J. CHEM. SOC. FARADAY TRANS., 1994, 90(2), 249-252 Dynamical Studies of the Reaction Be + HF(v, J) + BeF(v', J') + H on a New at,initio Potential-energy Surface Xinhou Liu Institute of Photographic Chemistry, Academia Sinica , Beijing 100101,People's Republic of China A new ab initio potential-energy surface for BeHF has been Fused for classical trajectory calculations on Be + HF(v,J) + BeF(v', J') + H. A reactive cross-section of 0.656 A2 is obtained for a collision energy of 83.58kJ mol-' on the ro-vibrational state of HF (0,0). This cross-section is increased by a factor of ca. five for the (1, 0) and ca. twelve for the (0, 30). It has been found that many trajectories pass through a deep well for the collinear complex FBeH. The role of the complex and the rotational excitation of HF is discussed.The energy dispersal in the products is also discussed. The simple atom-exchange reactions of the Group 2 atoms with hydrogen halides to form the metal monohalides have served over the past ten years to illustrate several conceptual principles in reaction dynamics. The reactions of Ba, Sr, and Ca with HX (X = F, C1, Br, I) have been studied in detail, experimentally and the~retically.'-~ Recently, trajectory calculations on the Ca + HF reaction have been reported by Jaffe." This study showed that a deep H-Ca-F potential-energy well dominates the collision dynamics of the reaction. For example, at a relative initial kinetic energy of 21 kcal mol-' more than 98% of the trajec- tories sample this well.Thus the Ca + HF reaction consti- tutes a type of neutral three-atom chemical insertion reaction which proceeds through a long-lived complex. A recent study16 of Ca + DF(u = 2, J) supported this reaction mecha- nism since the internal state distributions of the CaF are also well represented by statistical distributions. In particular, it has been found that the nearly isoenergetic reactions Ca + HF(v = 1, J = 7) and Ca + DF(v = 2, J = 1) give iden- tical product state distributions. This suggests that the reac- tion retains no 'memory' of the initial form of the reactant energy and the excess energy of the reaction is dispersed sta- tistically into all possible modes. It is clear from the experimental evidence that reactions of Group 2 atoms with hydrogen halides may proceed via the formation of a complex.This mechanism in the reactive encounters is important, particularly for the lighter alkaline- earth-metal atoms. Thus for the Ba + HX system, the reac- tion appears to be a direct abstraction. At high collision energies, Sr + HX behaves similarly, but at low collision energies complex reactions become important. However, Ca + HX reactions proceed mainly through complexes. Probably it may be speculated that for the lightest member of this family, Be, complexes should also play an important role. However, it is still not clear why the reactions show a forward-scattering behaviour. Generally speaking, for a reac- tion which proceeds via a complex that is long-lived com- pared with its rotational period, a forward-backward sym-metry angular distribution of the product should be obtained because the long-lived complex will lose the 'memory' of its initial translational vector so that the product will be scat- tered in all directions.Further experimental studies on this point are, therefore, still needed. In this paper, classical trajectory calculations on the reaction: Be + HF(v, J) + BeF(v', J') + H using a new ab initio potential-energy surface are given. Classical Trajectory Calculations Recently, we reported a new ab initio potential-energy surface using a large polarization basis set (6-311G**) for the BeHF system.32 Electronic correlation energies were given by fourth-order Moller-Plesset perturbation theory (MP4). Then the ab initio points were fitted to an analytical function using the many-body expansion method (PES2).The main features of this new function (PES2) will be mentioned briefly in this section. The reaction, Be + HF + BeF + H, is exothermic by 25 kJ mol-' on this surface. Like other surfaces for BeHF'7*'8,22 there is a very deep potential well corresponding to the stable, linear structure, F-Be-H, 373 kJ mol-' below the reactants. The transition state is very bent, at an angle of 70°, which is very different to those and the barrier height is only 79.99 kJ mol-'. The transition state on PES2 is slightly displaced towards the exit channel. Therefore, it belongs to the so-called 'late barrier'. It is very interesting that the transition state on this new surface is quite similar to that of the CaHF system reported by Jaffe et a1." In the CaHF system, the transition state is located in the product channel at an angle of 75" and the barrier is 68 kJ mol-' above the reactants.It can therefore be predicted that there may be some common dynamical features between the BeHF and CaHF systems. Classical trajectory calculations have been also performed on PES2.32 Relative translational energies ET of 84 kJ mol-', 105 kJ mol-' and 126 kJ mol-' were chosen. The initial ro-vibrational states of HF were taken as (v = 0, J = 0, 10, 20, 30) and (v = 1, J = 0) for each value of ET in order to investi- gate the effect of the reactant rotation on the reactive dynamics.More than 500 trajectories were run for each initial condition. The potential was monitored throughout the collisions in order to probe the reactive complex. Since the potential well on PES2 is deep, the energy threshold for the complex formation was chosen as 65 kJ mol- ' below that of the reactants. If the potential fell to this value and its con- figuration was near the linear complex, then the trajectory was deemed to have entered the region of the potential well. The calculated results are given in Table 1. The program, POT3DND,33 was used in the calculations. The values of b,,, obtained by carrying out a small number of trajectories, were found to vary between 1.2 A at the lowest collision energy and 2.4 8, at the highest collision energy and at the highest ro-vibrational state of HF.These b,,, values are much larger than those obtained for PES1.22 Similar b,,, values have been found for the Ca + HF reac- tion." Opacity functions P(b) for selected energies are given in Fig. 1. The decrease of P(b)with increasing b values is typical of reactions occurring on potential-energy surfaces having a barrier to reaction. For rotationally cold HF, increasing the translational J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Summary of dynamical calculations on the MP4/6-311G** surface 83.58 0, 0 1.2 53 0.656 83.58 14 21 65 104.50 0, 0 1.4 55 1.016 104.50 19 23 58 83.58 0, 10 1.5 65 2.721 108.98 15 20 65 125.40 0, 0 1.4 52 1.034 125.40 23 26 51 83.58 1, 0 1.6 59 3.224 127.48 16 21 65 104.50 0, 10 1.8 69 2.723 129.9 21 22 57 104.50 190 1.8 63 4.478 148.40 18 21 61 125.40 0, 10 1.9 72 2.722 150.8 28 22 50 125.0 1, 0 1.8 67 4.784 169.3 19 22 59 83.58 0, 20 2.2 74 6.3 10 180.97 19 23 58 104.50 0, 20 2.2 75 6.858 201.89 22 25 53 125.40 0, 20 2.5 79 9.07 1 222.79 25 28 47 83.58 0, 30 2.4 78 8.487 298.58 22 27 53 104.50 0, 30 2.4 81 9.029 319.50 23 19 48 125.40 0, 30 2.6 84 11.63 340.40 25 30 45 energy results in little overall change in either b,,, or P(b)so approach unity for small b values.This is different from the that cross-sections are little changed, but increasing vibra- result obtained using PES1.22 This implies that there is a tional energy increases both b,,, and P(b)and hence the reac- steric preference for the reaction even for J = 10.However, as tion cross-sections. The increase of 0.49eV (47kJ mol-') in the rotational quantum number of the reactant increases for the total energy will also be influential in increasing the any initial vibrational or translational energy P(b) cross-sections. approaches unity for small b values. This seems to show that The effect of increased rotational excitation of the HF on the reaction proceeds for high rotational states even when the the opacity functions is also shown in Fig. 1. From J =0-10, Be atom initially encounters the H end of the HF.However, a the overall change in P(b)is very slight, but from J = 10-20, factor which should be considered is the relative timescales of there is more than a three-fold increase in P(b).This is prob- the reactant. The rotational periods of HF for J = 10 and 20 ably because the total energy has been increased. The rota- are 86 x s and 43 x s, whereas the average tional excitation energies of the HF for J = 10, 20 and 30 are direct trajectory time is 40 x s on PES2. Thus an 25 kJ mol-', 97.5 kJ mol-' and 216.0 kJ mol-', respectively. asymptotic approach from the H end of the molecule with Therefore, it seems that at a given translational energy both J =20 may still be directed towards the F in the collision vibrational and rotational excitations enhance the reactivity region.For an even higher rotational state, say J = 30, there with the vibrational effects being more pronounced. A similar is a greater opportunity to reach the favoured approach result has been obtained using Chapman's MCSCF surface. '* angle of 70" during the trajectory so that for some b values, Such behaviour is expected, when the barrier is not displaced P(b)can reach unity. Thus the reaction on PES2 at low rota- early in the entrance channel. tional states of the reactants has a steric preference. Actually, Another dynamical feature shown by Fig. 1 is that for rota- that is not surprising because contour plots for Be moving tionally and vibrationally cold HF, opacity functions do not around the HF shows an angular preference to insert into the HF molecule.32 Therefore, PES2 shows a larger anisotropy and a much stronger energetic preference for the non-collinear reaction pathway. Fig.2 gives a qualitative view of the dependence of upon the reactant energies. It is clear that for cold initial states of i, I the HF, increasing translational energy increases the reacti- 0.25----I 0.251 000' " ' -t 1 .I.I,,.,.I I I . -t-,, 1 -1-L I o 05 1.0 1.5 20 25 o 0.5 1.0 1.5 2.0 2.5 o 0.5 i.0 1.5 2.0 2.5 impact parameter/A EJkJ mol-' Fig. 1 Opacity functions [P(b)].E, = A, 84; B, 105 and C, 126 kJ Fig. 2 Cross-sections. tr, J = (+) 0, 30; (+) 0, 20; ( X ) 40; (A) 0, 10 mol-'; u, J = (a)0,O; (b) 1,O; (c) 0, 10; (d)0,20 and (e)0.30 and (0)0,O. J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 vity very slightly, even for J = 10, but for higher ro-vibrational states of the HF as the translational energies rise, the reactivity will increase, particularly for J = 20 and 30. A fact to be noted is that the state (u = 1, J = 0) at ET = 84 kJ mol-has the same total energy as the state (u = 0, J = 0) at E, = 125 kJ mol-', and the state (v = 0, J = 10)at ET = 104 kJ mol-', but the order of the reactivity is (u = 1, J = 0) > (u = 0, J = 10) > (u = 0, 3 = 0). Thus the effect of increasing reactant energies on reactivity appears to follow the order, vibration > rotation > translation. Histograms showing product energy distributions are given in Fig. 3-5. Each panel is normalized to unit area.Fig. 3 presents the BeF product vibrational state distributions p(u'). For the same translational energy, the product vibrational 0.2500.125t i 0.3751 i0.125 (d' I0.125 0.0 0 5 10 15 20 5 10 15 20 5 10 15 20 25 vibrational state, N, at BeF Fig. 3 Distributions of product vibration states. A-C and (a)-(e)as in Fig. 1. 0.40 0.30 0.20 0.10 0.30 0.20 0.10 > c. *-0.30-.-a 0.2c2 g 0.10 n 0.30 0.20 0.10 0.30 0.2c tf +-+L 10.1c 0.300 0.2250.150 t 251 I I I (b) i I t n BeF scattering angles/degrees Fig. 5 Distributions of product scattering angles. AX and (a)-(e) as in Fig. 1. distributions become broader on increasing the reactant vibrational excitation.Increasing the translational energy also broadens the distribution somewhat. Small rotational excitation causes little change while high excitation leads to a much broader distribution. In part this may be a simple reflection of added total energy. Product rotational distribu- tions are shown in Fig. 4. A similar trend is obtained: increas- ing energy broadens the distributions. Angular distributions of the BeF product are shown in Fig. 5. As shown in Fig. 5(a) and (b)(where results for J = 0 are reported), the shape exhi bits approximate forward-backward symmetry peaks when the reactant is rotationally cold. As the values of J increase it slowly evolves to a forward scattering pattern [Fig. 5(c)-(e)]. In addition, as the translational energy is increased and the vibrational state of the reactant is excited from v = 0 to u = 1, forward scattering is also increased.Thus at higher total energies, the reaction exhibits a forward- scattering behaviour. Such behaviour can be attributed to the long-lived complexes whose number decreases with increas- ing energy. Table 1 shows that there are many trajectories which pass over the potential well on this surface. It should be expected that isotropic scattering would give a flat dis- tribution. Table 1 also gives the partitioning of the total energy into product translation, rotation and vibration; (A) is the frac- tion of energy in the ith mode. The reaction on the MP4/6- 31 1G**(PES2) surface strongly favours product translation, more than 50% of the available energy being channelled in this mode.This contradicts experimental observations on such reactions.' Product rotation is least sensitive to the reactant energy distribution. At the lowest total energy studied (Etota,= 84 kJ mol-') which is near the reaction threshold, less than 15% of the available energy goes into vibration but the fraction rises to ca. 20-30% at higher ener- gies. As the translational energy is increased the BeF vibra- tion takes an increasing share of the total energy. Rotational excitation has little effect on product energy distribution. LI,,,; LA,,L.i30 60 90 120 30 60 90 120 30 60 90 120 150 Therefore, to use the notation of P~lanyi,~~ near the thresh- rotational state, N, at BeF old,Fig.4 Distributions of product rotational states. A-C and (a)-(e) as in Fig. 1. AT AT' -k AR' (1) while at higher energies, AT +AT' -+ AR' 4-AV' (2) As mentioned before,22 it is known that the presence of a potential-energy well is not sufficient to produce long-lived complexes. Table 1 gives the percentage of reactive trajec- tories passing through the potential well. It can be seen that more than 50% of reactive trajectories sample the region of the well and usually they spend a long time in this region. The number of non-reactive trajectories which pass through the potential well was found to be very small. Thus, it can be concluded that encounters leading to the formation of the complex will enhance the reaction.Increasing translational or vibrational energies of the reactant do not favour the forma- tion of the complex. However, as the rotational quantum number of the reactant is increased, many more trajectories sample the well. A plausible explanation for this result is that at constant E,, a fairly slow moving heavy Be atom approaching a rapidly rotating HF molecule passes through the favourable 70" < Be-F-H configuration and thus is more likely to enter the well. In addition, it seems that a more bent transition state leads to easier insertion of Be into HF so that the opportunity to form the complex increases. Conclusions At present there have been no experimental results for BeHF reported in the literature. One reason for this is that the barrier to this reaction was thought to be much higher than for other reactions of this series, but our calculations using the large basis set and MP4 correlation give a barrier which is only half the height of earlier calculations.Another reason for the reaction not having been studied experimentally is the high toxicity of beryllium. The studies reported in this paper predict the following important features of Be + HF scattering: (1) At an initial translational energy, the reaction cross-section increases with increasing values of the initial HF vibrational, rotational and translational energies. Vibrational excitation of HF is more effective in promoting BeF forma- tion than in placing a corresponding amount of energy in initial translation or HF rotation.The order of promoting reaction is: vibration > rotation > translation. (2) The percentage of trajectories which sample the H-Be-F potential well is increased by increasing the HF rotational energy. (3) The complex, F-Be-H, plays an important role in the process of the reaction. A large number of reactive trajec- tories (> 50%) pass through this potential well. The author wishes to thank Prof. J. N. Murrell, Dr. P. J. Knowles and Dr. S. Carter for helpful discussions. The J. CHEM. SOC. 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