David W. Brooks. Edward A. ~ e y e r s ; and Fred Sicilio Texas A 8. M University
College Station, 77843 James C. Nearing De~orfmentof Phvsics university of Miami Coral Gables, Florida
I
I
I
Electron A f f i n i k
(
The Zeroth ~onhcltion
I
It is the purpose of this article to present the merits of adopting the terminology zeroth ionization potential, IPo, to describe the energy change, 4E,of the process indicated in eqn. (1).
(The symbol IPi is used to represent the ith ionization potential.) Our interest in this subject has been inspired by the excellent paperback of Pimentel and Spratley ( I ) , in which the physical basis and the importance of ionization potential is emphasized. Previously, the reverse of eqn. (1) has been written t o define the quantity electron affinity, EA, with a positive value for energy released. However, three advantages are associated with use of the zeroth ionization potential terminology. First, the defining reaction portrayed in eqn. (1) parallels that for other ionization potentials. Just as the first ionization potential, IPl, is the energy required to form the monopositive cation from the neutral atom by loss of an electro;, so the zeroth ionization potential is that energy rewired to form the electrically neutral atom from the .~ . monoanion. Second, the sign convention for zeroth ionization notential is identical to that for the other atomic ionization potentials. Conversely, the sinn convention for electron affinity often introd;ces unnecessary confusion, particularly when used in computation. For example, many textbooks use internally inconsistent sign conventions when determining the Mulliken electronegativity x (2) using the following equation X =
IP, + EA 2
(2)
Such difficulties are avoided when ionization potentials are used exclusively. Equation (2) would he rewritten as eqn. (3) without any ambiguity so that the Mulliken electronegativity in essence describes an average of the binding energies of the outermost electron in the anion and the atom from which the anion is derived.1
Finally, there is good reason to believe that experimental zeroth ionization potentials for atoms of each element are positive or zero and that conversion from monoanion to neutral atom is never an exothermic process, consistent with results for all other ionization aotentials. This uniformity in the sign of experimental zeroth ionization potential is not widely recognized as a distinct probahilitv. -, -
We would like to present a brief discussion of the methods used for the estimation of electron affinities. We shall then cite some experimental observation8 which conflict
with the estimated values. Finally, we will offer a highly simplified treatment which has the virtue of correctly predicting the sign observed in experimental situations. Two methods of calculation from available data prevail and are in general use. The extrapolation procedures are the most common. These rely upon extrapolation from available ionization potentials and generally use one of three procedures. The first involves extrapolation of different ionization potentials for constant atomic number ( 4 ) . The second involves extrapolation of ionization potentials for constant electronic configuration (5). The third involves extrapolation of ionization potentials for given degree of charge (6, 7). Each procedure has advantages and disadvantages as described in the referenced articles. In addition, several other empirical and semiempirical procedures have been suggested (8,9),and other extrapolation techniques have been attempted (10). The second general method involves the use of appropriate Born-Haher cycles. In these calculations, many data are required, including ionization potentials, lattice energies, heats of formation and bond energies (11). Both general methods for estimatina electron affinities give satisfactory results when appliei to the halogens. However, they have met with varying degrees of success in dealing with other atoms. In cases where electron affinities are estimated for neutral atoms in which there is a filled or half-filled outer electron shell (He, Be, N, Ne, Mg, etc.), contradiction abounds. Indeed, negative electron affinities (i.e., values indicating repulsion between the neutral atom and an unbound electron) are very frequently reported. Direct experimental determinations of electron affinities have, until recently, been rare (11). The experimental problem becomes magnified when the energy is low. For example, the electron affinity of He has been determined to be 0.080 f 0.002 eV by photodetachment (12) and 0.060 0.005 eV by electron impact (13). ~lockler's-earlyarticle-(4) probably has had a great deal to do with establishina ~recedentsconcernine the electron affinities of rare g a s e s r ~ i sextrapolated values for rare gas
*
1 Experimental values of zeroth and first ionization patentials may be used in eqn. (3) to calculate X. Good agreement between the x' values thus calculated and Pauling electronegativities is often observed (3). If the ionization potentials are expressed in eV, then the Pauling electronegativity is given as approximately 0.37 times the Mulliken eleetronegativity. However, eqn. (2) is often used with complicated non-experimental quantities such as average values for valence state functions. Mulliken's penetrating insight in the selection of appropriate ionization patentials is often impropitiously overlooked, perhaps on account of the simplicity of his equation. The agreement between Psuling and Mulliken electronegativities is particularly good for alkali metal and halogen atoms since their valence state functions as used in the Mulliken equation are quite close to the corresponding atomic functions.
Volume 50, Number 7, July 1973 / 487
electron affinities were negative, and he concluded that the anion species are unstable. He noted that only one tenuous report of a rare gas anion, He-, was available t o him, and that this was indicative of rare gas anion instability. Subsequently, however, there was a report of the identification of He- in a mass spectrographic analysis of He-H2 mixtures (14), although this result was in disagreement with an earlier study of the same system in which no He- was detected (15). The literature also includes a report of a rare gas molecule, CsXe, in which Xe- is presumably formed (16). Much of the modem literature takes on an uncertain tone when calculated values of rare gas electron affinities are positive. For example, one study included estimation of the cohesion of ionic solid alkali metal-rare gas salts. This report, partially inspired by positive calculated values for helium and neon electron affinities, concludes that finite hinding energies for the ionic salts are predicted if reasonable estimates are made for the rare gas anion radius 117). . , (Of . course anv calculated stahilitv for such compounds will depend heavily on the radii selected since these will affect the calculated lattice stabilization energy.) In this report however, no calculations are reported for argides, kryptides, or xenides since the calculated electron affinities then available for those three rare gases were negative. Quantum mechanical calculations of rare gas electron affinities have been undertaken (18-22). ~ h & ecalculations are difficult to evaluate when applied to atoms such as the rare gases whose affinities a r e expected to he very low. In one report (19) i t was concluded from consideration of the Hartree-Fock calculations of energy in the monoanion system that all one-center atom electron affinities would he positive or zero. I t has been pointed out that an electron, in a shielded coulomb field, has only a finite numher of negative energy states, and for certain potentials may have none (23). On this basis, it was concluded that negative values of the zeroth ionization potential might reasonably result, and some early Hartree-Fock calculations appeared to support this hypothesis. For this reason, the general theorem of Kaplan and Kleiner (19) is of great importance, since i t asserts that the Hartree-Fock energy of the ground state of M must always he less than or equal t o that of the e-. Thus, one-center Hartree-Fock calcuseparated M lations which have indicated that the energy of M- is greater that that of M + e- have been calculations for other than the mound state of M-. There is a lymited basis for making a general prediction of the sien of atomic electron affinities, or to use the proposed terminology, zeroth ionization potentials. Suppose we consider the electric field of an electron brought close to a neutral atom. A simple treatment is to consider the electronic energies of the neutral atom as its electrons and nucleus interact with the electric field. Such a model can be discussed in terms of the Stark effect. Except for hydrogen, the first-order Stark effect with only dipole terms always vanishes for the ground state because of the lack of accidental degeneracy. Even when quadrupole terms are included, spherically symmetric states (He, Be, N, Ne, etc.) will not he affected; non-symmetrjc states will have some binding orbitals. The second-order Stark effect (24) given using one-electron wavefunctions in eqn. (4)
+
-
that the monoanion systems (or, more precisely, neutralatom-plus-electron systems) will always have an energy lower than that of the neutral atom alone. In eqn. (4), E,O refers to the ground state energy, and thus the sign of the correction term is always nepative. The limitations of this treatment are clear and many in numher. In addition to nrohlems introduced hv use of one-electron wavefunctions, there is neglect of spin-orbital interaction by disregarding the spin of the attached electron. We are aware of no simple treatment that predicts a uniform sign for that spin-orbit interaction. Although the interaction goes as 23, i t is expected to he small for low-Z elements such as helium. Better Hartree-Fock calculations are availahle today (21). Still each calculation will need to he considered on its own merits, each calculation will he expensive to complete, and each calculation will still suffer from those well known limitations of even the modem HartreeFock calculations. Even calculations taking account of electron correlation are too imprecise to lend much aeight to an argument (22). The one-electron formula of eqn. (4) provides insight into the problem of zeroth ionization energies. In spite of its many limitations, it has the virtue of correctly predicting the sign of the zeroth ionization potential of, say, helium, an atom for which a 0.3-eV discrepancy exists hetween modern exneriment 112. 13) and accepted presentday "best values'; (7). indeed; mddern experimenial techniaues are heine anolied with increasine - freauencv . -to the measurement of electron affinities leading to heretofore unobtainable values and improvements upon older experimental values (25, 26). If continuing experimentation provides no examples of negative energies for the dissociation process of eqn. (11, then continued use of the older nomenclature of electron affinity seems to us to be unjustified. The pedagogical introduction of the zeroth ionization potential terminology is straightforward. The term is routinely introduced with other ionization potentials. It is then easily utilized when considering other phenomena such as ionic bonding. For example, consider the case of the atom M (alkali metal) with low first ionization potential and the atom X (halogen) with high zeroth ionization potential.
-
&.
M(g) + ~ ' ( g )
+ e-
IP,
(5)
XTg) X(g) + e-(g) IPo (6) Multiplying eqn. (6) by -1, and adding the result to eqn. (5) we get +
+ X(g)
I P , - IP, (7) Mt(g) + X-k) This simple algebraic manipulation of chemical equations is taught to most first year students. The energy for the sum reaction, eqn. (7), must he less than IPI, since both ZPl and ZPo are positive quantities. If IPo > ZPl, reaction (7) would he spontaneous a t zero K. There are no known cases wherein ZPo > IP1, so that some additional energy is required. This energy comes from the reactions M(g)
+
Mt(d
+ x-k)
+
MX(g)
No sacrifice is made in our ability to explain bonding and the new terminology is more consistent than the old. Literature Cited
(E.1, is the perturbed energy; Enl0and E,.,," are the unis the perturbed energies; e is the electronic charge; k~ectricfield strength; n, 1, m, n', 1'. rn' are quantum numbers; z is the z component) leads to the conclusion 488
/
Journalof Chemical Education
(1) Pirn."tol. G. C., and Spratley, R. D., "Chemical Bonding Clarified Through Quenturn Meehsnia: Holden-Day. lnc.. San Francisco, 1969. p. 58. 12) Mul1ikm.R. S..J Cham. Phys., 2.782119341. (3) Hakey, K. B., and Fortar, G. B., "Infmduetian to Physical Inorganic Chemistry." Addiwn-Wesley, Reading. Msar., 1963, p. 163. (4) GlockIer,G.,Phys. Rev., 46,11111934).
(5) Ed1en.B.. J Chem Phya., 33.9811960). (6) Edie, J. W.,andRohrlich, F.. J Cham. Phys., 36,623(1962). (7) Zollweg, R. J.,J Chsm Phys.. 50.4251 (1969). I81 Ginsberg, A. P., and Miller. J. M.. J. Inorg. Nucl Chpm., 7.351 (19581. 191 Ksufmsn. M.,Astrophys. J..137,1296 (19611. (101 Politxer, P..7 b n s . For Sor.. 64.2241(1968). (11) Pritchard,H. 0.. Chem Re", 52,529(19631. (L2) Biehm, B., Gusinow, M. A , and Hall, J. L..Phys. Rev. Lett., 19,737 119671. 1131 Smirnov, B. M., and Chibimv, M. I., Zh. Ekaporim. i Teor Fir.,19, 841 C.A. 64: 4266e. I141 Hiby, J. W.,Ann. Phya. (Lpz.), 34,473 119391. (151 Turen. O..Z./uPhyaik, 103.463119361.
1161 Thomas,G.,andHermsn. L.,Compt. Rendw, 229, 1313 (1M91. 1171 Clementi, E..andMcLean.A.D..Phya. Re". 133,A419119641. 1181 Holln. w . ~ . , ~ h y L s .a r . AZ6.5411967). 1191 Kaplan. T. A.. and Kieiner. W. H., Phi.8. R w . , 156, I(19671. (201 Losk,A. M..Phys. Rsu., 171,7119691. (211 Weisa, A. W.,Phys. Re". 166,70(19681. 1221 Ohuz, I.. and~inanoplu.O..Phyl. Re". 181,5411969~. (23) Mawey. H. S . W., "Negafivelons: Cambridge University Press, 1950, pp. 1-22. 1241 Davydov, A. S., '"Quantum Mechanics" (Tronslafor and Editor ter Hear. D l Addison-Wesley, Reading, Mass., 1965, pp. 280-283. 1251 Mil%tein.R..andBerrv. ., R.S...l. Chem. Phvs.. 55.4146119711. . 1261 SchecrM.L..andFine. J..J Chem. Phys., 50,4343 (19691.
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