SPECTROSCOPIC STUDIES OF HOOH

TOF MS

4.3 SPECTROSCOPIC STUDIES OF HOOH

Data analysis was performed by adapting the nonlinear least squares Marquardt algorithm²⁹ to lineshape analysis and exponential combined rise and decay analysis.

The essential changes to the standard programs (Ref. 29c) is in incorporating numerical evaluation of the fitted function and its derivative. A new recursion relation is used to evaluate the fitting function and derivative in the case of the combined exponential build-up and decay results.

Several theoretical studies are also of relevance to the present experiment. Ef- forts have been made to calculate the energies of the excited states of HOOH. 26 •41 The calculations do predict that only one excited state is involved in the dynamics for 266nm excitation.

A classical dynamics study42 of the dissociation of HOOH shows that the ro- tational excitation is induced by a small torque exerted by the repulsive 0-0 force around the center of mass of the OH radicals. This, in turn, leads to the conclusion that the rotational state distribution resulting from a given model PES was not very dependent on the photon energy. (Each surface is approximately linear in the Franck-Condon region.) However, the use of a steeper potential gave rise to more rotational excitation. It was concluded that the steep portion of the PES gener- ates the fragment angular momentum. These authors42 also included the effects of dipole-dipole interactions and observed that the added angular potential resulted in the joint probability distribution function, P(N_{1 ,} N2) where N is the nuclear rotational angular momentum of the OH product, giving N1

<

N2 or N₁ > N_{2 .} This is opposed to the trend observed without the di polar interaction where N ₁ ~ N 2.

Finally, another classical dynamics study43 shows good agreement with the scalar and vector properties observed in the 193nm experiments. Some disagreement exists for calculations at 266nm, where the inclusion of hot band excitations are more important. However, these studies show that the torsional dependence of the excited state potential is the most significant source of fragment rotational excitation. It is noted43 that this disagrees with the calculations of Ref. 42. The source of the disagreement is attributed to a deficiency in the potential used in Ref.

42.

The extensive range of measurements of the product state distribution, product angular distribution, Doppler-shift of the recoiling fragments and alignment studies of the OH fragment following the photolysis of HOOH at 266nm provides a solid basis upon which to develop an interpretation of the present experimental results.

The product state distribution⁴⁰ results display a narrow rotational distribution.

Doppler measurements⁴⁰ show, in the absence of any measurable amount of product

vibrational excitation,⁴⁰ that the energy available for translation is 2 x 10⁴

±

1 x 10³cm-¹, and 90% of this energy is apportioned to translation.

A recent description of the photodissociation product vector correlations has been presented.⁴⁰b The traditional A~ alignment parameter⁴•5 description has been rigorously advanced to the level of determination of the bipolar moments.⁴⁰b The important product vector correlation for the present analysis is the correlation of velocity and total angular momentum (v,J). The (v,J) correlation corresponds to the

,B~

(22) bipolar moment. This quantity has been analyzed from the Doppler studies.⁴⁰ Moreover, the product pair correlation P(N1,N2 ) has been obtained.³⁶ The value of

,B~

(22) was found to be close to its limiting value and became closer for larger ^JOH· This result was interpreted to mean that the OH product fragments exhibited a desire to align .JoH parallel to the recoil velocity,

v.

In other words, the dissociation produces products in which the planes of product rotation are mutually parallel but perpendicular to the 0-0 dissociation axis.

Klee et al.⁴⁰ explain this result by saying that the rotational angular momentum of the fragments arises from a strong torsional dependence for the ¹ Au excited electronic surface. The 0-0 bond dissociation is accompanied by excitation of the HO-OH torsional motion.⁴³ They concluded that the initial thermal excitation of

1 A₉ ground state does not have a significant effect on the observed correlations.

It is found, via the breakdown of the N 1 =N 2, complete correlation of the two OH products³⁶ that the recoil along the 0-0 bond ( slightly separated from the centers of mass) will produce some torque and rotational excitation. Also, the OOH bending mode dependence of the ¹ Au PES will create some rotational excitation. The latter two motions produce rotational momentum where JoH J_ iJ and loH

II

jl, where j1 represents the S1 ...- So transition moment. These authors estimate that the rotational excitation for the non-torsional processes contributes about 25% of the total rotational energy. Finally, the product correlations have the largest deviation from N1 = N2 when N=l, and N1 = N2 is obtained for N=6.³⁶

As was discussed above, the strong repulsion of the valence elecU,ons in the a* orbital dominate the Ro-o

<4A

range.⁴² The ¹ Au surface is described by

Eqn. ( 5.4) for the 0-0 coordinate. The shape of the Bu surface which correlates with the electronically excited

(2

E) OH product²⁶ is presently not known except at the equilibrium geometry of the ground state.⁴¹ Assuming that the Bu state is either more steeply repulsive than the ¹ Au surface or is described by a form approximately equivalent to Eqn. (5.4) yields an exponential separation of the two potential surfaces. Consequently, it is expected that a red-wing absorption would result.²³ (It is probably a reasonable assumption to say that the Bu and ¹ Au surfaces behave in a similar fashion in the large 0-0 separation region, because the ²E and ²II OH states exhibit nearly equivalent geometries.) Bersohn et al.⁴² position the center position of a dipole-dipole interaction at 4A 0-0 separation and turn the interaction off at smaller internuclear separations. Eqn. ( 5.4) gives value of V₁ =l.7cm-¹ at R=4A. Although it is not known, the Bu surface is presently assumed to have a similar asymptotic approach to zero interaction potential energy.

Therefore, the internuclear separation at and beyond 4A will be dominated by long- range electrostatic interactions.

The spectroscopy of the OH radical was most fully treated by Dieke and Crosswhite.⁴⁴ The notation of Ref. 44 follows the conventions for Hund's case (b ), which assumes that the spin is only weakly coupled to the internuclear axis. Hund's case (b ), which is applicable to the ²E levels ( e.g. A=0), implies a coupling of the electronic spin and the nuclear rotational angular momentum N. Each value of N in ²E manifold is split into two levels where J=N±½. For higher rotational states, case (b) may also be applied to the ground electronic state of OH radical, where A fO. In such case, the resultant angular momentum K, formed by A+N, interacts with the spin S to form J (e.g., J=K+S). For the ²II electronic state the total angular momenta {JoH} is, thus, expressed as K

+

½ and K - ½· (In the present experiment the A-doubling will not be resolved.)

However, for the low rotational level N (1 ::; N ::; 6) the angular momentum coupling is better approximated by Hund's case (a), in which the electronic orbital and spin angular momenta, denoted by A and S, respectively, couple strQngly to the internuclear axis. Namely, the resultant electronic angular momentum,

n,

which

is formed by A+S, interacts with the nuclear rotational angular momentum N to form the total angular momentum (e.g., J= f!+N). A-doubling splits each N level into two, but J remains the same for both levels. Although K is not defined in Hund's case (a), one can formally assign K values to be J

± ½

for ²11 electronic state. Furthermore, the selection rules for the ²1:;+ ~ ²11n (where

n

⁼

!, ½)

tran- sitions are 6J = 0, ±1 and

+

^{+-t -} (referring to the symmetry of the spin-rotation interaction: A-doublet). For case (b) systems, 6K = K' - K" = 0, ±1. Transitions that satisfy both the 6J and 6K rules constitute main branches. Transitions that violate the 6N rule are satellite branches.

For large K, where Hund's case (b) is a good approximation, the satellite in- tensities become small compared to the main branch line intensities. P, Q, and R branches are obtained for 6K=l,0, and -1, respectively. Q₁ (2) refers to 6K=0 transition for K=2 level in the ²II_{3 ; 2} manifold. The satellite transitions change J differently than the main branch transition. Q₂₁(2) implies 6N = 0, 6J = -1, but the transition originates from the same state as Q1 (2). Therefore, the main and satellite branch transitions probe the same ²II population. The transition radiative lifetimes have been tabulated in Ref. 45.