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Joanne R. Hetzler, Michael P. Casassa, and David S. King. J. Phys. Chem. , 1991, 95 (21), pp 8086–8095. DOI: 10.1021/j100174a017. Publication Date: ...
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J. Phys. Chem. 1991, 95, 8086-8095

energies in a straightforward way. The procedure appears well suited for calculations involving small widths or, equivalently, long decay times. In some dissociation phenomena, it may happen that there is only one energetically open channel. In this case the coefficient and decay matrices simply become functions of the energy, and one does not need to perform a diagonalization to construct the determinantal equation. The present study did not attempt to account for the time evolution of molecular states when the excitation is done with short light pulses;'9 it should however be possible to use the derived decaying states as basis functions for the description of the more complicated time evolution that follows pulse excitation.

Acknowledgment. This contribution is dedicated to the memory of Richard B. Bernstein, with whom I learned the related subject of molecular resonance phenomena. This work was partly sup ported by the National Science Foundation through Grant CHE-8918925 for the Institute for Theoretical Atomic and Molecular Physics at Harvard University and the Smithsonian Astrophysical Observatory, where it was started. I thank Prof. Alexander Dalgarno for his hospitality there. I also thank Profs. Michael Kasha and Joseph Lanutti for their hospitality a t the Chemistry Department and Supercomputer Computations Research Institute, respectively, of Florida State University, where this work was completed. Work at FSU was done under Contract No. DE-FG-5-87ER605 17 with the U S . Department of Energy.

Product Energy Correlations In the Dissociation of Overtone Excited NO Dimer Joanne R. Hetzler; Michael P. Casassa, and David S.King* Molecular Physics Division. National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (Received: April 24, 1991; In Final Form: June 25, 1991)

The photodissociation spectra, predissociative lifetimes, fragment internal state and translational energy distributions, and product energy and vector correlationsof overtone excited nitric oxide dimer, ( N o h have been measured using pulsed molecular beam and Doppler profile analysis techniques. The u I + us and 2us modes of (Noh were excited by infrared pumping, and NO fragments were detected with sub-Doppler resolution by laser-induced fluorescence. The predissociative lifetimes of u1 + us and 2us excited NO dimer are 34 f 6 and 20 f 3 ps, respectively. At least 97% of the dissociations produce NO(u=l) + NO(u=O); no product in the (v = 0) + ( v = 0) channel was detected. For both modes, about 85% of the energy available after vibrational energy distribution goes into relative translational energy of the fragments. Only 3% of this available energy appears in fragment rotational energy. The propensities of the three spin-orbit correlated channels were measured for both modes. For vI + v5 excitation 77 f 7% of the fragments are formed along the 'III/2JII3 channel and 21 f 5% via zIIl/2411/2. In contrast, 39 f 6% of the dissociations following 2v5 excitation proceed via the zh1/~-2111/2 channel. The only nonzero vector correlation observed is the fragment recoil anisotropy, which depends on the rotational transition excited in the parent. The results are discussed in terms of the dissociation and energy partitioning mechanisms.

I. Introduction Studies of vibrational excitation and subsequent dissociation of small weakly bound clusters have long served to elucidate the interactions between molecules, as well as being prototypical studies of unimolecular decay.'" The ground-state vibrationally induced dissociation of the N O dimer is interesting because it produces two free-radical species, analogous to actual chemical reactions that produce two radicals. The equilibrium structure of N O dimer is well-known7J (as shown in the inset in Figure 1, the dimer has C,, symmetry, with "r = 2.237 A, rNo = 1.161 A, and 8", = 99.6O) and the fundamental vibrational transitions have all been observed and a~signed.~Infrared photodissociation experiments pumping the vI N O symmetric stretch (1869 cm-I) and the us N O antisymmetric stretchlo (1790 cm-I) showed that the bond energy is about 800 cm-'." The electronic structure is not as well-known, but ab initio calculations12and experimental observations* indicate that the ground state is 'Al, with the N O singly occupied ?r* orbitals oriented to form an N-N u bond. These same studies also give clues as to the position of the other low-lying surfaces which correlate to the ,lT fragments. Unlike closed-shell systems such as (HF), which have been extensively studied,I the (NO), system is complicated by the ,lI configurations of the NO fragments, which combine in C , symmetry to form 16 potential energy surfaces (4 sets of triplets and 4 singlets). A curve-crossing mechanism was proposed nearly 30 years ago by Nikitin to explain the unusually large cross section for collisional vibrational relaxation of NO(v= 1) by NO(v=O).I3 More recent experiments suggest that similar nonadiabatic pro+NIST/NRC Postdoctoral Fellow 1990-91. Permanent address: Aerodyne Research Inc., 45 Manning Rd., Billerica, MA 01821.

cesses participate in the predissociation of vibrationally excited N O dimer."J4Js Still, little is known about the surfaces involved in the (NO), dissociation. Based on time" and frequency14 resolved data, Matsumoto conjectured that the rate and mode specificity of the vibrationally induced dissociations arise from a curve crossing to a 3B2surface, which might couple to the 'Al ground state via a spin orbit interaction. Although ab initio calculationsI2 place the 'B, surface 3630 cm-l above the ground state in the equilibrium configuration, seams of crossing might exist if the 3B2surface is depressed by deformation from the equilibrium geometry along a vibrational (1) (a) Miller, R. E. Acc. Chem. Res. 1990, 23, 10. (b) Dayton, D. C.; Jucks, K. W.; Miller, R. E. J . Chem. Phys. 1989,90,2631. (c) Pine, A. S.; Lafferty, W. J.; Howard, B. J. J. Chem. Phys. 1984, 81, 2939. (2) Janda, K. C. Ado. Chem. Phys. 1985,60, 201. (3) Bawick, J. A.; Jortner, J. Ado. Chem. Phys. 1981, 47, 363. (4) Levy, D. H. Adv. Chem. Phys. 1981,47, 323. ( 5 ) Nesbitt, D. J. Chem. Rev. 1988, 88, 843. (6) Casassa, M. P. Chem. Reo. 1988,88, 815. (7) Kukolich, S.G. J. Am. Chem. SOC.1982, 104, 4715. (8) Western, C. M.; Langridge-Smith, P. R. R.; Howard, 8. J.; Novick, S. E. Mol. Phys. 1981, 44, 145. (9) Menoux, V.;LeDoucen, R.; Haeusler, C.; Deroche, J. C. Can. J. Phys. 1984,62, 322. (10) The symmetric stretch of the NO dimer in the C, symmetry group is designated as Y,. The antisymmetric stretch of NO is designated here as us. This vibration has been referred to as u, in a number of previous reports. However, based on the symmetry assignments of the vibrations of (NO)*, v5 is the correct designation for the antisymmetric stretch. (11) Casassa, M. P.; Stephenson, J. C.; King, D. S. J . Chem. Phys. 1988, 89, 1966. (12) Ha, T. K. Theor. Chim. Acra 1981, 58, 125. (13) Nikitin, E. E. Opr. Specrrosc. 1960, 9, 8. (14) Matsumoto. Y.;Oshima, Y.;Michio, T. J. Chem. Phys. 1990,92,937. (15) Brechignac. Ph.; DeBenedicts, S.;Halberstadt, N.; Whitaker, B. J.; Avrillier, S.J.Chem. Phys. 1985, 83, 2064.

0022-365419 112095-8086302.50/0 0 1991 American Chemical Society

The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8087

Product Energy Correlations mode. A candidate promoter mode is the u3 in-plane bend, which

is shown by Nour's force field analysisI6 to be coupled to the us antisymmetric stretch; in this analysis the u1 symmetric stretch is shown to be a nearly pure N O stretching normal mode. The u3-uj coupling will influence the spatial extent of the vibrational wave function, providing probability density in those regions where the 'A, and )B2 surfaces cross. On the basis of these arguments one might anticipate dramatic effects to be observable for excitations at higher vibrational energies. For example, the NO overtones (3500-3800 cm-I) might sample the crossing region to a greater extent than the fundamentals. Such effects might appear as spectral perturbations, as mode-specific decay rates, or on the exit channels followed by the separated fragments, reflecting the character of the initial vibrational motion or symmetry. Previous investigations of (NO), infrared photodissociation revealed a mode dependence of the N O product dissociation rate when the y I or u5 N O stretching modes were e~cited.~.",'~,''-'~ The lifetime of the excited dimer was 880 f 260 ps and 39 f 8 ps following u I (1 868 cm-I) and u5 ( 1 789 cm-I) excitation, respectively." Homogeneous line widths of 193 i 20 MHz and 4-6 GHz fwhm determined" for these two bands give excellent agreement with the measured lifetimes. Fragment energy distribution measurements following both uI and us excitation showed that most of the available energy appeared in translation with only IO'%-1 2%of the available energy going into fragment rotation.'' Such an energy partitioning is unexpected based on distorted wave calculations using van der Waals pair potentials, yet it is consistent with dissociation along a repulsive surface. Because the details of the bonding potential are entirely unknown, this result does not prove that a nonadiabatic process is responsible for the kinetic energy release. In fact, Tachibana et aLzorecently modeled the dissociation process using a purely vibrational Hamiltonian, which quantitatively reproduced the mode-specific lifetimes and qualitatively accounts for the observed product kinetic and rotational energies. The best evidence for a nonadiabatic process is that the ratio of populations observed in the two fragment spin-orbit states depends upon the vibration initially excited, suggesting that dissociation proceeds on more than one fragment surface. In the present experiments, infrared light excited the u I + u5 combination band of (NO), at 3626 cm-' and the resulting states of N O and their correlations were characterized by laser-induced fluorescence (LIF). The general scheme can be written as (No12

hVlR

Td

(N0)2*(vl+v5) NOa(Ja,Qa,ua)

+ NOb(Jb,QbrUb) + EKE

where J , Q, and u are the fragment rotation, spin-orbit, and vibration quantum numbers, and EKEis the center of mass kinetic energy release. The subscripts (a, b) differentiate the geminate fragments. The IR excitation spectrum is sufficiently resolved to allow definitive assignment to the NO dimer and to assess the homogeneous line widths. After u1 us dissociation of the N O dimer, approximately 2900 cm-' of energy is available for distribution amongst the internal and translational degrees of freedom of the N O fragments. Energy conservation restricts u, + Ob I 1. If (NO), dissociates along the (u, = 1 ) + (ub = 0) channel, approximately 1050 cm-'remain for rotation and translation. The (0, = 0) (Ob = 0) channel would require all 2900 cm-l to go into rotation and translation of the fragments. Analyses of the N O LIF Doppler profiles and intensities give the fragment internal state and translational energy distributions, and product energy and vector correlations. These data lead to a refined value of the dimer bond energy, Do = 710 i 40 cm-l.

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(16) Now, E. M.; Chen, L.-H.; Strube, M. M.; Laane, J. J. Chem. Phys. 1984,88, 756. (17) Casassa, M. P.; Stephenson, J. C.; King, D. S.Faraday Discuss. Chem. Soc. 1986,82, 251. (181 Casassa, M. P.: Stephenson, J. C.; King, D. S.J. Chem. Phys. 1986, 85,'2333. (19) Casassa. M. P.; Woodward, A. M.; Stephenson, J. C.; King, D. S.J. Chem. Phys. 1986,85, 6235. (20) Tachibana, A.; Suzuki, T.; Yamato, M.; Yamabe, T. Chem. Phys. 1990, 146, 245.

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Like the fundamental bands, u1 us excitation results in minimal rotational energy release, with each N O fragment having an average of 15 cm-' of rotational energy. There is a near-complete correlation in product vibrational quantum numbers with only the (u, = 1) (ub = 0) channel being observed. There is also a pronounced correlation in product spin-orbit states, with approximately 75% of the dissociations proceeding by way of the NO(2111/2) N0(2113/2)channel, and the balance via the NO(2111,2)+ NO(2111,2)channel. Fragment kinetic energy is observed to decrease with increasing fragment rotational energy. There are no other strong correlations among fragment energy states. A large positive recoil anisotropy is observed which is related to the distribution of body-fixed recoil angles and the spatial form of the initially excited dimer rotational wave function. Limited results are also presented of (NO), dissociation following excitation of the 2u5 transition. A (u, = 0) (Ob = 1) correlation in the product vibrational quantum numbers is again observed. A correlation in the fragment spin-orbit states is evident, with a p proximately 60%of the dissociations following the NO(2111/2)+ NO('II312) channel and the balance via the N0(2111/2)+ NO(2111/2)channel. These results are discussed in terms of the character and consequence of the potential energy surfaces involved in the vibrationally excited NO dimer.

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11. Experimental Section

The experiments were performed on (NO), formed in a pulsed free jet expansion. The temporal duration of the molecular beam pulse was about 100 ps. Expansion conditions were optimized for producing the NO dimer by using a Fourier transform microwave spectrometer,' tuned to the dimer 303 212transition at 1 1 267.37 MHz.' All results presented here used a 10% mixture of vacuum-distilled NO in Ar at a pressure of 1.8 X 1 Os Pa (1.8 atm) expanded through a 0.7 mm diameter nozzle. The resulting expansion produced substantial amounts of (NO),, with a minimum amount of higher polymer. As shown below, the dimer was characterized by a rotational temperature of about 4 K, dependent on the backing pressure. All experiments were performed a t the temporal and spatial center of the ggs pulse where the dimer concentration was highest and signal contributions from beamcooled monomer lowest. All results presented here are specific to the (14NO), species. In the infrared photodissociation experiments an infrared pump pulse tuned to either the ul u5 or 2u5 transition vibrationally NO fragments were excited the dimers in the beam. Two X produced in the subsequent dissociation of each excited dimer. The fragments were detected by using an ultraviolet probe pulse tuned to the (0,O)and (1,l) bands of the A-X transition, resulting in LIF signals proportional to the population of NO fragments in each fragment level (Q,J,u). Doppler spectroscopy was used to obtain information on the kinetic energy release and vector and scalar correlations in the dissociation. The vI us infrared photodissociation pulses near 3626 cm-' were obtained by difference frequency generation (DFG) followed by optical parametric amplification (OPA).22323 Pulses at 659 nm (nominally 4 mJ/pulse, 6 ns duration, 6 mm beam diameter) from a YAG-pumped tunable dye laser were mixed with 532-nm pulses (12 mJ/pulse, 8 ns, 6 mm diameter) from the same YAG laser in an angle-tuned LiI03 crystal ( 1 cm length) to obtain infrared light at the difference frequency. The DFG energy was 5 pJ/pulse. These pulses served as idler pulses to seed an OPA. The OPA was a pair of angle-tuned LiNb03 crystals (each 5 cm long) which were pumped by 1064-nm pulses from the same YAG laser (60 mJ/pulse, 2 mm diameter). The net output was l 5 0 - d 3-pmpulses. The YAG laser was a single-mode injection seeded laser with a nominal bandwidth of 40 MHz fwhm. The resulting bandwidth of the IR was mainly determined by the bandwidth of the 659-nm dye laser which was either 0.3 or 0.05 cm-', de-

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(21) Lovas, F. J.; Suenram, R. D. J . Chem. Phys. 1987, 87, 2010. (22) Casassa, M. P.; Foy, B. R.; Stephenson, J. C.; King, D. S.J . Chem. Phys. 1991, 94, 250. (23) Baumgartner, R . A.; Byer, R. L. IEEE J. Quant. Electronics 1979, QE-15, 432.

Hetzler et al.

8088 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 TABLE I

-

WO

0.0 1868.25 1 1789 1757 3626.45 (10) 3559.32 (IO)

(14~0)2,0 Y 0

(14~O)2,b yI Q ~ N-... O Lu.*s ~ (I~NO)~? ( I ~ N O ) ~ ?+ ("NO)2? 2 ~ 5

.

a Reference

A 0.8616 0.85769 (4) 0.854 0.802 0.854 (4) 0.860 (2)

spectroscopic constants, cm-I B C 0.1872 0.1536 0.153906 (6) 0.187841 (io) 0.191 20 0.1564

0.00644 (70) -0.2 0.16 0.16 (2) 0.26 (2)

0.1 570 0.1573

0.1925 (5) 0.1925 (5)

AYL

8. *Reference 14. Reference 15. "This work

pending on the usage of an intracavity etalon. Pulses at 3560 cm-l to excite 2 3 were obtained in the same fashion. The entire infrared beam path was enclosed and purged with dry nitrogen to eliminate atmospheric H 2 0and C02absorption. Calibration of the pump frequency and bandwidth was achieved by using a reference spectrum taken with a low-pressure C02 absorption cell. The ultraviolet probe frequencies were obtained from the pulse amplified output of a single-mode CW ring laser operating around 568 nm. The pulsed dye amplifier is pumped by 532-nm pulses (45-50 mJ) from the single-mode YAG laser. The amplified dye laser pulses were frequency doubled in a KDP crystal, followed by sum frequency mixing in KD*P with 1064-nm pulses (40 mJ, 2 mm diameter) from the same YAG laser to yield 226-nm probe pulses. The bandwidth of the pulse-amplified visible output was determined to be 80 MHz f ~ h m .On ~ the ~ basis of this value, we estimate the bandwidth of the UV output at 226 nm as 120 MHz. A photomultiplier tube (PMT) detected the laser-induced fluorescence. Suitable collection optics, spectral filters, and a spatial mask allowed detection only of the central 1.5 mm long region of pump and probe laser and molecular beam overlap. This constrained field of view limits the contribution of parent transverse motion to the resultin fragment Doppler profile. Doppler scans across the Q1,10*0(0.5)2transition of beam-cooled monomer in the free-jet expansion gave a Gaussian line shape with 750 MHz fwhm. Although this is substantially larger than the probe laser bandwidth, it corresponds to a transverse beam translational temperature of 18 K, and was responsible for the limiting resolution of these experiments. In all of the experiments the IR pulse preceded the probe pulse by 15 ns. Data were collected by using gated integrators and were normalized to the probe and/or pump laser energies, depending on the measurement. Experiments were performed with linearly polarized light in several pump-probe geometries. Using geometrical designations given by Gericke et a1.,26 most measurements were made in geometries HI,IV and VI. The PMT axis and the stream flow of the free jet were collinear and at right angles to the Poynting vectors of both the pump and the probe lasers. In the collinear laser arrangements (111, IV) the pump laser beam was focused, using a confocal parameter of 100, to a beam waist of 0.3 mm at the center of the chamber. Prior to entering the chamber the probe laser beam was collimated with a beam diameter of 4 mm and attenuated to a level of 0.05-0.3 J (100-600 W/cm2), depending on bandwidth. This beam passed through a 200-pm aperture just prior to the chamber. In the perpendicular geometry (VI) the unapertured probe beam was focused with a 200-mm cylindrical lens with the elongated probe spot aligned with the pump beam. Two types of experiments were performed. IR photodissociation spectra were measured by fixing the probe laser on a specific A X NO(J,O,u) transition and scanning the pump laser wavelength. Fragment energy distributions and correlations were determined from Doppler profiles measured by fixing the pump laser at specific dimer rovibrational transitions and scanning the

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(24) Foy, B. R.; Casassa, M. P.; Stephenson, J. C.; King, D. S.J . Chem. Phys. 1990, 92, 2182. (25) In the notation Qd"%Q, u and u' refer to the initial and final vibrational levels of the transition, and m and m'to the fine-structure levels, where m 1 if D = 112, and m = 2 if D = 312. (26) Gericke, K.-H.; Klee, S.;Comes, F. J.; Dixon, R. N. J . Chem. Phys. 1986, 85, 4463.

t

b

1

-0 c

.-0, v)

4 -I 0 Z

3622

3624

3626 3628 3630 3632 Frequency (cm-') Figure 1. uI + u5 photodissociation spectrum of (NO), cooled in a molecular beam; Po = 1.1 X lo5 Pa (17 psia), 10%NO/Ar. The smooth curve is a simulation for T = 3.3 K. The stick spectrum is the same simulation showing the line positions.

probe laser through NO fragment transitions. 111. Results and Analysis A. Photolysis Spectra. The u1

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us photodissociation spectrum is shown in Figure 1. This was acquired with a pump laser bandwidth of 0.05 cm-' fwhm while probing the Q2p0(5.5) NO transition. The probe laser frequency was tuned slightly off of line center in order to minimize the pump laser independent contribution of cold NO present in the beam (Le., those NO monomers which are not a result of the dimer dissociation). The u1 + us level has B2 vibrational symmetry so the u1 + us transition is an a-type band, resembling a parallel transition of a prolate symmetric top. The P, Q, and R branches Can be readily identified in the spectrum. u1 u5 spectrum was simulatedz7 by using the An ground-state rotational constants derived from microwave datal5 and varying the upper state constants, A', B', and C'. The calculations incorporated nuclear-spin-weighted intensities and a Voigt profile convolution. The Lorentzian component of the Voigt profile, AvL, was varied, while the Gaussian component was fixed at the 0.05-cm-' laser bandwidth, determined from low-pressure COSabsorption measurements. The value of C'was set at l/C' = ( l / A ' + 1/B?. Three spectra, obtained with backing pressures of 1.1 X lo5, 1.8 X IOs,and 2.7 x lo5 Pa (17, 27, and 40 psia), were used in the evaluation of the derived rotational constants and line width. The initial attempt to fit the spectrum used values of AA and AB corresponding to the arithmetic sum of these terms obtained earlier for the two fundamentals, a value AYL = 0.14 cm-' corresponding to the uncertainty broadening of the observed 39-ps us predissociation lifetime, and a nominal 4 K rotational temperature. The initial fits were improved by varying AA and AB to simulate the positions of the prominent features in the high-pressure (e.& high temperature) spectrum. The best fit value for AVLwas selected based on the low-pressure (e.g. low temperature) spectrum.

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-

~~

(27) Asymmetric rotor spectra were calculated by using the MYMPD pro-

gram written by A. Maki at the National Institute of Standards and Technology.

Product Energy Correlations

The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8089

TABLE II: NO Fragment Internal Energy Partitioning (E,,), cm-l/fragment

fragment states 'II,/'

VI

+ y5

2v3

u = O 'n3/2 u= 1

u=I

63 f 9 50 f 5

71 & 8 78 & 9

15&2 14 & 2 15 & 2

*n1/2 'n3/2

Q '

VIa

u=0

114

Fragment Spin-Orbit Population Ratios [2n3/21/[2n1/21

0.72 & 0.07

[u = O ] / [ u = I ]

1.002g

0.46 & 0.10

0.90

0.45 & 0.15

0.20

Fragment Vibrational Po ulation Ratios 1.oo&

'Reference 11. Only the u, = 0 + ob = 0 channel is energetically accessible.

:

200t0 150

I

7 50

3554 3556

3558

3560

3562

3564 3566

Frequency (cm-')

Figure 2. 2u5 photodissociation spectrum of cooled in a molecular beam; Po = 1.8 X IO5 Pa (27 pia), 10% NO/Ar. The smooth curve is a simulation for T = 6 K. The stick spectrum is the same simulation

showing the line positions. Notably, changing PA affected the positions of the picketlike features while AB affected the shading of the Q branch. Changing AvL changed the peak to valley modulation across the entire spectrum. The Lorentzian contribution was essential to producing good fits, for without this broadening the calculated spectra were too structured. These three important parameters were fixed and all three spectra fit varying only T , where T ranged from 3.3 K (1.1 X 10s Pa) to 7 K (2.7 X IOs Pa). Qualitatively good fits were obtainable for a narrow range of PA, AB,and AvL values. These values and the band origin are presented in Table I along with previously determined values for the ground, vl, and v5 vibrational levels. The agreement of the experimental and calculated spectra confirms that we are observing N O fragments from dimer dissociation at all pressures and not from the dissociation of larger polymers of NO. The ( N O ) , 2v5 spectrum is displayed in Figure 2. It was obtained probing the QI11J(4.5)NO transition. The spectrum is an average of several spectra acquired at a backing pressure of 1.8 X lo5 Pa (27 psia). The 2v5 spectrum was simulated in the same fashion as was the combination band spectrum with the exception that spectra at only one backing pressure were measured. This was sufficient however to evaluate the rotational constants, line width, and rotational temperature. The rotational temperature of (NO), was 6 K. The line width, rotational constants, and the band origin are given in Table I. B. Fragment Internal State Distributions. The rotational and spin-orbit state population distributions of the NO fragments formed following v I + v5 excitation were determined by integrating Doppler profiles obtained probing a range of fragment levels and transitions. For these measurements a pump laser bandwidth of 0.3 cm-I was used, tuned to excite the R ( 2 ) and R ( 3 ) dimer subband transitions.28 Data for NO(u=l) 2111,2 and 211s/2 (28) We use diatomic molecule notation as short hand for the actual asymmetric top transition, e.g., the R(2) subband is composed of contributions from J = 2 with K,,K, = 0, 1, 2; each with an appropriate weight.

-50t' 0

' '

I

2

' ' '

I

4

"

'

I

6

' ' '

I

8

' ' '

' ' 10

'1 12

J

Figure 3. Rotational population distribution of NO fragments resulting from v I + v5 dissociation of (NO),, where 0 and X represent data for u = 1, 2n1/2 and u = I , 2n3/2 fragments, respectively.

products are displayed in Figure 3 . Each datum represents an average of many Doppler profiles. Since the p-J correlation is negligible (see below), no correction of integrated intensities for alignment effects was necessary. The precision of the data for any level, as determined by repetitive measurements of relative population, is nominally *IO%. The rotational state distributions are poorly fit by a Boltzmann distribution function. However, the data for each spin-orbit state give a linear dependence of In [ P ( J ) / ( 2 J l ) ] versus J . From this empirical relationship we obtain the average rotational energy for each spin-orbit level and and 211s/2populations. These numbers determine the relative 2111/2 are listed in Table I1 along with values previously obtained for v I and v5 photolysis. Due to low signal levels for 2v5 excitation, detailed rotational population distributions were not obtained. Comparison of relative intensities of the Ql11~1(J=1.5,2.5,3.5) lines indicates the N O formed from 2v5 excitation to be slightly "colder" than from u1 + v5 excitation. The u1 + us data in Table I1 show that fragment channels resulting in each of these three measured (Q,u) fragment states result in the same average rotational energy release. Figure 3 shows that the angular momentum distributions for and 211!/2 fragments are essentially indistinguishable and that these distributions are very narrow; peaking at the lowest value of J , with a half-width of 1-2 units of angular momentum. Only fragment vibrational levels u = 0, 1 are energetically accessible. Direct comparison of absolute signals probing NO( ~ 0versus ) N O ( u = l ) fragments could, in principle, give the corresponding population ratios, [u = O ] / [ u = 11. Doing this accurately, however, requires detailed knowledge of the wavelength dependence of the PMT, collection optics, and filters and is critically dependent on laser beam alignment. Tuning the probe laser frequency between the NO fragment (0,O)and ( 1 , l ) bands results in movement of the beams due to dispersive optical elements (much greater than for tuning through rotational levels). This makes intensity comparisons imprecise, even though the necessary realignments were aided by apertures. The comparison of (u = 0) to ( u = 1) populations using the available NO spectroscopic

+

Hetzler et al.

8090 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991

0

z t

0

5

10

15

20

‘i,, I

25

GHz Figure 4. Doppler profiles of NO Q11’*’(4.5)and QllLs1(0.5) transitions measured in geometries VI (curve a) and 111 (curve b).

data and published wavelength dependencies of the PMT and filters indicates these populations are the same, within a factor of 2. A more precise ratio is obtained from Doppler analysis of the fragments (see below) and shows that the v, = 0 + Ob = 0 channel is unimportant. Therefore, [u = O ] / [ u = I ] is essentially unity. The NO monomer units have spin and orbital angular momentum, giving rise to the 2111/2and 2113/2 spin-orbit states, with an energy separation of 123 cm-’. Coupling of the nuclear rotation and orbital angular momentum gives rise to the two A doublet states that at high values of J differ in reflection symmetry of the electron coordinates with respect to the plane of rotation [MA’) is symmetric; A(A”), anti~ymmetric].~~ Though the reflection symmetry is only rigorous a t high J , the A doublets at low J still correspond to spatially distinct electronic charge distribution^.^*^' Spectroscopically, the doublets can be distinguished; e.g., Q l l branch transitions preferentially probe the h(A’) component, and RIItransitions the A(A”) component. The ratio of A(A’)/“A’’) was obtained by comparing integrated intensities of Doppler profiles for Q I land R I I ,and Q22 and R22branch transitions for each of several values of J . The result is that in the predissociation of (NO)2uI + u5 the A doublet components are formed with equal probability for the examined levels J < 8.5. C. Fragment Doppler Profiles. Doppler profiles of the NO product L I F transitions were analyzed to obtain product recoil velocities (v) and correlations between fragment states, as well as possible correlations among fragment momenta (v,J) and the parent transition moment ( I ) , The Doppler profiles of the Q l l ~ ’ ( o . 5and ) Qll’*’(4S)transitions of NO measured with detection geometries to emphasize 1-v correlations are displayed in Figure 4. A small contribution from beam-cooled monomer has been removed from the data of Figure 4 by subtracting data obtained with the pump laser blocked. Each trace is the sum of several scans. The lower trace was obtained with the pump laser electric vector and probe Poynting vectors parallel (geometry 111) while they were perpendicular for the top trace (geometry VI). The pump laser, of 0.3 cm-I bandwidth, was tuned to the R(2) and R(3) transitions of the dimer. The different shapes of the profiles in the different geometries show that there is a significant p-v correlation. The NO Doppler profiles were analyzed in the manner described by D i x ~ nGericke , ~ ~ et a1.,26 and Casassa et a1.,22where a single-particle Doppler profile has the form 1 g ( V ) = @O + g2P,((v - U o ) / A V ) ) =

(29) Alexander, M., et ai. J. Chem. Phys. 1988.89, 1749. (30) Dixon, R. N.; Field, D.; Zare, R. N. Chem. Phys. Lerr. 1985, 122, 310. (31) Andresen, P.;Rothe, E. W.J. Chem. Phys. 1985, 83, 3634. (32) Dixon, R. N. J . Chem. Phys. 1986, 85, 1866.

Figure 5. QiiiJ(0.5)profile measured in geometry 111. The curve has been folded over at its center frequency to produce the half profile shown. The three curves are nonlinear fits of the data (see text). The smooth solid curve is the best fit of the data, given with le, = -0,322, bo= 0.70 GHz and Au = 2.68 GHz. The dashed and dotted lines correspond to fits where Au is fixed to 2.55 or 2.81 GHz, respectively.

where yo is the rest frequency, Au is the maximum Doppler shift, and P2(X) g0

=

= (39-

1 ) / 2 9

@err

= g2/go

+ bl@d, g2 = b28rr + b34.J + b4@#vJ

The anisotropy parameters Pi, which are to be determined, are known as the bipolar moments of the velocity distribution. The bipolar moments, Dd, OF,, @,J, and @,,,J [defined as O&O 2), A 2 ( 2 O), @$(2 2), and BO2(22), respectively, in ref 321 have physical significance reflected by their subscripts. The conventional recoil anisotropy parameter is @ = 2@,,, and the alignment parameter is AJ2) = 4/54,,, The bipolar moments characterize correlations among the orientation of the transition moment p of the parent at the instant of excitation (more correctly, the orientation of the photolysis electric vector), the fragment velocity vector v, and the fragment rotational angular momentum vector J. The vI + v5 spectrum indicates that 1 is along the dimer CI axis. The bipolar multipliers, b,, are calculated and depend only on the experimental geometry and on the angular momentum quantum numbers involved in the LIF transition. Assuming a b-function speed distribution, the observed profiles were fit by using eq 1 convoluted with a Gaussian resolution profile (AVOfwhm) to obtain values for the average kinetic energy and effective anisotropy parameters. A distribution of cofragment internal energy states could, in principle, cause the Doppler profiles to depart from the b-function form described above. For example, if both the v, = 0 + = 1 and us = 0 4- vb = 0 channels were important, the u, = 0 profiles would be a superposition of profiles with widths Au i+: 2.6 and Av i= 4.6 GHz, respectively. The observed u = 0 profiles show no observable second component with such a large Doppler shift for either spin-orbit state. We conclude that the u, = 0 + v b = 0 channel is not important. Given the signal-to-noise ratio, this component is certainly less than 3% of the u, = 0 + ob = 1 component. The value of the vibrational population ratio given in Table I1 is based on these considerations. In contrast to the fragment vibrations, the NO rotational distributions and the NO spin-orbit splitting give Doppler splittings of approximately 0.1 and 0.2 GHz, respectively, which are less than the effective Gaussian resolution (0.75 GHz fwhm). Thus the &function speed distribution suffices to model the observed profiles, and no attempt was made to extract the form or width of the kinetic energy distributions from the shape of the individual Doppler profiles. While not included explicitly in the fitting procedure, cofragment internal state distributions (mainly the spin-orbit energies) do slightly influence the Doppler profiles. Fits of eq 1 to model profiles which included trial cofragment distributions showed that

The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8091

Product Energy Correlations TABLE III: Anisotropy Panmeters Determined In Doppler Profile AMIYW~of NO(J,0=3/2,v=l) Formed from (NO),v1 + v5

J(W 0.5 2.5 6.5 8.5

B#J 0

0.31 0.21 0.36 0.01 f 0.003 0.26 -0.03 f 0.01 0.32 -0.15 f 0.05 0.37

f 0.09

B#J

Bd

BLV

0

0

f 0.07b f 0.2W f 0.08 f 0.10

0.11

0.06 f 0.02 -0.04 f 0.01 -0.004 f 0.01 0.03 f 0.01 0.03 f 0.01 0.01 f 0.01

'Pump laser bandwidth 0.3 cm-I, tuned to the vicinity of the dimer and R(3) band. bPump laser bandwidth 0.05 cm-I, tuned to the dimer Q subband. 'Pump laser bandwidth 0.05 cm-I, tuned to the dimer R(3) subband. R(2)

this influence appears entirely in the width parameter Au. In fact, by comparing Au for different transitions, one can extract information about interfragment energy correlations. The results of three trial fits to eq 1 are overlaid in Figure 5 on an averaged Q111*1(0.5) profile. The full profile has been folded over at its center frequency for analysis purposes. The best fit (solid line) in Figure 5 was one in which Av, Bestand AVO were allowed to float in a nonlinear least-squares routine, which resulted = -0.322, and AuG = 0.70 GHz. in values Au = 2.68 GHz, The data are well fit by the model of eq 1, as Figure 5 shows, and fits of similar quality were obtained for all other transitions measured. The other two curves (dotted, dashed) in Figure 5, which do not fit the data as well, are best fits calculated by fixing Au at values equal to 2.68 f 0.13 GHz and allowing and PUG to float. These fitted curves give the total kinetic energy release, EKE= mNo(Auc/uo)2,concurrent with the formation of fragments in specific (J,Q,u ) quantum states, and an estimate of the uncertainty in this parameter. For fragments (J = 0.5, Q = I/?, u = l), a value of EKE= 924 f 40 cm-' was obtained. A similar procedure was followed to find the best values and uncertainty for the effective anisotropy parameter Ben. 1. Anisotropy Parameters. Effective anisotropy parameters, BCrr,and integrated intensities, go,were determined for Doppler profiles observed in different geometries for rotational levels in both spin-orbit states of the NO(u=l) fragments following u1 u5 photolysis. Procedures outlined in refs 22 and 26 were used to further reduce this set of parameters to the bipolar moments Bi given in Table 111. The parameters listed in Table I11 were all obtained with a pump laser with 0.3 cm-I bandwidth tuned to the vicinity of the dimer R ( 2 ) and R ( 3 ) subbands. The correlation of p and J affects the integrated intensities of the lines and not their shapes. The value of j3,,, was derived from the ratios of the integrated intensities of Doppler profiles of a given transition measured in geometries I11 and IV, scaled for line strength and laser power. The other three bipolar moments affect the shapes of the Doppler line profiles. They were calculated from the measured effective anisotropy parameters of Q2,IJ and R221J branch transitions obtained in case I11 and I V pump/probe geometries. Linear combinations of the &'s of a particular rotational level yield the values of &, &, and &,, As shown in Table 111, the derived anisotropies flvJand are approximately equal to zero while p,, = 0.31 f 0.09, indicating a positive recoil anisotropy. In order to further characterize the F-v correlation, the bandwidth of the pump source was decreased to 0.05 cm-l to allow individual (NO), u I + us subbands to be excited. Since for the Q111*'(o.5)transition the J-dependent moments are zero, the shapes of these fragment Doppler profiles depend solely on &. Doppler profiles for the transition were recorded as a function of pump laser wavelength. Table I11 includes the value of ,@, obtained following the excitation of different dimer subbands. 2. Fragment Kinetic Energy. The values of Au obtained for u = 1 fragments are presented in Figure 6 . This figure shows a linear dependence of Au on J , with higher rotational levels carrying less kinetic energy. The dashed line in the figure, which lies close to the data, shows the slope expected if the rotational energy of the fragments were completely uncorrelated, Le., all fragments NO,(J) have cofragments NOb with the same distri-

+

2.01 " ' ~ " " " ' " ' ~ " ' ~ " ' ~ 0 2 4 6 8 10 12 J Figure 6. Doppler shifts of NO(J,Q,o= 1) levels as a function of J and Q following vI us excitation. Data for zlll/2levels are represented by 0 , 'll3/2 levels by X. The five lines correspond to the following: (-) fit of Doppler shifts of 2111/2levels; (----) expected 'll3/2 locus if there is statistical branching of spin-orbit levels; (---) expected 2113/2locus

+

-

if only 2111/2 2111/2and zlls/2 2113/2 occur; expected slope of 2113 locus if correlated rotations (J, = Jb); (--) expected '1I3/2 locus if 2fIlpc-, '&/2 correlation occurs with uncorrelated J. (..e)

bution of rotational energies. The lesser slope of the data implies that the highest rotational states tend to have cofragments with slightly lower average rotational energy. The dotted line shows the slope expected in the limit that rotations are correlated such that J, = Jbr which clearly does not occur. Figure 6 also shows that fragments with the same value of J but in different spin-orbit states form with essentially the same kinetic energy. This observation allows us to discern a correlation among the NO fragment spin-orbit states. We shall denote the possible spin-orbit channels as 2111/2 + 'II1/2, 2113 2 + 2113/2. and the doubly degenerate 2111 + 2 n 3 / 2 channel. The solid line in Figure 6 is a linear fit to the 2111/2data; a fit to the 2113/2 data is the same within the uncertainty. This is the result expected if the dominant dissociation channel is 2111/2+ 21132. If the other relaxation channels were important the fitted widths, Au, would be different for the 2111/2 and 2113 fragments. The two additional lines in Figure 6 which parallei the data represent the widths expected for the ,II?l2 fragments given the observed 2111/2Doppler widths for two limiting dissociation mechanisms. The line with the 2.6-GHz intercept corresponds to a statistical mechanism wherein the four channels occur with equal propensity. The expected profiles were simulated by sums of profiles of the type given in eq 1 with appropriate weights and widths, convoluted with the Gaussian resolution function, and fit in the same way as the actual data. The expected separation of the 2111/2and 2113/2 data sets for statistical spin-orbit branching ratios, as shown by the lines in Figure 6 , is well outside the observed grouping of points. Even further removed from the observations is the line with the 2.3-GHz intercept, which corresponds to a mechanism with strict ,JI3 + 2113/2 and 211!/2.+ 2111/2correlations and with the *111,, + 2 h 3 / 2 channel negligible. The data and models illustrated in Figure 6 show that the 2111/2 + ,II3/2 channel is dominant in uI + us dissociation, while the intensity data given in Table I1 indicate that the dissociat,iondoes not proceed entirely by this mechanism. A more general modeling procedure, similar to that described above, but constrained by the data of both Figure 6 and Table 11, gives normalized propensities for the correlated spin-orbit channels: P(2111/2+2113/2) = 0.77 f 0.07, P(211J/2+2111/2) = 0.21 f 0.05, and P(21132+2113/J 0.06. The kinetic energy of fragments produced fohowing 2u5 excitation was also measured. The values of Au evaluated for a range of J of both spin-orbit states are given in Figure 7. The Doppler shift is shown to again depend linearly on J. But unlike the u1 + vs data, the values of Au obtained for the two spin-orbit fragments fall on two parallel lines, slightly offset from each other. The additional lines in Figure 7 are analogous to those in Figure 6 , calculated here according to the energetics of 2vs excitation.

8092 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991

Hetzler et al. TABLE I V (NO)*Fragment Energy Partitioning 2v5"

L

vI

+ v,"

US

VI

1040 0.03 0.10

1079 0.10 0.05

1158 0.12

0.87 "For b = -1 vibrational channel.

0.85

EaVail. cm-' fmt

fw

xm,

973 C0.03 0.06 0.91

0.10 0.78

Photodissociation Spectrum and Lifetimes. The origin of the

u I + us band was determined to be a t 3626.45 f 0.1 cm-'. The origin of the 2us band was determined to be at 3559.32 f 0.1 cm-I.

-. -.-.

.

L :; ''C

2.0

L

0

a

I

2

"

'

4

a

"

I

6

a

n

I

8

'

*

'

10

J Figure 7. Doppler shifts of NO(J,O,u=I) levels as a function of J following 2v5 excitation. Data for 2111/2levels are represented by 0 , 2113,2 levels by X. The solid line with 2.7 GHz intercept is a linear tit to 2111/2 data and the other solid line is a fit to the 2113,2 data. The other four lines are analogous to those in Figure 6.

As with u I + us excitation, the highest rotational states have cofragments with lower average rotational energy. The data represented in Figure 7 indicate that, although the dominant dissociation channel is 2111/2+ 2113/2, the 2111 + 2111/2channel occurs to a more significant extent than in the uI + u5 induced dissociation. A modeling procedure constrained by the data of Figure 7 and the available energy (using the dimer bond energy determined from the u1 us results) gives the propensities for the spin-orbit channels: P(2111/2+21132) = 0.58 f 0.10, P(2111/2+2111/2) = 0.39 f 0.06, and P(2d3/2+2n3/2) < 0.03. Based on these propensities, the ratio of the total population of the two is 0.46 f 0.10, which is similar spin-orbit states, [2111/2]/[2113/2], to that obtained from the us excitation of NO dimer. Casassa et al. previously reported a spin-orbit ratio [2113,I/ [2111/2] = 0.9 f 0.2 following uI excitation with no details ofjthe interfragment spin-orbit correlation." We returned to the u I excitation, probing the Doppler profiles of fragments in ( J = 10.5, Q= u = 0) and ( J = 6.5, Q = 3/2, u = 0). Analysis of these ratio gives the results together with the measured [2113/2]/[2111/2] = 0.95 f 0.21. propensity: P(2111/2+2113/2)

+

IV. Discussion A. NO Dimer Energetics. A value for the weak-bond dissociation energy, Do, may be obtained from the correlated product state distributions. The vibrational channel u, = 0 + ob = 1 is taken to operate exclusively, the rotational distributions are taken to be completely uncorrelated, and the average spin-orbit energy is obtained from the spin-orbit correlations discussed in section III.C.2. For each probed J state we obtain a value for the total kinetic energy release, EKE, from the fitted Doppler profiles. Consider, for example, results obtained probing the Q221,1(4.5) transition. The value of Au = 2.60 f 0.13 GHz obtained gives a value for the total kinetic energy release EKE = 851 f 40 cm-'. The 2113,2(J=4.5,u=1) level being probed has rotation plus spinorbit energy of 161 cm-' and vibrational energy of 1876 cm-'. Essentially all cofragments have been shown to be in 2111/2(J,u=O) levels. On average, the geminate fragment has an average rotational energy of 14 f 2 cm-' and spin-orbit energy 10 f 2 cm-I. Excitation of the u , + us R(2) and R(3) transitions gives the parent dimer an average 2.5 cm-l of rotation and 3626.45 cm-' of vibration energy. Conservation of energy is then used to derive a value for the bond energy from the difference in average energy in parent and geminate fragments. Such a calculation for this level gives a value of 71 7 f 40 cm-'. Similar calculations for all probed levels give an average measure of the bond energy of Do = 710 f 40 cm-I. This value for the bond energy is more accurate than previous determinations based on ul dimer dissociation" and on the temperature dependencies of y I and y I + us absorption meas~rements.~J~

There are no noticeable perturbations in these (14NO)2 overtone spectra. As shown in Table I, there are no large differences in rotational constants between ground, fundamental, and overtone levels. A measure of the dissociation lifetimes of following u, + us and 2 4 excitation was obtained from the observed photodissociation spectra. The fitted Lorentzian components of the line widths correspond to lifetimes of 7 = 34 f 6 ps for u1 + us and 20 f 3 ps for 2 4 . Although this broadening could result from mixing with other vibrational levels, such a process seems unlikely. For dissociation from the us fundamental, a comparable width was measured and corresponded to the 39 f 8 ps dissociation lifetime measured in real time. In the case of us then, the homogeneous line width reflects coupling to the dissociation coordinate, and not to other metastable vibrational levels. Dissociation from the overtone levels is a Au = 1 process and so parallels the fundamental dissociation. Discounting the spectating NO@=1 ) vibrational quantum, the two processes are nearly isoenergetic. Given the similarity in energetics and line widths and the mode dependence of the fragment spin-orbit ratios, we expect the overtone line widths also correspond to dissociation lifetimes. B. Energy Partitioning. The principal reaction channel following excitation of vI + us proceeds to form one NO(Q=I/,) and one NO(Q=3/2)fragment, with 1876 cm-I of vibrational energy, 29 cm-I of average rotational energy, and 890 cm-I of translation energy. For the minor channel proceeding to two NO(Q=I/,) fragments, the amount of fragment rotation is assumed to be the same since the measured 2111/2rotation population distribution is so similar to that of the 2113/2 fragments. The average energy partitioning for all reaction channels for the overtones and fundamentals is included in Table IV. Since these reactions are all Au = 1 processes, the energies available for the nonvibrational degrees of freedom (rotation, spin-orbit, and translation) are comparable for all excitations studied. In all cases, most of this energy appears in fragment translation. The fraction appearing in rotation,f,,,, is significantly lower for dissociation from u1 + us and 2us than for the fundamentals. The spin-orbit population ratios observed for dissociation from these four vibrational states are significantly mode dependent, varying by a factor of 2. Photofragment angular distributions were used by Dayton, Jucks, and to determine the hydrogen bonding Do (1065 f 5 cm-I) and interfragment scalar J-J correlation for the vibrational predissociation of (HF),. There are major differences between NO and HF compounds of these complexes; most notable are that NO is open-shelled with a small rotational constant, B = 1.69 cm-l, while H F is closed shell with a large B = 20 cm-I. A major difference in the dissociation dynamics is the large Cr, 90%)kinetic energy release from (NO), and small ( ~ K E4 6%) kinetic energy release from (HF),. In the absence of detailed potential energy surfaces for these species, it is difficult to attribute these differences to specific mechanical or electrical properties of the complexes, especially since the bonding and equilibrium geometries of these two complexes are so dissimilar. In fact, the dissociative forces acting in (HF), and (NO), are qualitatively different. Below we show that nonadiabatic processes which are impossible in H F dimer do play a role in determining (NO)2 fragment states. Additionally, the specific near resonant, correlated high-J-low-J channels favored in the dissociation of (HF), do not exist for NO dimer.

-

(33) Dinerman, C. E.; Ewing, G.E. J . Chem. Phys. 1970, 53, 626.

The Journal of Physical Chemistry, Vol. 95, No. 21, I991 8093

Product Energy Correlations

1. Vibrationnl-StateDistributions. The observation of only the + (Ob = 0) channel for dissociation from u1 + us and 2us is expected in light of similar observations of vibrational predissociation for many weakly bound van der Waals complexes. Theoretical treatments of van der Waals molecular dissociation show that the efficacy of Au = 1 processes is an energy gap e f f e ~ t . ~Energetically .~~ accessible Au = 1 processes offer better overlap between initial- and final-state radial wave functions than Au > 1 processes. The energy gap effect should operate whether the dissociation mechanism is mediated by vibrational potential coupling or by an electronic curve crossing. Since the (0, = 1) (ob = 0) channel operates exclusively, the following discussion sections implicitly refer to dissociation on the (u, = l)...(Ub = 0) potential energy surface. The notion of a Au = 1 process suggests that the initial excited state resembles (u, = 1)...(ub = 1) or (0, = 2) ub = 0), which at first glance do not appear to correspond to u, + u5 or 2u5. However, a nodal map constructed in either the normal-mode or local-mode basis shows that the uI + u5 and 2us motions sample both these configurations, differing only in the phase of the stretching motion on the two N O groups. 2. Spinarbit-State Distributions. The mechanism of the dissociation of vibrationally excited N O dimer has been a puzzling problem, particularly with regard to the role of the many electronic surfaces which correlate to the two 211 fragments. Several hypotheses have been offered, but none have been proven. Table I1 and the Doppler profile analyses (Figures 6 and 7) show how the N O product spin-orbit-state distributions and the correlation between geminate fragment spin-orbit states depend upon which vibrational motion is excited. These observations offer some additional insight into the dissociation mechanism of vibrationally excited N O dimer. One mechanistic description is dissociation mediated by a vibrational potential, analogous to the vibrational predissociation of van der Waal m ~ l e c u l e s A . ~recent ~ calculationm with a model potential quantitatively reproduced the mode-specific lifetimes observed for the NO-stretching fundamentals” and the insensitivity of lifetimes to isotopic ~ubstitution.’~ This calculation also was in qualitative agreement with the low extent of rotational excitation observed in the fragments. Consideration of the fragment spin-orbit states is, however, absent from this model. An alternative description is dissociation mediated by an electronically nonadiabatic process.” Several expectations based on this model are seen in experiments, including the rapid time scale of dissociation, the low degree of rotational excitation in the fragments, and the observation of both spin-orbit states in the fragments. Contrary to experimental results, such a nonadiabatic model should exhibit an energy gap effect, resulting in lifetimes sensitive to energy shifts obtained by isotopic substitution. Matsumoto et al. have suggested a hybrid mechanism:14 dissociation occurs upon crossing from the ground-state singlet to a repulsive triplet, in a configuration distorted from the equilibrium geometry. This determines the order-of-magnitude of the dissociation rate. Vibrational potential coupling causes the different modes to explore different regions of the multidimensional ground-state surface, affecting the relative rates. Like the vibrational predissociation model, this description does not consider the spin-orbit-state correlations. If the dissociation processes are governed entirely by a sudden transition a t short fragment separations, as in the nonadiabatic model or in vibrational predissociation followed by fast separation of the fragments, one would expect to observe significant propensities in all three distinct spin-orbit channels. The reason for this expectation is that the N O dimer is strongly bound, Do 700 cm-l, with a b initio calculations12 and microwave spectras showing a u bond arising from alignment of the NO T * orbitals containing the unpaired electrons in the dimer plane. Using monomer wave functions as a basis, aligning the orbitals mixes IA = + I , E) and IA = -1, 2). so the dimer wave functions are mixtures of N O 2111/2 and 2113/2. N O dimer is most probably in the strong-interaction, strong-alignment limit where the mixing (u, = 1)

+

..a(

-

(34) Ewing, G. Chem. Phys. 1978, 29, 253.

coefficients are equal (see below). A sudden mechanism would project these mixed monomer wave functions onto the fragments, giving equal probability to each of the spin-orbit channels. Such a statistical distribution is not observed, arguing against such a mechanism. The magnitude of the 2111/2-Q3/2 mixing in the N O dimer can be estimated by using an electrostatic model, or by comparison to results reported for NO-HF. NO-HF is hydrogen-bound in an approximate T-shaped geometry.35 The N O electronic orbital angular momentum is quenched by a potential of the form VQ = e cos 24, where 4 is the azimuthal angle of the unpaired electron relative to the molecular plane.36-37 For NO-HF, e = 313 cm-I. In the IAZ) monomer basis VQhas off-diagonal matrix elements ( A’Z’I V Q ~ A Z= ) e/28At,A&!,E which compete with diagonal spin-orbit matrix elements AsoAZ, resulting in a splitting of the zero-order states by (A2 + eZ)l/Z. The mixing coefficients in the resulting eigenvectors give relative probabilities [211,/2]/ [’II3/21 = ( [ ( A 2+ A ] / E ]=~2.2 for sudden dissociation from the ground state to form N O + HF. For NO dimer, VQ may be estimated by using the free N O quadrupole moment tensor35 to calculate the quadrupole-quadrupole energy for different orientations of the N O unpaired electron clouds. The result shows the different configurations in N O dimer will be split on the order of 500-1000 cm-I, giving [21112J/[2113/2]= 1.6-1.3. In all likelihood, this electrostatic model underestimates the extent of mixing of 2111/2and 2113/2 in N O dimer, since it ignores other electronic effects which must be important. Thus we expect that a sudden dissociation would produce fragments in each of the spin-orbit channels and that [21112]/[21132] = 1. We note that u I + u5 excitation results in a [ d l / 2 ~ / [ 2 ~ 3 / 2ratio ~ near unity. However, analysis of the resulting Doppler profiles shows one spin-orbit channel dominates, unlike the statistical branching expected for a sudden mechanism. The excitation of ul also results in a [2111/2]/[211312] ratio near unity, while analysis of the fragment Doppler profiles indicates a propensity for one spin-orbit channel. All of the N O dimer vibrational excitations begin on the dimer ground-state potential energy surface, but the different vibrational modes sample and emerge with varying propensities on different fragment surfaces, as shown by the spin-orbit-state results presented here. This can be explained if the dissociation process has both adiabatic and nonadiabatic attributes. (The word ‘adiabatic” here refers to processess in which the electronic state evolves smoothly with fragment separation.) In order to visualize this, it is helpful to think of the N O dimer as a diatomic composed of two 2P atoms, and to divide the dissociation coordinate into regions characterized by the relative size of the interfragment electrostatic energy (V,) and the N O spin-orbit splitting (Am.). This separation has proved quite useful in describing slow atomic collisions.3* At large separations, Aso > Vi,, and electronic surfaces are dominated by the spin-orbit interaction. These surfaces adiabatically correlate to the separated-fragment spinorbit states. In this distance range, Coriolis and velocitydependent radial forces can cause nonadiabatic transitions. At short interfragment distances near the equilibrium geometry KNT.> Aso, and states are dominated by the bonding interaction. Spin-orbit and other interactions enter as perturbations to effect transitions among these states. These types of transitions are also called nonadiabatic. Figure 8 shows a correlation diagram connecting the long- and short-range terms for the rotationless N O dimer. This diagram has mainly illustrative value, for the states shown are a rather restricted set of the states available to N O dimer and the true picture will be considerably more complex. The diagram shows at short range the four lowest terms found in ab initio calculations

+

(35) Fawzy, W. M.; Fraser, G. T.; Hougen, J. T.; Pine, A. S. J. Chem. Phys. 1990, 93, 2992. (36) Mills, P. D. A.; Western, C. M.; Howard, 9. J. J . Phys. Chem. 1986, 90,3331; Mills, P. D. A.; Western, C. M.; Howard, B. J. J. Phys. Chem. 1986, 90, 1986. (37) Fawzy, W. M.; Hougen, J. T. J . Mol. Specrrosc. 1989, 137, 154. (38) Nikitin, E. E.; Umanskii, S.Ya. Theory ofSIow Atomic Collisions; Springer-Verlag: New York, 1984.

8094 The Journal of Physical Chemistry, Vol. 95, No. 21, 199'1 S P I n - m I T S T A R CcemlATIOnS C,

pwridiatmic

.t.t..

separated

fragnt

t*N

C * m

I 4

-

-

1,

\

Figure 8. Correlation diagram connecting the long and short-range terms for the rotationless NO dimer. At short range only the four lowest terms for NO dimer in C, symmetry are shown.

for N O dimer in C, symmetry.12 Next to the C, designations are the corresponding terms for quasidiatomic NO dimer in Hund's case a. These are obtained simply by inspection of the configurations given in ref 12 for the C, term, and identification with configurations and terms possible for 2P2P diatomics. The case a notation is appropriate in the short-range region since VI,, > Am As the distance increases Aso becomes more important, each fragment establishess its own value of Q, and the case c designations given in the figure become appropriate. The correlations are drawn by invoking the noncrossing rule for states of the same Q and parity.39 Among the states shown in the diagram, the only terms accessible by nonadiabatic transitions from the ground state are I l l (by spin-orbit or Coriolis coupling at short range) and l p (by doriolis coupling a t longer range).38 If the vibrationally induced dissociation processes were strictly adiabatic, the fragment would, irrespective of initial excitation, emerge on a single surface. This would be expected for vibrational predissociation at short range followed by adiabatic evolution of the spin-orbit states. The diagram shows that the lowest energy term 'Al has only one Q component, Os+,and so for a slow adiabatic process the fragments must emerge only on the 2111/22111/2 (2P1/2~2Pl/2) surface. Since this is not observed for any of the vibrational modes excited, we conclude that a nonadiabatic process occurs at some point in the dissociation. We cannot say whether it happens in lieu of, or subsequent to, vibrational predissociation. The observations do show activity in the 2111/22111/2channel. This activity is mode selective and might be a measure of the extent to which the purely adiabatic mechanism is operative. uI us dissociates mainly on the 2Pl/22P3/2 surface (77%) but with significant probability on the zP1/22Pl~z surface (21%). The arrow drawn in the correlation diagram, Figure 8, illustrates just one way this might arise: competing spin-orbit coupling and vibrational predissociation processes followed by adiabatic evolution of the spin-orbit states. Conceivably the other vibrations studied couple to these paths with different relative strengths, producing the mode-specific spin-orbit distributions. We emphasize that Figure 8 is greatly simplified. Addition of other NO dimer terms and geometries, and consideration of other nonadiabatic couplings or vibronic interactions, could vastly change its appearance. More ab initio calculations on the NO dimer in different geometries would be extremely helpful in this regard. The main point to be made here is that excited electronic surfaces do play an important role in the dissociation of vibrationally excited NO dimer, affecting the spin-orbit states of the fragments. At the same time, a competing purely adiabatic process cannot be ruled out. Nonadiabatic process(es) with mode-selective propensities direct the fragments along the various spin-orbit

+

(39) Mulliken,

R. S.J. Chem. Phys. 1971, 55, 288.

Hetzler et al. surfaces. Further evolution along these surfaces must be mainly adiabatic since nonstatistical and mode-selective spin-orbit correlations are observed. 3. RotationnEStateDistributions. The N O fragments produced in v I + us dissociation form with average J values of 1.5 in the 2111/2 state and of 2.5 in the '?3/2. state. As indicated in Table 11, the rotation population distnbution results in average fragment rotation energies of 15 cm-l. This represents a small fraction of the energy available, even excluding fragment vibrational energy. As will be discussed below, the most plausible origin of these rotational-state distributions is transformation of zero-point motion in the parent bending and torsional modes into fragment rotation. The low fragment rotational excitation is inconsistent with purely impulsive or phase-space models, although both can be modified to agree with observations. For an impulse acting between nitrogen atoms in the NO dimer in its equilibrium configuration, the impulsive model imparts 26%of the available energy into rotation of each fragmentna Similarly, phase-space calculations following Eres et a1I: grossly overestimate the average fragment rotation. In the impulsive model the rotational energy release would be reduced if the impulse acts instead along the fragment centers of mass. The phase-space calculations can likewise produce low rotational excitation if the impact parameter and available energy are restricted to very small values (b C 0.1 A, E C 70 cm-I); under these conditions however fragment states with J > 4 are forbidden. Parent bending and torsional motions should influence the fragment rotations to some extent and may be the predominant source of the very low rotational excitations observed here. We estimated the degree of rotational energy release using the model given by Vasudev et al. to describe the vibration-to-rotation transformation in HONO d i s s o c i a t i ~ n . ~ ~Using the dimer equilibrium geometry and fundamental frequencies (263,198, and 88 cm-' for the symmetric bend, antisymmetric bend, and torsion, respectively): one expects to observe approximately E,,,, = 56 cm-I rotational energy in each fragment if the low-frequency dimer modes are in the zero-point levels. The u1 + us combination state, however, produces significantly less fragment rotational energy. Qualitative agreement is obtained if the van der Waals frequencies in the transition state are reduced from their equilibrium values by factors of 3-4 and only zero-point motion in these modes is available for fragment rotation following uI + us and 2us excitation. This picture implies the dissociation proceeds through a loose transition state with a barrier to the reverse, association reaction. Since fragment rotation observed following excitation of the (NO)2 u = 2 states is minimal, we postulate that these states are near the hv = -1 threshold for a nonadiabatic transition to a repulsive surface. If we assume each of the dissociations encounters an equivalent transition state with an association barrier of -900 cm-I, we may use the vibration-to-rotation model to predict the fragment rotational energies. Neglecting impulse-derived rotation and allowing all energy above the postulated barrier to be in transition state vibrations, one then predicts average per fragment rotational energies of nominally 14 cm-I (zero-point energy only), 28, 36, and 52 cm-' following 2us, vi + us, us, and v1 excitation, respectively. These numbers are qualitatively in agreement with the observed values of C14, 15, 56, and 75 cm-I. A quantum mechanical treatment of the transformation of parent zero-point motion to fragment rotation predicts Gaussian-like rotational-state distributions peaked at low J,43 similar to our observations. Inclusion of bend and torsion excitation above this zero-point level should give P(J) peaked at J > 0 as observed for excitation of the fundamentals." This may be compared to the vibrational predissociation of HNJ 7uNH for which a barrier of ca. 1000 cm-l was also observed, but for which the amount of availability energy above the barrier was (40) Tuck, A. F. J. Chem. Soc., Faraday Trans. 2 1977, 73, 689. (41) Eres, D.; Gurnick, M.; McDonald, J. D. J. Chem. Phys. 1984, 81. 5552. (42) Vasudev, R.;Zare, R. N.; Dixon, R. N. J. Chem. Phys. 1984, 80, 4863. (43) Freed, K. F.; Morse, M. D.; Band, Y . B.Discuss. Faraday Soc. 1979, 67. 297.

Product Energy Correlations

The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8095

greater. The NH(alA) and N2 (X’Z+8) rotational states and vector correlations showed that a significant fraction of the availability energy is conveyed above the barrier through transition-state bends and torsion. The vibration-to-rotation transformation also has implications for the J vector correlations. The calculation shows the fraction of energy associated with rotation in the plane perpendicular to the dimer a axis is ERI/ER = 0.2. The balance is associated with rotation in the dimer plane. If the recoil velocity v is strictly parallel to the a axis, a small negative v-J correlation would be expected, Le., BVJ= [3(ERI/ER) - 1]/2 -0.2. A slight increase in energy in the torsional mode, or a distribution of recoil angles, would reduce this anisotropy parameter to zero, as observed. The same mechanisms could reduce all the other bipolar moments associated with J(B,,,I@,J) to the observed near-zero values. The equal propensities observed for the A(A’) and A(A”) A doublet states have several possible origins. In the high-J limit, the A doublet states have electronic wave functions which are symmetric (A’) or antisymmetric (A”) with respect to reflection in the plane of rotation. For N O in the h i g h 4 limit, the singly occupied A* orbital lies in the plane of rotation for the A(A’) state and perpendicular to it for the A(A”) state. At the low values of J observed here, the electronic symmetry is not exact, but the doublets still represent distinct distributions of electronic charge with respect to the plane of rotation. If the N O dimer dissociation were restricted to a plane, and if the dissociation is sudden in the electronic coordinates, then the fragments would be expected to show electronic A’ symmetry, since the dimer bond is a u bond. These states would necessarily be superpositions of the low-J A doublets. Based on this model, the ratio of A(A’)/A(A”) populations should range from 1 to 1.6 for the range of J states measured (J = 1.5 to J = 8.5). One effect which could lead to the equal populations observed is nonplanar dissociation, as predicted by the parent vibration to fragment rotation model. Another origin could be an electronic process, either electronically adiabatic or nonadiabatic, which reorganizes the electron distribution during the course of the dissociation. C. Recoil Anisotropy. The recoil anisotropy, = 2&, is the only nonzero vector correlation. In experiments where the pump laser had a resolution of 0.3 cm-’and primarily excited dimer R(2) and R(3) transitions, a value of @?,, = 0.31 f 0.09 was obtained. The NO fragments recoil in a direction parallel to the initial alignment of the transition moment and E. As seen in Figure 1, the rotational structure of the v I v5 band is resolved. This necessarily means that the T 35 ps predissociation lifetime is long compared to the dimer rotational period and the optically prepared states are well described as stationary rotational eigenfunctions of the dimer.” The initial alignment of the dimer and the consequent recoil anisotropy then depend upon the transition of the dimer which is excited. The recoil anisotropies observed pumping individual subbands with 0.05 cm-’resolution, as well as the result obtained with 0.3 cm-’ pump resolution, are equal to values calculated by using a symmetric top model,m within experimental uncertainty. This calculation is an average over several excited transitions, weighted according to the pump spectral profile and the fitted Lorentzian contour of the photodissociation lines. The agreement between the observed and calculated @s indicates that the distribution of body-fixed recoil angles, which would dilute 8, is quite small with an average recoil angle ( 7 ) 5 14O. D. Lmplicatiom for Collisional Relaxation of NO. Cross sections for rotation (R-T) and spin-orbit (S-T) changing collisions and vibration-to-translation (V-T) and vibration-to-vibration (V-V’) transfer between NO molecules are known. For low J states of NO in collision with N O at thermal (a293 K) energies, the cross sections for AJ = *I, 2 changing collisions are 5-10 AZe4 Cross sections for AR = fl changing collisions are nominally one-half

-

+

-

~~

(44)Sudbo, Aa. S.;Loy, M.M.T . J . Chem. Phys. 1982, 76, 3646.

of that for AJ = f l , 2.c4 In these experiments the fate of the collision partner is unknown. In the present vibration-induced dissociation of the separating geminate fragments are in proximity for a fairly long time. One might therefore question the extent to which rotation and/or spin-orbit relaxation might proceed. (The fragments separate at a rate of 12 A/ps.) Since depends on initial excitation the the final ratio [2111/t]/[2113/2] spin-orbit relaxation must not be complete. Additionally, there is no evidence for T-S excitation resulting in geminate 2113/2 fragments, even though energetically allowed. Self-relaxation through a V-T process, i.e. NO(u=l) + NO(u=O) NO(u=O) + NO(u-0) AE = 1876 cm-’ proceeds at thermal energies with cross sections around 0.01 A2,“ which is substantially higher than mast V-T processes with similar AE. The self-relaxation also shows an anomalous temperature dependence, with deactivation probabilities increasing with decreasing temperature in the range 300-100 K.& The process appears to proceed with no barrier. The results can be explained quantitatively using the electronic resonance model of Nikitin” together with an attractive well. The self-relaxation results are seemingly at odds with the notion of a barrier as discussed above. However, the nonadiabatic transitions involved in dimer decomposition have associated barriers which must lie below the u, u b = 1 asymptote for (NO)z(U=l) 2NO(U,+Ub=O), and below the U, + Ub = 2 asymptote for the (NO),(u=2) 2NO(u,+ub=l) decomposition. This means that the reactions corresponding to vibrational energy transfer, i.e., 2NO(Ua+Ub=2) (N0)2(~=2)’ 2NO(U,+Ub=l) + EKE

-

-

2NO(u,+Ub=l)

+

+

-

--

+

(N0)2(~=1)’

+

+ EKE

2NO(U,+L’b=O)

may proceed with effectively no barrier to association.

V. Conclusions We have employed high-resolution frequency-domain techniques to explore the dynamics of the dissociation of N O dimer induced by excitation of overtone vibrations. The lifetimes of v 1 us and 2v5 excited N O dimer were determined to be about 34 and 20 ps, respectively. Each dissociation produces one N O fragment in the u = 1 state and an N O cofragment in the u = 0 state. The fragments have very little rotational energy, (Em,) 15 cm-I, and the remaining available energy, -900-1000 cm-I, appears as spin-orbit and translational energy. The recoil anisotropy is the only nonzero vector correlation. The results indicate that the fragment velocity vectors are constrained to a narrow range of body-fixed recoil angles, while the fragment J vectors are unconstrained and are derived from lowfrequency bends and torsions in the excited dimer. Product energy correlations indicate a preference for dissociation by the z I I l 2-21f3/2 channel with approximately 75% and 60% of the (N6), dissociating by this channel subsequent to vi us and 2v5 excitation, respectively. The balance dissociates mainly via the 2111,2-211,/2 channel. There is essentially no dissociation via the 211yz-211s~zchannel. A combination of adiabatic and nonadiabatic processes appears to be responsible for the observed nonstatistical and mode-selective spin-orbit correlations. These processes may or may not account for the mode specificity of the dissociation lifetimes. The bond energy was calculated to be 710 f 40 cm-’ based on the conservation of energy in the reaction.

+

-

+

Acknowledgment. We thank R. N. a r e , G. Fraser, and J. C. Stephenson for helpful discussions. This work was supported in part by the Air Force Office of Scientific Research. (45) Stephenson, J. C. J. Chem. Phys. 1973,59, 1523. (46) Stephenson, J. C. J. Chem. Phys. 1974, 60,4289.