HBrCO suggests that the fast decomposition of HBrCO at room temperature is the result of heterogeneous processes instead of homogeneous ones. (3) The reaction Br HCO is predicted to proceed rapidly to form HBr CO through HBrCO as a hot intermediate. This reaction may have important effects on reaction systems involving both Br and HCO. (4) The frequencies for the us bands of HBrCO and HBrI3CO are derived from the calculated isotopic frequencies and that of the DBrCO. The values are 358.6 cm-' for HBrCO and 355.8 cm-' for HBrI3CO, respectively.
+
+
References a d Notes ( 1 ) Barnes, I.; Bastian, V.; Becher, K. H.; Tong,Z . In?.J . Chem. Kiner. 1989, 21, 499. (2) Maker, P. D.; Niki, H.; Breitenbach, L. P.; Savage, C. M. 39th Sym-
posium on Molecular Spectroscopy, Ohio State University, Columbus, OH, 1984. (3) Niki, H.; Maker, P. D.; Savage, C. M.; Breitenbach, L. P. In?. J. Chem. Kine?. 1985, 17, 525. (4) Timonen, R. S.;Ratajczak, E.;Gutman, D. J. Phys. Chem. 1988,92, 651. (5) Yanvood, G.; Niki, H.; Maker, P. D. J . Phys. Chem. 1991,95,4773. (6) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.;Gonzalez, C.; DeFrecs, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.;Kahn, L. R.; Stewart, J. J. P.; Topiol, S.;Pople, J. A. Gaussian 90, Revision H; Gaussian, Inc.: Pittsburgh, PA, 1990. (7) Binning, R. C., Jr.; Curtiss, L. A. Compuf. Chem. 1990, 11, 1206. (8) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (9) Scuseria, G. E.; Schaefer, H. F. J. Chem. Phys. 1989, 90, 3629. (10) Morokuma, K.; Kato, S.; Hirao, K. J . Chem. Phys. 1980, 72,6800. Goddard, J. D.; Schaefer, H. F. J. Chem. Phys. 1990,93,4907. Kamiya, K.; Morokuma, K. J. Chem. Phys. 1991,94,7287. Francisco, J. S.;Zhao, Y.J. Chem. Phys. 1992,96,7587. (11) Francisco, J. S.;Zhao, Y . J . Chem. Phys. 1992, 96, 7587. (12) Tyrrell, J.; Lewis-Bevan, W. J. Phys. Chem. 1992, 96, 1691. (13) Pople, J. A,; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.;Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W.J. Inf. J. Quantum Chem. Symp. 1981, 15, 269. (14) Sulzle, D.; Drcwello, T.; Baar, B. L. M. van; Schwarz, H. J. Am. Chem. Soc. 1988, 110, 8330. ( I S ) Brown, J. M.; Ramsay, D. A. Can. J. Phys. 1975, 53, 2232. (16) Huber, K.; Herzberg, G. Molecular Specrra and Molecular Structure 4. Constanrs of Diaromic Molecules; Van Nostrand: Princeton, NJ, 1979. (17) Milligan, D. E,; Jacox, M. E. J . Chem. Phys. 1969, SI, 277.
The Nature of Core Excited States in C, As Exhibited by the Auger Line Shape David E. Ramaker, Chemistry Department, George Washington University, Washington, D.C. 20052
Noel H. Tumer,* and JOAM Milliken Chemistry Division, Naval Research Laboratory, Washington, D.C. 20375 (Received: May 4, 1992) We have measured the C KVV Auger line shape for Csoand compared it with that previously obtained for graphite and benzene. A theoretical interpretationreveals the presence of two shakeup satellites. One satellite results from shakeup upon creation of the initial core hole, the second, upon filling of the core hole in the Auger final state. The relative intensity and energy shift of the first satellite indicate that the ls-'lr-'w* shakeup state is localized on the core excited atom. In contrast, for graphite, only a fraction of the ls-'?r-'r* excitations (i.e. only the low energy electron-hole pairs excited at the Fermi level) remained sufficiently localized to contribute to the line shape. The absence of Auger satellites in both Cm and graphite from either the resonant ls-'w* or the shakeup ls-'v-l excitation indicates that these excitations delocalize in times that are short relative to core hole decay. The structure of Cm is known to be a truncated icosahedron with 20 six-membered rings and 12 five-membered rings.' The molecule, with all C atoms equivalent, has a closed shell electronic
structure and comprises a unique, new pure form of carbon. Although Csoand other fullerenes have been known for several years now, recently developed synthetic techniques2have allowed
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