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Department of Chemistry and Biochemistry
University of Colorado at Boulder
Voice: 303 492-8603
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Lab: 303 492-5406

Photoelectron Spectroscopy of Negative Ion Beams: Measurements of Electron Affinities

The electron affinity (EA) of a molecule is the binding energy of the electron to the neutral molecule. It is useful to think of this in analogy to a spectroscopic transition, Fig. 1. Consider a negative ion, [R]¯, that is stable with respect to the corresponding neutral, R, and a free electron. The electron affinity of R is the transition energy, EA(R) = ΔE(R ← R¯). Familiar examples of [R]¯ might be the hydroxide, methide, or the vinyl anions {[OH]¯, [CH3]¯, or [CH2=CH]¯}; all are bound with respect to the corresponding neutral and a free electron, e¯. More specifically, Fig. 1 indicates that, the electron affinity of R is the transition energy from the ground vibrational/rotational state of the anion to the ground vibrational/rotational state of the neutral: EA(R) |R, v’=0, J’=0>←|R, v"=0, J"=0>; the electron affinity associated with the (0,0) band in Fig. 1 is sometimes referred to the "adiabatic EA". It is common for spectroscopists to refer to the ground electronic state of a polyatomic species as ˜ X while the excited electronic states are Ã, ˜ B, etc. From time to time it happens that the spectroscopic threshold corresponding to the (0,0) band cannot be identified so the proper EA is not experimentally measureable. In which cases the transition corresponding to the most intense Franck-Condon features of the detachment spectrum is sometimes reported as the "vertical detachment energy", VDE.

Qualitative diagram of potentail energy curves for anion and neutral species
Fig. 1: A qualitative diagram of potential energy curves for the anion [R]¯ and the neutral R. These curves are meant to represent all diatomic and polyatomic molecules. In the case of a non-linear polyatomic with n atoms, there are 3n-6 modes and this figure shows a cut through a Franck-Condon active mode.

An electron affinity is only a fraction of the size of the ionization energy [1] (IE). Photoionization of a neutral species (R) induces charge separation and produces a free electron – positive ion pair; R + hν → R+ + e¯. In consequence of Coulomb's law, charge separation requires a considerable amount of energy. In contrast to photoionization, photodetachment of an anion [R]¯ produces a free electron and an neutral atom or molecule; [R]¯ + hν → R + e¯. For example consider the simplest atom, hydrogen, and recall [2] that IE(H) is 13.6 eV while [3] EA(H) is only 0.75 eV. For most molecules, ionization energies are around 10 eV and the electron affinities are roughly 1 eV; IE(R) ≡ 10 eV but EA(R) ≡ 1 eV.

Although every molecule has a positive IE, this is not true for EAs. There is a huge class of anions that are not bound species. Many common molecules like N2, H2O, and C6H6 do not form stable anions. In the gas phase the "water anion" [H2O]¯decays to H2O plus a free electron and [C6H6]¯ is not stable with respect to benzene and e¯; the carbon dioxide anion is metastable for roughly 100 µsec before it too disintegrates: [CO2]¯ → CO2 + e¯. Generally radicals, such as OH, CH3, or CH2=CH, bind an electron into their "half-filled molecular orbital" and form a stable anion. In contrast, closed shell species, such as N2, H2O, or C6H6, have filled valencies and cannot bind an electron. Of course water or benzene will bind an electron in clusters [4] or in solution; [C6H6]¯ has a beautiful EPR spectrum in cryogenic matrices. [5] In condensed phases, solvent molecules help stabilize binding of the electron to the host molecule by a complex set of dipole and multipole couplings. [6]

In the gas phase "temporary" negative ions, such as [N2]¯, [H2O]¯, and [C6H6]¯ can be studied by resonant electron scattering.[7] [8] Several of these temporary negative ions are of great practical importance; an electrical discharge generates the [N2]¯; ion that drives the CO2 laser. The scattering resonances are "negative"; electron affinities because the potential curves of the ion and neutral in Fig. 1 are inverted. The ion curve is above the neutral species. Useful reviews of the spectroscopy of temporary negative ions have been written. [9] [10] Jordan and Burrow's review has a complete list of electron transmission spectroscopic resonances for all molecule up through 1986.

The Photoeffect

Several methods have been employed to measure the electron affinities of isolated molecules. Charge transfer reactions in a mass spectrometer, collisional ionization with fast alkali beams, plasma and optogalvanic spectroscopies, and collisional ionization have been used to deduce molecular electron affinities.[11] However, the most effective method to measure electron affinities is the photoelectric effect.[12] This measurement routinely produces EA values of "chemical accuracy" with uncertainties less than 1 kJ mol-1.

The essential experiment is to bombard a target ion, [R]¯, with a light beam of frequency ν and to monitor the photodestruction of [R]¯ or the appearance of the scattered electrons, e¯.

[R]¯ + hν → R + e¯    (1)

How does the photoeffect in (1) work?[13], [14] Consider a light beam that strikes an ion beam as shown in Fig. 2. Suppose the frequency of the light beam is fixed at υ0 and the photon flux, measured as photons s-1, is Φ0. The target anions, called [R]¯ in (1), are formed into a beam of velocity, υ0 (cm s-1), and beam width, l0 (cm). By simple conservation of energy, if hν0 < EA(R) then no photodetachment can occur and no scattered electrons will be produced. If hν0 equals or exceeds the photodetachment threshold, then photoproduction of electrons is possible. Typically one uses Beer's law to describe the probability of photodetachment [R].

Anion photodetachment occurs at intersection of beam of negative ions with the laser beam
Fig. 2: Negative ion photodetachment occurs at the intersection of a beam of negative ions with a laser beam.

In Fig. 2, the incident flux of photons that strike the ion beam is Φ and the intensity of the transmitted light is Φexp(-ρσDl0). Consequently the current of scattered photoelectrons, jelect (electrons s-1), in Fig. 2 is related to the incident photon flux Φ, through the photodetachment cross section, σD (cm2), the ion density, ρ(cm3), and the optical path length, l0 (cm).

jelect = Φ[1 - exp(-ρσDl0)]    (2)

The photoelectrons in Fig. 2 are not scattered randomly or isotropically. Instead the angular distribution of the scattered electrons can be described by a simple expression[15] that is based on dipole selection rules and angular momentum conservation. For linearly polarized light producing photoelectrons of kinetic energy, E, the angular distribution has the general form:

general equation for angular distribution     (3)

where P2(cosΘ) = ½(3 cos2Θ - 1), ¯σD represents the total photodetachment cross section, Θ measures the angle between the direction of the ejected electron and the polarization of the incident light, and β(E) is an asymmetry parameter. Commonly experimentalists fix the angle Q to be 54.7º so P2(cos 54.7º) is zero; consequently eq. (3) insures that the angular distribution of the detached photoelectrons will be completely independent of β(E) at this "magic angle".

Time dependent optical perturbation theory, with dipole selection rules, yields a simple expression[16], [17] for the photodetachment cross section, ¯σD.

photodetachment cross section equation     (4)

In (4), m and e are the electron mass and charge, whereas υ is the asymptotic electron velocity and ν is the photon frequency. If we write the dipole transition moment operator as µ(q) (where q is the nuclear coordinate), then the transition moment integral is <Ψ"(q)µ(q)Ψ'(q)> with Ψ"(q) being the state of the initial anion and Ψ'(q) the state of the final neutral. It is common to assume that the rotational, vibrational, and electronic degrees of freedom are separable in both the anion, Ψ"(q), and the final neutral, Ψ'(q). If µ(q) is slowly varying or a constant, then µ(q) ≡ µ0 and the Condon approximation yields:

Condon approximation equation     (5)

The vibrational wavefunctions, Ψvib”(Q"), are functions of the Q" normal coordinates, Q"; the vibrational overlaps, <ψ;vib”(Q)ψvib’(Q)>, give rise to the familiar Franck-Condon factors.

Can we make an estimate of how many photoelectrons, jelect, will be produced when a laser crosses a stream of anions, janions/ions s-1? The expression for Beer's law in (2) is not so convenient for us. Typically experimentalists manipulate properties of the negative ion beam (the current, the beam width, and velocity) and try to generate the most laser light possible. By doing some elementary sums, the Beers' law expression in (2) can be manipulated into a different form that relates the scattered photoelectrons to the current of negative ions (or anions), janions. It can be shown[18] that eq. (2) can be recast so that the current of scattered photoelectrons, jelect, is:

jelect = janions[1 - exp(-σDΦ/υ0l0)]     (6)

In (6), the current of scattered photoelectrons, jelect, can never exceed the flux of anions, janions. If the detachment cross section (σD) becomes huge or if the photon flux (Φ) is gigantic, then exp(-σDΦ/υ0l0) → 0 and jelect ≡ janions. On the other hand, if the ion beam velocity (υ0) is very large then exp(-σDΦ/υ0l0) ≡ 1 with the consequence that jelect ≡ 0.

What are some common experimental values? Typically the ion current, janions, is approximately 0.1 nA or 109 ions s-1. Ar III laser radiation at 351 nm has a frequency (ν) of 8.5 x 1014 Hz or a wavenumber of 28 490 cm-1 (3.53 eV). If we think of the laser beam in Fig. 2 as a stream of photons, then Φis nhν where h is Planck's constant, 6.6 x 10-34 J s. Consequently a 50 W Ar III laser generates roughly 9 x 1019 photons s-1. Suppose the photodetachment[16], [19] cross section, σD, is 6 x 10-18 cm2 and that the ions are focused down to a small beam diameter, typically l0 ~ 0.1 mm. The ion beam kinetic energy is roughly 40 eV so the ions have a velocity, υ0, of 2.2 x 106 cm s-1. Inserting parameters, one estimates (σDΦ/υ0l0) to be 0.02. This small number assures us that we can linearize (6) to compute the flux of scattered photoelectrons.

jelect = janions[σDΦ/υ0l0]     (7)

If we insert numbers into (7), we conjecture that the rate of photodetachment will be 2 x 107 electrons s-1. This estimate of the photodetached electrons supposes that they are scattered into all space (4π steradians) but the apparatus generally uses a hemispheric analyzer to count the electrons. This detector only collects the small fraction of the photoelectrons that are scattered into a 5º acceptance angle so dΩ ≡ 4π/2000. This implies that the electrostatic analyzer will experience count rates of (4?/2000) x (2 x 107 electrons s-1) or roughly 2 x 105 electrons s-1. This is the approximate electron count rate that is observed from most atoms. The count rates for molecules are commonly much smaller because of molecular Franck Condon factors and lower ion beam currents.

References

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