Dynamical stereochemistry and the polarization of reaction products

Analysis of Stereodynamical Effects in Terms of Order Parameters and Steric Factors ... The Journal of Physical Chemistry A 1997 101 (41), 7476-7485 ...
0 downloads 0 Views 1MB Size
Download PDF
J . Phys. Chem. 1987, 91, 5378-5387

5378

FEATURE ARTICLES Dynamical Stereochemistry and the Polarization of Reaction Products J . P. Simons Department of Chemistry. The University. Nottingham NG7 2RD, England (Received: January 12, 1987)

A broad overview of an important and developing aspect of dynamical stereochemistry is presented-the experimental measurement of electronic orbital and molecular rotational alignment in the products of both full collisions (reactive and inelastic) and half-collisions (photodissociation). Interconnections between some of the related aspects of vector correlations in reactive and inelastic scattering are emphasized throughout the review.

1. Introduction

The experimental science of molecular reaction dynamics germinated in the golden glow of the sodium diffusion flame and flowered through the development of three classic techniques, flash photolysis and kinetic spectroscopy, infrared (and UV/visible) chemiluminescence, and molecular beam scattering. Michael Polanyi’s sodium flame experiments gave the first inkling of specificity in exothermic reaction energy disposal.1 That specificity was mapped initially at the vibrational level by Norrish, Porter, and Thrush2 using flash photolysis and by John Polanyi using IR chemiluminescence3 and later at the vibrational-rotational level through Polanyi’s introduction of the “arrested relaxation” method.4 The practical outcome of these experiments was the chemical laser. Application of microscopic reversibility to the discovery of specific energy disposal led naturally to the concept of specific energy utilization in endoergic reactions, or more generally, in reactions proceding via an energy barrier. The chemical laser, resulting from specificity in the products, provided a convenient pump to probe specificity in the reagents5 The scalar attributes of reactive collisions were expressed in the language of detailed rate constants and attractive, repulsive, or mixed energy The parallel development of molecular beam scattering techniques, particularly by Herschbach,’ Lee,* and their co-workers, provided the first means of probing vector proper9es in reactive or inelastic collisions. The angular correlation (k, k’) between the reagent and product relative velocity vectors, k and k’, was expressed in the language of differential cross sections and stripping, rebound, or complex collision dynamics. A pioneering series of experiments from Herschbach’s laboratory focused attention for the first time on rotational angular momentum, as opposed to rotational energy disposal in the separating products of reaction, by measuring the alignment of product rotational angular momenta- JLwith respect to the reagent relative ~ e l o c i t y . ~ The correlation (k, J’) reflects the division of angular momentum between orbital L’ and internal rotation J’. For example, repulsion (1) Polanyi, M. Atomic Reactions; Williams and Norgate: London, 1932. Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1939, 35, 178, 192, 195. (2) Norrish, R. G. W. “Liversidge Lecture”; Proc. Chem. SOC.London, 1958, 247. (3) Carrington, T.; Polanyi, J. C.; In Chemical Kinetics; Polanyi, J. C . , Ed.; M. T. P. International Reviews in Science; Butterworths: Oxford, U.K., 1972; Physical Chemistry, Series One, Vol. 9, p 135. (4) Polanyi, J. C.; Woodall, K. B. J . Chem. Phys. 1972, 57, 1574. ( 5 ) Bernstein, R. B. Chemical Dynamics uia Molecular Beam and Laser Techniques; Clarendon: Oxford, U.K., 1982. (6) Polanyi, J. C.; Schreiber, J. J. In Physical Chemistry. An Advanced Treatise; Jost, W., Ed.; Academic: New York, 1974; Vol. VIA, p 383. (7) Herschbach, D. R. Adc. Chem. Phys. 1966, 10, 319. (8) Lee, Y. T.; Shen, Y. R. Phys. Today 1980, 33, 52. (9) Herschbach, D. R. Faraday Discuss. Chem. SOC.1973, 55, 233.

between the separating fragments (late energy releasel iicreases (L’/(L’+ J’)) and tends to reduce the correlation (k, J’). The dynamics of molecular photodissociation could be probed by replacing one of the molecular or atomic reagent beams with a laser beam. Measurements of the angular resolved velocity distributions of_the scattered fragments by Wilsonlo led to the correlation (& k’) between the molecular transition dipole p and the fragment recoil vector k’. The correlation was expressed by the sign and magnitude of the anisotropy parameter, p.” Again paralleling the developments in reactive scattering, the phoLofragment rotational angular momentum vector correlation (p, J’) was first probed through measurements of photofragment fluorescence polarization.’*J3 The correlation was expressed by the sign and magnitude of the alignment parameter, AL2).l4 The measurement and interpretation of the vector attributes of reactive or inelastic collisions has since captured the imagination of many reaction dynamicists-including those whose vision has focused on the gas-surface interface. It is not hard to understand why. Conceptually, the measurement of correlations involving axial or angular momentum vectors provides an entry into the anisotropy of molecular interactions, an approach to understanding the stereospecificityof chemical reactivity, and a means of charting the collision dynamics in stereoscopic 3-D. Experimentally the measurement of vector correlations has been facilitated by the ready availability of tunable, narrow-line, polarized laser probes to monitor the internal state distributions among the scattered reaction products; by the development of Doppler probe techniques; by the advent of state-selected reagent molecular beam sources focused by tunable, electrostatic multipolar fields; and by a host of other ingenious methods to probe or prepare polarized products or reagents (for examples, see the rest of this article and those which accompany it). Analytically, and perhaps most importantly, the interpretation of the surge of new experimental data has been set on rigorous foundations, especially through the guidance of Case, McClelland, and Her~chbach,’~ Fano and Macek,16Greene, Altkorn, and Zare,14~’7~‘s Dixon,I9 Hertel,20 and Alexander.2’ ( I O ) Wilson, K. R. In ExcitedStafe Chemistry; Pitts, J. N., Ed.; Gordon and Breach: New York, 1970. (11) Lin, S. H.; Bersohn, R. Ado. Chem. Phys. 1969, 16, 67. (12) van Brunt, R. J.; Zare. R. N. J . Chem. Phvs. 1968. 48. 4304. (13) Chamberlain, G. A.; Simons, J. P. J . ChemISoc., Faraday Trans. 2 1975, 71, 2043. (14) Greene, C. H.; Zare, R. N.; J . Chem. Phys., 1983, 78, 6741. (1 5 ) Case, D. A.; McClelland, G. R.; Herschbach, D. R. Mol. Phys. 1978, 35, 541. (16) Fano, U.; Macek, J. H. Reu. Mod. Phys. 1973, 45, 553. (17) Altkorn, R.; Zare, R. N. Annu. Reo. Phys. Chem. 1984, 35, 265. (18) Zare, R. N. Ber. Bunsen-Ges. Phys. Chem. 1982, 86, 422. (19) Dixon, R. N. J . Chem. Phys. 1986, 85, 1866. (20) Hertel, 1. V.; Schmidt, H.; Bahring, A,; Meyer, E. Rep. Progr. Phys. 1985, 48, 375.

(21) Alexander, M. H.; Dagdigian, P. J . Chem. Phys. 1984, 80, 4325.

0022-3654187 12091-5378%01.50/0 , 0 1987 American Chemical Society T

I

-

Feature Article

The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5379

“locking. decoudine radius”

&!gn&

.e!’

quadrupoiar a (P&

IN COLLISlOh BODY-FIXED

Figure 1. Schematic representations of isotropic, oriented, and aligned vectorial distributions.

This article provides a broad overview of one aspect of dynamical stereochemistry-the measurement of product alignment, both from full collisions (reactive and inelastic processes) and half-collisions (fragmentation processes) and including both electronic orbital motion and molecular rotation. It is not meant to be an exhaustive (or exhausting) catalogue: it is meant to expose the interconnections between some of the related aspects of vector correlations in reactive and inelastic scattering. Much of the review will, unashamedly, be centered on researches of which the author has an intimate and personal knowledge.

2. Vocabulary Any system in which the spatial distribution of angular momentum or axial vectors is not isotropic is said to be polarized. Oriented distributions are ones in which the odd moments are non-zero; aligned distributions are ones in which the even moments are nonzero. The vector diagrams shown in Figure 1 indicate classical vector distributions that are monopolar, reflecting population; dipolar, reflecting orientation; and quadrupolar, reflecting alignment. In an, oriented population the average Legengre polynomial ( P , ( J - Z ) ) # 0; in an aligned population, (P,(J.Z)) # 0. In a quantal system, an isotropic distribution would correspond to one in which all mJ states were equally populated, and an oriented or aligned system would exhibit a unidirectional or bidirectional weighting of the populated m J states. Angular momentum distributions are often expressed in terms of the state multipoles, expectation values of the spherical tensor For a monopolar distribution only the zero rank operators multipole ( is nonvanishing. An oriented population has nonzero components, (7&) = the orientation; an aligned population has nonzero components, ( 7$:!l,iz) A6f!1,i2r the alignment. Frequently, the polarized populations are prepared with axial symmetry, e.g., about the relative velocity vector of two collision partners or the polarization vector of an incident photon beam: in this situation all multipole components with q # 0 vanish. Those of the first and second rank, 06’)( J , ) / ( J ( J + l))’l2 and AO(z) (3J: - J z ) / [ J ( J+ l)], reflect the first and second moments of the angular momentum distribution about the symmetry axis.I4

TI.

3. Electronic Orbital Alignment When chemical bonds are made or broken there is a redistribution of the electronic charge: in a diatomic system the redistribution corresponds to a realignment of the electronic angular momentum about the molecular/body-fixed axis to or from the center of mass/space-fixed axis. Figure 2 summarizes the simple “orbital following” model, proposed by HertelZ0as a basis for discussing the consequences of orbital alignment in colliding atoms. While not to be taken too literally, it serves as a convenient framework for subsequent discussion. The model postulates the existence of an effective “locking radius” R L , at which the electronic angular momentum originally aligned about an axis in the LAB frame (space-fixed)

@

&

POST COLLISlOl SPACE FIXED

Figure 2. ”Orbital following”: the realignment of electronic orbital angular momentum in atomic collisions 2o

realigns onto the molecular (body-fixed) frame and precesses about the interatomic axis. As the collision proceeds, and the axis rotates about the center of mass, the electronic angular momentum remains locked into the body-fixed frame-hence the phrase “orbital-following”-until the collision partners have moved far enough apart for the electronic angular momentum to become decoupled once more at a radius RDEC.The “locking-decoupling” sequence requires an initial impact parameter b > R L ( R D E C ) , would retain any space-fixed alignment originally conferred on the atomic system. The separations represented in Figure 2 provide a convenient way of categorizing three types of experimental situation, though the reality of so clearly defined a locking radius is questionable and the simple picture can be clouded by the introduction of Coriolis and spin-orbit coupling. i. Precollision alignment, where the electronic orbital alignment is referenced to the LAB frame prior to collision, e.g., through polarized laser excitation parallel or perpendicular to the center of mass velocity; the interactions which occur during collision are probed through the polarization dependence of the scattering cross-sections. ii. In-collision alignment, where an electronic state of the collision complex is selectively populated as a transient collision pair; the transfer from body to space-fixed alignment is monitored via the depolarization of the atomic fluorescence. A (more chemical) variant probes the dissociation of a weakly bonded van der Waals complex, stabilized in a free jet expansion, after selective laser ... excitation into a Z or I’I electronic state of the complex. 111. Postcollision alignment, where the electronic orbital alignment is introduced as a consequence of the inelastic or reactive scattering of initially nonaligned collision partners: the alignment can be probed via selective population of magnetic sublevels in atoms or A-doublet states in diatomic molecular products. Precollision Excitation-Polarized Laser Excitation of Atomic Beams. An orbitally aligned atomic beam of electronically excited atoms, e.g., Ca*(4s5p; ‘PI), can be generated by absorption of linear polarized laser radiation directed parallel, pu, or perpendicular, p r , to the beam axis, or to the relative velocity in a crossed-beam system. Collisions of Ca* with He, or other rare gas atoms, are able to promote intersystem crossing, transferring the Ca*(’P,) atoms into the lower lying triplet states Ca**(4s5p;3PJ). The transfer can be monitored via the weak fluorescence emitted to the red of the absorbed laser frequencyz2 Ca(4sz;’S0) + hvl(pol) Ca*(lP,)

-

Ca*(4s5p;’P1)

-

hv,

(1)

+ He, Ar, ... -,C a * * ( 4 ~ 5 p ; ~ P+~hu2 )

(2)

(22) Hale, M. 0.;Hertel, I . V.; Leone, S. R. Phys. Rev. Lett. 1984, 53, 2296.

Simons

5380 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987

(b)

(U 1

Figure 3. Schematic potentials illustrating curve-crossing pathways for atomic excitation-deexcitation collisions:20(a) Ca*(’P,) + He; (b) Nat Na*(3p), ungerade potentials only.

The schematic potential energy diagram shown in Figure 3 suggests that the transfer should be promoted by spin-orbit interaction of the Inl and 3Z1potentials and favored therefore by “n” preparation of the incident Ca* beam: with H e as the collider this is precisely the behavior ~ b s e r v e d . ~ ~Unfortunately ~*~ n preparation also favors the reverse process: with the heavier rare gases the polarization dependence of the Ca(’P-3P) transfer decreases and is reversed for The u, n description is clearly inappropriate when spin-orbit coupling is strong although the four asymptotic spin-orbit potentials do group into two pairs of l3-like and Z-like molecular states at short range.25 The orbital-following model appears to be more useful in discussing the collisional excitation/deexcitation of orbitally aligned N ~ * ( ~ P ; by ~ PNa’ ~ ) ions,20+26 where the excitation (3) and deexcitation steps (4)are favored by u and n preparation, respectively (see Figure 3)

N ~ * ( ~ P , ~+P ~ Na’)

-17

Na+

+

NaH(3d,‘DJ)

(3)

NaC

+

Na(3s.‘S)

(4)

The model has also been invoked in the first (and only?) study of the influence of reagent orbital alignment in a reactive collision, namely Ca*(3s3p;lP1) + HC1, C1,

-

CaC1*(AZII),(B’2)

+ H, C1 (5)

Rettner and Zare found that u and n preparation of Ca*(3s3p:’Pl) favored production of CaC1*(22) and (%), respectively, from HC12’ but unfortunately, the opposite behavior was found when the HCl was replaced by Cl,. Perhaps in the latter case, a larger reactive cross section restricts impact parameters to those where b >> RL so that u (asymptotic) n+ (close range)? Clearly, there are interesting things to be discovered from orbital prealignment experiments but in view of the complexities of the transition from the space- to the body-fixed frame their interpretation can be more subtle than first imagined. In-Collision Preparation: Depolarization of Atomic Resonance Radiation. Polarized laser excitation in the red or violet wings of a collisionally broadened atomic p s resonance line, e.g.,

+

-

Ba(5s5p, ]PI 5sz, ‘So), will selectively populate ‘Z and III components of the collision complex; e.g., IBa(5s2)***Arl

+

I

-

[Ba*(5s5p).--Arl

?Z)

(61

[Ba*(5~5p)-..Arl

c’n)

(7)

hvl(pO‘)

‘hv,(pol)

Measurement of the atomic resonance fluorescence intensity (Le., of the free Ba* after its separation from the collision complex) shows strong depolarization when the violet (IZ)wing is excited but weaker depolarization from the ‘II wing.,* Here, the concept of orbital following is most helpful since rotation of the excited u (or n’) orbitals, with increasing interatomic distance from R C RDEC to R E R D E must ~ cause depolarization of the eventual fluorescence. II preparation would lead to weaker depolarization than 2 since the alignment of the a- component cannot change as the orbital rotates (see Figure 2). An elegant demonstration of the differential reactivity of orbitally aligned atoms in stabilized “collision” complexes generated through free jet expansion has been accomplished by Soep, Jouvet, and their c o - w o r k e r ~ . Excitation ~~ of [Hg-H,] van der Waals complexes to the red or violet of the Hg(6IP1 6ISo) atomic transition preferentially excites (Hg(6s6pn).-H2] or [Hg(6s6pu).-H2] complexes. The former separate reactively leading to chemistry-the production of HgH, detected via laser-induced fluorescence. The latter separate nonreactively, leading to the emission of atomic mercury resonance fluorescence (cf. ref 6 and 7). The differential behavior is simply understood in terms of the nodal properties of the orbitals involved,” given the T-shaped geometry of the complex

-

-

-

(23) Devdariani, A. Z.;Zagrebin, A. L. Chem. Phys. Lett. 1986,131. 197. (24) Leone, S. R., personal communication. (25) Alexander, M. H.; Pouilly, P. J . Chem. Phys., in press. (26) Bahring, A.; Hertel, I. V.;Meyer, E.; Schmidt, H. Z . Phys. A. 1983, 312, 293; Phys. Reu. Len. 1984, 53, 1433. Bahring, A.; Hertel, I. V.; Meyer, E.; Meyer, W.; Spiess, W.; Schmidt, H. J . Phys. B 1984, 17, 2859. (27) Rettner, C. T.; Zare, R. N. J . Chem. Phys. 1981, 75, 3630 1982, 77, 2417.

(9)

Many more experiments of this kind can be expected in the future. (28) Alford, J.; Anderson, N.; Burnett, K.; Cooper, J. Phys. Reu. 1984, 30, L366.

(29) Breckenridge, W. H.; Jouvet, C.; Soep, B. J . Chem. Phys. 1986,84, 1443.

The Journal of Physical Chemistry, Vol. 91. No. 21, 1987

Feature Article

5381

TABLE I: A Selection of Examples Illustrating Preferential Population of A-Doublet Levels in Inelastic Reactive Scattering Processes”

process excitation transfer Ar*(3P2,0)+ N2

--

atom transfer H NO2

+

0 + HR

-

Ar

ref

+ N2*(C311,)

+

+

+

+

surface scattering NO

> “1

OH(,II) + NO OH(,II) R

photodissociation NH, hu “I

planar transition state

32, 33 31

-

“I

TI

36

pyramidal planar maser action?

> “I

“I

rotation plane tends to contain k’

1

torsional motion

38, 39 35 40 34 41, 42

scattering from two potentials

43

planar recoil from a ‘A” potential

> *I

“ rI,, rI represent components where the electron density lies preferentially parallel, perpendicular to the plane of rotation. Postcollision Preparation: Population of A-Doublet States. When diatomic or linear polyatomic molecules are generated in electronic states of II symmetry, their rotational levels are split into A-doublet components whose wave functions are either symmetric or antisymmetric to reflection in the plane of rotation. The generating process could be a bimolecular reaction, a photodissociation, an inelastic collision, a gas-surface collision, or any other scattering process you may fancy. Likely molecules could be CH(u2a1:X211), NO(-.u2a1;X211), OH(-.U~T~;X*II), NH* (.-u’7r3;c111) and so on. What many of these processes have in common is an ability to generate unequal populations in the pairs of A-doublet component states, and the excitement that such observations promote is associated with their ability to provide information on the spatial distribution of electron density referenced to the molecular rotation and ultimately to the molecular collision frame. How is this information gained? The crucial point is the asymmetry of the electron density distribution in the partially filled a-orbitals, which are either symmetric or antisymmetric to reflection in the plane of rotation and can be associated with one or other of the A-doublet components. Many excellent discussions are available: two of the best and most recent are those of Alexander and Dagdigian2’ and Andresen and Rothe30 and there is no need to rehearse their discussions again. Suffice it to note the following before introducing some specific, illustrative examples: i. Fragments in 2 J I n or 3110,2electronic states e.g., OH(X), N2*(C), only exhibit a strongly differentiated electronic density distribution when the A-doublet components are derived from levels with high rotation, J (Hund’s case b). When J is low and the spin-orbit interaction constant A is of the same order as the rotational spacing 2BJ (Hund’s case a), the electronic density in each component approaches cylindrical symmetry, and there is little distinction between the electron densities in-plane and perpendicular to the plane. Their association with a preferred electronic orbital alignment is greatest, therefore, when the rotational level, J >> 0, and the ratio X = IA/BJ5 1.30 ii. This constraint does not apply to fragments generated in ‘II,or 3111electronic states, e.g., NH*(c) or N2*(C); for these the asymmetric distribution of electron density obtains even under case a conditions, Le., when X >> 1. iii. There is a reversal of behavior for 211 fragments possessing a’and a3orbital occupancy, e.g., CH(X) and OH(X)-a subtlety which has created some confusion in interpreting past experimental data, now happily r e ~ o l v e d . ~ ’ * ~ ’ When the electron occupancy is a’,the electron density tends to lie in the plane of rotation if the wave function of the A-doublet component is symmetric to reflection in the plane and perpendicular to the plane when the wave function is antisymmetric. This behavior is reversed for a3occupancy. There are now many examples of systems in which the scattered products, probed by laser-induced or occasionally spontaneous

J

(b)

Figure 4. Preferential population of &doublet levels in rotating molecular photofragments: (a) OH(XZII)from H 2 0 , rI > r,,; (b) NH(c’II) from NH3, rlI> ri.

fluorescence spectroscopy, exhibit unequal A-doublet populations, particularly those involving atom transfer or photodissociation. A selection is presented in Table I; alland al are used to symbolize preferential populations of the components lying parallel or perpendicular to the plane of rotation. Consider first the two systems H + NO2 ---* HO(’II)N + NO; (ail > ~ 1 ) (10)

+ hv

HONO(’A’)

350 nm

(all

> T I )(1 1)

The atom-transfer reaction 10 is assumed to proceed via a planar H O N O transition state, with electronic symmetry A’, since the O H fragment emerges with its a-electron density preferentially aligned in the plane of r ~ t a t i o n . ~ lThe - ~ ~preferentially occupied A-doublets also have A’ symmetry, suggesting a preferential population of the (as yet unobserved) A’ components in NO(*II) as well. In contrast the N0(211) generated via the photodissociation of electronically excited HONO(’A’’) (reaction 11) should display the opposite preference.2’ While experimental difficulties have so far prevented confirmation of the prediction, the opposite preference has been found for the analogous photodiss~ciation~~ CH,ONO

+ hv

364 nm

CH30

Another photodissociation

H2O

+ h~

157 nm

+ NO(211); (aL > all)

(12)

-

H,O[(lb1)-’(3~)’] OH(*II)+ H; (aI > all) (13)

(32) Mariella, R. P. Jr.; Luntz, A. C. J . Chem. Phys. 1977, 67, 5398. Mariella, R. P. Jr.; Lantzch, B.; Maxson, V. T.; Luntz, A. C. J . Chem. Phys. 1978. -.. -, 69. -. , 541 - .1..

(33) Murphy, E. J.; Brophy, J. H.; Arnold, G. C.; Dimpfl, W. F.; Kinsey,

J. L. J . Chem. Phys. 1981, 74, 324. (30) Andresen, P.; Rothe, E. W. J . Chem. Phys. 1985, 82, 3634. (31) Kinsey, J. L. J . Chem. Phys. 1984, 81, 6410.

-

HONO(IA/’) HO(211)N + NO;

(34) Lahmani, F.; Lardeux, C.; Solgadi, D. Chem. Phys. Letr. 1986, 129, 24. Bruhlmann, U.; Dubs, M.; Huber, J. R., J . Chem. Phys. 1987, 86, 1249.

5382 The Journal of Physical Chemistry, Vol. 91, No. 21, I987

Simons j BC

TABLE 11: A Selection of Examples Illustrating Methods of Generating and Detecting Rotationally Aligned Reaction Productso process ref excitdtion transfer A* + BC A + (BC*), (1) 4r(3P2) + W 2 Ar + N2*(C3IIU)\ 46 51 Kr(3P2)+ Br2 Kr + Br2(D’(2,)),

- -- + +

atom transfer A + BC (AB), C A * + BC (AB*), C K + HBr KBr H Xe(’P,) C1, X e C I * ( B , q , + C1 photodiwciation (AB)i, + C

-

+

+

ABC

ABCD

hw

+ hu +

H20

-+

hu

+

+ + (CD),

L ( A B ,,)

(AB),

C

+

OH

-I- H

(A),,

ClCN hu CN*(B), CI H2O2 + hu OH(X),\ OH(X), (HC0)2 + hu H2 2(CO)j \urfdce scattering I\rO A g ( l l 1 ) \O(X)\

-

-

+

+

52. 53 55. 62 (3) (1) (3)

OH(X),,

i:*+

( 2 ) (3) (1)

71

H

70, 72 73 41, 42 74

+

(3)

76

‘Detection by ( I ) spontaneous fluorescence polarization, (2) electric field deflection of a scattered beam, (3) polarization-dependent laserinduced fluorescence spectroscopy.

has aroused interest in view of its possible (probable?) role in fuelling interstellar maser action.35 Simple representations of the orbital rearrangements which accompany the dissociation (1 3) as well as that of NH, (14)

NH,

+ hv



7rL)

(14)

are shown in Figure 4. A final word before closing this section, concerned with spin polarization. A considerable stir was created among the community of “photodissociators” by Wittig’s discovery of unequal spin-orbit populations in the CN(X2Z1+) fragments generated through photodissociation of ICN.44

ICN

+ hv

266 nm

I(3/2, 1/2)

+ CN(X2Zf)N

(15)

Child and Zare4s have attributed the polarization effect to coupling of the electron spin with the electronic angular momentum of the heavy iodine atom and thence with the rotational angular momentum of the CN fragment. The critical factor in the model was the strong field associated with the heavy atom; similar behavior was not expected in the photodissociation of HCN. This unique experiment, which explores the question of spin correlation in molecular photodissociation, has opened the possibility of conducting a new variety of CIDEP experiments in the gas phase. (35) Andresen, P.; Ondrey, G.S.; Titze, B.; Rothe, E. W . J . Chem. Phys. 1984.80, 2548.

(36) Derouard, J.; Nguyen, T. N.; Sadeghi, N. J . Chem. Phys. 1980, 72, 6698. (37) Andresen, P.; Luntz, A. C. J . Chem. Phys. 1980, 72, 5842. (38) Alberti, F.; Douglas, A. E. G e m . Phys. 1978, 34, 399. (39) Quinton, A. M.; Simons, J. P. Chem. Phys. Lett. 1981, 81, 214. (40) Vasudev, R.;Dixon, R. N.; Zare, R. N. J . Chem. Phys. 1984, 80, 4863. (41) Docker, M. P.; Hodgson, A.; Simons, J. P. Chem. Phys. Letr. 1986, 128, 264; Faraday Discuss. Chem. Soc., in press. (42) Gericke, K.-H.;Klee, S.; Comes, F. J.; Dixon, R. N. J . Chem. Phys. 1986, 85, 4463. (43) Luntz, A. C.; Kleyn, A. W.; Auerbach, D. J. J . Chem. Phys. 1982, 76, 721. (44) Nadler, I.; Margerefteh, D.; Reisler, H.; Wittig, C. J . Chem. Phys. 1985, 82, 3885. Nadler, I.; Reisler, H.; Wittig, C. Chem. Phys. Lett. 1984, 103, 451. Shokoohi, F.; Hay, S.; Wittig, C. Chem. Phys. Lett. 1984, 110, I , (45) Joswig, A,; O’Halloran, M. A,; Zare, R. N.; Child, M. S. Faraday Discuss. Chem. Soc., in press.

I

n

Figure 5. The superthermal beam Maxwellian gas chemilupinescence polarization experiment. R (I -I Zl)/(Z(l l + 21,) a (P,(J’*Z)).

4. Molecular Spatial Polarization Molecules or molecular fragments involved in a collision (or half-collision) system may be polarized either as a result of the collision, with the collisional interaction acting as a kind of polarizing lens, or during the collision, with the anisotropy of the intermolecular potential serving to orient or align the collision partners, or prior to the collision (or half-collision), through application of focusing multipolar electrostatic (or magnetic) fields or through the anisotropy of photon absorption. There is a strong analogy with the three uzones” of electronic orbital alignment, or in more general terms, electronic angular momentum polarization. The “before” and the “during” zones are reviewed in the accompanying articles by Bernstein, Parker, and Stolte, by Soep, and by Wittig. The emphasis here will be directed toward the “alternative”, Le., the “products” polarization, how it can be measured, and what it can reveal about the reaction dynamics. We shall be concerned principally with the proc!u_cts’ rotaiional alignme$, reflected in the vector correlations (k,J’) and (k’,J’), where k, k’-are the reagent and product relative velocity unit vectors and J’ is the unit vector for the product’s rotational angular momentum. Table I1 lists the range of systems under review. Excitation Transfer. The collisional transfer of electronic excitation from an excited atomic donor to a molecular acceptor is the primary event in photosensitized chemical reaction. Occasionally, the acceptor may spontaneously fluoresce and measurements of the sensitized fluorescence intensity and its dispersed spectrum provide insight into the collision dynamics, particularly when the spectral intensities can be determined over an extended range of selected collision energies. At the present time, relatively few studies have addressed this aspect of inelastic scattering dynamics. Even fewer have focused on the polarization of the sensitized fluorescence. They ought to, since it allows determination of the average alignment of th,e acceptor molecule after excitation transfer has occurred, (P,(J’.k)). The interaction of Ar(3P2,0)with N2 provides a rare example46 Ar*(3P2,0)+ N2

-

N2*(C311,)

-

+ N2*(C(311,))N, N2**(B311g)+ hv(po1) Ar

(16) (17)

When a superthermal beam of Ar(3P2,0)is directed into a N2gas cell, the sensitized N,(C-B) fluorescence is found to be preferentially polarized parallel to the beam axis. In the high rotation limit the N2(C+B) transition dipole lies perpendicular to the molecular rotation axis so the fluorescence polarization reflects an alignment of the rotational angular momentum J’. If the fluorescence intensities Zl, and I, are measured parallel and perpendicular to the beam axis z (see Figure 5 ) it is easy to relate the observed polarization to the average product rotational alignment; for a “parallel” transition (E‘, R J )

and for a “perpendicular” transition, the polarization of the additional Q branch lines is4’

RQ = + ( P 2 ( & 4 ) ) ;

-yz

C

RQ < +1

(19)

(46) Johnson, K. M.; Pease, R.; Simons, J. P., unpublished work. (47) Johnson, K.; Pease, R.; Simons, J. P. Mol. Phys. 1984, 52, 955.

Feature Article

The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5383

b

7

Ill

I5

111

2-

111

F, ,I hJ in101

-

Figure 6. Rotational alignment of N2(C311,)produced through excitation transfer from an atomic beam of Ar(3P2,0):Ar*(”,,J + N, Ar + N2*(C31T,)J,.46

The positive polarization found for the N,(C-B) fluorescence reflects a negative alignment of its rotation with respect to the incident atomic beam axis, Le., a tendency for J’ to be directed perpendicular to z (see Figure 1). What aboui the alignment referenced to the relative velocity vector, k, (P,(J’.k))? That could have been found directly by employing crossed-beam conditions to define precisely the direction of k, but the reduced fluorescence signal causes signa1:noise problems: hence the choice of beam-gas conditions. Fortunately the azimuthal symmetry allows the factorizati~n~~.~~ and the “kinematic” blurring factor, ( P&2)), reflecting the divergence of the cone of relative velocity vectors about the beam axis, can readily be calculated by using Monte Carlo averaging technique^.^^^^^ As the relative velocity and/or the mass of the target molecule increases, its magnitude rapidly approaches unity; for almost all practical purposes, the polarizations measured under beam-gas conditions are only reduced by SO%.47 The first experimental data for the Ar*(3P2,0)/N2system are shown in Figure 6. The average rotatio_n+lalignment, although lying well below the kinematic limit (P,(J’.k)) = -1/2, does reflect an average tendency for J’ to be directed perpendicular to k, particularly at low collision energies. When this result is combined with the preferential A-doublet population (section 3), which reflected a simultaneous preference for the alignment J’ I k’, Le., perpendicular to the exit relative velocity, the dynamics of the excitation transfer (16) are seen to generate N,*(C) in rotationally excited levels where the rotation axis tends to lie perpendicular to the collision plane. The decreasing alignment at elevated collision energies argues against rotational excitation being associated with orbital angular momentum transfer L J’; the higher alignment at low collision energies more likely indicates a preference for a nonlinear collision geometry. Two final remarks before moving on: i. Although the average alignment measured via unresolved fluorescence polarization represents an average over all scattering angles and all populated rovibronic states, the most recent experimental developments allow the latter averaging to be broken down.49.50 Fluorescence intensities generated under beam-gas conditions are sufficient to allow partial spectral resolution, using signal averaging techniques. This will enable measurements of rotational alignment to be made as a function of both the collision energy and the final vibronic state. With partial resolution of the rotational envelopes, it may even be possible to estimate its variation with the final rotational state. ii. Different methods of monitoring product rotational alignment can give different kinds of average and experimental results obtained by different methods and should be compared cautiously. Measurements via spontaneous fluorescence polarization are summed over all scattering directions, and the derived alignments are averages over the full center of mass (CM) angular scattering

-

(48) Prisant, M. G.;Rettner, C. T.; Zare, R. N. J . Chem. Phys. 1981, 75, 2222. (49) Ottinger, Ch., personal communication. (50) Hartree, W. S . ; Johnson, K. M.; Simons, J. P., unpublished work. (51) Hennessy, R. J.; Simons, J. P. Chem. Phys. Left. 1980, 75,43.

distributions. The electric beam deflection technique, however, sample:; only those products where C M scattering angles lie within the acceptance cone of the polarization analyzer; for the systems M / H X where the “leaving” atom is very light there is very little angular discrimination, but this is not the case with M/X, or other systems which are not kinematic “special cases”. Measurements using the polarization dependence of laser-induced fluorescence intensities must be integrated over the full Doppler width of the sampled spectral line to ensure averaging over the full angular scattering distribution. Particular problems (and advantages!) can arise when this is not done if there is a correlation between the rotational angular momentum J’ and the recoil velocity k’15; see section 5. Atom Transfer. Angular momentum conservation in the archetypal reaction A

-

+ BC(J)

AB(J’)

+C

(21)

requires Jtotal

= LA-BC+ JBC = L’AB-C+ J’AB

where L,L’ and J,J’ are orbital and internal angular momenta. When the reagent A is . ,epared as a superthcrmal atomic beam, and BC is entrained in a supersonic nozzle beam expansion ILI >> 14. If in addition, the atom-transfer reactions were proceeding at the “spectator stripping limit”, with IL1 1, memory of the initial correlation between p,bs and ep may dimi?ish, with a corresponding reduction in the alignment 2(P2(J’-tp)).69When dissociation is fast on the time scale of the parent rotational clock, there is no possibility of “amnesia”. The two extremes are neatly encapsulated in a study of the photodissociation of H2O.’O Two-photon absorption of tunable laser radiation near 248 nm excites both the rotationally_structured (but strongly predissociated) RyGberg state, H 2 0 (C’B,), and the dissociative continuum H20(B1A,)upon which it is superimposed (see Figure 8). The former survives for about a picosecond, the latter for much less; both lead to generation of OH(A2Z?) and OH ( X 2 n ) photo fragment^.^^^^^ The OH(A2Z+) fragments, preferentially generated in high rotational levels, emit fluorescence which is strongly polarized when the laser is selec_tivelytuned into the continuum absorption lying between the H20(C+X) rotational features; the fragments are strongly aligned and both the sign and magnitude of the alignment are consistent with fast dissociation from a state of A, symmetry.’O When the laser is tuned onto the sharp rotational features, the obs_erved-alignments fall and the greater the contribution from the C X component, the greater the reduction. FLagments generated via predissociation of the long-lived H20(C1B,) carry little or no rotational alignment. Other factors which may also diminish the observed product rotational alignments, particularly of fragments in low rotational 14968

-

(68) Macpherson, M. T.; Simons, J. P.; Zare, R. N. Mol. Phys. 1979,38, 2049. (69) Nagata, T.; Kondow, T.; Kuchitsu, K.; Loge, G. W.; Zare, R. N. Mol. Phys. 1983, 50, 49.

(70) Hodgson, A.; Simons, J. P.; Ashfold, M. N. R.; Bayley, J. M.; Dixon,

R. N. Mol. Phys. 1985, 54, 351. (71) Krautwald, H. J.; Schneider, L.; Welge, K. H.; Ashfold, M. N. R. Faraday Discuss. Chem. SOC.,in press. (72) Simons, J. P.; Smith, A. J.; Dixon, R. N. J . Chem. SOC.,Faraday Trans. 2 1984, 80, 1489.

Figure 9. The trianglcof photofragment vector correlations: k , photofragment recoil axis; J’, photofragment rotation axis; Pah, parent molecular transition moment direction; ep, r-vector of photolysis beam.

levels, include precessional effects promoted by coupling of the fragment molecular rotation to its nuclear and/cr e l e ~ t r o n lspin ~,~~ or external magnetic fields.73 In practice, reductions due to external fields (e.g., that of the earth) present no problems; those promoted by spin precession are generally small but care has to be taken in analyzing the experimental data associated with fragments populating low rotational states.

5. Photofragment Vector Correlations and Beyond There is a rapidly growing range of systems in which the angular momentum (and energy) disposal in the molecular photofragments has been probed by using tunable laser-induced fluorescence techniques. When, as is often the case, the laser line width is narrower than the Doppler-broadened spectral profile, it selects a subset of fragments associated with a particular scattering direction and if the recoil velocity k’ and the rotational angular momenta J’ are correlated, the alignment will vary across the Doppler profile. Under such conditions, direct determination of the alignment via polarization measurements, necessarily requires summation over th,e eJtire Doppler-broadened profile. The correlation (k’, J’), which can be termed the photofragment helicity, is a dynamical quantity of great interest in its own right, directly reflecting the dissociation dynamics during the fragment recoil. It is referenced not to the LAB frame but to the body frame since pabS(and hence tP) are not involved. The correlation persists even when there is a long interval between excitatio? and dissociation. The alignment (J’, &bs) and the anisotropy (k, Pabs)both suffer from “amnesia” when dissociatio_n!i delayed (see Figure 9). In broader terms the correlation (k’, J’) is not restricted to photodissociation; we have already met it in connection with excitation transfer from Ar(3P2) to N2and it surely exists in many (most) bimolecular collision systems where there is a rapid release of momentum in the exit channel. As with all the other correlations there are two limiting cases corresponding to parallel and perpendicular polarization: the first, J’ 11 k’ would arise from torsional motion about the recoil axis, the second J’ Ik’, from a bending motion in a plane containing the recoil axis. The first is exemplified by the photodissociation of H20;1942 (see below) and the second by the dissociation of any nonlinear triatomic molecule, e.g., SC0,74or less trivially, any polyatomic molecule in which there is a propensity for dissociation via a, planar configuration, e&, (HCO),.74 The existence of a (J’, k’) correlation can be revealed through analysis of the Doppler-resolved photofragment spectral profiles. These will change as t h e probe laser direction k, and polarization ea are a l t e r e d relative to those of the photolysis laser, kpand tP;typical alternative configurations would include k, 11 ep and k, I tp. If the probe excites a perpendicular transition (AA or Ai2 = & l ) the profiles (73) Guest, J. A,; OHalloran, M. A,; Zare, R. N. Chem. Phys. Lett. 1984, 103, 261. (74) Hall, G. E.; Sivakumar, N.; Houston, P. L.; Burak, I. Phys. Reo. Lett. 1986, 56, 1671. Hall, G. E.; Sivakumar, N.; Ogorzalek, R.; Chawla, G.; Haerri, H. P.; Houston, P. L.; Burak, I. Faraday Discuss.Chem. Soc., in press.

Simons

5386 The Journal of Physical Chemistry, Vol. 91, No. 21, 1987

-

kP

reduced to a set of bipolar moments ,f3f(kl,k 2 ) ,which are determined by the translational and rotational vectorial angular distributions. The spectral line shapes associated with laser-induced fluorescence detection are expressed by the summation

ILp

I

where A’D = v0(v/c) is the Doppler shift, X D = ( u - v 0 ) / A v D measures the relative displacement from the line center v0, and the terms gk,are linear combinations of the bipolar moments with beam geometry dependent coefficients. The expansion in even Legendre polynomials up to P6reflects the “three-photon” nature of the overall pumpprobe sequence. In practice, the more rapid oscillations introduced by the higher terms are unlikely to be resolved experimentally. The remaining polynomials are associated with the terms go = bo

+ b,PlwQ)

(35)

and

where (b’

EaiJ‘ -

:

P,R?bronch excitation

=

kalk’ :

Figure 10. Simplified representation of a triatomic molecular photodissociation showing how the photofragment vector correlations can influence the Doppler profiles of rotational branches in its laser-induced fluorescence spectrum. The illustration represents a system where the parent molecular transition moment lies in the ABC plane.

will be sensitive to the choice P,Rf or Qt. As a simple illustration consider the dissociation of a triatomic molecule ABC hu AB(J’) + C (32)

+

-

via a bent configuration. Suppose that (i) the transition moment pabslies in the molecular plane, (ii) the product AB(J’) is probed via a perpendicular transition, and (iii) the photolysis and probe lasers are directed coaxially, k, 11 kp (see Figure IO). Conservation of angular momentum requires J’ I k’ while the cylindrical symmetry about pa&ensures a cylindrical distribution of k’ in the polarization plane of the probe beam: the fragments are thrown off like water droplets from a spinning wheel. AB(J’) fragments recoiling along the probe beam axis k, will be aligned with J’ 11 t,, favoring Qt branch excitation (in the high J’ limit) but fragments recoiling perpendicular to k,will find themselves aligned with J’ I e, favoring P,Rt branch excitations. Recoil along the “line of sight” promotes the maximum Doppler shift and leads to the Qt branch Doppler profiles displaying enhanced intensities in the wings and a dip at the line center. Recoil perpendicular to the probe beam favors the opposite behavior with the P,Rf branch profiles peaking at the center. Provided the atomic fragment C is generated in a unique electronic state, the selection of a single rovibronic state in the sister fragment AB, ensures a monoenergetic velocity distribution, apart from the thermal motion of the parent molecule, which greatly simplifies analysis of the Doppler profiles. Houston has turned this to advantage in an investigation of product branching in the photodissociation of sc0.74

SCO

Pa(02) = ( 5 / 4 ) A f ) gives the alignment ( j ’ , ZP)

(37)

sideways recoil perpendicular to&,

+ hv(222 nm)

-

CO(X’Z+)

+ S(’D) or (3P)

(33)

Application of energy conservation to the expected velocity distributions in the recoiling CO fragments, monitored by laser excitation of the CO(A’II X’Z’) fluorescence, established the predominance of the single spin-orbit channel leading to S(lD). The bimodal rotational distribution in the CO had earlier encouraged the view that the CO molecules occupying the highest rotational levels were generated via the alternative more exoergic channel, leading to S(3P). DixonI9 has provided a detailed analysis of (&, k’) photofragment correlations which enables the experimental data to be

-

Pi(20)

(1 / 2 ) P gives the anisotropy

(i’,ip)

(38)

Pg(22)

(P2(k’d’))gives the helicity (k’, j’)

(39)

-

The coefficients bo b4 are (tabulated) multipliers dependent on the choice of the excitation-detection beam geometry and polarization, and the selected rotational branch, AJTAJJ;the moment &22) describes the mutual correlation of k’ and J’ with pabs Equations 35 and 36, together with the tabulated coefficients bo b4, can be used to extract each of the vector correlations from measurements of a series of Doppler spectral profiles, prouided the fragments recoil with a single or known velocity distribution. In the absence of that constraint or knowledge, the analysis must remain qualitative. An Example f r o m Life. The best characterized system in which the vector correlations are nontrivial and where fortune smiles kindly in respect of the sharpness of the fragment recoil velocity distribution is provided by the photodiss~ciation.~~-~~~~~

-

H 2 0 2+ hu (266 or 248 nm)

-

20H(X),=o,Ar. (40)

The OH(X) fragments are generated with no vibrational excitation, modest rotational excitation, but very high translation. The assumption of a near-monoenergetic velocity distribution for any selected rotational level provides a very good match to the observed Doppler shift^.^^,^^ The lif Doppler profiles of the OH(X) fragments are sensitive to the choice of relative probe beam geometry and polarization, the choice of rotational branch, and the rotational level selected; typical profiles are shown in Figure 11. The translational anisotropies determined through their analysis establish photofragment recoil perpendicular to_the transition dipole, k’ Ij ~ , ~supporting , the assignment A’A X’A to the continuum absorption, with pa& directed parallel to the C2symmetry a ~ i s ~ ’ , ~ ~ , see Figure 12. The rotational alignments are found to be small and positive, but the Doppler profiles reveal a much stronger positive correlation between JtOHand k’-compare the contours of the Q and P branches in Figure 11. The positive correlation reflects a preference for the rotation to be aligned parallel to the recoil vector, with the OH fragments executing a “cart-wheel” motion generated by torsion about the 0axis. Figure 12 provides a qualitative picture of the way in which the Doppler profiles shown in Figure 1 l a are developed. The principal source of the correlated motion is thought to be a strong torsional dependence

-

(75) Ondrey, G.; van Veen, N.; Bersohn, R. J . Chem. Phys. 1983, 78. 3732

The Journal of Physical Chemistry, Vol. 91, No. 21, 1987 5381

Feature Article

(b)

Q!>>P,R(whenlv-vol

=0

Figure 12. Simplified representation of photodissociation dynamics in H202. Torsion about the 0-0 bond promotes a “cartwheel” motion in the

i

:

:

O H fragments and a tendency for J’oH 11 ktOH. With the transition moment 1 11 C2, this leads to an enhanced intensity in the wings of the Doppler broadened P , R t laser-induced fluorescence features and the center of the Qt branch features (cf. Figure 1 l a ) .

!

Figure 11. Photodissociation of H202 a t 248 nm. Doppler-resolved profiles of laser-induced fluorescence excitation of OH(X211312)in rotational level N-= 14 showing the dramatic effects of the photofragment helicity, (k’, J’), for different branches and alternative photolysis (p); probe (a) laser beam geometries (Docker, M. P.; Hodgson, A.; Simons, J. P., unpublished work).

in the photoexcited parent molecular p ~ t e n t i a l . ~ ~ , ~ ~ With hindsight, this result might well have been anticipated (by someone with remarkabk vkion). Certainly, the sensitivity of Doppler line shapes to (J’, k’) correlation in the scattered fragments had been anticipated in a prescient paper by Case, McClelland, and Herschbach.Is However, even they would have been (were?) surprised by the discovery of a preferential alignment of CO molecules generated through the photodissociation of gIy0xa1’~perpendicular to their recoil velocity. The alignment must reflect a preference for a planar configuration at the instant when the molecule eventually decides, after a delay s, to dissociate

-

(HCO),

+

hv H2

+

2CO(J’)

(41b)

6. Final Thoughts There is much to be gained from experimental studies of angular momentum polarization in reactive and inelastic collisions and in molecular fragmentations: this article has tried to give a flavor of their breadth and value. It contains much material, yet the surface has only been scratched, in more ways than one, since collisions with and desorption from solid surfaces can undoubtedly impose alignment and orientation upon the scattered molecule^.^^*'^

Where is ignorance most prevalent? Virtually nothing is known about i. The vector correlations in collisions involving excitation transfer e.g., A* BC(J) A + BC(*)(J’) (42) ii. The state-to-state dependence of vector correlations in reactive collisions, e.g., A(*) BC(D,J) AB(*)(~:J? + c (43)

-

+

+

iii. Electronic orbital alignment or spin polarization in fragmentation processes, e.g., ABC hv AB(*) c(*) (44) or in processes 42 and 43; iv. The influence of orbital alignment on the reactive or inelastic scattering of excited atoms; v. The (Jl’, J2/) correlations in systems such as ABCD h~ AB(J1’) CD(J2’) (45)

+

A

+ + BCD

-

4

AB(J1’)

+

+ + CD(Ji)

(46) vi. Angular correlations involving more than two vectors; and vii. The vector correlations associated with scattering at gas-surface interfaces. Dynamical stereochemistry still has a long way to go-it welcomes fellow travellers. Acknowledgment. The author is more than grateful to Raphy Levine, Dudley Herschbach, and Dick Bernstein for their encouragement of the preparation of this article, to his colleagues over the years, whose work is featured in it, and to Mrs. Margaret Krause for help in preparing the manuscript. (76) Kleyn, A. W.; Luntz, A. C.; Auerbach, D. J. Surf. Sci. 1982, 113, 33.