Resonances in Electron-Molecule Scattering: Metastable States in Chemistry, Lab Reports of Physics

Download Resonances in Electron-Molecule Scattering: Metastable States in Chemistry and more Lab Reports Physics in PDF only on Docsity! Reprinted from ACS SYMPOSIUM SERIES, No. 263 RESONANCES IN ELECTRON-MOLECULE SCATIERING VAN DER WAALS COMPLEXES, AND REACTIVE CHEMICAL DYNAMICS Donald G. Truhlar, Editor Copyright 1984 by the American Chemical Socjety Reprinted by permission of the copyright owner 1 Roles Played by Metastable States in Chemistry JACK SIMONS Department of Chemistry. University of Utah, Salt Lake City. UT 84112 Metastable states are important in chemistry for reasons which relate to the fact that Buch states have finite lifetimes and finite Heisenberg energy widths. They are observed in spectroscopy as peaks or resonances superimposed on the continua in which they are buried. Their fleeting existence provides time for energy transfer to occur between consti- tuent species which eventually become separated fragments. It is often the rat e of Buch intra- fragment energy transfer which determines the ~ifetimes of resonances. The theoretical explora- tion of metastable states presents special diffi- cult'ies because they are not discrete bound states. However, much of the machinery Which bas proven so useful for stationary electronic and vibrational-rotational states of molecules bas been extended to permit resonance energies and lifetimes to be evaluated. In this contribution, examples of electronic shape and Feshbach, rotational and vibrational predissociation, and unimolecular dissociation resonances will be examined. Finally, anovel situation will be treated in which the energy transfer dictating the deca y rate of the metastable species involves vibration-to-electronic energy flow foliowed by electron ejection. The purposes of this chapter are to provide overviewand perspective concerning the various kinds of metastable species found in chemical systems as we II as to focus at tent Jon on an interesting class of temporaryanions (1-4) whose lifetimes are governed by vibration- electronic coupling strengths. To emphasize the importance of met as tab le states in experimental chemistry, it is useful to first analyze how they are created via collisional or photon absorption processes. This prov!ides.' a basia for discussing the signatures which metastable states leave in the instrumental responses seen in the laboratory. Having introduced metastable states in relat ion to the experimental situations in which they arise, it is useful to 0097-6156/84/0263-0003$06.00/0 @ 1984American Chemical Socjety 4 RESONANCES distinguish between twa primary categories of Buch species and to classify maRY of the systems treated in this symposium. This overview and categorizing focuses attention on the properties (e.g.. mass. angular momentum. energy. potential energy surfaces. internal energy distribution) 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 in somewhat more detail a class of highly vibrationally excited molecular anions which undergo electron ejection at rates determined by the strength of vibration-electronic coupling present in the anion. The findings of theoretical simulations of the electron ejection process as well as the experimental relevance of Buch temporary anions are discussed. Metastable states as the~ occur in collisions and half collisions. One caR form metastable states (denoted here by AB*) either by bringing together twa fragments (A and B) in a collision 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 excitation is employed. the subsequent decay of the metastable to produce fragments (A and B) is termed a '~alf collision". The decay rate or lifetime (T) of the excited state can. in same cases. be inferred from the Heisenberg component to the width (r) of the measured resonance feature in the bound-state absorption or excitation spectrum. It is often very difficult to extract from the total observed linewidth the component due to the decay of the corresponding state. Unresolved rotational structure and Doppler broadening often dominate the linewidth. Only for life- times shorterthan 10-9 s (orr ~ 0.03 cm-l) is it likelythat the Heisenberg width will be a major component. For very laRg 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. If one or both of the fragments are ionic. ion detection methods caR be used. The appearance of structure in the absorption spectrum superimposed upon a background continuum is a result of the strong-interaction region component of the resonance- state wavefunction. This is the component of the metastable specie's wavefunction in which the fragments A and B reside within the region where their interfragment potential energy is significant. For fragment separations outside this region. the term "asymptotic" is employed. It is this "in ciose" part of the wavefunction that characterizes resonances and that may carry strong oscillator strength from the underlying bound state. Since in the lower AB state the A--B relative motion is bound and hence localized. it is only the localized part of the excited-state wavefunction which will appreciably overlap the ground-state wavefunction. Hence for excited metastable states. which possess large valence-region components. theelectric dipole transition matrix element caR be substantial. In contrast. excitation from the lower bound state to nonresonant dissociative excited states gives rise to emalier transition dipoles. because Buch excited states have smalI valence-region components and heRce weaker absorption int ens it ies . I. SIMONS Figure 2: Me/as/oble Sto/es 7 t Voff E~;+EBj /[=25 ~L=20 \.- L=O r- Figure I: Effective potentials V + -tr2J(J(I)/2\.Ir2 for R. = O, 20, 25. t E ~ EAi+EBj---~ 1 ~i~~kEEAi-1+EBj r- A Feshbach resonance exists below EAi + EBj but above dissociation to EAi-1 + EBj' The kinetic energy (KE) of the ejected A and B fragment s is alBo shown. 8 RESONANCES Table I. Electronic Shape Resonance Examples Formation Proces s Decay Products Z a HZ(lag ,v')+ e(p wave) z - Z e(3.7 eV) + HZ(la ,v)... H z (la la)'"g g u e(Z.3 eV) + NZ (lI:;,V) ... N;(Z'lTg'vU) e(0.3eV)+ Mg(lS)...Mg-(ZpO) - Z~+ - Z NaCI, ( L ) + hv(Z.l eV) ... NaCI, ( 'IT) ...H + H-, at 3.73 eV (Ref.lO) ...NZ(lI+,v') + e{d-wave)bg ...Mg(lS) + e(p-wave)c l~+ d ...NaCI, ( L ) + e(p-wave) a) Vibrational excitation of HZ occurs. The ejected electron comes orf primarily in a p-wave distribution because the lali orbital of HZ is dominated by the p symmetry when it is expanded about the center of mass of the molecule. The width,of this state is greater than Z eV (Refs. 6-9). b) Again vibrational excitation occurs. The d-wave character is dictated by the d-like symmetry of the active 1'ITantibonding g orbitalof NZ. The width r - 0.6 eV correspondsto a lifetime -14 of - 10 s (Refs.11-14). The width r - O.l-O.ZeV correspond~to a lifetimeof Z - 4 x 10-14 s (Refs.15-18). -lZ The lifetime is - 10 . s (Refs. 19-Z0). c) d) electron-target effective potential arises tram charge-dipole, charge-induced dipole (i.e., polarizability) and valence-level interactions. The shape resonance occurs when the energy of the ejected electron gives rise to deBroglie wavelengths in the strong- interaction region, which in this case is the valence region, that permit the electron's radial wavefunction to establish a standing wave pattern in the region between the twa tuner turning points of the effective potential (see Figure l). In ali of the examples illustrated here, only the ground electronic-state fragment is involved. Such does not have to be the case, however; orbiting resonances can arise tram the binding of an electron withl, * O to an excited electronic state of the fragment. The relevance of the above kind of electronic shape resonance to chemistry is twofold. First, in environments Buch as plasmas, electrochemical cells, and the ionosphere, where free electrons are prevalent, the formation of Buch temporary anions can provide avenues for the free electrons to "cool down" by transferring kinetic energy to the internal (vibrational and/Dr electronic) degrees of freedom of the fragment. (6-14) Second, metastable states may play important roles in quenching excited electronic I. SIMONS Metastable States 9 states of atoms and molecules by providing a mechanism through which electronic ener~y can2be transformed to fragment internal energy. For example, H2 (la la) is invoked as an intermediale to explain the quenching of ileetroMically excited (21-21) Na(3p; po) and (23 Mg(lp) by H2 (lag ,v) to yield vibrationally hot H2: --- 2 + - l 2 Na( P) + H2(v) + Na H2 + Na( S) + H2(lag ,v'), Mg(lpo) + H2(v) + Mg+(2S)H2- + Mg(lS) + H2(v'). In these examples, the metas~able H2- does not actually undergo electron less because the Na or Mg+ lon "retrieves" the electron as the complex dissociates leaving the H2 vibrationally excited and the Na or Mg atom in its ground state. Recent werk on electron transmission spectroscopy studies of unsaturated hydrocarbons (24) demonstrates that electronic shape resonances maJ be essentially ubiquitous in chemical systems which possess low-energy vacant orbitals and the availability of electron density to enter such orbitals. Electronic Feshbach Resonances. In Table II are a few examples of target-excited or Feshbach resonances in which the ejected electron is initially attached to an electronically 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- tries of the metastable state and the lo!er lying target state to which it decays. In the case of H-(2p , Fe), parity constraints even forbid direct ejection of a p-wave electron (odd parity) to leave the H atom in the H(ls,2S) (even parity) ground ~tate. H-(2p2,3pe) must first radiate to produce the H-(2s2p, po) < metastable state which can then undergo Feshbach decay to produce H(ls,2S) and a p-!av~ electron. In contrast, the seemingly similar metastable Na-(3p, Fe) state of Na- can undergo radiative decay to Na-(3s3p,3po) and subsequent tunneling (not Feshbach) decay to Na (3s,2S~ and e(p-wave); direct Feshbach decay of Na-(3p2,3pe) to Na(3s, S) and e(p-wave) is parity forbidden as was the case in 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, it proceeds via the two-electron terms e2/rio in the Hamiltonian. For example, the rate of electron lass id H-(2s2p,3po) is proP2rtional to the square of the two-electron integral <2s2ple /r Ils kp), where kp represents the continuum p-wave orbit"al. tfiisintegral,and hence Ehe decay rate, is often quite small because of the size difference between the 2s or 2p and ls orbitals and because of the oscillatory nature of the kp orbital. In fact, series of Feshbach resonances involving, for example, nsnp + ~'s kp decay often show (29) lengthening lifetimes as functions of increasing n. This trend can be explained in terms of both the greater radial size difference and the increasing oscillatory character (due to increased kinetic energy of the ejected electron) of the kp orbital as n increases. Both trends tend to make the coupling integral <nsnple2/r12In'skp) smaller. 12 RESONANCES One can, of course, have orbiting resonances for larger molecules and for molecules in which chemical banda (rather than van der Waals interactions) are operative. For example, H2 (v = O, j = 38) undergoes rotational predissociation to produce twa H atoms. This metastable shape resonance state bas a Heisenberg width (31) of 90 cm-l; the v = O, j = 37 state of H2 decays with a width of ~cm-l and the v = 14, j = 4 state does so with r - 0.007 cm-l (even thoughthe v = 14, j = 4 state bas.far more total energy than the v = O, j = 38 one). Orbiting resonances are very important in chemistry. They have observable effects on the transport properties of dense gases and liquids (32), and they are thought to provide a mechanism for atom- atom recombination to occur via metastable shape resonances which live long enough to become stabilized by collision (33) with another molecule or with a surface. Shape resonances algo give rise to broadening in experimentally observed absorption spectra; transi- tlona into high rotational levels often result in populating rota- tionally predissociating shape resonances whose natural lifetime is reflected in the spectral broadening. Heavy-Particle Feshbach Resonances. Vibrationally and rotationally predissociating van der Waals complexes Buch as those listed in Table III provide examples of Feshbach states which decay via intramolecular energy transfer; The first three examples involve transfer of vibrational energy, which initially resides essentially in one molecular fragment, to the radial coordinate of the weak van der Waals band. The lifetimes of Buch species span many orders of magnitudes. The fourth example shown in Table III illustrates a case in which rotational energy of H2 in the H2Ar complex is transferred to the van der Waals coordinate upon which the system candissociate. In the final example, the electronically excited HCN can, if it is prepared with excess energy in its bending vibra- tional mode (V2)' underg6 CH band rupture if the excess bending energy transfers to the CH stretching mode (VI)' The coupling between v2 and vi is caused by strong orf-diagonal curvature of the HCN molecule's potential energy surface between the bending and CH stretching coordinates, so the strength of this strong orf-diagonal curvature determines the decay rate of CIA' HCN. The chemical importance of heavy-particle Feshbach resonances cannot be overstated. They are present in unimolecular rearrangements, both thermal ones and those which occur in organie photochemical reactions, in mass spectroscopic lon fragmentations, and in bimolecular collisions which proceed through long-lived intermediates. A Novel Class of Target-Excited Resonance Experiments have recently been carried out (~ in which polyatomic molecular antena trapped in an essentially collisionless lon cyclotron resonance celI are vibrationally excited using an infrared laser laser of 0.1-6 J/cm2 fluence and - 1000 cm-l energy. Electron ejection from the antena is observed to occur at rates which are fluence dependent. The mechanism of this ejection is the subject of these remarks. 1. SIMONS Metastable StaleJ l3 Table III. Heavy-Particle Feshbach Resonance Examples Metastable Species Decay Products IZ(B 3n,v)He . ... IZ(B 3n,v') + Hea b (CIZ)Z . ZCIZ NOz(ZB)He ... NOZ(ZB) + Hec d HZ(j,v)Ar ... HZ(j',v) + Ar HCN(C lA"VlVZV3) . CN(B Z~) + He a) A very strong propenslty is observed for the v' = v - l channel. The rate of decay is 4. Sx 109 s-l for v = lZ and increases to Z.6 x 1010 s-l for v = Z6 (Refs. 35,36). b) The vibrationally excited (CIZ)Z requires -10-4 s to decay. This time is 108_109 times the vibrational period of the CIZ molety (Ref. 37). The observed lifetime for the vibrationally hot ZB state of NOZ to eject the van der Waals bound He atom is 10-11 s (Ref. 38). c) d) The rotationally hot HZ molety in HZAr decays via transfer of rotational energy to HZ...Ar relative motion wito a width of - 10-3 cm-l for j = Z and 4 x 10-4 cm-l for j = 4 (Refs. 39,40). The bent excited state of HCN, when photochemically prepared l\;'+ from the X L ground state, requires transfer from the bending (vZ) motion to the CH stretchingmotion (vI) before dissociation can occur (Refs. 4l,4Z). e) Laser pulses of 3 ~s duration and a typical fluence of 1.0 J/cmZ and infrared absorption cross sections of 10-18_l0-Z0 cmZ yield photon absorption rates of 105_107 photons/s, which are much slower than the rate of intramolecular vibrational energy redistribution in systems Buch as benzyl anion. Hence, the anions are excited in a sequential process in which the vibrational energy is redistributed before the next photon is absorbed. This means that Buch experiments cannot determine in which vibrational mode(s) the energy resides. It bas algo been demonstrated(3), by studyingthe competition between electron loss and a unimolec:ulardecomposition of known activation energy, that sequential infrared absorption continues to occur even after the anion bas achieved enough total internal energy to reach its electron detachment threshold. This implies that, near threshold, electron ejection must not be occuring faster than the 105_107s-l photon absorptionrate. These experimentsdo not, however, allow one to conclude wito much certainty how far above 14 RESONANCES threshold photon absorption continues to occur; clearly, ance the electron loss rate exceeds the absorption rate the anion will no longer absorb. The above experiments are hampered by lack of knowledge of the total energy content and internal energy distribution of the anions. This interpretation would be helped by order of magnitude estimates of the rate of electron ejection as a furictionof energy above threshold. The author's group recently undertook (4) an ab initio simulation of soch ejection rates for twa prototYPE!anioru; (OH- and LiH-) which are viewed as limiting case~ of slow (OH-) and rapid (LiH-) vibration induced e1ectron ejection. Diatomic anions were chosen to obviate questions about where (i.e., in what vibra- tiona1 mode) the internal energy is residing. OH- is an idea1 candidate for slow e1ectron 10ss because the energy of its 1w active orbital is only weakly dependent opon band length and because its detachment thresho1d is large (1.82 eV). In contrast, the 3a active orbita1 of LiU-, which consists primari1y of a non- bonding 2s-2pa hybrid localized on the Li center and directed away tram the H center, is quite strong1y affected by movement of the very polar (Li+H-) band. As a result, the detachment energy of LiH- varies substantially with band length; even at the equi1ibrium band length it is only 0.3 eV. For neither LiH- nor OH- do the Oppenheimer potentia1 energy curves be the case for the energy surfaces in the experiments of Refs. (1) and 2~+ - 1 + 3" (B L) C2 and (X L or a n) C2 where Lineberger(43) bas u 2 + g u observed (B L) C2- to be metastable with respect to electron ejection. Henge the e1ectron 10ss mechanism does not invo1ve the anion samp1ing, through its vibrationa1 motion, geometries where e1ectronic shape or Feshbach resonances or direct detachment occurs. It requires coup1ing between e1ectronic and vibrationa1 motion and can be viewed as a radiation1ess transition between the twa components of the metastab1e state (the vibrational1y excited anion and the vibrationa11y coo1er neutra1 with an outgoing electron) induced by the nonadiabatic coup1ing terma which the Born- Oppenheimer Hami1tonian neg1ects. In this sense, soch metastab1e states can be viewed as target-excited states. They are ana10gous to vibrationa11y excited Rydberg states which undergo autoionization (44). --- It was found in Ref. (4) that the 1ifetimes for e1ectron ejection ranged tram 10-9 to 10-10 s ~or LiH- in vibrationa1 1eve1sbetween v = 3 and v = 10 and tram 10- to 10-6 s for OH- tram v = 5 to v - 11: The ejection rates did not increase strong1y with increasing vibrationa1 energy above thresho1d. In a11 cases, the anions were found to decay preferentia11y to the energetica11y c10sest vibrationa1 state of the neutra1; the branching ratios for decay luto various neutra1 vibrationa1 1eve1s corre1ated wel1 with ion-neutra1 Franck-Condon-1ike f~ctorf. This range of 1ifetimes (10- -10- O to 10-5_10-6 s) for prototype fast and slow e1ectron ejectors is entire1y consistent with the estimates made in Refs. (1), (3) and (43). The weak dependence of these rates on the eIlergy--abovethreshold indicates that many po1yatomic anions (i.e., those for which the ejection rate anion and neutra1 Born- cross. Soch is a1so thought to of the po1yatomic anions studied (3) and for the curves of