Isotope Effect in the Vibrational Predissociation of van der Waals Molecules: Complexes of Glyoxal with H and D

In this work photodissociation studies of glyoxal-H2 (D:) molecules have been conducted in order to analyze the effect of the mass in the vibrational predissociation of van der Waals complexes. The glyoxal-H2 (DE) molecules have been formed in a supersonic expansion and photodissociated by means of a tunable dye laser. The final state of the glyoxal fragments has been determined by the analysis of the fluorescence spectrum. A significant isotope effect on the branching ratios for predissociation has been found. An interpretation in terms of a distorted wave diabatic treatment is presented.

In this work photodissociation studies of glyoxal-H2 (D:) molecules have been conducted in order to analyze the effect of the mass in the vibrational predissociation of van der Waals complexes. The glyoxal-H2 (DE) molecules have been formed in a supersonic expansion and photodissociated by means of a tunable dye laser. The final state of the glyoxal fragments has been determined by the analysis of the fluorescence spectrum. A significant isotope effect on the branching ratios for predissociation has been found. An interpretation in terms of a distorted wave diabatic treatment is presented.
The dissociation of van der Waals molecules exhibits a clear cut example of vibrational predissociation which constitutes a particular case of the very important problem of vibrational energy redistribution in polyatomic molecules. TM We have recently undertaken the study of the photodissociation pathways of van der Waals molecules involving a polyatomic (glyoxal) and a rare-gas atom (He, Ne or Ar), or a diatomic molecule (a2). 3'4 Those experiments have shown selective pathways for vibrational predissociation which depend on the complex partner.
In an attempt to further understand the dynamics of the process of Work supported in part by Universit6 Pierre et Made Curie, UER 52. vibrational predissociation, we have conducted new expedrnents on glyoxal-D2: isotope substitution of H2 by D2 gives a unique way of changing the reduced mass for the van der Waals vibrational motion without changing the intermolecular potential. The purpose of this note is to present the results of those experiments together with a theoretical interpretation based on a distorted wave diabatic treatment of vibrational predissociation.
The experimental setup has been described elsewhere. 3"6 In brief, the glyoxal-H2 (D2) molecules are formed in a supersonic expansion with He as a carder gas, excited by a pulsed tunable dye laser to the 81 vibrational level of the $1 1Au electronic state of glyoxal and the final state of the glyoxal fragment is determined by analysis of the fluorescence spectrum.
In Figure 1, we present the fluorescence excitation spectrum of glyoxal-H2 and glyoxal-D2 molecules. Each vibrational transition of the uncomplexed molecule is accompanied by satellite peaks (a,b,c,d,e). We attribute the (b), (c), (d), (e) peaks to a vibrational progression in the van der Waals mode (0 0,1,2,3), and the (a) peak to a hot band (1 0). For glyoxal-H2 we have determined to 17 cm -1 and fox 1.4 crn -1 for the frequency and anharmonicity of the van der Waals mode in the electronic excited state. 3 If this interpretation is correct we expect for glyoxal-D2 a reduction of the frequency by a factor x11/2, where -q is the ratio between the reduced masses xl =p (glyoxal-D2) Ix (glyoxal-H2) 1.98, while the anharmonicity should be reduced by the factor . We expect then to 12.2 cm -1 and tox= 0.7 cm -1 for glyoxal-D2. From our results presented in This result can be understood in terms of the distorted wave diabatic treatment for vibrational predissociation in polyatomic systems. 1,4,7 In this model, the bound and dissociative states of the complex are described by diabatic functions: where r stands for all the internal coordinates of the glyoxal molecule, and R denotes the distance between the centers of mass of H2 (D2) and glyoxal.
The function q(r) is the solution of the Hamiltonian describing the vibration of the uncomplexed glyoxal molecule, while 0(R) is the eigenfunction describing the van der Waals motion when the glyoxal molecule is "frozen" at its equilibrium geometry re. In the distorted wave treatment of vibrational predissociation, the individual rates are given by ruby, (2) where V(R,r) is the van der Waals intermolecular potential. In Eq. (2), v denotes the initial vibrational state of the glyoxal molecule in the bound state of the complex, while v' is the final vibrational state of the glyoxal molecule after dissociation. The branching ratio between two different dissociation pathways v' and v" obtained from the same initial state v will then be given by If the van der Waals interaction potential V(R,r) is described in terms of a sum of atom-atom interactions, and if the potential at the equilibrium geometry of the glyoxal V(R,re) is fitted by a Morse function (4) it has been shown1, that the coupling term [V(R,r) V(R,re)] in Eq. (2) can be given approximately by A exp(-2(xR), the proportionality constant A depending on the complex geometry and on the decomposition of the normal coordinates on the cartesian displacements. If we formed the ratio y Rn2/Ro2, this constant cancels and y is function only of the potential parameters or, D and of the relative kinetic energy of the fragments as well as of the reduced mass for the relative motion of H2 (D2) with respect to the glyoxal molecule.
We have performed calculations using the analytical results developed for Morse functions 1. The parameters and D were estimated in the range 1 A -< ct < 3/-1 and 50 cm -< D < 150 crn-1. The results for the vibrational predissociation of the 81 state of glyoxal giving 71 and O , are displayed on Figure 2.
It can be seen that y is always greater than 1 and varies from 2 to 4 for the range of parameters chosen. These results agree with the experimental finding that y > 2.5.
The reason why y is always greater than 1 in our calculations is the following: the rates are proportional to the overlap between an initial bound wavefunction and a continuum dissociative function. The former has a width proportional to ct -1 while the latter oscillates with a wavelength h (2 Ix e/h) where e is the relative kinetic energy. The rates will then be a strong increasing function of the product ha. From our analytical results, it is possible to show that F oc exp (-"rr/hct). Now h increases when H2 is substituted by D2 because the reduced mass increases, but it is also larger for the 81 O than for the 81 71 dissociation process. As a result, the branching ratio between the final states O and 71 is greater for H2 than for D2 in agreement with the experimental results. Similar isotope effects should be present for other initial states in glyoxal as well as in other molecular systems such as 12 H2(D2)8.