State and orientation selected reactivity of O(1D) + HCl from wavepacket calculations¤ Valentina Piermarini,a Antonio and Gabriel G. Balint-Kurtib Lagana ` a a Dipartimento di Chimica, di Perugia, V ia Elce di Sotto 8, 06123, Perugia, Italy Universita ` b School of Chemistry, University of Bristol, Bristol, UK BS8 1T S Received 12th March 2001, Accepted 14th August 2001 First published as an Advance Article on the web 21st September 2001 State and orientation selected reaction properties of O(1D) ] HCl have been calculated using a wavepacket method and a recently proposed potential energy surface. The e†ect of increasing translational, rotational and vibrational energy on the reactivity of the system has been investigated. A non-negligible e†ect of the orientation of the target molecule on the efficiency of the reaction process has also been found. 1 Introduction Recently a signiÐcant amount of theoretical work has been undertaken on the O(1D) ] HCl reaction. Ab initio calcu- lations of the potential energy values have been performed with the aim of producing potential energy surfaces (PES)1h5 suitable for dynamics calculations. On those PESs both quasi- classical trajectory (QCT)5 h9 and quantum mechanical (QM)10 h16 dynamical calculations have already been carried out for this reaction. Our interest in this system started with the calculation of an extended set of ab initio values of the electronic energy and the construction of the PES.5 Then a check of its dynamical properties using QCT calculations5,8 was performed. These calculations led to an improvement of the potential energy surface of ref. 9 and to a satisfactory comparison of state selec- ted and state-to-state reaction probabilities calculated on the improved PES with experimental results. Experimental results considered for comparison include measurements of the ClO produced in a beam study of the process17 O(1D) ] HCl(v, j) ] ClO(v@, j@) ] H (R1) as well as measurements of laser induced Ñuorescence (LIF) (including Doppler e†ects)18h20 and infrared chemilumi- nescence21 for the OH product resulting from the reaction O(1D) ] HCl(v, j) ] OH(v@, j@) ] Cl (R2) These measurements contain, in fact, a great deal of informa- tion on the importance of the di†erent product channels in the reaction and on the energy partitioning in the products. Due to the structure of the PES of this system and to the di†erent nature of the two reaction channels [heavyÈheavyÈlight (HHL) for the ClO producing channel and heavyÈlightÈheavy (HLH) for the OH producing channel] detailed reaction prob- abilities also deliver information on the reaction mechanisms and on the inÑuence of the PES on the energy distribution among the internal states of the products. On the PES of ref. 9 we have already performed quantum wavepacket calculations at v \ 0 and j \ 0 using both the reactant and the product coordinate techniques. From these ¤ Presented at the Stereodynamics 2000 Conference on Dynamics and Stereodynamics of Chemical Reactions, El Escorial, Madrid, Decem- ber 1È5, 2000. results and an energy shifting model we have been able to compare theoretical predictions with measured branching ratio, product vibrational distributions and cross sections.16 The three dimensional quantum calculations reported here investigate the e†ect of exciting (either vibrationally or rotationally) the reactant molecule and of constraining the initial atomÈdiatom geometry. They also investigate the detail of product rotational (PRD) and product vibrational (PVD) distributions under the e†ect of varying the internal energy of the reactants for the two product channels. The calculations were performed using a quantum real wavepacket technique based on a centrifugal sudden approximation22,23 and a simple damped Chebyshev iteration.24,25 At time zero the wavefunction of the overall system is expressed in terms of the initial diatomic molecule HCl vibrational wavefunction (Jacobi coordinates of the reactant arrangement R, r and H are used for this purpose). For a given total angular momen- tum quantum number J and a given projection K of the total angular momentum J on the body Ðxed axis z, the other terms of the initial wavepacket are a phase factor in R (the OÈHCl separation) multiplied by the normalized associated Legendre polynomial (for calculations using product Jacobi coor- P J K (H) dinates a sinc wavepacket was used in place of a Gaussian16) and, for orientation selected calculations, a normalized Gauss- ian function in H. If only the total reaction probability is required, this may be calculated by describing the wavepacket in terms of reactant Jacobi coordinates. An analysis of the asymptotic form of the wavepacket in terms of these coordinates permits us to deter- mine the fraction of the wavepacket that did not react at any particular energy. The reaction probability may then be com- puted as one minus this non-reactive fraction. If it is also desired to study product-state distributions, Jacobi coordi- nates R@, r and H@ of the product arrangement have to be used. The propagation is performed by repeatedly applying the pro- pagator. During the propagation the wavepacket is analysed at every time step along an analysis line placed in the asymp- totic region of the product channel.22,23 The resulting infor- mation is accumulated in order to evaluate the S matrix elements for a range of values of the collision S vjK , v{j{K { J (E tr ) energy at the end of the propagation. E tr By summing the square modulus of the detailed S matrix elements calculated in product coordinates over K and K@ one can evaluate state-to-state reaction probabilities P vj, v{j{ J (E tr ). By further summing over v@ and j@ one gets initial-state state selected reaction probabilities This quantity can also P vj J (E tr ). DOI : 10.1039/b102325j Phys. Chem. Chem. Phys., 2001, 3, 4515È4521 4515 This journal is The Owner Societies 2001 (