Vibrational Dynamics of the I 3 Radical: A Semiempirical Potential Surface, and Semiclassical Calculation of the Anion Photoelectron Spectrum C. J. Margulis, D. A. Horner, S. Bonella, and D. F. Coker* Department of Chemistry, Boston UniVersity, 590 Commonwealth AVenue, Boston, Massachusetts 02215 ReceiVed: July 26, 1999; In Final Form: September 24, 1999 The semiempirical diatomics in molecules (DIM) approach is used to model the potential surface for ground- state vibration of a linear I 3 molecule. We use this system to explore semiclassical methods for treating quantal nuclear vibrations by computing the photoelectron spectrum of I 3 - which produces vibrationally excited I 3 . We compare semiclassical results with full quantum calculations and experimental results recently reported by Neumark and co-workers. (Taylor, T. R.; Asmis, K.R.; Zanni, M. T.; Neumark, D. M. J. Chem. Phys. 1999, 110, 7607.) 1. Introduction Since the 1950s the existence of the triiodide radical has been proposed as an intermediate species to explain how iodine atoms, produced by photodissociating I 2 , can recombine in the gas phase to reproduce the diatomic species. The accepted mechanism involves an I • radical first colliding I 2 to form stable I 3 which subsequently undergoes collision with another I • radical, then this collision complex breaks apart to give two I 2 molecules. Despite its proposed importance in this most fundamental reaction of gas-phase chemical kinetics, direct experimental observation of the I 3 molecule has only very recently been accomplished in the high-resolution photoelectron spectroscopy studies of Neumark and co-workers. 1 The first goal of this paper is to demonstrate that a very simple description of the I 3 molecule offered by the semiempirical diatomics-in-molecules (DIM) approach is actually capable of providing a very reliable representation of this molecule, reproducing the recently measured binding energies, and vibrational frequencies with surprising accuracy. Next we summarize how time dependent perturbation theory can be used to compute the distribution of ejected photoelectron kinetic energy P  (ǫ) in the thermal equilibrium photoelectron spectrum of I 3 - in which vibrationally hot I 3 is produced according to the following process: Finally we will compare the results of fully quantum dynamical calculations of this photoelectron spectrum, with classical and semiclassical calculations of the I 3 vibrational dynamics probed by these measurements, and we compare our theoretical results with the experimental photoelectron spectrum of Neumark and co-workers. 1 2. Methods 2.1. A DIM Potential Model for Ground Electronic State Intramolecular Vibrations of I 3 . The model assumes that the I 3 molecule is linear, hence the projection of the total angular momentum of the system into the molecular axis is a good quantum number. Following the same scheme used in previous work 2 we write the basis set as Hund’s case C kets where J k and m jk are the total angular momentum and it’s projection on the molecular axis for each of the iodine atoms. Our purpose in this paper is to focus on the properties of the ground electronic state of I 3 , hence we will reduce our basis set to a minimum subspace that will include only the necessary kets mixing to form this lowest energy eigenstate. Thus the approach we present here will not produce all the subsequent excited states, but only some of them. We suppose that the ground-state eigenket has total angular momentum projection so only kets satisfying this condition will combine to generate this assumed lowest energy eigenstate. 3 Our knowledge of the ground-state dissociation limits of the I 3 radical can be used to further limit the basis set. Thus if one of the bonds is stretched, the molecule should dissociate to ground-state I 2 and an I • radical species. The ground state of I 2 in our representation is and the I • radical ground state is These considerations thus enable us to limit the basis kets to only those having all the J k ) 3 / 2 and the m jk )( 1 / 2 . This procedure is only valid in the gas phase, in solution other states that we are not including in the calculations described here will be coupled by anisotropic interactions with the solvent and thus make contributions to the lowest energy solution phase eigenket, but this is beyond the scope of the current paper. The DIM Hamiltonian operator has the form 4,5 and we choose the zero in energy to be that of the isolated I • radicals; therefore, the second sum in the above expression can be disregarded. For convenience in the notation we will drop the J index in the angular momentum expression since it is the I 3 - (therm) + pν f I 3 (vib) + e - (ǫ) (1) |J 1 m j1 〉|J 2 m j2 〉|J 3 m j3 〉 ) |J 1 m j1 , J 2 m j2 , J 3 m j3 〉 M J ) ∑ k)1 3 m jk )( 1 / 2 1/ 2(| 3 / 2 , 1 / 2 〉| 3 / 2 ,- 1 / 2 〉 - | 3 / 2 ,- 1 / 2 〉| 3 / 2 , 1 / 2 〉) | 3 / 2 ( 1 / 2 〉 ∑ i<j H ˆ i, j - n ∑ i H ˆ i (2) 9552 J. Phys. Chem. A 1999, 103, 9552-9563 10.1021/jp992596m CCC: $18.00 © 1999 American Chemical Society Published on Web 11/06/1999