A Combined Experimental-Theoretical Study of the OH + CO H + CO 2. Reaction Dynamics

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1 A Combined Experimental-Theoretical Study of the OH + CO H + CO 2 Reaction Dynamics Adriana Caracciolo, 1,# Dandan Lu, 2,# Nadia Balucani, 1 Gianmarco Vanuzzo, 1 Domenico Stranges, 3 Xingan Wang, 4 Jun Li, 2,* Hua Guo, 5 and Piergiorgio Casavecchia 1,* 1 Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Perugia, Italy 2 School of Chemistry and Chemical Engineering, Chongqing University, Chongqing , China 3 Dipartimento di Chimica, Sapienza - Università di Roma, Roma, Italy 4 Department of Chemical Physics, School of Chemistry and Materials Science, University of Science and Technology of China, Hefei, Anhui , China 5 Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico, 87131, USA Supporting Information I. Experimental details Briefly, two supersonic beams of the reactants are crossed at 90 in a scattering chamber kept at about mbar in operating conditions. Product angular and velocity distributions are measured by a rotatable electron impact ionization quadrupole mass spectrometer detector and TOF analysis. The whole detector can be rotated in the plane defined by the two beams of the reactants, with the laboratory angle Θ=0 corresponding to the OH beam direction. The long used electron multiplier as ion detector was recently replaced by a Daly detector which led to an 1

2 enhanced collected signal, following also an improved ion focalization on the Daly cathode (held at -14 kv) by two electrostatic cylindrical lenses inserted at the quadrupole exit. 1 The OH radical beam was produced by a Radio-Frequency (RF) discharge supersonic beam source starting from a dilute mixture of H 18 2 O in He. 2, 3 By discharging 220 mbar of the He/H 18 2 O gas mixture (He gas was bubbled in a flask containing H 18 2 O kept at 277 K) through a water cooled quartz nozzle (0.26 mm dia.) at 300 W RF power, an intense beam of 18 OH radicals was produced with peak velocity of 2787 m/s and speed ratio of 5.4. The hydroxyl radical beam contains also other species, such as atomic oxygen and hydrogen, as well as undissociated water, but they do not interfere because the detected reaction product C 18 O 16 O (m/z=46) under singlecollision conditions can only originate from the reaction of C 16 O with 18 OH. The OH radicals are expected to be in the ground electronic state, 2 Π, because possible electronically excited states of OH are short lived (<1 μs) 4 and would relax to the ground state before reaching the collision region (about 5 cm away from the nozzle). OH is also expected, following supersonic expansion, to be essentially in the ground vibrational level and in the lowest several rotational levels, as shown by previous characterization in our laboratory of similar beams of OH radicals by Laser- Induced-Fluorescence (LIF). 3 The CO beam was produced by a supersonic expansion of a 10% mixture of CO in He at about 1 bar through a stainless steel nozzle (0.1 mm dia.) kept at room temperature, leading to a beam peak velocity of 1356 m/s and a speed ratio of 9.8. The CO molecules are expected to be essentially in the lowest (j=0,1,2) rotational levels. The two reactant beams, after a stage of differential pumping and further spatial definition by a collimating slit, were crossed in the main scattering chamber with the resulting collision energy of 12.6 kcal/mol. Because of the not too high speed ratios, especially of the OH beam, there is a significant spread of the relative translational energy (collision energy) of the two beams, which 2

3 leads to a very significant experimental averaging of the measured angular and TOF distributions. The FWHM (full-width-half-maximum) spread of the collision energy amounts to about 6 kcal/mol for the experiment at E c =12.6 kcal/mol, as shown in Figure S1, where the collision energy spread is plotted together with the best-fit P(E T ) distribution. The angular distribution was measured, as usual with continuous beams, by modulating the CO beam (at 160 Hz) for background subtraction. Product TOF distributions were measured using the pseudo-random TOF technique at 6 μs/channel only at the CM angle, because of the lower signal-to-noise ratio (S/N) with respect to the previous, higher E c experiment (as a consequence of a somewhat lower E c, and hence lower reactive cross section, and especially of the use of a 10% CO mixture in He, which was used to accelerate CO using a room temperature nozzle). We recall that we retrieve the product differential cross section (DCS) in the CM frame, I CM (θ, u), from measurements in the LAB of the product intensity as a function of the scattering angle Θ (the laboratory angular distribution, N(Θ)), and the product intensity as a function of Θ and arrival time t (TOF spectra, N(Θ, t)), via the relation N LAB (Θ, v) = I CM (θ, u)v/u 2 (where v and u are product LAB and CM velocities, respectively, and θ the CM angle). The Jacobian v 2 /u 2 relating the CM and LAB fluxes is written as v/u 2 because of the 1/v dependence of the number density measurements using an electron impact ionization mass spectrometer detector (which is a number density detector). The lifetime of the HOCO intermediate was estimated according to the relation T( =180 )/T( =0 ) = exp(-τ r /2τ), where τ r is the complex rotational period (used here as an internal clock). 5 The rotational period of the complex is estimated from the relation τ r = 2πI/L max, where I is the moment of inertia of the complex and L max (= μv r b max ) is the maximum total orbital 3

4 angular momentum. The maximum impact parameter, b max, (b max =2.25 Ǻ) from the calculated opacity function (see Figure S2) was used. Finally, the fraction of translational energy in the product, f T, is defined as <E T >/E tot, where <E T >= E T P(E T )/ P(E T ) and E tot =E c -ΔH. II. Details of PES fitting and QCT calculations. The same ab initio data set used in PES was employed for PES Unlike PES- 2014, PES-2017 is fit by using a single neural network for all regions. Briefly, the feed-forward NN functional form with two hidden layers can be generalized as 7 K 3 3 J I V b1 1, k f2 bk k, j f1 bj j, i Gi k 1 j 1 i 1 (S1) where I denotes the number of PIPs (G i ) of the input layer; 8, 9 J and K denotes the number of the neurons of the two hidden layers, respectively; f i (i=1, 2), transfer functions for the two hidden l layers; are weights that connect the ith neuron of (l-1)th layer and the jth neuron of the lth ji, layer; l b are biases of the jth neurons of the lth layer. ω and b are determined by non-linear j fitting of NN. In this work, the maximum order of the PIPs is 2, which is sufficient to ensure correct permutation invariances among the two identical oxygen atoms, resulting in 17 PIPs in the input layer. The data set was randomly divided into the training (90% of the data points), validation (5%), and testing (5%) sets. To avoid false extrapolation due to edge points in the randomly selected validation and test sets, only fits with similar RMSEs for all three sets were accepted. In 4

5 addition, the maximum deviation is also used in selecting the final PIP-NN fits. For each architecture, 200 different training calculations were performed and the early stopping method 7 was used to avoid overfitting. The training converges fast for all the fitting reported here, typically finishing within a few hundred steps. The final PIP-NN PES was chosen as the average of three best fits, as suggested by the NN ensemble approach to minimize random errors. The VENUS dynamical calculation program 10 is used to perform the quasi-classical trajectory (QCT) calculations on the PES The trajectories were initiated with a reactant separation of 7.5 Å and terminated when products or reactants are separated by 6.0 Å. The maximal impact parameter (b max ) determined using small batches of trajectories with trial values. The statistical errors are all less than 1.2%. Other scattering parameters including the impact parameter, vibrational phases, and spatial orientation of the initial reactants were determined according to the Monte Carlo approach implemented in VENUS. 10 The electronic angular momentum of OH is ignored so that the ground rotational state corresponds to N=1. The propagation time step was selected to be 0.02 fs. The reactive integral cross section (ICS) is determined according to the following formula: 2 E b E P E ( ) max (S2) r c c r c where the reaction probability P r (E c ) at the specified collision energy E c is given by the ratio between the number of reactive trajectories (N r ) and total number of trajectories (N total ): P r (E c ) = N r / N total (S3) with the standard error given by ( Ntotal Nr ) / Ntotal Nr. 5

6 Figure S4 shows the opacity function at fixed impact parameter b for E c =13.0 and 14.5 kcal/mol. As expected, the reaction probability is attenuated gradually with b increased. The differential cross section (DCS) is determined according to d r rpr ( ) d 2 sin( ) (S4) with the scattering angle θ given by cos r r r r (S5) i f 1 i f Here, r denotes the relative velocity vector with the subscripts i and f for initial and final, respectively, r i r 18 r CO HO r r r. Note that the current definition of the scattering, f 18 OCO H angle is consistent with the experiment. Furthermore, there might exist zero point energy leakage in QCT. Therefore, we removed those trajectories with the 18 OCO vibrational energy less than its zero point energy. As shown in Figure S11, the ZPE effect on the DCSs at E c =13.0 and 14.5 kcal/mol is minimal. III. Additional results Table S1 reports the relative population of the various N OH =1 to 10 levels ( as those reported in Table 1 of ref. 3, the relative ICS for the reaction of the various N OH levels at E c =14.5 kcal/mol calculated on the present PES (see also Fig. S4 and S8), and the relative weight of the various N levels used in the simulation of the experimental data (according to the procedure outlined elsewhere. 3 ) 6

7 Figure S1 shows the FWHM spread of the relative translational energy (collision energy) of the reactants for the experiment at E c =12.6 kcal/mol, compared with the best-fit P(E T ) distribution of the products. Figure S2 shows the opacity function from the QCT calculations at the indicated E c s. Note that the impact parameter is fixed. Figure S3 depicts the residence time distribution of the trajectories in the HOCO well. Figure S4 shows the integral reactive cross section for the OH + CO reaction at E c =14.5 kcal/mol as a function of OH (top panel) and CO (bottom panel) rotational quantum numbers. Figure S5 compares the CO 2 product angular distribution at E c =14.5 kcal/mol for CO(j=0) and CO(j=3). As can be seen the shape of the DCS remains essentially unchanged by increasing the CO rotational energy. Figure S6 depicts the (normalized at the peak) QCT CM CO 2 product angular distributions calculated for each OH rotational level N from 1 to 10 (for the relative weights, see ref. 3 and Table S1). As can be seen, they all look similar for the various N levels, and similar to the global one, i.e., backward-forward distributed, with a slight bias toward the forward direction. The corresponding QCT product translational energy distributions for the same 10 rotational levels of 18 OH are shown in Figure S7. The shapes are rather similar, with the peaking and the energy cut-off increasing slightly with increasing rotational level, as a consequence of the higher total available energy with increasing N OH. Quite interestingly, there is no difference in the rise of P(E' T )s with the value of N OH. Finally, the relative ICSs for the first 10 rotational levels of 18 OH as a function of collision energy, as obtained from the QCT calculations on the present PES, are shown in Figure S8. Also for the ICS the trends are similar for all N levels of OH. As is well visible, ICSs increase with E c and the effect of the rotational excitation of OH is 7

8 negligible. Overall, the results of previous QCT calculations 3 of the quantities shown in Figures S6, S7, and S8 on three different previous OH+CO PESs showed also little differences between them, which were traced back in some different details in the entrance channels of the various PESs. References 1. Caracciolo, A.; Vanuzzo, G.; Balucani, N.; Stranges, D.; Cavallotti, C.; Casavecchia, P. Observation of H displacement and H 2 elimination channels in the reaction of O( 3 P) with 1-butene from crossed beams and theoretical studies, Chem. Phys. Lett. 2017, 683, Alagia, M.; Balucani, N.; Casavecchia, P.; Stranges, D.; Volpi, G. G. Crossed beam studies of four - atom reactions: the dynamics of OH+CO, J. Chem. Phys. 1993, 98, Laganà, A.; Garcia, E.; Paladini, A.; Casavecchia, P.; Balucani, N. The last mile of molecular reaction dynamics virtual experiments: the case of the OH(N = 1 10) + CO(j = 0 3) reaction, Faraday Disc. 2012, 157, Okabe, H. Photochemistry of Small Molecules. Wiley: New York, Herschbach, D. Molecular dynamics of elementary chemical reactions. In Nobel Lectures in Chemistry , Malmstrom, B. G., Ed. World Scientic Publishing: Singapore 1993; pp Li, J.; Chen, J.; Zhang, D. H.; Guo, H. Quantum and quasi-classical dynamics of the OH + CO H + CO 2 reaction on a new permutationally invariant neural network potential energy surface, J. Chem. Phys. 2014, 140, Raff, L. M.; Komanduri, R.; Hagan, M.; Bukkapatnam, S. T. S. Neural Networks in Chemical Reaction Dynamics. Oxford University Press: Oxford, Jiang, B.; Guo, H. Permutation invariant polynomial neural network approach to fitting potential energy surfaces, J. Chem. Phys. 2013, 139, Li, J.; Jiang, B.; Guo, H. Permutation invariant polynomial neural network approach to fitting potential energy surfaces. II. Four-atom systems, J. Chem. Phys. 2013, 139, Hu, X.; Hase, W. L.; Pirraglia, T. Vectorization of the general Monte Carlo classical trajectory program VENUS, J. Comput. Chem. 1991, 12,

9 Figure Captions Figure S1: FWHM spread of the relative translational energy (collision energy) of the reactants for the experiment at E c =12.6 kcal/mol, compared with the best-fit P(E T ) distribution of the products. Figure S2: Opacity function from the QCT calculations at the indicated E c s. Note that the impact parameter is fixed. Figure S3: Residence time distribution of the trajectories in the HOCO well. Figure S4: Integral reactive cross section for the OH + CO reaction at E c =14.5 kcal/mol as a function of OH (top panel) and CO (bottom panel) rotational quantum numbers. Figure S5: Comparison of the CO 2 product angular distribution at E c =14.5 kcal/mol for CO(j=0) and CO(j=3). As can be seen the shape of the DCS remains essentially unchanged by increasing the CO rotational energy. Figure S6: Center-of-mass CO 2 angular distributions of the 18 OH + CO reaction for the first 10 rotational levels of OH at E c =14.5 kcal/mol. Figure S7: Product translational energy distributions of the OH + CO reaction at E c =14.5 kcal/mol for the first 10 rotational levels of OH, as from the QCT calculations. Figure S8: Relative integral cross section for the reaction 18 OH + CO as a function of collision energy for the first 10 rotational levels of 18 OH as from QCT calculations at four E c s. Figure S9: QCT calculated relative differential cross sections (DCSs) for the reaction H 18 O + CO H + 18 OCO at the collision energies of 7, 11.5, 13.0, 13.9, 14.5, 17.0 and

10 kcal/mol. The error bars are not given for clarity. Note the slightly increasing trend towards more forward scattering with increasing E c. Figure S10: The effect of the 18 OH rotational excitation on the distributions of the product translational energy. This might account for the underestimation of the product translational energy in QCT, partly. (see main text). Figure S11: The ZPE effect on the DCSs at E c =13.0 and 14.5 kcal/mol. 10

11 Table S1. Effect of OH rotational excitation on ICS N OH Relative rotational Relative ICS (Ǻ 2 ) P ICS (Relative population, P (a) from present QCT weight used in the calculations QCT simulations) (0.99) (1.00) (0.79) (0.56) (0.41) (0.23) (0.14) (0.07) (0.04) (0.04) (a) ref

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