Electron Affinities of the Alkaline Earth Metals and the Sign

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Electron Affinities of the Alkaline Earth Metals and the Sign Convention for Electron Affinity John C. Wheeler Department of Chemistry and Biochemistry, University of California–San Diego, La Jolla, CA 92093-0340

Background and Synopsis Most general chemistry textbooks published in the last six years contain tables or figures showing the alkaline earth metals with large endothermic electron affinities. These data come from outdated extrapolations and are seriously in error. It has been known since 1987, both theoretically and experimentally, that the ion Ca{ is stable. It is now certain that Sr{, Ba {, and Ra{ are also stable, and accurate values for the electron affinities of Ca{, Sr{ , and Ba{ have been determined. Recommended values for these electron affinities, in the units commonly employed in introductory texts and with the sign convention used here, are 2.37, 5.03, and 13.95 kJ/mol for Ca, Sr, and Ba, respectively. The endothermic electron affinities often quoted for Be and Mg are also too large and should be reported simply as “≤0”. An argument for a return to the original sign convention for the electron affinity is presented in this paper. Introduction Most recent general chemistry textbooks, along with many published over the past decade, contain tables or figures giving large endothermic values for the electron affinities of the alkaline earth metals and noble gases. (Several more advanced texts on physical and inorganic chemistry contain similar values or assertions.) Because many, but not all, of these texts also introduce a change in the original sign convention for the electron affinity, it is necessary to state clearly which sign convention is being used. I use the convention that if energy is required to detach an electron from the isolated negative ion in a vacuum then the electron affinity is positive. This is the original definition, and the one most prevalent in the current research literature. I argue for returning to it later in this note. With this convention, the electron affinity is positive for elements such as fluorine, for which energy is released when an electron is added to make an ion, while the widely quoted values for the alkaline earth metals and noble gases are negative. Electron Affinities of the Alkaline Earth Metals With the sign convention chosen above, typical values quoted for the alkaline earth metals are {241 kJ/mol for Be, {231 kJ/mol for Mg, {156 kJ/mol for Ca, {167 kJ/ mol for Sr, and {52 kJ/mol for Ba. None of the several texts I found quoting these values gave any reference to where the data were obtained. These numbers agree with those quoted (in eV) by Chen and Wentworth in this Journal (1), but those authors do not clearly indicate the origin of their numbers. Other authors quote identical values for all but strontium, with divergent negative values for this element. Another text quotes different negative values for the alkaline earth metals, all more nega-

tive than {25 kJ/mol. All of these values are certainly seriously in error. It has been known since 1987, both theoretically (2) and experimentally (3), that the Ca{ ion is stable. These original calculations and measurements agreed well, and indicated that the Ca{ ion is stable by about 43 meV. That is, the electron affinity for Ca, using the sign convention adopted here, was found to be about +4 kJ/mol. A number of subsequent theoretical calculations (4, 5) involving various techniques obtained values ranging from 0 to 130 meV. The electron configuration in Ca{ is found to be dominated by 4s24p (2P). This makes it an interesting example of the effects of nuclear charge on the relative energies of the 4s, 4p, and 3d orbital energies. The electron configurations (6) of the isoelectronic species Ca(4s 2), Sc+ (4s3d) and Ti2+(3d2) can be rationalized with the explanation that better penetration of the 4s orbital compared to the 3d makes the energy of 4s lower than that of 3d in Ca, but that the 3d orbital decreases more rapidly in energy than the 4s with increasing nuclear charge (7, 8) because it is smaller on the average than the 4s. Thus, (it could be argued) in Sc+ the energy difference between 4s and 3d has become less than the pairing energy to be gained by unpairing the electrons, while in Ti2+ the energy of the 3d orbital has actually fallen below that of the 4s. This type of argument is also helpful in understanding the irregular pattern of “promotion” of one or both ns electrons to (n–l)d orbitals in the electron configurations of the transition metal neutral atoms. The electron configurations of the isoelectronic series Ca{(4s24p), Sc(4s23d), Ti+ (4s3d2), V2+(3d3) reinforce this interpretation and suggest that in the calcium anion the trend of increasing energy of 3d with decreasing nuclear charge has apparently reached the point that 3d is actually above 4p as well as 4s. This interpretation is further reinforced by the configurations (6, 9) of the isoelectronic sequence with one-higher nuclear charge: Sc{(4s24p3d), Ti(4s23d2), V+(3d4) and Cr2+(3d4). (The subtleties of this sort of argument and another interpretation are noted in a recent article in this Journal by Vanquickenborn et al. [8].) The electronic configuration of Ca{ is also consistent with that of the excited states of neutral K and Ca atoms (6), in both of which the 4p level lies below the 3d. In 1992, two independent experiments obtained substantially smaller values of the electron affinity of Ca. One of these (10) is a laser photodetachment experiment, like that in ref 3, but it measures a threshold for photodetachment to an excited state of neutral Ca by using a tunable laser rather than measuring the energy of the ejected electrons resulting from detachment by a fixed frequency laser as in ref 3. The value obtained is 18.4 ± 2.5 meV. The other (11) is an electric field dissociation experiment, giving the value 17.5 +4.0/{2.0 meV. These smaller values are supported by the measure-

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Information • Textbooks • Media • Resources ment (12) of a finite lifetime of 590 µs for the stable Ca{ ground state, attributed to electron photodetachment by room-temperature black-body radiation. This finite lifetime for the negative ion does not, of course, contradict the existence of Ca { as a stable species. Rather, it is a manifestation of the fact that, at room temperature, the small binding energy of the electron is actually less than kT. As a consequence, the lifetime of any given negative ion formed in the bath of room-temperature black-body radiation is rather short. A clear review of the work on Ca up to that point is given by Peterson (13). Subsequently, an extensive CI calculation including core polarization (14) obtained a value for the electron affinity of Ca of 17.7 meV, in good agreement with the newer experimental results. A theoretical analysis (15) of the decay of weakly bound states in an electric field suggested that the value quoted in ref 11 should be revised upward to about 21 meV. Those authors have recently quoted the value 21 ± 2.5 meV (16). Another experimental study (17), interpreted as resonant electron transfer from Rydberg excited-state Ca to ground state Ca, gave the value 24 ± 1.4 meV, but the theoretical analysis of this experiment (18) did not include the effect of the coulomb attraction between departing Ca{ and Ca + ions. Including this effect makes the process of interest strongly nonresonant (Fabrikant, I. I., personal communication, 1995; 19), in contradiction with the original interpretation of the experimental results. In addition, it has recently been reported (20) that the observed signal is dependent upon the intermediate state through which the excited Ca is obtained, also in contradiction with the proposed mechanism. Moreover, it appears that the original signal may have been due to three-photon effects (Leone, S. R., personal communication, 1995). For these reasons, this experiment does not contribute reliable information on the electron affinity of Ca. Very recently, a remarkably accurate determination of the electron affinity of Ca has been made (Andersen, T., personal communication, 1995; 21) using a method first employed on Ba (22) and described in more detail below. These authors are able to resolve the fine structure resulting from spin-orbit coupling in the 2P term, finding 24.56 meV for the ground-state 2P1/2 component and 19.73 meV for the 2P3/2 component with an uncertainty in each of 0.10 meV. Once it is known that Ca{ is stable, it becomes highly plausible that Sr{, Ba {, and Ra{ are stable as well. Like calcium, Sr, Ba, and Ra have low-lying d orbitals and a small energy gap to the p orbitals that decreases steadily with increasing period number (6). Quantum calculations (4, 23, 24) confirmed this expectation almost immediately after the discovery of stable Ca{. Experimentally, the existence of Sr { and Ba{ was reported (25) in 1990, and of Ra{ in 1993 (26). Observation of a negative ion is not a guarantee of its stability, and a definitive measurement of the electron affinities of these elements was not yet available, but those authors estimated from the survival in the electric fields involved that the binding energy of an electron to Ba and Sr must be at least 15 meV, and to Ra, at least 50 meV. Measurements of electron affinity have recently been reported for Sr and Ba. The value 48 ± 6 meV for Sr (27) is obtained from a threshold measurement, similar to that of ref 10. An elegant two-photon resonant ionization method was used to obtain the extraordinarily precise value 144.62 ± 0.06 meV for Ba (22). This remarkable experiment involves photodetachment of an elec-

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tron from Ba{ via an s-wave threshold, which has a much sharper onset than the p-wave thresholds used in refs 10 and 27. The resulting excited state of the Ba atom is detected by state-selective resonant photoionization to Ba+, resulting in dramatic signal-to-noise enhancement. These authors also resolve the fine-structure splitting of the 2P state, finding the splitting to be 55.02 ± 0.09 meV between the lower-lying 2P1/2 component and the higher-energy 2P3/2 component, which is found to have an electron affinity of 89.60 ± 0.06 meV. This experiment sets a new standard of precision for electron affinity measurements. The authors have measured electron affinity for Ca by the same method (21) and are planning to obtain that for Sr, as well (Andersen, T., personal communication, 1995).1 These results suggest the values 2.37 kJ/mol, 5.03 kJ/mol, and 13.95 kJ/mol for the electron affinities of Ca, Sr, and Ba, respectively, in the units commonly used in introductory chemistry texts. The electron affinity for Ra, EA(Ra), remains unmeasured except for the limits 50 meV ≤ EA(Ra) ≤ 200 meV resulting from resistance to field ionization and abundance in sputtering of Cs, respectively (Litherland, A. E., personal communication, 1995). It would be expected to be comparable to or larger than that of Ba. It is highly likely that Be{ and Mg{ are unstable, but the large endothermic electron affinities often quoted are unrealistic. Quantum mechanical calculations (4, 28) establish that there is a resonant scattering state with symmetry corresponding to a 4s24p (2P) state for Be{ only about 365 or 323 meV, respectively, above the ground state of Be. Both theory (4, 29) and experiment (30) establish such a state for Mg{; the experiments indicate it lies only about 0.15 eV above the ground state of neutral Mg. These results place an upper limit on the magnitude of what it is sensible to call the electron affinity of these elements, if one wishes to assign a number at all. In general, it is probably preferable simply to give the value “≤ 0” for electron affinities that have not yet been determined to be positive (using the sign convention chosen here), rather than quoting estimates that are negative. This practice conforms to the practice in the literature by those actually measuring electron affinities (31). A negative electron affinity corresponds to electron detachment from a species that spontaneously loses an electron. Consequently, there is no stable species from which to detach the electron. While tentative negative values can sometimes be assigned using resonant scattering states or calculated using confinement of the ion in a box or scattering matrix methods, these results are fraught with even greater difficulties, both of technique and of interpretation, than are the already difficult measurements and calculations of positive electron affinities. Estimates obtained with other extrapolation methods have proven notoriously unreliable, as the electron affinities of the alkaline earth metals illustrate. In this regard, the substantial negative values often quoted for the noble gases are almost certainly not reliable and should be replaced by “≤ 0” unless a reliable source can be quoted. On the Sign of the Electron Affinity I argue for a return to the original convention that a positive electron affinity corresponds to a positive electron detachment energy of the negative ion. There are three arguments for this that, I believe, strongly outweigh any perceived advantage of the current fashion in the opposite direction in introductory chemistry texts.

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First, there is an extensive older literature on electron affinities following the original convention, as well as a vigorous current literature, both experimental and theoretical, that overwhelmingly continues to follow that convention. A brief perusal of any of the on-line abstracting services reveals extensive and vigorous current literature on the experimental and theoretical determination of the electron affinity of atoms, molecules, clusters, liquids, and solid surfaces. The concept has been generalized so that one also sees current papers describing determinations of the proton affinity of various compounds, again with the sign convention that the proton affinity is positive if the addition of a proton to the target species is exothermic. Moreover, this is the sign convention used most widely even in junior-level textbooks on physical chemistry and inorganic chemistry. Consequently, students taught with the new convention will have to relearn the definition if they go on to study or practice chemistry, physics, or materials science. It is perhaps no accident that the only introductory textbook (32) I found that exhibited any awareness by the author of the stability of Ca{ is also one of those that follow the sign convention used by the current literature on the subject. Second, there is compelling reason to preserve the original definition of electron affinity, both in the conventional meaning of the word affinity and in the historical precedent set by the technical term chemical affinity, introduced by deDonder. In conventional English, the word affinity means (33) “a natural liking or attraction to a person or thing”. In my experience, students readily perceive the absurdity of a construction such as “I feel a great affinity for you; it is very negative!” In 1922, deDonder (34) introduced the “affinity” of a chemical reaction as A = {∆G so that the affinity is positive when the reaction is spontaneous. This definition of affinity of reaction has been and continues to be used in the literature of both equilibrium and nonequilibrium thermodynamics (35–38). The Condensed Chemical Dictionary (39) defines (chemical) affinity as “the tendency of an atom or compound to react or combine with atoms or compounds of different chemical constitutions” and gives as an example “The Hemoglobin molecule has a much greater affinity for carbon monoxide than for oxygen.” It concludes with “The free energy decrease is a quantitative measure of chemical affinity” (emphasis mine). This meaning of the term affinity has found widespread use in the biochemical and biophysical literature to indicate preferential binding of one species over another to a target species. In that usage, if the binding equilibrium constant of A to B is greater than that of A to C, then A has a greater affinity for B than it does for C, as in the example of hemoglobin quoted above. In addition, the term has come to be used to describe a wide variety of techniques (affinity labeling, affinity chromatography, affinity partitioning), all using the same qualitative meaning for the word affinity. In the same way, the original definition makes the electron affinity positive when the binding of an electron to an atom or molecule is energetically favorable. This corresponds to the conventional meaning of the word affinity and is consonant with the technical definition. Third, the advantages gained from the changed definition are modest, while the disadvantages are significant. The advantage (as I understand the arguments of those who advocate it) is that it allows the electron affinity (EA) to be equal to ∆E for the reaction

A + e{ = A{

(1)

and that this allows one to consistently emphasize the point that changes of energy (and, later, free energy) are negative for spontaneous processes. It also makes the bookkeeping in the Born–Haber cycle slightly easier because then EA is just ∆E for adding an electron to an atom to make a negative ion. This is not a very compelling argument. The original convention defines the electron affinity to be ∆E for the reaction A{ = A + e {

(2)

One can use this as an example of the observation that processes with positive change in energy (free energy) tend not to be (are not) spontaneous. The student surely will either have already learned or will learn immediately that reversing the order of reactants and products in a reaction always changes the sign of ∆E, so it is a simple exercise to see that the process described by eq 1 must have ∆E = {EA. The original choice of sign actually helps to unify the teaching and understanding of electron affinities and ionization energies. With this choice, electron affinity is, in analogy with the ionization energy (IE) of atoms, the energy needed to detach an electron from the negative ion of the atom in question. This, it should be noted, corresponds to how one actually measures electron affinity experimentally: by forming the negative ion and then detaching an electron from it. Since one almost invariably introduces EA immediately after IE, this provides a unifying link to the earlier material. The electron affinity shows the same periodicities and same interruptions of smooth trends due to the filling of shells and to pairing energy at half-filled shells as do the first, second, third, … ionization energies. Indeed, it has been noted (40) that EA might well be called the “zeroth ionization energy”, IE0, in analogy with the first, second, third, … ionization energies, IE 1, IE2, IE3, …. The pedagogical benefits of focusing on the periodicity of electron affinity have been noted in this Journal before (1, 41). With the new sign convention for EA, a further sign change is needed to see the similarity in periodicities of the ionization energies and electron affinities. Several texts, after introducing EA with the new sign convention, then plot the EA with negative values up and positive values down to illustrate the periodic properties. This contortion is unnecessary with the original definition. In the transition from ionization energies and electron affinities to electronegativity, it is helpful to introduce the Mulliken definition, X = IE + EA, and show how this smooths out the “hitches and glitches” that appear in either IE or EA alone. The difficulty in measuring EA then motivates Pauling’s procedure for estimating electronegativity. With the changed sign of EA, one must either forgo mention of the Mulliken idea or else introduce yet another sign change into Mulliken’s definition, thereby rewriting history once again. For textbook writers to presume to redefine a quantity that has been in the literature for many years and is currently the subject of active investigation, and to do so by simply changing its sign while keeping the same name, and further to do so in a manner that makes the term inconsistent with the conventional meaning of the word, is neither good science nor good pedagogy. If it is felt that the change of sign is really essential—I have argued that it is neither necessary nor desirable—then at least a new name and symbol, such as electron at-


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tachment energy (or enthalpy) (EAE) should be coined, so that there is not a direct conflict between quantities with the same name and exactly opposite meaning and sign. I believe that better science and better pedagogy would result from: 1. defining the electron affinity as the electron detachment energy of the negative ion; 2. pointing out the periodicities held in common by the ionization energies and electron affinity; 3. noting that with this definition EA is the ∆E for reaction 2 and that, therefore, ∆E for the reaction l is equal to {EA; 4. pointing out the reason for choosing a word with an understood conventional meaning, such as affinity, and the connection with the corresponding choice in sign for EA; 5. perhaps mentioning some of the term’s other uses (electron affinity of molecules, proton affinity, hemoglobin binding affinity, antigen binding affinity)

In this way, students would not have to relearn the definition of electron affinity when they proceed to a more advanced course or to research, and they would be led to see connections between the concept of electron affinity and other uses of the affinity concept in chemistry, physics, and biology. In closing, I note that the periodicity shared by the electron affinity and successive ionization energies can be made particularly clear by using the device of the “effective nuclear charge” felt by the leaving electron. If one formally defines the effective charge through the hydrogen-atom-like equation

IE ≡ IE(H) ×

Z 2eff n2

(3)

where IE is the ionization energy of the species in question, IE(H) is the ionization energy of atomic hydrogen, and n is the principal quantum number of the electron removed, so that

Zeff = n

IE IE(H)

(4)

then the electron affinities and first several ionization energies of the elements through atomic number 20 can be conveniently displayed on a single figure, as shown in Figure 1. The periodicities are particularly apparent in such a figure, with the start of the pattern being shifted by one to the right with each increase of one in the charge on the species being ionized. An advantage of Z eff is that it varies only by about unity on passing from EA to the IEl, from IEl to IE2, etc., and also between elements within a given IE. This is in sharp contrast with the energies themselves, which vary by a factor of more than 103 between the typical small (but nonzero) EA and the largest IE 3, making a simultaneous plot of the energies almost unusable. (This scheme is less useful for the transition metals because of irregularities in the electronic configurations of the transition metal atoms and ions and the ambiguity in the appropriate values of n.) The electron affinities used in Figure 1 (other than that for Ca) are from Hotop and Lineberger (31); the ionization energies are from Moore (6). Acknowledgments I thank P. Taylor, J. Peterson, I. Fabrikant, and S. R. Leone for illuminating conversations, J. Peterson for calling to my attention the most recent references to Sr and Ba, and M. Paul and T. Andersen for making their results available prior to publication. Note 1. The EA for Sr has been determined since this paper was accepted for publication (Andersen, H. H; Petrunin, V. V.; Kristensen, P.; Andersen, T. Submitted to Phys. Rev. A). These authors find 52.06±0.06 meV for the ground-state 2P1/2 component, in good agreement with the results of ref 27, and 32.17±0.03 meV for the higher-energy 2P3/2 component (Andersen, T., personal communication, 1996).

Literature Cited

Figure 1. Effective nuclear charge, Zeff, defined in eq 4, as a function of nuclear charge from the first three ionization energies and electron affinities of elements with Z ≤ 20. The line Zeff = Z passes through the hydrogen-like atoms and ions; the origin, 0, 0, represents the free electron (electron “bound” to a nucleus with zero nuclear charge). The additional nearly parallel, nearly straight lines join isoelectronic ions, while the jagged gently upward sloping lines join adjacent atomic numbers. The points are labeled with the symbol for the species being ionized. The isoelectronic lines that have been drawn emphasize the fact that dips below the general upward trend in ionization energies occur when the electron being removed starts a new shell (shielding) or subshell (shielding and penetration) or begins the pairing of electrons in a previously halffilled shell (pairing energy).

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Electron Affinities of the Alkaline Earth Metals and the Sign

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