Ab Initio Calculations on the Vinyl Fluoride ... - Springer Link

Structural Chemistry, Vol. 12, No. 2, 2001

Ab Initio Calculations on the Vinyl Fluoride Fragmentation Reactions ˜ 1 and Saulo A. Va´ zquez1,2 Emilio Mart´ınez-Nu´ nez Received October 31, 2000; accepted January 11, 2001

High level ab initio calculations for the fragmentation reactions of vinyl fluoride were performed. The relative energies calculated at the QCISD(T)/ 6-311G(2d,2p) level of theory, corrected with MP2/ 6-311G(2d,2p) zero-point energies (ZPEs), differ significantly from those obtained previously at a lower level of theory. The calculations suggest that both the three- and four-center HF elimination processes are likely to occur, with the three-center elimination favored over the four-center at high energies. KEY WORDS: Vinyl fluoride; fluoroethylene; fluoroethene; ab initio calculations; potential energy surfaces.

INTRODUCTION

in their experiment the translational energy distributions are associated to the ground-state potential energy surface (PES) of neutral vinyl fluoride. In fact, in the same study, they performed MP2/ 6-31G(d,p) calculations on the ground-state PES of neutral vinyl fluoride in order to confirm the reaction mechanism they initially proposed from the experimental observations. According to their ab initio calculations [13], the open channels at the experimental energy are

Recently, we have been studying the unimolecular dynamics of moderately large polyatomics using the classical trajectory method [1–7]. In particular, we have focused our attention on the RRKM versus non-RRKM behavior of these systems. In most cases, we performed traditional classical trajectory calculations, that is, trajectory simulations employing an analytical potential energy function fit to ab initio and/ or experimental data. Very recently, we have also employed the direct dynamics procedure [7 and references therein], with which the construction of a global potential energy surface is avoided. Specifically, we used the AM1 method with specific reaction parameters (AM1-SRP). The vinyl fluoride decomposition dynamics has been extensively studied in past years [8–14]. Sato et al. [13] used mass-resolved photofragment time-of-flight spectroscopy to measure the relative translational energy distributions of the fragments produced in the photolysis of vinyl fluoride at 157 nm (182.1 kcal/ mol). The photofragments were detected by a quadrupole mass spectrometer, which ionizes them. Note, however, that

CH2 — CHF r CH — CH + HF r CH — CF + H2 r C2 H2 F + H r C2 H3 + F r CH — CH + H + F

They found that HF elimination is the main primary dissociation process and concluded from their translational energy distributions that this reaction channel has a substantial exit barrier [13]. HF eliminations can occur through a three- or four-center transition state and, on the basis of their results [13], they concluded that the latter is more likely to occur. The same research group also reported a dynamics study [14], but they only considered the four-center HF elimination process among

1 Departamento

de Qu´ımica F´ısica, Universidad de Santiago de Compostela, Santiago de Compostela E-15706, Spain. 2 To whom all correspondence should be addressed.

95 1040-0400/ 01/ 0400-0095$19.50/ 0  2001 Plenum Publishing Corporation

˜ and Va´ zquez Mart´ınez-Nu´ nez

96

those specified above. Therefore, it would be desirable to undertake a dynamics study taking the other reactive channels into account. To this end, one first needs to characterize all the stationary points at an accurate ab initio level of theory. The MP2/ 6-31G(d,p) level used by Sato et al. [13] may not be accurate enough to model the energetics of the unimolecular decomposition of vinyl fluoride. This is especially true for those channels involving radical species, for which the UMP2 method may perform poorly due to significant and variable spin contamination [15]. In the present study, we performed ab initio calculations at the QCISD(T)/ 6-311G(2d,2p)/ / QCISD/ 6311G(2d,2p) level of theory for all stationary points of the vinyl fluoride fragmentation processes. In addition, we carried out MP2/ 6-311G(2d,2p) computations to evaluate vibrational frequencies and zero-point energies (ZPEs) for the species involved in these reactions. The calculations presented here are at a much higher level of theory than those reported previously by Sato et al. [13] and cover more stationary points. The purpose of this work is twofold. First, to provide more reliable ab initio outcomes for geometries, vibrational frequencies (not reported previously), and energies. Second, to serve as input data for the calibration of the AM1-SRP method, which will be used in a separate classical trajectory study [16].

COMPUTATIONAL DETAILS All the electronic structure calculations were carried out using the GAUSSIAN94 program package [17].

The standard 6-311G(2d,2p) basis set was employed in all the computations. We have performed global optimizations at both the MP2 and QCISD levels of theory for all the stationary points involved in the ground-state fragmentation reactions of vinyl fluoride. The vibrational frequencies for these stationary points were evaluated at the MP2/ 6-311G(2d,2p) level of theory. To obtain more reliable relative energies, we used the QCISD(T) method at the optimized QCISD energies with the same basis set as above. Finally, the energies were corrected to take the ZPEs into account, evaluated from the MP2 vibrational frequencies.

RESULTS Geometrical parameters for the minima optimized at the QCISD/ 6-311G(2d,2p) level are collected in Table I. The QCISD optimized geometries for the five transition states (saddle points of index one) found in the present work are displayed graphically in Fig. 1. Except for the monoatomics (H and F) and diatomics (H2 and HF), all the structures optimized in this work show Cs symmetry. Following the notation of Sato et al. [13], TS1 is a saddle point of index one for the four-center HF elimination, TS2 corresponds to the three-center HF elimination, and TS3 to the three-center H2 elimination. No transition state for a four-center H2 elimination was found in the present study. Finally, TS4 and TS5 connect H2 C — C with HC — — CH and HFC — C with HC — — CF, respectively. These two relevant transition states were not studied in the work of Sato et al. [13]. The geometrical features for TS1, TS2, and TS3 predicted with

˚ ) and Bond Angles (in Degrees) for the Minimaa Optimized at the QCISD/ 6-311G(2d,2p) Level Table I. Bond Lengths (in A C — C C1 — H C1 — F C2 — H1 C2 — H2 H — C1 — F F — C1 — C H — C2 — C H — C2 — C H — X (H — H, F) HFC — CH2 FC — CH2 cis-HFC — CH trans-HFC — CH — CH HC — — HF H2 C — C HFC — C H2 — FC — — CH HC — CH2 a All

1.3238 1.3174 1.3098 1.3093 1.2036

1.0794 1.0830 1.0790 1.0613

1.3457 1.3146 1.3461 1.3566

1.0786b 1.0825b 1.0725 1.0728 1.0613

1.0775 1.0761

1.0832

1.0832

112.6 112.4

121.9 129.1 123.0 122.5

119.2 120.1b 135.6 139.6 180.0

121.1 120.0

120.0

120.0

0.9128 1.3039 1.3281

1.0888

1.3333

117.2

128.9 0.7422

1.1960 1.3128

1.2828 1.0771

1.0593 1.0825

180.0 1.0878c

the structures, except diatomics, present CS symmetry. C — H bond eclipses the C — F bond. c The H atom is in cis arrangement. b The

112.4

180.0 121.2

117.9

Vinyl Fluoride Fragmentation Reactions

97

Fig. 1. Transition states optimized at the QCISD/ 6-311G(2d,2p) level of theory, showing the ˚ ) and bond angles (in degrees). bond distances (in A

the QCISD method are, in general, very similar to those obtained previously at the MP2/ 6-31G(d,p) level [13]. The MP2/ 6-311G(2d,2p) also afford similar structures, except for TS3. Strikingly, for this transition state, our MP2 distance separating the H2 and HFC — C moi˚ ) is much longer than those calculated at eties (≈2.6 A the QCISD/ 6-311G(2d,2p) and MP2/ 6-31G(d,p) levels ˚ in both cases). (≈0.06 A The energy results are collected in Table II. For the sake of completeness, we include our MP2/ 6311G(2d,2p) values as well as those calculated by Sato et al. [13] at the MP2/ 6-31G(d,p) level. The last entry of Table II, denoted by QCISD(T)ZPE , refers to the QCISD(T) relative energies plus ZPE corrections. These ZPE corrections were evaluated from our MP2 vibrational frequencies listed in Table III. For TS3, the ZPE obtained from MP2/ 6-311G(2d,2p) calculations was so

small that the QCISD(T)ZPE energy path for the formation of HFC — C + H2 became “loose.” For this reason, we evaluated the ZPE of TS3 at the MP2/ 6-31G(d,p) level (which affords a transition structure similar to that predicted by QCISD). For convenience, a potential energy diagram for the unimolecular processes involved in the decomposition of vinyl fluoride is shown in Fig. 2. The numbers depicted in the figure are our best relative energies, that is, the ZPE-corrected QCISD(T) values. We note here that the energetic values reported in ref. [13, Fig. 3] were not corrected to take the ZPE into account. As can be seen from Table II, there are substantial discrepancies between the MP2 and QCISD energy results. Thus, for C — H scissions, the differences are about 5 kcal/ mol. More acute discrepancies are found for the C — F dissociation and for TS3. For the former, we found a discrepancy of ≈5 kcal/ mol. On the other hand,


98

Table II. Relative Energiesa for the Stationary Points Found in This Work

HFC — CH2 [FC — CH2 + H] [cis-HFC — CH + H] [trans-HFC — CH + H] — CH + HF] [HC — — — CH + H + F] — [HC — [H2 C — C + HF] [HFC — C + H2 ] — [FC — — CH + H2 ] [HC — CH2 + F] TS1 TS2 TS3 [TS4 + HF] [TS5 + H2 ]

MP2b

MP2

QCISD

QCISD(T)

QCISD(T)ZPE c

0.0 — — — 32.0 162.6 — — 64.1 126.2 82.2 85.3 118.0 — —

0.0 120.8 124.3 124.4 24.5 162.6 76.2 117.8 62.6 134.0 79.2 83.6 116.4 75.6 117.8

0.0 116.0 119.0 119.2 27.7 160.6 69.8 109.6 65.4 118.9 82.3 82.4 108.7 75.5 112.8

0.0 116.4 119.7 119.9 27.5 161.8 70.9 110.2 64.4 121.6 79.7 80.2 108.4 75.1 111.8

0.0 108.9 112.0 112.3 22.2 150.6 63.9 99.9 55.6 117.9 74.3 74.7 101.2 66.8 101.2

kcal/ mol. The 6-311G(2d,2p) basis set was used in the calculations. / 6-31G(d,p) calculations from Ref. [13]. c QCISD(T) values plus ZPE corrections obtained from MP2 vibrational frequencies (see text). a In

b MP2

the QCISD(T) relative energy for [HC — CH + F + H] decreases by ≈11 kcal/ mol when the ZPE is considered. Finally, our QCISD(T)ZPE barriers for the three- and four-center HF eliminations (74.7 and 74.3 kcal/ mol, respectively) compare very well with the experimental activation energy for the molecular elimination of HF, estimated to be 70.8 ± 3.6 kcal/ mol [18]. As stated elsewhere [13] and shown in Fig. 2, the three-center HF elimination leads to the subsequent isomerization of vinylidene (H2 C — C) to acetylene. Jensen et al. [19] have reported that the barrier height for the isomerization from vinylidene to acetylene is 0.9 kcal/ mol at the MP4/ 6-311+G(d,p) level. Higher-level calculations performed by Gallo et al. [20] led them to conclude that the classical barrier for this process is ≈3 kcal/ mol. Our QCISD(T) computations predict a value of 2.9 kcal/ mol, in good agreement with the latter. Our results indicate that the overall exit barrier for the threecenter elimination is comparable to that for the four-center elimination. As a consequence, one may expect that the percentage of HF formation through each of these channels is very similar. To verify this, we have undertaken RRKM calculations [21] for these two channels, using the QCISD(T) barrier heights and the MP2 vibrational frequencies. Figure 3 shows the ratio three-/ fourcenter HF elimination in the 60–200 kcal/ mol energy range, calculated as k 2 / k 1 , where k 2 (k 1 ) stands for the RRKM rate constant for the three-center (four-center) HF elimination. As seen in the figure, for energies very

near the threshold, the four-center is favored over the three-center HF elimination. This fact is explained on the basis of the small critical energy difference (0.4 kcal/ mol) favoring the former channel. However, as the energy rises, the ratio k 2 / k 1 reaches a constant value of Table III. Vibrational Frequencies (in cm − 1 ) Obtained at the MP2/ 6-311G(2d,2p) Level for Species Involved in Decomposition of Vinyl Fluoride HFC — CH2 FC — CH2 cis-HFC — CH trans-HFC — CH — CH HC — — HF H2 C — C HFC — C H2 — CH FC — — HC — CH2 TS1 TS2 TS3a TS4 TS5 a MP2

483, 738, 857, 943, 975, 1182, 1347, 1434, 1710, 3211, 3250, 3324 467, 728, 945, 965, 1204, 1425, 1950, 3195, 3322 503, 787, 792, 981, 1142, 1340, 1941, 3206, 3377 453, 837, 842, 1037, 1082, 1352, 1939, 3255, 3376 580 (2), 743 (2), 1966, 3443, 3530 4206 241, 717, 1228, 1683, 3162, 3263 113, 642, 945, 1163, 1784, 3048 4530 385 (2), 577 (2), 1057, 2249, 3512 747, 979, 1048, 1098, 1438, 1885, 3133, 3235 2018i, 540, 606, 695, 748, 759, 934, 1034, 1718, 1824, 3359, 3422 1327i, 278, 519, 573, 774, 816, 950, 1303, 1641, 2279, 3183, 3291 325i, 293, 307, 359, 510, 659, 735, 1021, 1206, 1747, 3216, 4341 1009i, 628, 916, 1833, 2533, 3396 114i, 616, 924, 1154, 1806, 3008

/ 6-31G(d,p) calculations (see text).

Vinyl Fluoride Fragmentation Reactions

99

Fig. 2. Potential energy diagram for the fragmentation reactions of vinyl fluoride. QCISD(T)ZPE values are given in kcal/ mol.

about 1.7, thus slightly favoring the three-center elimination process. This may be explained by the fact that, as the energy increases, the entropy factor (governed by the frequencies at the transition states) becomes more important than the barrier height and consequently the HF elimination through TS2, which is “looser” than TS1, is favored. However, Sato et al. [13] concluded that HF

is mainly produced via four-center elimination, since, in their experiment, a large amount of available energy is partitioned in relative translational energy between HF — CH. Our results contrast with their conclusion and HC — and suggest that one or both of these two reaction channels might be nonstatistical. This possibility is explored in a separate work [16]. Finally, the reaction endothermicity for the channels leading to HC — — CH + HF is also very important for the correct interpretation of the experimental product energy distributions. The experimental endothermicity has been reported to be about 19 kcal/ mol [22, 23]. In the present work, we obtained a value of 22 kcal/ mol, which is more similar to the experimental result than is the theoretical value reported previously (32 kcal/ mol) [13].

CONCLUSIONS Fig. 3. Branching ratios for the three- vs. four-center HF elimination channels in the energy range 60–200 kcal/ mol.

In the present work we report high level ab initio calculations for the ground-state fragmentation reac-


100

tions of vinyl fluoride. While for geometries our QCISD results are very similar to those obtained by Sato et al. [13] at the MP2 level, for energies there are marked differences. The barrier heights for the three-center and four-center HF eliminations are predicted to be similar. The ab initio results of this work were employed to calculate RRKM rate constants for the three- and fourcenter HF elimination processes. Our RRKM results suggest that the two processes are likely to occur, with the three-center elimination favored over the four-center at high energies. These results suggest that some dynamical (non-RRKM) effects might be present in the experiment of Sato et al. [13], since they concluded that HF elimination is mainly produced through the four-center transition state. ACKNOWLEDGMENTS We thank Centro de Supercomputacion de Galicia (CESGA) for their computational facilities. We also thank R. Rodr´ıguez-Ferna´ ndez for his help as system manager of our computer resources. REFERENCES 1. Mart´ınez-Nu´ n˜ ez, 5393. 2. Mart´ınez-Nu´ n˜ ez, 8907. 3. Mart´ınez-Nu´ n˜ ez, 9783. 4. Mart´ınez-Nu´ n˜ ez, 10501.

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