7878
J. Phys. Chem. 1995,99, 7878-7890
FEATURE ARTICLE Full- and Half-Collision Studies of Metal Atom Singlet-to-Triplet Deactivation Induced by Rare-Gas Atoms Solomon Bililign Department of Physics, North Carolina A&T State University, Greensboro, North Carolina 2741 I
John G. Kaup and W. H. Breckenridge” Department of Chemistry, University of Utah, Salt Luke City, Utah 84112 Received: December 6, 1994; In Final Form: March 8, 1995@
Experiments and ab initio calculations are described involving singlet-to-triplet deactivation of nsnp(’P) to n~np(~P or) ns(n - l)d(3D) valence excited states of Mg, Ca, Sr, Ba, Zn, Cd, and Hg atoms induced by “full” and “half’ collisions with rare-gas (RG) atoms. The evidence presented is consistent with a mechanism originally postulated by Breckenridge and Malmin: if an attractive M.RG(’n1) potential curve is crossed by a repulsive M*RG(32t)potential curve below or near the energy region accessed experimentally, predissociation may occur to form the M(nsnp 3Pz)or M(ns(n - l)d 3D) state. The efficiency of this singlet-to-triplet energy transfer process depends on the magnitude of the spin-orbit coupling which mixes the and ’2; states in the curve-crossing region.
I. Introduction The concept that electronic spin angular momentum must be conserved for a chemical reaction or energy-transfer process to take place efficiently has been important in physics and chemistry for many As a relevant example, the Wigner spin-conservation rules, derived from the early work of Wigner and Wittmer,’.2had been used by Laidler3 and others4 up to the mid-1960s to rationalize and predict the rates of, and major products in, the collisional deactivation of electronically excited atoms by various species. By the late 1960s, however, reports of major exceptions to the spin-conservation “rules” were beginning to appear. For example, the quenching of the first excited singlet M(nsnp ‘PI)states of metal atoms such as Zn, Cd, and Hg by alkane hydrocarbons RH had been p r e d i ~ t e d ,using ~ . ~ spin conservation, to produce either vibrationally excited ground-state R P M (two singlets), MH R (two doublets), or, when energetically possible, M H R (a singlet and two doublets). The possible spin-disallowed process
+ +
+
+
M(nsnp ‘P,) 4- RH
-
M(nsnp 3PJ>4-RH*
(1)
to produce the lower-energy M(nsnp 3 P ~ triplet ) states of the metal atom was not even listed as a possible quenching p r o c e ~ s . ~Breckenridge .~ and Callear,5-6using a resonanceradiation flash photolysis technique, showed in 1969 that Cd(5s5p ’PI)is deactivated by CHq molecules at essentially every collision and that the major products appeared to be the lowerlying Cd(5s5p 3 P ~states, ) in clear violation of the Wigner spin rule. This was quantitatively confirmed later by Breckenridge and co-workers’ using state-to-state pulsed laser methods; the yield of Cd(5s5p 3 P ~states ) in the quenching of Cd(5s5p ‘PI) by C& was 284%. In fact, it was shown that most alkane, @
Abstract published in Advance ACS Abstracts, May 1, 1995.
0022-365419512099-7878$09.00/0
alkene, and alkyne hydrocarbons, as well as N:! and CO, collisionally deactivate Cd(5sSp ‘PI)very efficiently and that the Cd(5s5p 3 P ~states ) are the major products.8 In 1972, in a qualitative study, Madhaven et aL8 similarly observed strong emission from Hg(6s6p 3P1)when Hg(6s6p ‘PI) was collisionally deactivated by several molecules, including Nz, CO, and hydrocarbons. Later s t u d i e ~provided ~ ~ ’ ~ evidence that for N2 and CO at least, the energy transfer was a direct, one-step, efficient (but spin-forbidden) process: Hg(6s6p ‘P,)
+ N,(CO) - Hg(6s6p 3PJ) + N;(CO*)
(2)
Of course, it was also known from the earliest days of quantum mechanics that the Wigner spin rule was expected to be truly valid only when the direct couplings between spin and orbital electronic angular momenta were negligibly small, e.g., for electronic states of light atoms where the magnitudes of the spin-orbit coupling matrix elements H ~ were o small. As the nuclear charge of an atom with the same outer-shell electronic configuration increases, the rapid change in potential energy (as a function of distance r from the nucleus) experienced by electrons which penetrate close to the higher nuclear charge can cause strong relativistic coupling of spin and orbital electronic angular momenta.’’ Thus, electron spin is no longer a good quantum number, and an initial “singlet” state, for example, has some probability of becoming a “triplet” state in an excitedatodatom or an excited-atodmolecule collision when the excited atom is “heavy”. The values of the atomic spin-orbit coupling constants for the valence Cd(5s5p) and Hg(6s6p) states are, of course, quite large for these second- and third-row transition elements (HSO = 1141 and 4264 cm-’, respectively), and in hindsight it is not really surprising that the Wigner spin rule should break down for such heavy-atom cases. In contrast, studies in our laborat o r i e ~ ’have ~ . ~ shown ~ that the efficient collisional quenching 0 1995 American Chemical Society
Feature Article
J. Phys. Chem., Vol. 99, No. 20, 1995 7879
Energy Levels of Group 2, 12 Metal Atoms
-
50,000 -
40,000
T E(cm”)
-
-
-2
5s5p’P1
-1
-0 3s3p1P1
30,000 -
20,000 -
-
4s4p lPl
6 ~ 6 p’P,
-
=4s4p3P,
- 12
-
6s6p3P,
5s5p3P,
3s3p 3P,
10,000-
0-
-
-
-
-
Mg
Zll
Cd
Hg
3s2 ’So
4s2 ’So
5s2 ‘So
6s2 lS0
Figure 1. Energies of the nsnp ‘PI and nsnp 3 P states ~ of Mg, Zn, Cd, and Hg.
of the 3s3p ‘PI excited state of the “light” magnesium atom by a variety of hydrocarbons and other molecules produces no detectable Mg(3s3p 3 P ~ (for ) alkane hydrocarbons, the main product is the MgH molecule, indicating efficient chemical reactionI3). This is, of course, quite reasonable given the very low value of HSO= 41 cm-I for the Mg(3s3p) atomic states. Earlier resonance-radiation flash photolysis studies by Breckenridge and RenlundI4 of deactivation of the 4s4p ‘PI state of the zinc atom, where HSO= 386 cm-’ for the Zn(4s4p) states (substantially larger than that for the Mg(3s3p) states) also revealed no clear evidence for Zn(4s4p 3 P ~products ) for any molecule studied. (Note that very similar earlier flash photolysis experiments by Renlund and Bre~kenridge’~ on Cd(5sSp ‘PI) deactivation with the same apparatus had shown large yields of Cd(5s5p 3 P ~products, ) consistent with the later time-resolved laser work.’) Similarly, Zn(4s4p ‘PI) reacts chemically with alkane hydrocarbons to produce ZnH,I4 a conclusion confirmed by the recent state-to-state laser studies of Umemoto et a l . I 6 It appears, then, that for metals with low Hso(nsnp) values, spin-forbidden ‘PI 3 P energy ~ transfer is so slow that other spin-allowed processes, such as chemical reaction to form two doublet radicals or deactivation to form the singlet ground states of both metal atom and molecule, dominate the deactivation processes of the nsnp ‘PI states. What seems odd, however, is that the “failure” of the spinconservation rule manifests itself so suddenly in going from the Zn(nsnp) states ( H ~ o= 386 cm-I) to the Cd(nsnp) states (HSO= 1141 cm-I). But (see below) the coupling between appropriate singlet and triplet potential surfaces (which presumably have similar character in the isovalent Zn and Cd cases) is proportional to the square of the H ~ matrix o element, so it is possible that an almost “all” or “nothing” switch from dominant spin-allowed to dominant spin-disallowed processes could occur from Zn to Cd, where the ratio of (Hso)* is 0.114.
-
The problem, of course, with interpreting M*-polyatomic or even M*-diatomic interactions is that there are usually several multidimensional diabatic potential energy surfaces involved (as well as possible electronic, vibrational, andor rotational dynamical couplings among them) which are difficult to estimate or even calculate using state-of-the-art ab initio methods, especially for heavy metal atoms. Both experimental and theoretical efforts have been reported recently on this difficult problem, the Cd*Hzand CdC& systems being two good example^,'^-^^ and further experimental and theoretical studies are in progress. In the meantime, it is important to point out that singlet-totriplet collisional energy transfer from valence M(nsnp ‘PI)states to M(nsnp 3 P ~ states ) can be induced even by collisions with the simplest of quenchers, namely, chemically inert rare-gas (RG) atoms, albeit with widely varying e f f i c i e n ~ i e s . ~ ~ ~ ~ ~ ~ ~ ~ * ~ This feature article reviews our current knowledge of such “simple” collisional processes:
M(nsnp ‘P,) -tRG
-
M(nsnp 3PJ)-I- RG
(3)
We will discuss and attempt to rationalize experimental and theoretical results related to this “full-collision” collisional deactivation process for M = Mg, Zn, Cd, Hg, and Ba. Deactivation of valence Ca(4s4p ‘PI) and Sr(5s5p ‘PI) states by RG atoms to form Ca(4s3d 3 D ~and ) Sr(Ss4d 3 D ~ states, ) respectively, will also be discussed. Results of a new “half-collision’’ method developed in our laboratories for studying singlet-to-triplet energy transfer in these cases will also be presented and utilized to help understand the mechanisms for such processes. Briefly, the weakly-bound ground-state van der Waals complex M(nsns ‘So).RG is prepared and laser excited to M(nsnp ‘Pl).RG van der Waals states. It is then determined (as a function of excitation energy) whether
7880 J. Phys. Chem., Vol. 99, No. 20, 1995
Bililign et al.
A l‘P,1+ As
>
g
e
x
?
31 000
I-
30 500
M
30 000
1
~
2.00
4.50
3.25
5.75
7.00
R (Angstroms)
Figure 2. Morse function estimates of the potential curves of ground state and the first excited triplet and singlet states of the Cd-Ar van der Waals molecule correlating with Ar(3p6 ‘SO)and Cd(5s5s ’SO),Cd(5s5p 3P~), and Cd(5s5p ‘PI), r e s p e c t i ~ e l y . ~Details ~ - ~ ~ about the construction of the potentials may be found in ref 32.
the M(nsnp ‘PI).RG complex eventually fluoresces or predissociates to form M(nsnp 3 P ~ atomic ) products: supersonic
M(nsns ‘So) -I- RG j etM
-
-
(4)
( ~ S Is,)-RG ~ S
+
M(nsns ‘So)*RG hv’
(6b)
(bound-bound)
M(nsns IS,)
+ RG + hv”
(bound-free) (6c)
11. “Full-Collision” Deactivation of Cd(5s5p ‘PI) by RG Atoms: The Breckenridge-Malmin Mechanism
In a pioneering laser pump-probe study by Breckenridge and Malmin7 of collisional deactivation of Cd(5s5p ‘PI) by various species, it was noted that even collisions with inert Ar atoms7 can deactivate Cd(5s5p ‘PI) to the Cd(5s5p 3P~)states, albeit with a very low quenching cross section3’ of OQ < 0.01 A2. It was also determined that the highest-energy Cd(5s5p 3P2)state was the major product of the three possible 3P2.1,0 product states. (We now believe that Cd(5s5p 3P4 is produced in 100% yield in the deactivation of Cd(5s5p ‘PI) by Ar and that the small amounts of the 3P0 and 3Pl states detected were due3’ to quenching by very small amounts of NZ impurity in the argon gas.) See Figure 1 for a pictorial depiction of the energy levels of the valence excited states of Mg, Zn, Cd, and Hg. Breckenridge and Malmin’ proposed a general mechanism for such singlet-to-triplet collisional deactivation by RG atoms which has stood the test of time remarkably well. Shown in Figure 2 are the potential curves which result from the van der Waals interactions of the Ar atom with the first excited (5s5p ‘PI)singlet state and the first excited (5s5p 3P2,1,0) triplet states
of the Cd atom.32-36 The curves have either been constructed to fit data from laser-induced fluorescence (LIF) experiments on the cold Cd-Ar van der Waals m ~ l e c u l e ~ *in- a~ supersonic ~ jet or estimated from an empirical treatment of spin-orbit coupling.36 These potential curves can be understood qualitatively in the following way. Sigma alignment of the Cd(5p) orbital is more attractive at very long range, since the axial 5pa electron density provides a greater dispersive interaction along the bond axis. However, Cd(Spo).Ar(3pa) electron-electron repulsion also sets in at very large distances. Hence, the Cd(5s5p ’P,).Ar(’Z+) state is essentially repulsive but has a very shallow potential minimum at large R. In contrast, for x alignment of the Cd(5p) orbital, the dispersive attraction is less at large R, but because the Ar atom is approaching along the nodal axis of the 5pn orbital, electron-electron repulsion does not become appreciable until very much smaller values of R. The argon atom can thus penetrate closer to the Cd(5s)’ “core”, which is relatively unshielded by the diffuse and transversely aligned Cd(5pn) orbital. The Cd(5s5p ‘P~)*Ar(’nl)state is therefore much more strongly bound and has a rather small Re value, as can be seen in Figure 2. Similar considerations apply to the lower-lying triplet a and n states which correlate with the Cd(5s5p 3 P ~ ) A r ( ’ S 0 ) atomic states, but the coupling between spin and orbital angular momentum for such states complicates the picture somewhat.36 In the Cd(5s5p 3 P ~ case, ) spin-orbit coupling is quite large, and the splitting between the Cd(5s5p 3 P ~ , asymptotic ~,~) levels can be comparable to or greater than the electrostatic interactions (attraction or repulsion) with Ar at moderate distances R. Hund’s case “c” is therefore approached, where the only good quantum number is 51 (Hund’s case “a” notation is still used in Figure 2 since it is more familiar to most readers). The states with the same value of 51 (and the same overall parity) interact strongly, and thus can have “mixed” p x and p a alignment ~ h a r a c t e r . ~The ~ - ~31T2 ~ and 31T~+states (see Figure 2) remain “pure x” in nature, but the 3111and 3n0states are mixed (by the l+s- component of the spin-orbit operator) with the ’2; and states, respectively.” Because of the p a character which is thereby introduced into their wave functions by the spin-orbit interaction, the latter two 311 states are only quite weakly bound. At smaller internuclear distances, and much higher energies (comparable to the ‘I31state energies near 43 500 cm-I), where all the triplet states are repulsive, a Hund’s case “a” description will be appropriate, since the electrostatic interactions are much greater than the spin-orbit coupling terms. The 32+states are much more repulsive than the 313 states at small R, and the Z ’ ; curve could therefore cross the bound potential curve. If so, these two states (both of which have values of S2 = 1) would also be mixed near the crossing region (again, by the l+s- component of the spin-orbit operator”). Thus, a “headon” collision in which the Cd(5s5p ]PI)state is n-aligned with an Ar atom would begin on the bound ’HIpotential curve but could end up on the repulsive ’2; curve, producing the Cd(5s5p 3P2)state. In the particular case of Cd(5s5p ‘PI) Ar, the ‘ I l l and Z ’ : curves apparently do not come close in energy until high on the repulsive inner wall of the IIIIpotential curve above its dissociation limit, thus rationalizing the fact that the cross section for quenching of Cd(5s5p ‘PI) by Ar is very low, xO.01 A’. In contrast, the cross section for the quenching of the Cd(5s5p ‘PI) state by Xe atoms is quite high,27 25 f 5 A*. Also, the Cd(5s5p 3Pz)multiplet is the exclusive product of the deactivation process by Xe atoms; no Cd(5s5p 3 P ~ or ) Cd(5s5p 3P0)
+
3g
+
J. Phys. Chem., Vol. 99,No. 20, 1995 7881
Feature Article
I
I
0.11
L
Figure 4. Higher resolution L F spectrum35of the (6,O) band in Figure 3, showing the overlapped P, Q, R branch rotational structure of the CdSAr isotopomers. Top: experimental. Bottom: simulation. I
I
--
Figure 3. Low-resolution laser-induced fluorescence (LIF) spectrum Cd(5s5s ]S&Ar(’Z+,v”=O) showing the Cd(5s5p lP1)*Ar(’nl,v’) vibrational transition^.^^ The Cd(5s5p ]PI 5s5s ‘SO)atomic transition is at higher energy, 43 692 cm-I. Top: experimental. Bottom: simulation.
,
I A
-7
C4l~P1
