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Three-center vs. four-center HF elimination from vinyl fluoride: a direct dynamics study
29 December 2000
Chemical Physics Letters 332 (2000) 583±590
www.elsevier.nl/locate/cplett
Three-center vs. four-center HF elimination from vinyl ¯uoride: a direct dynamics study ~ez, Saulo A. V Emilio Martõnez-N un azquez * Departamento de Quimica Fisica, Universidad de Santiago de Compostela, Santiago de Compostela E-15706, Spain Received 7 August 2000; in ®nal form 29 September 2000
Abstract Two fragmentation reactions of vinyl ¯uoride (three-center and four-center HF eliminations) were investigated by AM1 direct classical trajectories. Product energy distributions (PEDs) were computed for dierent initial excitation schemes and the results compared with the experimental observations. The results support that the four-center elimination is the preferred decomposition process but HF elimination through the three-center mechanism is predicted to be signi®cant. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The vinyl ¯uoride decomposition dynamics has been extensively studied in past years [1±7]. Particularly, Sato et al. [6] used mass-resolved photofragment time-of-¯ight spectroscopy and ab initio calculations to investigate the photodissociation of vinyl ¯uoride at 157 nm (182.1 kcal/mol). According to their MP2/6-31G(d,p) calculations [6], the open channels at the experimental energy are CH2 @CHF ! CHBCH HF
1
! CHBCF H2
2
! C2 H2 F H
3
! C2 H3 F
4
! CHBCH H F
5
*
Corresponding author. Fax: +34-981-595012. E-mail address: [email protected] (S.A. VaÂzquez).
HF eliminations (channel 1) can be produced from a four-center or a three-center transition state (see Fig. 1). The MP2/6-31G(d,p) calculations [6] predict classical barriers of 82.2 and 85.3 kcal/mol for the four-center and three-center eliminations, respectively. More recent calculations at the QCISD(T)/6-311G(2d,2p) level of theory aord barriers of about 80 kcal/mol (74 kcal/mol including the zero-point energy, ZPE) for both channels [8]; the others (channels 2±5) present energy barriers substantially higher [8]. Sato et al. [6] suggested that `the exit barrier for the four-center elimination is easily converted into the relative translational energy between acetylene and HF, while the exit barrier energy for the three-center elimination is largely partitioned into the internal energy of acetylene'. From this and the large amount of average translational energy observed in their experiment (42 kcal/mol), they concluded that HF is predominantly produced via the fourcenter elimination process. However, the most probable translational energy was found to be about 20 kcal/mol, suggesting that the three-center
0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 1 9 8 - 2
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E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
Fig. 1. The three-center and four-center transition states calculated by ab initio [8], AM1±SRP and AM1 methods. The ab initio methods are: QCISD(T) for energies, QCISD for geometries and MP2 for frequencies; all with the 6-311G(2d,2p) basis set.
process might be signi®cant. In addition, RRKM calculations [8] predict that both processes are likely to occur, with the three-center one slightly favored over the four-center at 182 kcal/mol above the vinyl ¯uoride ZPE. On the other hand, Watanabe et al. [3] reported distributions of HF produced by Hg-photosensitized reactions of ¯uorethylenes. At ca. 111.6 kcal/ mol of excitation energy, they found that 19% of the available energy goes to HF vibration, a value
much higher than the statistical one. The authors discussed two possible sources of disagreement. Firstly, a non-random distribution of the available energy among the internal degrees of freedom at the transition state, and secondly, the presence of a potential barrier that causes a strong force upon the separating fragments. The latter possibility was previously suggested by Berry [9] and Zamir and Levine [10]. In addition, Quick and Wittig [2] found similar trends at 20±35 kcal/mol of excess
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
energy with respect to the transition state ZPE, and concluded that the large HF vibrational excitation can be explained on the basis of the signi®cant stretching of the HF bond in the transition state with respect to its equilibrium value. Takayanagi and Yokoyama [7] performed ab initio (RHF/3-21G) classical trajectory calculations for the four-center HF elimination. They used an orthant-like sampling method at the transition state geometry, with no account of the ZPE. They obtained product energy distributions (PEDs) at several excess energies. While their average translational energy is similar to the experimental result [6], the vibrational state distributions of HF are not in good agreement with experiment. The above results prompted us to undertake a classical dynamics study for both the four-center and the three-center elimination processes of vinyl ¯uoride in order to assess the extent to which the three-center process is competitive. In this Letter, we present a direct dynamics simulation [11±14] by using a code that interfaces the classical trajectory program GE N D Y N [15] with the semiempirical electronic structure theory package MO P A C 7.0 [16,17]. The AM1 parameters [18] in MO P A C , supplemented with speci®c reaction parameters [12±14,19] (SRPs), are used in the present study. PEDs for several ensembles are calculated at two excitation energies, 111.6 and 182.1 kcal/mol (above the reactant ZPE), and the results compared with experiment [3,4,6]. 2. AM1±SRP semiempirical model We use the AM1 Hamiltonian [18] in the MO 7.0 [16,17] semiempirical package modi®ed by the use of speci®c reaction parameters (AM1± SRP) [12±14,19]. The use of speci®c reaction parameters was ®rstly proposed by Truhlar and co-workers [19], who adjusted the parameters of a NDDO wave function to reproduce experimental or ab initio data for speci®c reactions. The original AM1 parameters and the new AM1±SRP ones are listed in Table 1. Our own ab initio data [8] was used in the reparameterization procedure. More speci®cally, the new values were chosen to model the ab initio geometries and frequencies of the PAC
585
Table 1 AM1 and AM1±SRP parametersa Atom
Parameter
AM1 value
AM1±SRP value
H
Uss bs zs a Gss
)11.396 )6.174 1.188 2.882 12.848
)11.306 )6.554 0.998 3.102 12.808
C
Uss Upp bs Zs Zp a Gsp Gpp Gp2 Hsp
)52.029 )39.614 )15.716 1.809 1.685 2.648 11.470 11.080 9.840 2.430
)51.909 )39.914 )15.916 1.909 1.505 2.588 11.400 10.800 10.400 1.900
F
Uss Upp bp zs Gss Gsp
)136.106 )104.890 )27.922 3.770 16.920 17.250
)146.206 )105.510 )27.902 3.800 16.820 17.350
a
Only those parameters that were changed in the AM1±SRP model PES are listed in the table.
four-center and three-center transition states (see Fig. 1) as well as the energetics involved in the two elimination channels that are being studied here (shown in Fig. 2). The parametrization was performed in an iterative way until it was judged that an optimum point (at which the above properties were calculated about as well as possible) was reached. Peslherbe and Hase [20] have shown that product energy partitioning may depend on how the SRPs are chosen. Fig. 1 shows the four-center (TS1) and threecenter (TS2) transition states with the energies, imaginary frequencies, and some selected geometrical parameters calculated by ab initio [8], AM1, and AM1±SRP models. As seen in the ®gure, the AM1±SRP model predicts structures more similar to the ab initio ones than does the AM1 model. The AM1 energies are approximately 20 kcal/mol higher than the QCISD(T)/6-311G(2d,2p) and AM1±SRP values, and the AM1 imaginary frequencies are also very high, especially for TS2. Overall, the AM1±SRP model predicts reasonable
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E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
Fig. 2. Potential energy diagram for the three-center and four-center elimination processes. The numbers are the AM1±SRP energies (without ZPE) and those in parentheses the corresponding QCISD(T)/6-311G(2d,2p) values [8].
structures, energies, and frequencies for these transition states. Fig. 2 shows a schematic potential energy diagram showing the energetics of the HF elimination processes calculated at the AM1± SRP and QCISD(T)/6-311G(2d,2p) [8] levels of accuracy. As seen in the ®gure the agreement is quite good, with the average deviation being 2.7 kcal/mol only. 3. Trajectory computational details Throughout this paper and unless otherwise stated, the excitation energies are given with respect to the vinyl ¯uoride ZPE. The trajectories were initialized in three ways. First, the ecient microcanonical sampling (EMS) [21] without angular momentum was used to prepare a microcanonical ensemble at 182.1 kcal/mol, an energy for which experimental data are available [6]. For this ensemble (referred to as EMS), 5 105 steps
starting from the equilibrium geometry were taken for the warm up Markov walk and 104 between individual trajectories. In addition, at each step of the Markov walk, all the atoms were moved with a leading to an acceptance ratio step size of 0.125 A, between 0.3 and 0.5. Finally, to con®ne the sampling to the reactant con®guration space, maximum bond extensions allowed during the random for all the bonds. walk were 3 A In the second excitation scheme, a group of normal modes were selectively excited to obtain a total energy of 182.1 kcal/mol. Several ensembles were constructed in this way. In the one called WAGG, the wagging and twisting vibrational modes were initially excited. The FCC/CH2 ensemble corresponds to an initial excitation of the FCC bending and the CH2 rocking normal modes. Ensemble FCH/CH2 corresponds to the excitation of the FCH bending mode, and the CH2 rocking. The CC and CF stretching modes were initially excited together with the HCH scissoring mode in
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
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Then, various classimasses were separated 10 A. cal mechanical molecular properties, such as relative translational energy, product vibrational and rotational energies, were calculated [25,26]. In addition, vibrational quantum numbers for the product HF were evaluated by the Einstein±Brillouin±Keller (EBK) [27±29] quantization of the action integral.
ensembles CC/HCH and CF/HCH, respectively. Finally, the three CH stretching normal modes were excited in ensemble CH. In the third method, the internal energy was distributed according to a quasi-classical microcanonical sampling of the normal mode vibrational states at the barrier [14]. The method is based on the classical barrier sampling [22] and selects each state with equal probability so that the momentum distribution in the reaction coordinate agrees with RRKM theory [23,24]. With this method, trajectories were initialized from TS1 (ensemble QCBS-TS1) or TS2 (ensemble QCBSTS2) at two selected energies: 111.6 and 182.1 kcal/ mol above the reactant ZPE. Once the initial conditions were set, the trajectories were integrated by using a fourth order Runge±Kutta±Gill routine with a ®xed step size of 0.05 fs. At each step of the integration the Schr odinger equation was solved for electronic energies and forces on the nuclei. After the SCF convergence, the ®rst derivatives of the energy with respect to the Cartesian coordinates were evaluated numerically within MO P A C 7.0, obtaining an energy conservation of at least four significant ®gures. Batches of 1000 trajectories were propagated until the HF and acetylene center of
4. Results Table 2 lists the PEDs evaluated in this work at the excitation energy of 182.1 kcal/mol (and additionally at 111.6 kcal/mol for the QCBS ensembles) as well as the experimental ®ndings [2,3,6]. The last column of this table collects the ratio N3 / N4 , where N3 and N4 are the number of trajectories that decomposes through the three-center and four-center transition states, respectively. As can be seen, for ensembles EMS, CF/HCH, FCC/CH2 , and WAGG the four-center channel is the preferred one, although the three-center process appears to be competitive. Note that although the energy dierence between the TS1 and TS2 structures predicted by the AM1±SRP model is significant (5.6 kcal/mol) compared with the QCISD(T)/
Table 2 PEDs and ratio N3 /N4 at 182.1 kcal/mol of excitation energy with respect to the vinyl ¯uoride ZPE
a
Ensemble
hEtrans i
hErot;HCCH i
hEvib;HCCH i
hErot;HF i
hEvib;HF i
N3 =N4
QCBS-TS1 QCBS-TS2 EMS CH CF/HCH CC/HCH FCC/CH2 FCH/CH2 WAGG Experimenta
43.5 27.4 20.3 21.9 19.7 21.1 48.7 26.0 29.6 42
7.8 12.8 11.8 11.8 11.7 11.8 10.6 14.5 12.2
67.6 81.9 109.0 93.7 88.6 91.4 77.1 86.0 87.4
22.5 25.6 14.6 17.2 15.7 17.4 13.1 21.2 19.2
35.6 29.3 21.3 32.4 42.3 35.3 27.5 29.3 28.6
± ±
QCBS-TS1b QCBS-TS2b Experimentc Experimentd
40.0 14.5
3.8 6.2
36.3 62.1
10.4 10.2
15.8 13.3 19 6 10
± ±
Taken from [6]. At 182.1 kcal/mol of excitation energy. At 111.6 kcal/mol of excitation energy. c Taken from [3]. At 111.6 kcal/mol of excitation energy. d Taken from [2]. At 94±109 kcal/mol of excitation energy. b
0.90 1.24 0.72 1.00 0.31 10.38 0.53
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E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
6-311G(2d,2p) result (see Fig. 2), it is not critical for the calculation of the ratio N3 /N4 at the excitation energy of 182.1 kcal/mol. For the CH and FCH/CH2 ensembles, elimination through the three-center transition state is more likely to occur. The result for ensemble FCH/CH2 (N3 /N4 10.38) can be easily understood by a simple inspection of the FCH bending eigenvector. As stated in Section 1, Sato et al. [6] concluded that HF is basically produced through the four-center elimination process. Our average translational energy computed for the QCBS-TS1 ensemble (43.5 kcal/mol) is similar to their average value (42 kcal/mol). The value obtained for the QCBS-TS2 is markedly lower (27.4 kcal/mol). These results seem to support their conclusion. However, as shown later, a more rigorous comparison between the calculated and observed translational energies should involved not only the average values but also the form of the distributions. The experimental values for the vibrational energy content in the product HF are 610 [2] and 19 kcal/mol [3] at excitation energies of 94±111.6 kcal/mol. Both the QCBS-TS1 and QCBS-TS2 results, 15.8 and 13.3 kcal/mol (9.8 and 7.3 kcal/ mol without ZPE), respectively, are in good agreement with experiment. On the other hand, the internal energy content in acetylene calculated for QCBS-TS2 (94.7 kcal/mol) is substantially higher than that obtained for QCBS-TS1 (75.4 kcal/mol), as Sato et al. [6] suggested. It is well known that, in general, classical trajectories initiated at the reactant phase space do not aord accurate PEDs due to the improper treatment of zero-point motion [22]. The product relative translational energy calculated for the EMS ensemble (20.3 kcal/mol) is signi®cantly smaller than the experimental quantity and, unexpectedly, than those predicted for the QCBS ensembles. Trajectories initiated in the reactant phase space may cross the transition state without ZPE in modes orthogonal to the reaction coordinate so that one would expect enhancement of the average translational energy in comparison with the outcomes aorded by QCBS. This unexpected result led us to conclude that the decomposition dynamics in the EMS ensemble is non-statistical, more speci®cally, intrinsically non-RRKM [23], a
behavior frequently observed in classical trajectory calculations at high energies [30]. As shown in Table 2, the average vibrational energy in acetylene calculated for the EMS ensemble (109.0 kcal/ mol) is substantially higher than the corresponding values obtained for the QCBS-TS1 and QCBS-TS2 ensembles (67.6 and 81.9 kcal/mol, respectively). For other ensembles in which vibrational modes involving the HCCH fragment are initially excited, such as CH or CC/HCH, the calculations show high vibrational energy contents for acetylene, too. Thus, it seems that a phase space bottleneck (or bottlenecks) may be associated to the HCCH moiety in our model and, as a consequence, the eective excitation energy in the EMS ensemble is lower than that in the QCBS ensembles, leading to this unexpected trend. The clear discrepancy found between the EMS and the experimental results, however, points out that this non-statistical behavior, exhibited in the EMS ensemble, may not take place in the experiment. The maximum HF vibrational energy content was obtained for the CF/HCH ensemble. This result could be expected because, for this ensemble, many trajectories crossing a transition state dividing surface will present very large HF bond distances due to the initial excitation of the CF stretch. The same can be applied to ensembles CH, and CC/HCH, which also aord a high content of HF vibrational energy. It is also remarkable the average translational energy obtained for ensemble FCC/CH2 (48.7 kcal/mol). To a large extent, this is a consequence of the fact that most of the trajectories produces HF via the four-center transition state (the ratio N3 /N4 is 0.31). So far, our comparisons between classical trajectory results and experimental data involved averaged properties. From now on, we will concentrate on vibrational state distributions and translational distributions, which may provide further insights into the dissociation dynamics of vinyl ¯uoride. Table 3 compares the HF vibrational state distributions obtained in this study with those determined experimentally [2,3] and those calculated in the previous dynamics study [7]. Our results for both the QCBS-TS1 and QCBS-TS2 ensembles are substantially dierent from the previous trajectory results [7] and more
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
589
Table 3 Comparison of the vibrational state distributions of HF produced in the photodissociation of vinyl ¯uoride at several excess energies Energya
v0
v1
v2
v3
v4
Experiment Experimentc
38 20±35
± ±
1.00 1.00
0.56 0.55
0.42 0.15
0.24 <0.05
QCBS-TS1 QCBS-TS2 Trajectoryd Trajectoryd
33 37 10 50
0.74 1.10 3.76 1.14
1.00 1.00 1.00 1.00
0.43 0.43 0.00 0.24
0.13 0.03 0.00 0.02
0.03 0.05 0.00 0.02
Method b
v5
0.00 0.00 0.00 ±
a
Excess energies (in kcal/mol) with respect to the transition state ZPE. Taken from [3]. c Taken from [2]. d Taken from [7]. The authors do not specify whether the zero-point energies were considered. b
similar to the experimental observations (especially to those of [2]). The QCBS-TS1 values are more similar to the experimental ones than are the QCBS-TS2, supporting the previous conclusion that HF is predominantly formed via the fourcenter channel [6]. Fig. 3 compares the experimental translational energy distribution obtained by Sato et al. [6] (solid line) with those calculated here (vertical bars) for ensembles QCBS-TS1 and QCBS-TS2. As can be seen, neither the QCBS-TS1 nor the QCBS-TS2 ensemble ®ts the experimental distribution. The QCBS-TS1 distribution peaks at a higher translational energy (ca. 40 kcal/mol, very near its average value). The QCBS-TS2 distribution peaks at a value similar to the most probable translational energy observed experimentally (ca. 20 kcal/mol) but the populations of trajectories with higher translational energy are signi®cantly smaller than the experimental distribution. Therefore, although the QCBS-TS1 results aord the best agreement with the average translational energy determined experimentally, disagreement is found for the most probable translational energy. The contrary is found for the QCBS-TS2 ensemble: the most probable translational energy predicted for this ensemble is in very good agreement with the experimental value but the average quantities dier considerably. Being more rigorous, the comparison of our results with experiment should involved a weighted average of the QCBS-TS1 and QCBSTS2 ensembles. Using the weighting factor cal-
culated from the N3 /N4 ratio for the EMS ensemble, the distribution thus obtained (Fig. 3c) ®ts the experimental one signi®cantly better than does the QCBS-TS1 or the QCBS-TS2 ensemble alone, although the experimental distribution peaks at a lower translational energy and is broader than the theoretical distribution. This comparison suggests that the percentage of HF eliminations evolving through the three-center transition state might be signi®cant in the experiment. To sum up, the results presented in this work seem to support that the dissociation of vinyl ¯uoride proceeds preferentially through the four-center elimination but the percentage of molecules decomposing via the three-center process should be signi®cant. Finally, it seems interesting to remark the role that a possible non-random initial excitation may play on the PEDs. As shown previously, dierent excitation schemes led to substantially dierent N3 / N4 ratios and PEDs. Now, for the sake of example, we include in Fig. 3 the translational energy distribution obtained from averaging the FCH/CH2 and WAGG distributions (panel d). As can be seen, the resulting distribution ®ts reasonably well the experimental curve. Note, on the other hand, that ensembles FCH/CH2 and WAGG clearly favor the four-center channel (the percentages of four-center eliminations are 76% and 65%, respectively). Our intention here is not to suggest that these modes are preferentially excited in the experimental conditions of Sato et al. [6], but to note that the possibility of a non-random initial
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References
Fig. 3. Translational energy distributions for: (a) the QCBSTS1 ensemble, (b) the QCBS-TS2 ensemble, (c) a weighted average of both QCBS ensembles, and (d) the average of FCH/ CH2 and WAGG ensembles. For all the plots, the solid line corresponds to the experimental distribution [6].
preparation of vinyl ¯uoride in the experiment should not be disregarded. Acknowledgements We thank `Centro de Supercomputaci on de Galicia' CESGA for time allocation for the calculations.
[1] M.J. Berry, G.C. Pimentel, J. Chem. Phys. 51 (1969) 2274. [2] C.R. Quick Jr., C. Wittig, J. Chem. Phys. 72 (1980) 1694. [3] H. Watanabe, H. Horiguchi, S. Tsuchiya, Bull. Chem. Soc. Jpn. 53 (1980) 1530. [4] D.J. Donaldson, D.G. Watson, J.J. Sloan, Chem. Phys. 68 (1982) 95. [5] S. Kato, K. Morokuma, J. Chem. Phys. 74 (1980) 6285. [6] K. Sato, S. Tsunashima, T. Takayanagi, G. Fijisawa, A. Yokoyama, Chem. Phys. Lett. 242 (1995) 401. [7] T. Takayanagi, A. Yokoyama, Bull. Chem. Soc. Jpn. 68 (1995) 2245. ~ ez, S.A. V [8] E. Martinez-N un azquez (submitted). [9] M.J. Berry, J. Chem. Phys. 61 (1974) 3114. [10] E. Zamir, R.D. Levine, Chem. Phys. 52 (1980) 253. [11] J.M. Milliam, V. Bakken, W. Chen, W.L. Hase, H.B. Schlegel, J. Chem. Phys. 111 (1999) 3800. [12] K. Bolton, W.L. Hase, G.H. Peslherbe, in: D.L. Thompson (Ed.), Modern Methods for Multidimensional Dynamics Computation in Chemistry, World Scienti®c, Singapore, 1998, p. 143. [13] C. Doubleday Jr., K. Bolton, W.H. Hase, J. Phys. Chem. A 102 (1998) 3648. [14] C. Doubleday Jr., K. Bolton, G.H. Peslherbe, W.H. Hase, J. Am. Chem. Soc. 118 (1996) 9922. [15] D.L. Thompson, GE N D Y N program. [16] J.P.P. Stewart, MO P A C 7.0, a General Molecular Orbital Package QCPE, 1993, p. 455. [17] J.P.P. Stewart, J. Comput. Chem. 10 (1989) 209. [18] M.J.S. Dewar, E.G. Zoebish, E.F. Healy, J.P.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [19] A. Gonzalez-Lafont, T. Truong, D.G. Truhlar, J. Phys. Chem. 95 (1991) 4618. [20] G.H. Peslherbe, W.L. Hase, J. Chem. Phys. 104 (1996) 7882. [21] G. Nyman, S. Nordholm, H.W. Schranz, J. Chem. Phys. 93 (1990) 6767. [22] W.L. Hase, D.G. Buchowski, Chem. Phys. Lett. 74 (1980) 284. [23] T. Baer, W.L. Hase, Unimolecular Reaction Dynamics: Theory and Experiments, Oxford University Press, New York, 1996. [24] R.G. Gilbert, S.C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scienti®c Publications, Oxford, 1990. [25] D.L. Bunker, Meth. Comput. Phys. 10 (1971) 287 (and references therein). [26] L.M. Ra, D.L. Thompson, in: M. Baer (Ed.), Theory of Chemical Reaction Dynamics, CRC Press, Boca Raton, 1985. [27] A. Einstein, Verh. Dtsch. Phys. Ges. 19 (1917) 82. [28] M.L. Brillouin, J. Phys. (Paris) 7 (1926) 353. [29] J.B. Keller, Ann. Phys. 4 (1958) 180. [30] D.V. Shalashilin, D.L. Thompson, J. Chem. Phys. 105 (1996) 1833.
Chemical Physics Letters 332 (2000) 583±590
www.elsevier.nl/locate/cplett
Three-center vs. four-center HF elimination from vinyl ¯uoride: a direct dynamics study ~ez, Saulo A. V Emilio Martõnez-N un azquez * Departamento de Quimica Fisica, Universidad de Santiago de Compostela, Santiago de Compostela E-15706, Spain Received 7 August 2000; in ®nal form 29 September 2000
Abstract Two fragmentation reactions of vinyl ¯uoride (three-center and four-center HF eliminations) were investigated by AM1 direct classical trajectories. Product energy distributions (PEDs) were computed for dierent initial excitation schemes and the results compared with the experimental observations. The results support that the four-center elimination is the preferred decomposition process but HF elimination through the three-center mechanism is predicted to be signi®cant. Ó 2000 Elsevier Science B.V. All rights reserved.
1. Introduction The vinyl ¯uoride decomposition dynamics has been extensively studied in past years [1±7]. Particularly, Sato et al. [6] used mass-resolved photofragment time-of-¯ight spectroscopy and ab initio calculations to investigate the photodissociation of vinyl ¯uoride at 157 nm (182.1 kcal/mol). According to their MP2/6-31G(d,p) calculations [6], the open channels at the experimental energy are CH2 @CHF ! CHBCH HF
1
! CHBCF H2
2
! C2 H2 F H
3
! C2 H3 F
4
! CHBCH H F
5
*
Corresponding author. Fax: +34-981-595012. E-mail address: [email protected] (S.A. VaÂzquez).
HF eliminations (channel 1) can be produced from a four-center or a three-center transition state (see Fig. 1). The MP2/6-31G(d,p) calculations [6] predict classical barriers of 82.2 and 85.3 kcal/mol for the four-center and three-center eliminations, respectively. More recent calculations at the QCISD(T)/6-311G(2d,2p) level of theory aord barriers of about 80 kcal/mol (74 kcal/mol including the zero-point energy, ZPE) for both channels [8]; the others (channels 2±5) present energy barriers substantially higher [8]. Sato et al. [6] suggested that `the exit barrier for the four-center elimination is easily converted into the relative translational energy between acetylene and HF, while the exit barrier energy for the three-center elimination is largely partitioned into the internal energy of acetylene'. From this and the large amount of average translational energy observed in their experiment (42 kcal/mol), they concluded that HF is predominantly produced via the fourcenter elimination process. However, the most probable translational energy was found to be about 20 kcal/mol, suggesting that the three-center
0009-2614/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 0 ) 0 1 1 9 8 - 2
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E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
Fig. 1. The three-center and four-center transition states calculated by ab initio [8], AM1±SRP and AM1 methods. The ab initio methods are: QCISD(T) for energies, QCISD for geometries and MP2 for frequencies; all with the 6-311G(2d,2p) basis set.
process might be signi®cant. In addition, RRKM calculations [8] predict that both processes are likely to occur, with the three-center one slightly favored over the four-center at 182 kcal/mol above the vinyl ¯uoride ZPE. On the other hand, Watanabe et al. [3] reported distributions of HF produced by Hg-photosensitized reactions of ¯uorethylenes. At ca. 111.6 kcal/ mol of excitation energy, they found that 19% of the available energy goes to HF vibration, a value
much higher than the statistical one. The authors discussed two possible sources of disagreement. Firstly, a non-random distribution of the available energy among the internal degrees of freedom at the transition state, and secondly, the presence of a potential barrier that causes a strong force upon the separating fragments. The latter possibility was previously suggested by Berry [9] and Zamir and Levine [10]. In addition, Quick and Wittig [2] found similar trends at 20±35 kcal/mol of excess
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
energy with respect to the transition state ZPE, and concluded that the large HF vibrational excitation can be explained on the basis of the signi®cant stretching of the HF bond in the transition state with respect to its equilibrium value. Takayanagi and Yokoyama [7] performed ab initio (RHF/3-21G) classical trajectory calculations for the four-center HF elimination. They used an orthant-like sampling method at the transition state geometry, with no account of the ZPE. They obtained product energy distributions (PEDs) at several excess energies. While their average translational energy is similar to the experimental result [6], the vibrational state distributions of HF are not in good agreement with experiment. The above results prompted us to undertake a classical dynamics study for both the four-center and the three-center elimination processes of vinyl ¯uoride in order to assess the extent to which the three-center process is competitive. In this Letter, we present a direct dynamics simulation [11±14] by using a code that interfaces the classical trajectory program GE N D Y N [15] with the semiempirical electronic structure theory package MO P A C 7.0 [16,17]. The AM1 parameters [18] in MO P A C , supplemented with speci®c reaction parameters [12±14,19] (SRPs), are used in the present study. PEDs for several ensembles are calculated at two excitation energies, 111.6 and 182.1 kcal/mol (above the reactant ZPE), and the results compared with experiment [3,4,6]. 2. AM1±SRP semiempirical model We use the AM1 Hamiltonian [18] in the MO 7.0 [16,17] semiempirical package modi®ed by the use of speci®c reaction parameters (AM1± SRP) [12±14,19]. The use of speci®c reaction parameters was ®rstly proposed by Truhlar and co-workers [19], who adjusted the parameters of a NDDO wave function to reproduce experimental or ab initio data for speci®c reactions. The original AM1 parameters and the new AM1±SRP ones are listed in Table 1. Our own ab initio data [8] was used in the reparameterization procedure. More speci®cally, the new values were chosen to model the ab initio geometries and frequencies of the PAC
585
Table 1 AM1 and AM1±SRP parametersa Atom
Parameter
AM1 value
AM1±SRP value
H
Uss bs zs a Gss
)11.396 )6.174 1.188 2.882 12.848
)11.306 )6.554 0.998 3.102 12.808
C
Uss Upp bs Zs Zp a Gsp Gpp Gp2 Hsp
)52.029 )39.614 )15.716 1.809 1.685 2.648 11.470 11.080 9.840 2.430
)51.909 )39.914 )15.916 1.909 1.505 2.588 11.400 10.800 10.400 1.900
F
Uss Upp bp zs Gss Gsp
)136.106 )104.890 )27.922 3.770 16.920 17.250
)146.206 )105.510 )27.902 3.800 16.820 17.350
a
Only those parameters that were changed in the AM1±SRP model PES are listed in the table.
four-center and three-center transition states (see Fig. 1) as well as the energetics involved in the two elimination channels that are being studied here (shown in Fig. 2). The parametrization was performed in an iterative way until it was judged that an optimum point (at which the above properties were calculated about as well as possible) was reached. Peslherbe and Hase [20] have shown that product energy partitioning may depend on how the SRPs are chosen. Fig. 1 shows the four-center (TS1) and threecenter (TS2) transition states with the energies, imaginary frequencies, and some selected geometrical parameters calculated by ab initio [8], AM1, and AM1±SRP models. As seen in the ®gure, the AM1±SRP model predicts structures more similar to the ab initio ones than does the AM1 model. The AM1 energies are approximately 20 kcal/mol higher than the QCISD(T)/6-311G(2d,2p) and AM1±SRP values, and the AM1 imaginary frequencies are also very high, especially for TS2. Overall, the AM1±SRP model predicts reasonable
586
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
Fig. 2. Potential energy diagram for the three-center and four-center elimination processes. The numbers are the AM1±SRP energies (without ZPE) and those in parentheses the corresponding QCISD(T)/6-311G(2d,2p) values [8].
structures, energies, and frequencies for these transition states. Fig. 2 shows a schematic potential energy diagram showing the energetics of the HF elimination processes calculated at the AM1± SRP and QCISD(T)/6-311G(2d,2p) [8] levels of accuracy. As seen in the ®gure the agreement is quite good, with the average deviation being 2.7 kcal/mol only. 3. Trajectory computational details Throughout this paper and unless otherwise stated, the excitation energies are given with respect to the vinyl ¯uoride ZPE. The trajectories were initialized in three ways. First, the ecient microcanonical sampling (EMS) [21] without angular momentum was used to prepare a microcanonical ensemble at 182.1 kcal/mol, an energy for which experimental data are available [6]. For this ensemble (referred to as EMS), 5 105 steps
starting from the equilibrium geometry were taken for the warm up Markov walk and 104 between individual trajectories. In addition, at each step of the Markov walk, all the atoms were moved with a leading to an acceptance ratio step size of 0.125 A, between 0.3 and 0.5. Finally, to con®ne the sampling to the reactant con®guration space, maximum bond extensions allowed during the random for all the bonds. walk were 3 A In the second excitation scheme, a group of normal modes were selectively excited to obtain a total energy of 182.1 kcal/mol. Several ensembles were constructed in this way. In the one called WAGG, the wagging and twisting vibrational modes were initially excited. The FCC/CH2 ensemble corresponds to an initial excitation of the FCC bending and the CH2 rocking normal modes. Ensemble FCH/CH2 corresponds to the excitation of the FCH bending mode, and the CH2 rocking. The CC and CF stretching modes were initially excited together with the HCH scissoring mode in
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
587
Then, various classimasses were separated 10 A. cal mechanical molecular properties, such as relative translational energy, product vibrational and rotational energies, were calculated [25,26]. In addition, vibrational quantum numbers for the product HF were evaluated by the Einstein±Brillouin±Keller (EBK) [27±29] quantization of the action integral.
ensembles CC/HCH and CF/HCH, respectively. Finally, the three CH stretching normal modes were excited in ensemble CH. In the third method, the internal energy was distributed according to a quasi-classical microcanonical sampling of the normal mode vibrational states at the barrier [14]. The method is based on the classical barrier sampling [22] and selects each state with equal probability so that the momentum distribution in the reaction coordinate agrees with RRKM theory [23,24]. With this method, trajectories were initialized from TS1 (ensemble QCBS-TS1) or TS2 (ensemble QCBSTS2) at two selected energies: 111.6 and 182.1 kcal/ mol above the reactant ZPE. Once the initial conditions were set, the trajectories were integrated by using a fourth order Runge±Kutta±Gill routine with a ®xed step size of 0.05 fs. At each step of the integration the Schr odinger equation was solved for electronic energies and forces on the nuclei. After the SCF convergence, the ®rst derivatives of the energy with respect to the Cartesian coordinates were evaluated numerically within MO P A C 7.0, obtaining an energy conservation of at least four significant ®gures. Batches of 1000 trajectories were propagated until the HF and acetylene center of
4. Results Table 2 lists the PEDs evaluated in this work at the excitation energy of 182.1 kcal/mol (and additionally at 111.6 kcal/mol for the QCBS ensembles) as well as the experimental ®ndings [2,3,6]. The last column of this table collects the ratio N3 / N4 , where N3 and N4 are the number of trajectories that decomposes through the three-center and four-center transition states, respectively. As can be seen, for ensembles EMS, CF/HCH, FCC/CH2 , and WAGG the four-center channel is the preferred one, although the three-center process appears to be competitive. Note that although the energy dierence between the TS1 and TS2 structures predicted by the AM1±SRP model is significant (5.6 kcal/mol) compared with the QCISD(T)/
Table 2 PEDs and ratio N3 /N4 at 182.1 kcal/mol of excitation energy with respect to the vinyl ¯uoride ZPE
a
Ensemble
hEtrans i
hErot;HCCH i
hEvib;HCCH i
hErot;HF i
hEvib;HF i
N3 =N4
QCBS-TS1 QCBS-TS2 EMS CH CF/HCH CC/HCH FCC/CH2 FCH/CH2 WAGG Experimenta
43.5 27.4 20.3 21.9 19.7 21.1 48.7 26.0 29.6 42
7.8 12.8 11.8 11.8 11.7 11.8 10.6 14.5 12.2
67.6 81.9 109.0 93.7 88.6 91.4 77.1 86.0 87.4
22.5 25.6 14.6 17.2 15.7 17.4 13.1 21.2 19.2
35.6 29.3 21.3 32.4 42.3 35.3 27.5 29.3 28.6
± ±
QCBS-TS1b QCBS-TS2b Experimentc Experimentd
40.0 14.5
3.8 6.2
36.3 62.1
10.4 10.2
15.8 13.3 19 6 10
± ±
Taken from [6]. At 182.1 kcal/mol of excitation energy. At 111.6 kcal/mol of excitation energy. c Taken from [3]. At 111.6 kcal/mol of excitation energy. d Taken from [2]. At 94±109 kcal/mol of excitation energy. b
0.90 1.24 0.72 1.00 0.31 10.38 0.53
588
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
6-311G(2d,2p) result (see Fig. 2), it is not critical for the calculation of the ratio N3 /N4 at the excitation energy of 182.1 kcal/mol. For the CH and FCH/CH2 ensembles, elimination through the three-center transition state is more likely to occur. The result for ensemble FCH/CH2 (N3 /N4 10.38) can be easily understood by a simple inspection of the FCH bending eigenvector. As stated in Section 1, Sato et al. [6] concluded that HF is basically produced through the four-center elimination process. Our average translational energy computed for the QCBS-TS1 ensemble (43.5 kcal/mol) is similar to their average value (42 kcal/mol). The value obtained for the QCBS-TS2 is markedly lower (27.4 kcal/mol). These results seem to support their conclusion. However, as shown later, a more rigorous comparison between the calculated and observed translational energies should involved not only the average values but also the form of the distributions. The experimental values for the vibrational energy content in the product HF are 610 [2] and 19 kcal/mol [3] at excitation energies of 94±111.6 kcal/mol. Both the QCBS-TS1 and QCBS-TS2 results, 15.8 and 13.3 kcal/mol (9.8 and 7.3 kcal/ mol without ZPE), respectively, are in good agreement with experiment. On the other hand, the internal energy content in acetylene calculated for QCBS-TS2 (94.7 kcal/mol) is substantially higher than that obtained for QCBS-TS1 (75.4 kcal/mol), as Sato et al. [6] suggested. It is well known that, in general, classical trajectories initiated at the reactant phase space do not aord accurate PEDs due to the improper treatment of zero-point motion [22]. The product relative translational energy calculated for the EMS ensemble (20.3 kcal/mol) is signi®cantly smaller than the experimental quantity and, unexpectedly, than those predicted for the QCBS ensembles. Trajectories initiated in the reactant phase space may cross the transition state without ZPE in modes orthogonal to the reaction coordinate so that one would expect enhancement of the average translational energy in comparison with the outcomes aorded by QCBS. This unexpected result led us to conclude that the decomposition dynamics in the EMS ensemble is non-statistical, more speci®cally, intrinsically non-RRKM [23], a
behavior frequently observed in classical trajectory calculations at high energies [30]. As shown in Table 2, the average vibrational energy in acetylene calculated for the EMS ensemble (109.0 kcal/ mol) is substantially higher than the corresponding values obtained for the QCBS-TS1 and QCBS-TS2 ensembles (67.6 and 81.9 kcal/mol, respectively). For other ensembles in which vibrational modes involving the HCCH fragment are initially excited, such as CH or CC/HCH, the calculations show high vibrational energy contents for acetylene, too. Thus, it seems that a phase space bottleneck (or bottlenecks) may be associated to the HCCH moiety in our model and, as a consequence, the eective excitation energy in the EMS ensemble is lower than that in the QCBS ensembles, leading to this unexpected trend. The clear discrepancy found between the EMS and the experimental results, however, points out that this non-statistical behavior, exhibited in the EMS ensemble, may not take place in the experiment. The maximum HF vibrational energy content was obtained for the CF/HCH ensemble. This result could be expected because, for this ensemble, many trajectories crossing a transition state dividing surface will present very large HF bond distances due to the initial excitation of the CF stretch. The same can be applied to ensembles CH, and CC/HCH, which also aord a high content of HF vibrational energy. It is also remarkable the average translational energy obtained for ensemble FCC/CH2 (48.7 kcal/mol). To a large extent, this is a consequence of the fact that most of the trajectories produces HF via the four-center transition state (the ratio N3 /N4 is 0.31). So far, our comparisons between classical trajectory results and experimental data involved averaged properties. From now on, we will concentrate on vibrational state distributions and translational distributions, which may provide further insights into the dissociation dynamics of vinyl ¯uoride. Table 3 compares the HF vibrational state distributions obtained in this study with those determined experimentally [2,3] and those calculated in the previous dynamics study [7]. Our results for both the QCBS-TS1 and QCBS-TS2 ensembles are substantially dierent from the previous trajectory results [7] and more
E. Martõnez-N u~ nez, S.A. V azquez / Chemical Physics Letters 332 (2000) 583±590
589
Table 3 Comparison of the vibrational state distributions of HF produced in the photodissociation of vinyl ¯uoride at several excess energies Energya
v0
v1
v2
v3
v4
Experiment Experimentc
38 20±35
± ±
1.00 1.00
0.56 0.55
0.42 0.15
0.24 <0.05
QCBS-TS1 QCBS-TS2 Trajectoryd Trajectoryd
33 37 10 50
0.74 1.10 3.76 1.14
1.00 1.00 1.00 1.00
0.43 0.43 0.00 0.24
0.13 0.03 0.00 0.02
0.03 0.05 0.00 0.02
Method b
v5
0.00 0.00 0.00 ±
a
Excess energies (in kcal/mol) with respect to the transition state ZPE. Taken from [3]. c Taken from [2]. d Taken from [7]. The authors do not specify whether the zero-point energies were considered. b
similar to the experimental observations (especially to those of [2]). The QCBS-TS1 values are more similar to the experimental ones than are the QCBS-TS2, supporting the previous conclusion that HF is predominantly formed via the fourcenter channel [6]. Fig. 3 compares the experimental translational energy distribution obtained by Sato et al. [6] (solid line) with those calculated here (vertical bars) for ensembles QCBS-TS1 and QCBS-TS2. As can be seen, neither the QCBS-TS1 nor the QCBS-TS2 ensemble ®ts the experimental distribution. The QCBS-TS1 distribution peaks at a higher translational energy (ca. 40 kcal/mol, very near its average value). The QCBS-TS2 distribution peaks at a value similar to the most probable translational energy observed experimentally (ca. 20 kcal/mol) but the populations of trajectories with higher translational energy are signi®cantly smaller than the experimental distribution. Therefore, although the QCBS-TS1 results aord the best agreement with the average translational energy determined experimentally, disagreement is found for the most probable translational energy. The contrary is found for the QCBS-TS2 ensemble: the most probable translational energy predicted for this ensemble is in very good agreement with the experimental value but the average quantities dier considerably. Being more rigorous, the comparison of our results with experiment should involved a weighted average of the QCBS-TS1 and QCBSTS2 ensembles. Using the weighting factor cal-
culated from the N3 /N4 ratio for the EMS ensemble, the distribution thus obtained (Fig. 3c) ®ts the experimental one signi®cantly better than does the QCBS-TS1 or the QCBS-TS2 ensemble alone, although the experimental distribution peaks at a lower translational energy and is broader than the theoretical distribution. This comparison suggests that the percentage of HF eliminations evolving through the three-center transition state might be signi®cant in the experiment. To sum up, the results presented in this work seem to support that the dissociation of vinyl ¯uoride proceeds preferentially through the four-center elimination but the percentage of molecules decomposing via the three-center process should be signi®cant. Finally, it seems interesting to remark the role that a possible non-random initial excitation may play on the PEDs. As shown previously, dierent excitation schemes led to substantially dierent N3 / N4 ratios and PEDs. Now, for the sake of example, we include in Fig. 3 the translational energy distribution obtained from averaging the FCH/CH2 and WAGG distributions (panel d). As can be seen, the resulting distribution ®ts reasonably well the experimental curve. Note, on the other hand, that ensembles FCH/CH2 and WAGG clearly favor the four-center channel (the percentages of four-center eliminations are 76% and 65%, respectively). Our intention here is not to suggest that these modes are preferentially excited in the experimental conditions of Sato et al. [6], but to note that the possibility of a non-random initial
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References
Fig. 3. Translational energy distributions for: (a) the QCBSTS1 ensemble, (b) the QCBS-TS2 ensemble, (c) a weighted average of both QCBS ensembles, and (d) the average of FCH/ CH2 and WAGG ensembles. For all the plots, the solid line corresponds to the experimental distribution [6].
preparation of vinyl ¯uoride in the experiment should not be disregarded. Acknowledgements We thank `Centro de Supercomputaci on de Galicia' CESGA for time allocation for the calculations.
[1] M.J. Berry, G.C. Pimentel, J. Chem. Phys. 51 (1969) 2274. [2] C.R. Quick Jr., C. Wittig, J. Chem. Phys. 72 (1980) 1694. [3] H. Watanabe, H. Horiguchi, S. Tsuchiya, Bull. Chem. Soc. Jpn. 53 (1980) 1530. [4] D.J. Donaldson, D.G. Watson, J.J. Sloan, Chem. Phys. 68 (1982) 95. [5] S. Kato, K. Morokuma, J. Chem. Phys. 74 (1980) 6285. [6] K. Sato, S. Tsunashima, T. Takayanagi, G. Fijisawa, A. Yokoyama, Chem. Phys. Lett. 242 (1995) 401. [7] T. Takayanagi, A. Yokoyama, Bull. Chem. Soc. Jpn. 68 (1995) 2245. ~ ez, S.A. V [8] E. Martinez-N un azquez (submitted). [9] M.J. Berry, J. Chem. Phys. 61 (1974) 3114. [10] E. Zamir, R.D. Levine, Chem. Phys. 52 (1980) 253. [11] J.M. Milliam, V. Bakken, W. Chen, W.L. Hase, H.B. Schlegel, J. Chem. Phys. 111 (1999) 3800. [12] K. Bolton, W.L. Hase, G.H. Peslherbe, in: D.L. Thompson (Ed.), Modern Methods for Multidimensional Dynamics Computation in Chemistry, World Scienti®c, Singapore, 1998, p. 143. [13] C. Doubleday Jr., K. Bolton, W.H. Hase, J. Phys. Chem. A 102 (1998) 3648. [14] C. Doubleday Jr., K. Bolton, G.H. Peslherbe, W.H. Hase, J. Am. Chem. Soc. 118 (1996) 9922. [15] D.L. Thompson, GE N D Y N program. [16] J.P.P. Stewart, MO P A C 7.0, a General Molecular Orbital Package QCPE, 1993, p. 455. [17] J.P.P. Stewart, J. Comput. Chem. 10 (1989) 209. [18] M.J.S. Dewar, E.G. Zoebish, E.F. Healy, J.P.P. Stewart, J. Am. Chem. Soc. 107 (1985) 3902. [19] A. Gonzalez-Lafont, T. Truong, D.G. Truhlar, J. Phys. Chem. 95 (1991) 4618. [20] G.H. Peslherbe, W.L. Hase, J. Chem. Phys. 104 (1996) 7882. [21] G. Nyman, S. Nordholm, H.W. Schranz, J. Chem. Phys. 93 (1990) 6767. [22] W.L. Hase, D.G. Buchowski, Chem. Phys. Lett. 74 (1980) 284. [23] T. Baer, W.L. Hase, Unimolecular Reaction Dynamics: Theory and Experiments, Oxford University Press, New York, 1996. [24] R.G. Gilbert, S.C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell Scienti®c Publications, Oxford, 1990. [25] D.L. Bunker, Meth. Comput. Phys. 10 (1971) 287 (and references therein). [26] L.M. Ra, D.L. Thompson, in: M. Baer (Ed.), Theory of Chemical Reaction Dynamics, CRC Press, Boca Raton, 1985. [27] A. Einstein, Verh. Dtsch. Phys. Ges. 19 (1917) 82. [28] M.L. Brillouin, J. Phys. (Paris) 7 (1926) 353. [29] J.B. Keller, Ann. Phys. 4 (1958) 180. [30] D.V. Shalashilin, D.L. Thompson, J. Chem. Phys. 105 (1996) 1833.