Roles Played by Metastable States in Chemistry - ACS Symposium

1 Roles Played by Metastable States in Chemistry JACK SIMONS

Downloaded by 97.74.230.16 on May 17, 2018 | https://pubs.acs.org Publication Date: September 28, 1984 | doi: 10.1021/bk-1984-0263.ch001

Department of Chemistry, University of Utah, Salt Lake City, UT 84112

Metastable states are important i n chemistry for reasons which relate to the fact that such states have f i n i t e lifetimes and f i n i t e Heisenberg energy widths. They are observed i n spectroscopy as peaks or resonances superimposed on the continua i n which they are buried. Their fleeting existence provides time for energy transfer to occur between c o n s t i tuent species which eventually become separated fragments. It i s often the rate of such intra fragment energy transfer which determines the lifetimes of resonances. The theoretical explora t i o n of metastable states presents special diffi c u l t i e s because they are not discrete bound states. However, much of the machinery which has proven so useful for stationary electronic and v i b r a t i o n a l - r o t a t i o n a l states of molecules has been extended to permit resonance energies and lifetimes to be evaluated. In this contribution, examples of electronic shape and Feshbach, rotational and v i b r a t i o n a l predissociation, and unimolecular d i s s o c i a t i o n resonances w i l l be examined. F i n a l l y , a novel s i t u a t i o n w i l l be treated i n which the energy transfer dictating the decay rate of the metastable species involves vibration-to-electronic energy flow followed by electron ejection. The purposes of this chapter are to provide overview and perspective concerning the various kinds of metastable species found i n chemical systems as well as to focus attention on an interesting class of temporary anions (1-4) whose lifetimes are governed by v i b r a t i o n electronic coupling strengths. To emphasize the importance of metastable states i n experimental chemistry, i t i s useful to f i r s t analyze how they are created via c o l l i s i o n a l or photon absorption processes. This provides a basis for discussing the signatures which metastable states leave i n the instrumental responses seen i n the laboratory. Having introduced metastable states i n r e l a t i o n to the experimental situations i n which they a r i s e , i t i s useful to 0097-6156/84/0263-0003$06.00/0 © 1984 American Chemical Society

Truhlar; Resonances ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

4

RESONANCES


distinguish between two primary categories of such species and to c l a s s i f y many of the systems treated i n this symposium. This overview and categorizing focuses attention on the properties (e.g., mass, angular momentum, energy, potential energy surfaces, internal energy d i s t r i b u t i o n ) which determine the decay rates or lifetimes of particular species. After giving an overview and interpretative treatment of a wide variety of metastable systems, this paper treats i n somewhat more d e t a i l a class of highly v i b r a t i o n a l l y excited molecular anions which undergo electron ejection at rates determined by the strength of vibration-electronic coupling present i n the anion. The findings of theoretical simulations of the electron ejection process as well as the experimental relevance of such temporary anions are discussed. Metastable states as they occur i n c o l l i s i o n s and half c o l l i s i o n s . One can form metastable states (denoted here by AB*) either by bringing together two fragments (A and B) i n a c o l l i s i o n experiment or by exciting a bound state of the AB system using, for example, photon absorption or electron impact excitation. In situations where bound-state e x c i t a t i o n i s employed, the subsequent decay of the metastable to produce fragments (A and B) i s termed a "half c o l l i s i o n " . The decay rate or lifetime (T) of the excited state can, i n some cases, be inferred from the Heisenberg component to the width (r) of the measured resonance feature i n the bound-state absorption or excitation spectrum. It is often very d i f f i c u l t to extract from the t o t a l observed linewidth the component due to the decay of the corresponding state. Unresolved rotational structure and Doppler broadening often dominate the linewidth. Only for l i f e times shorter than 10"^ s (or T *• 0.03 cnT*) i s i t l i k e l y that the Heisenberg width w i l l be a major component. For very long lived states, the lifetime may be measured by monitoring the time evolution of the product fragment species, by, for example, laser induced fluorescence or the absorption spectrum of one of the fragments produced. I f one or both of the fragments are ionic, ion detection methods can be used. The appearance of structure i n the absorption spectrum superimposed upon a background continuum i s a result of the strong-interaction region component of the resonancestate wavefunction. This i s the component of the metastable specie's wavefunction i n which the fragments A and B reside within the region where t h e i r interfragment potential energy i s s i g n i f i c a n t . For fragment separations outside this region, the term "asymptotic" i s employed. It i s this " i n close" part of the wavefunction that characterizes resonances and that may carry strong o s c i l l a t o r strength from the underlying bound state. Since i n the lower AB state the A—B r e l a t i v e motion is bound and hence l o c a l i z e d , i t is only the localized part of the excited-state wavefunction which w i l l appreciably overlap the ground-state wavefunction. Hence for excited metastable states, which possess large valence-region components, the e l e c t r i c dipole t r a n s i t i o n matrix element can be substantial. In contrast, excitation from the lower bound state to nonresonant dissociative excited states gives r i s e to smaller t r a n s i t i o n dipoles, because such excited states have small valence-region components and hence weaker absorption intensities.



1. SIMONS

5

Metastable States

For experiments i n which two fragments c o l l i d e to produce metastable species which subsequently undergo decay, the lifetime of the metastable state is reflected i n the kinetic energy dependence of the e l a s t i c , i n e l a s t i c , and reactive cross-sections character izing the c o l l i s i o n events. Such experiments measure cross-sections as the i n i t i a l r e l a t i v e kinetic energy of the fragments i s scanned. They may also monitor the kinetic energy of one or both of the fragments ejected from the metastable species. Such crosssections when plotted as functions of the fragment r e l a t i v e kinetic energy display resonance features i n the v i c i n i t y of each metastable-state energy. C o l l i s i o n a l l y formed states are called metastable or resonances i f their lifetimes are substantially longer than the "transit times" which one would calculate for the fragments based upon knowledge of their asymptotic r e l a t i v e k i n e t i c energies. The simple fact that the fragments remain i n close contact longer than expected based on their transit time i s what allows interfragment energy transfer to be so e f f i c i e n t i n meta stable species. Given interaction times of the order of l O - l O ^ times the transit time, [a t y p i c a l transit time for molecules c o l l i d i n g at room temperature i s ~ 10 s ] , even small rates of energy transfer per i n t e r f ragment vibration can result i n large net energy transfers during the state's l i f e t i m e . Such enhanced e f f i c i e n c y for energy transfer results i n higher p r o b a b i l i t i e s that the product fragments exit i n different internal states than were occupied i n the i n i t i a l c o l l i s i o n pair. This is one of the most chemically important c h a r a c t e r i s t i c s of metastable states. 1

Two P r i n c i p l e Categories of Resonance States. Denoting the internal energies of the separated fragments (A and B) by + Eg*, a l l metastable or resonance states can be subdivided into those whose t o t a l energy E l i e s either below or above each such asymptotic energy. As i s shown below, this d i v i s i o n i s chemically meaningful because the physical features which determine the energies and lifetimes of the two types of resonances defined i n this manner are different. At energies above each E^ + Egj one can expect to find orbiting resonances (also known as shape resonances) i f the fragments experience an a t t r a c t i v e potential (V) varying more strongly than r ~ and have non-zero r e l a t i v e angular momentum (£) . Here r represents the coordinate which asymptotically i s the distance between the centers of mass of the two fragments. In e l a s t i c or i n e l a s t i c c o l l i s i o n s , the entering and exiting fragments have i d e n t i c a l chemical composition but their internal (e.g., v i b r a t i o n a l , r o t a t i o n a l , electronic) states may d i f f e r . For reactive processes which proceed through a metastable state, the entering and exiting species are chemically d i f f e r e n t . The e f f e c t i v e radial potentials V + -ft l(l+l)/2r u depicted i n Figure (1) for various JL values may then support states whose t o t a l energy exceeds E^ + Egj but which can decay only by the two fragments of r e l a t i v e reduced mass u tunneling through the "angular momentum b a r r i e r " a r i s i n g from the *ti fc(fc+l)/2pr factor i n i n t e r f ragment angular kinetic energy ( i . e . , the interfragment r o t a t i o n ) . The tunneling lifetimes of these resonances are determined by the height and thickness of the angular b a r r i e r and the fragment reduced massy. r

z


RESONANCES

6

At energies below each fragment energy E^ + Eg*, target-excited or Feshbach resonances are to be expected. Although these metastable states cannot decay to the E^ + Egj asymptotic state, they possess enough energy to couple to the continua of lower fragment states (e.g., to E + Eg^ or E £ + Eg• j ; see Figure (2)). What makes these states metastable i s the ract that not enough of t h e i r t o t a l energy i s i n i t i a l l y ( i . e . , as they are created) contained i n the dissociative coordinate r . They have ample energy i n the internal intrafragment degrees of freedom; however, some of this energy must be redistributed to the asymptotically d i s s o c i a t i v e motion before the resonance state can decay. The lifetimes of such target-excited states are determined by the strength of the coupling between the fragment internal degrees of freedom and the interfragment motion which, i n turn, depends upon the curvature and anharmonicity of the system's potential energy surface. The position or energy E of the resonance state r e l a t i v e to i t s asymptotically closed reference energy E^ + Eg- i s determined by the strength of the a t t r a c t i v e potential between the A and B fragments i n the E £ and Egj states; the stronger this a t t r a c t i o n , the further below E^ + Egj the Feshbach resonance should l i e . A decay channel i s said to be closed i f the t o t a l energy of the system l i e s below the asymptotic energy of this channel. Thus metastable species can only decay to produce open-channel products. It i s also possible to have target-excited resonances that l i e above the E^ + Egj asymptotic; these are discussed elsewhere ( 5 ) .


A i - 1

A

r

A

Examples of Orbiting and Target-Excited

Resonances

To better appreciate the chemical significance of both classes of metastable species i t i s helpful to examine several examples of such species. This overview i s by no means intended to be exhaustive either with respect to the systems i t covers or concerning references to workers i n the area. Its purpose i s to i l l u s t r a t e how metastable states can have important effects i n chemical experiments. Therefore, the treatment given here i s rather q u a l i t a t i v e and directed toward the interested but non-expert reader. Because electrons have much smaller mass than atomic nuclei, i t is natural to distinguish between situations i n which an electron i s one of the fragment p a r t i c l e s and those i n which both fragments are so called heavy p a r t i c l e s ( i . e . , atoms, molecules or ions). In the former case, the asymptotic fragment internal energies E^ + Egj reduce to the energies of the atomic or molecular fragment since the electron fragment has no internal energy levels of i t s own (external magnetic f i e l d effects are ignored). Electronic Shape Resonances. In the f i r s t three examples given below i n Table I, the orbiting resonance can be viewed as forming when an electron of kinetic energy E enters an empty low-energy o r b i t a l of the atomic or molecular target fragment. As indicated i n Table I, the active o r b i t a l has, i n every case, nonzero angular momentum components which give r i s e to the barrier through which the electron must tunnel to escape. The a t t r a c t i v e part of the r


I. SIMONS

Metastable States

7

i

r

t


Veff

Figure 1:

E f f e c t i v e potentials V + 2

-tf J(j(l)/2ur

2

for I = 0, 20, 25.

+

•EAi E j B

J Final kE E

Figure 2:

AH

+ E

Bj

A Feshbach resonance exists below E ^ + Egj but above d i s s o c i a t i o n to E £ _ + Egj. A

1

The kinetic energy (KE)

of the ejected A and B fragments i s also shown.


8

RESONANCES

Table I. Electronic Shape Resonance Examples Formation Process 2

e(3.7

eV) + H ( l a , v ) 2

Decay Products H ~(la *lc )

L

g

g

H (la

2

f

v ) + e(p wave)

9

U

Z

g

• H + H"

t

2

e(2.3

eV) + N

e(0.3

eV) + Mg( S) • Mg"( P°)

2

( ^ v ) - N~( TT ,v") g

1

2

2

+


NaC£"( ^ ) + hv(2.1 eV) a)

at 3.73 eV (Ref.10)

• ^ ( ^ v ' ) + e(d-wave) 1

+ Mg( S) + e(p-wave) 2

NaCjT( Tr)

Vibrational excitation of H2 occurs.

a

NaC*

b

C

+ e(p-wave)

d

The ejected electron comes

off primarily i n a p-wave d i s t r i b u t i o n because the la

orbital

of H2 i s dominated by the p symmetry when i t i s expanded about the center of mass of the molecule.

The width of this state i s

greater than 2 eV (Refs. 6-9). b)

Again v i b r a t i o n a l excitation occurs.

The d-wave character i s

dictated by the d-like symmetry of the active lir antibonding o r b i t a l of N . The width r ~ 0.6 eV corresponds to a l i f e t i m e -14 9

of ~ 10 c)

s

(Refs. 11-14).

The width T ~ 0.1-0.2 eV corresponds to a l i f e t i m e of 2 - 4 x 10"

d)

A

14

s (Refs. 15-18).

The l i f e t i m e i s - 1 0 "

12

s (Refs. 19-20).

electron-target e f f e c t i v e potential arises from charge-dipole, charge-induced dipole ( i . e . , p o l a r i z a b i l i t y ) and valence-level interactions. The shape resonance occurs when the energy of the ejected electron gives r i s e to deBroglie wavelengths i n the stronginteraction region, which i n this case i s the valence region, that permit the electron's r a d i a l wavefunction to establish a standing wave pattern i n the region between the two inner turning points of the e f f e c t i v e potential (see Figure 1). In a l l of the examples i l l u s t r a t e d here, only the ground electronic-state fragment i s involved. Such does not have to be the case, however; o r b i t i n g resonances can arise from the binding of an electron with £ * 0 to an excited electronic state of the fragment. The relevance of the above kind of electronic shape resonance to chemistry i s twofold. F i r s t , i n environments such as plasmas, electrochemical c e l l s , and the ionosphere, where free electrons are prevalent, the formation of such temporary anions can provide avenues for the free electrons to "cool down" by transferring k i n e t i c energy to the i n t e r n a l ( v i b r a t i o n a l and/or electronic) degrees of freedom of the fragment. (6-14) Second, metastable states may play important roles i n quenching excited electronic


I.

Metastable States

SIMONS

9

states of atoms and molecules by providing a mechanism through which electronic energy can^be transformed to fragment i n t e r n a l energy. For example, H ~ ( l a l a ) i s invoked as an intermediate to explain the quenching of e l e c t r o n i c a l l y excited (21-21) Na(3p; P°) and (23^ Mg( P) by H ( l a ,v) to y i e l d v i b r a t i o n a l l y hot H : 2

2

X

2

g

2

2

Na( P) + H (v) 2

1

Mg( P°) + H (v) 2

+

+ Na H " +

2

Na(*S) +

2

2

?

H (la ,v ), 2

g

1

+ M g ( S ) H " * Mg( S) + H ( v » ) . 2

2

In these examples, the metastable H ~ does not actually undergo electron loss because the Na~*~ or Mg ion "retrieves" the electron as the complex dissociates leaving the H v i b r a t i o n a l l y excited and the Na or Mg atom i n i t s ground state. Recent work on electron transmission spectroscopy studies of unsaturated hydrocarbons (24) demonstrates that electronic shape resonances may be e s s e n t i a l l y ubiquitous i n chemical systems which possess low-energy vacant o r b i t a l s and the a v a i l a b i l i t y of electron density to enter such orbitals. 2

+


2

E l e c t r o n i c Feshbach Resonances. In Table II are a few examples of target-excited or Feshbach resonances i n which the ejected electron i s i n i t i a l l y attached to an e l e c t r o n i c a l l y excited state of the fragment. Note that the angular properties ( i . e . , p-wave, s-wave, etc.) of the ejected electron are again constrained by the symme t r i e s of the metastable state and the lower lying target state to which i t decays. In the case of H~(2p , P ) , parity constraints even forbid direct ejection of a p-wave electron (odd parity) to leave the H atom i n the H ( l s , S ) (even parity) ground state. H " ( 2 p , P ) must f i r s t radiate to produce the H~(2s2p, P°) metastable state which can then undergo Feshbach decay to produce H ( l s , S ) and a p-wave electron. In contrast, the seemingly s i m i l a r metastable Na~"(3p , P ) state of Na" can undergo radiative decay to Na~(3s3p, P°) and subsequent tunneling (not Feshbach) decay to Na (3s, S) and e(p-wave); direct Feshbach decay of Na""(3p, P ) to Na(3s, S) and e(p-wave) i s parity forbidden as was the case i n H . Electronic Feshbach resonances are often very long lived and hence have narrow (often < 0.01 eV) widths. Their lifetimes are determined by the coupling between the quasibound and asymptotic components of their electronic wavefunctions. Because the Feshbach decay process involves ejection of one electron and deexcitation of a second, i t proceeds via the two-electron terms e /r .^ i n the Hamiltonian. For example, the rate of electron loss In H"(2s2p, P°) i s proportional to the square of the two-electron i n t e g r a l , where kp represents the continuum p-wave o r b i t a l . This i n t e g r a l , and hence the decay rate, i s often quite small because of the size difference between the 2s or 2p and Is o r b i t a l s and because of the o s c i l l a t o r y nature of the kp o r b i t a l . In fact, series of Feshbach resonances involving, for example, nsnp * n-'s kp decay often show (29) lengthening lifetimes as functions of increasing n. This trend can be explained in terms of both the greater r a d i a l size difference and the increasing o s c i l l a t o r y character (due to increased k i n e t i c energy of the ejected electron) of the kp o r b i t a l as n increases. Both trends tend to make the coupling i n t e g r a l smaller. e

3

e

2

e

2

e

2

;

1 2

2

1

2


10

RESONANCES

Table I I . Electronic Feshbach Resonance Metastable Species 2

Decay Product

2

2

He"(ls2s , S) 2

3

e

H"(2p , P )

Examples

1

H e ( l s , S ) + e(s-wave)

b

a

3

H"(2s2p, P°) + hv ,

J z

H ( l s , S ) + e(p-wave) 0 ~ ( l i r 3s O g . ^ ) + Na" ( 3 p , P ) > Na~(3s3p, P°) + hv 2

2

2


a)

2

0

g

3

e

3

( l l T

2 , 3

+ )

6

W

a

V

6

13

The

s) (Ref. 25).

This resonance l i e s ~ 0.01 eV below the 2p state of H and has a 3

3

6

1

s" .

The

P ° state then decays v i a a Feshbach mechanism to H(ls) and e(p)

at a rate of 6 x 10

8

s"

1

(Ref. 26).

At 8.04 eV above the ground state of 0 2 i this resonance i s thought to involve two electrons i n a Rydberg-like 3so* bound to e s s e n t i a l l y an 0

d)

)

d

The electron i s ejected with 19.4 eV of k i n e t i c energy.

radiative decay rate to the P ° state of 2.5 x 10

c)

( p

2

width of the resonance i s 0.008 eV (x ~ 5 x 1 0 " b)

+

°2 g ^g Na(3s, S) + e(p-wave)

orbital

core (Ref. 27).

2

3

As explained i n the text, the decay of Na"(3s3p, P°) i s not a Feshbach decay.

This example i s l i s t e d i n this Table only to

demonstrate that i t s seeming s i m i l a r i t y to the above H~ case i s deceiving.

3

The P

e

3

state of Na" l i e s 0.06 eV below the P

state

of Na (Ref. 28).

The chemical importance of electronic Feshbach resonances derives from e s s e n t i a l l y the same effects as were given e a r l i e r for shape resonances. They allow either free electrons or electron density from a c o l l i s i o n partner to give energy to the i n t e r n a l ( v i b r a t i o n a l , r o t a t i o n a l , or electronic) degrees of freedom of the target. Heavy P a r t i c l e Shape Resonances. The van der Waals a t t r a c t i o n between two Ar atoms i s shown i n Figure 3. It supports eight bound v i b r a t i o n a l states i f the diatom's r o t a t i o n a l quantum number j i s zero. For j - 30, only two v i b r a t i o n a l states are bound. The angular momentum barrier a r i s i n g from the j(j+l)fi /2]jr factor i n the A r rotational k i n e t i c energy gives r i s e to an e f f e c t i v e r a d i a l potential (see Figure 3) which for j = 30 supports only two bound states and one metastable orbiting resonance state. Lower j values give r i s e to more bound states and more shape resonance states. The lifetimes of these states depend upon the height and thickness of the barrier, which depend upon j and the reduced mass and actually range (30_) from 1 0 " s to 1 0 s. 2

2

11

1 0


Metastable States

1. SIMONS

11


V(R)

V ff Centrifugal Barrier k .mi 2 C

w

\

0

—/ /

3

o ^-20 >o a:-40 Id Z

Metastable Stote

V=0 2 1 J

•

i

=

j=30

0

v =0

H00 6

8

0 R(

Figure 3:

8

2 A)

Intermolecular potential for A r . 2

On the l e f t

potential curve for non-rotating (j=0)Ar . 2

i s the

On the

right is the e f f e c t i v e potential for rotating (j=30)Ar . 2


RESONANCES

12

One can, of course, have orbiting resonances for larger molecules and for molecules i n which chemical bonds (rather than van der Waals interactions) are operative. For example, H (v = 0, j = 38) undergoes rotational predissociation to produce two H atoms. This metastable shape resonance state has a Heisenberg width (31) of 90 cm" ; the v = 0, j - 37 state of H decays with a width of 6 cm" and the v = 14, j - 4 state does so with T ~ 0.007 cm" (even though the v - 14, j - 4 state has far more t o t a l energy than the v = 0, j = 38 one). Orbiting resonances are very important i n chemistry. They have observable effects on the transport properties of dense gases and l i q u i d s (32), and they are thought to provide a mechanism for atomatom recombination to occur via metastable shape resonances which l i v e long enough to become s t a b i l i z e d by c o l l i s i o n (33) with another molecule or with a surface. Shape resonances also give r i s e to broadening i n experimentally observed absorption spectra; t r a n s i tions into high r o t a t i o n a l levels often result i n populating rotat i o n a l l y predissociating shape resonances whose natural lifetime i s reflected i n the spectral broadening. 2

1

1

2


1

Heavy-Particle Feshbach Resonances. V i b r a t i o n a l l y and r o t a t i o n a l l y predissociating van der Waals complexes such as those l i s t e d i n Table III provide examples of Feshbach states which decay v i a intramolecular energy transfer. The f i r s t three examples involve transfer of v i b r a t i o n a l energy, which i n i t i a l l y resides e s s e n t i a l l y in one molecular fragment, to the r a d i a l coordinate of the weak van der Waals bond. The lifetimes of such species span many orders of magnitudes. The fourth example shown i n Table III i l l u s t r a t e s a case i n which r o t a t i o n a l energy of H i n the H Ar complex i s transferred to the van der Waals coordinate upon which the system can dissociate. In the f i n a l example, the e l e c t r o n i c a l l y excited HCN can, i f i t i s prepared with excess energy i n i t s bending v i b r a t i o n a l mode ( v ) , undergo CH bond rupture i f the excess bending energy transfers to the CH stretching mode ( v ^ ) . The coupling between v and i s caused by strong off-diagonal curvature of the HCN molecule's potential energy surface between the bending and CH stretching coordinates, so the strength of this strong off-diagonal curvature determines the decay rate of C-^A' HCN. The chemical importance of heavy-particle Feshbach resonances cannot be overstated. They are present i n unimolecular rearrangements, both thermal ones and those which occur i n organic photochemical reactions, i n mass spectroscopic ion fragmentations, and i n bimolecular c o l l i s i o n s which proceed through long-lived intermediates. 2

2

2

2

A Novel Class of Target-Excited Resonance Experiments have recently been carried out (1,3) i n which polyatomic molecular anions trapped i n an e s s e n t i a l l y c o l l i s i o n l e s s ion cyclotron resonance c e l l are v i b r a t i o n a l l y excited using an infrared laser laser of 0.1-6 J/cnr fluence and ~ 1000 cm" energy. Electron ejection from the anions i s observed to occur at rates which are fluence dependent. The mechanism of this ejection i s the subject of these remarks. 1


1.

Metastable States

SIMONS

13

Table I I I . Heavy-Particle Feshbach Resonance Examples Metastable Species

Decay Products

3

I ( B n,v)He (Ci ) 2

3

>

2

I ( B H,v') + He

+

2

2C*

2

c

2

H (j,v)Ar

f

+

2

H (j ,v) + A r 2

HCN(C A ' , v v v ) x

2

d

2

1

CN(B £ ) + H

3

e

A very strong propensity i s observed for the v' = v - 1 Q _1 channel.


2

N0 ( B) + He

2

The rate of decay i s 4.5 x 10

increases to 2.6 x 1 0 b)

b

2

N0 ( B)He

a)

a

2

1 0

s

f o r v = 12 and

1

s " for v - 26 (Refs. 35,36). 4

The v i b r a t i o n a l l y excited (CJ& ) requires ~ 10~ s to decay. 2

8

This time i s 10 -10

9

2

times the v i b r a t i o n a l period of

the C* moiety (Ref. 37). 2

c)

2

The observed l i f e t i m e for the v i b r a t i o n a l l y hot B state of N0 to eject the van der Waals bound He atom i s 1 0 "

d)

The r o t a t i o n a l l y hot H

2

11

2

s (Ref. 38).

moiety i n H Ar decays v i a transfer of 2

rotational energy to H ...Ar r e l a t i v e motion with a width 2

3

1

of ~ 10~ cm"

4

1

f o r j = 2 and 4 x 10" cm"

for j - 4 (Refs.

39,40). e)

The bent excited state of HCN, when photochemically prepared l

from the X

ground state, requires transfer from the

bending ( v ) motion to the CH stretching motion (v^) before 2

d i s s o c i a t i o n can occur (Refs. 41,42).

Laser pulses of 3 ys duration and a t y p i c a l fluence of 1.0 J/cm and infrared absorption cross sections of 10" -10" ^ cm y i e l d photon absorption rates of 10^-10^ photons/s, which are much slower than the rate of intramolecular v i b r a t i o n a l energy r e d i s t r i b u t i o n i n systems such as benzyl anion. Hence, the anions are excited i n a sequential process i n which the v i b r a t i o n a l energy i s redistributed before the next photon i s absorbed. This means that such experiments cannot determine i n which v i b r a t i o n a l mode(s) the energy resides. I t has also been demonstrated (3), by studying the competition between electron loss and a unimolecular decomposition of known a c t i v a t i o n energy, that sequential infrared absorption continues to occur even after the anion has achieved enough t o t a l i n t e r n a l energy to reach i t s electron detachment threshold. This implies that, near threshold, electron ejection must not be occuring faster than the 10^-10' s " photon absorption rate. These experiments do not, however, allow one to conclude with much certainty how far above 18

2(

2

1


RESONANCES


14

threshold photon absorption continues to occur; c l e a r l y , once the electron loss rate exceeds the absorption rate the anion w i l l no longer absorb. The above experiments are hampered by lack of knowledge of the t o t a l energy content and i n t e r n a l energy d i s t r i b u t i o n of the anions. This interpretation would be helped by order of magnitude estimates of the rate of electron ejection as a function of energy above threshold. The author's group recently undertook (4) an ab I n i t i o simulation of such ejection rates for two prototype anions (0H"~ and LiH") which are viewed as l i m i t i n g cases of slow (0H~) and rapid (LiH") v i b r a t i o n induced electron ejection. Diatomic anions were chosen to obviate questions about where ( i . e . , i n what vibra t i o n a l mode) the i n t e r n a l energy i s residing. OH" i s an i d e a l candidate for slow electron loss because the energy of i t s lir active o r b i t a l i s only weakly dependent upon bond length and because i t s detachment threshold i s large (1.82 eV). In contrast, the 3a active o r b i t a l of LiH", which consists primarily of a nonbonding 2s-2pa hybrid l o c a l i z e d on the L i center and directed away from the H center, i s quite strongly affected by movement of the very polar ( L i H " ) bond. As a r e s u l t , the detachment energy of L i H " varies substantially with bond length; even at the equilibrium bond length i t i s only 0.3 eV. For neither LiH" nor 0H~ do the anion and neutral BornOppenheimer potential energy curves cross. Such i s also thought to be the case for the energy surfaces of the polyatomic anions studied in the experiments of Refs. (1) and (3) and for the curves of +

2

+

1

+

3

(B Y ) C " and (X Y or a n ) Co where Lineberger (43) has u 2 + 8 u * observed (B £ ) C "" to be metastable with respect to electron e j e c t i o n . Hence the electron loss mechanism does not involve the anion sampling, through i t s v i b r a t i o n a l motion, geometries where electronic shape or Feshbach resonances or direct detachment occurs. I t requires coupling between electronic and v i b r a t i o n a l motion and can be viewed as a radiationless t r a n s i t i o n between the two components of the metastable state (the v i b r a t i o n a l l y excited anion and the v i b r a t i o n a l l y cooler neutral with an outgoing electron) induced by the nonadiabatic coupling terms which the BornOppenheimer Hamiltonian neglects. In this sense, such metastable states can be viewed as target-excited states. They are analogous to v i b r a t i o n a l l y excited Rydberg states which undergo autoionization (44). I t was found i n Ref. (4) that the lifetimes for electron ejection ranged from 10"" to 1 0 " s for LiH" i n v i b r a t i o n a l levels between v = 3 and v = 10 and from 10" to 10" s for OH" from v = 5 to v - 11. The ejection rates did not increase strongly with increasing v i b r a t i o n a l energy above threshold. In a l l cases, the anions were found to decay p r e f e r e n t i a l l y to the energetically closest v i b r a t i o n a l state of the neutral; the branching ratios for decay into various neutral v i b r a t i o n a l levels correlated well with ion-neutral Franck-Condon-like factors. This range of l i f e t i m e s (10" -10" to 10" -10" s) f o r prototype fast and slow electron ejectors i s e n t i r e l y consistent with the estimates made i n Refs. (1), (3) and (43). The weak dependence of these rates on the energy above threshold indicates that many polyatomic anions ( i . e . , those for which the ejection rate 9

2

9

10

5

9

10

6

5

6


1.

SIMONS

15

Metastable States

near threshold i s not faster than the photon absorption rate) continue to absorb infrared photons far above their detachment thresholds. This information, when combined with the observation of a propensity to decay to the closest vibrational l e v e l of the neutral, suggests that v i b r a t i o n a l l y hot neutrals can be expected to be produced i n such infrared pumping experiments. When considering the reverse reaction, the attachment of an electron to a molecular target to produce a v i b r a t i o n a l l y hot anion, the rate of electron ejection as studied here can be combined with estimates of the equilibrium constant f o r


e + A(v) t A"(v») to estimate the rate constant for the attachment step. actually done so (45) i n a recent study of SF^~.

Benson has

Acknowledgments Acknowledgment i s made to the National Science Foundation (Grant #8206845), as well as to the Donors of the Petroleum Research Fund, administered by the American Chemical Society (PRF 14446-AC6), f o r their support.

L i t e r a t u r e Cited 1.

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11,

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Roles Played by Metastable States in Chemistry - ACS Symposium

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