LUMO Energies and Negative Electron Affinities Henry A. Kurtz Memphis State University, Memphis. TN 38152 Many modern theories of chemical bonding and chemical reactions are built on the concents of occunied and unoccunied orhitals. The importanve of thrit: theories was demonstrated hv the awnrdine of thr 1981 Nobel Prine in ('hemistw to two oi their developers: R. Hoffmaun and K. ~ u k u iI.t is usually the orhital properties, such as symmetry and energy, that are utilized to explain and predict chemical behavior. Further, it is the highest occupied molecular orhital (HOMO) and the lowest unoccupied molecular orbital (LUMO) which are often of the meatest use. This leads to the question of what t o use as the vaiues for these orbital energies. Within the framework of what is known as Koopmans' theorem (I), the occupied orbital energies are associatkd with ionization energies (i.e., the energy required t o remove an electron from a-given orbital), andthese values can be measured quite accurately by photoelectron spectroscopy (2). The unoccunied orhital enereies are associated with the enerw release2 upon the addition of an electron. This quantity is ti; electron affinity, EA, and is positive when a stable anion can be formed. Identifying the LUMO is complicated since there are two twes: enerw) .. bound (neeative . ".. corresnondine to stable anions and unbound (positive energy) corresponding to unstable anions. Like occupied orbitals, the energies of bound unoccupied orbitals present no real problem in that they can be assigned to well-defined positive electron affinities such as those measured by photoelectron detachment (3). A very good discussion of the selection and behavior of positive atomic electron affinities was provided by Chen and Wentworth (4). However, their results for systems without positive EA's (i.e., the filled sub-shell atoms in Groups IIA and IIB) are in error bv almost an order of magnitude, and these errors have, unfortunately, heen p~rprtuntedhy srveral general chemistrv texthuoks. The question remains how to select the values for the unbound, unoccupied orbital energies. Brooks, Meyers, Sicilia, and Nearing (51,while suggesting that the terminology IPo be adopted for the detachment energy of an electron from an anion, cited ah initio calculations to show that for atoms this value should never be negative. This approach is unsatisfactory, as the energy of the negative ion formed upon the addition of an electron to an unbound orhital lies above the energy of the neutral system. Therefore, i t must corresnond to a time-denendent electron-scattering problem, not to a time-independent stationary state. If such neeative ions can he identified. thev would have finite (and us;ally quite short) lifetimes. These temporary negative ion states have been found in electron-scattering experiments and are called resonances (6). They are characterized by their nosition (enerav) and width (lifetime). Following Tavlor's definitions (7);three types of resonances can he identified in atomic systems: single-particle shape resonances, core excited type I (Feshbach) resonances, and core-excited type I1 (excited-state shape) resonances. Of these types only the single-particle shape resonances correspond~tothe addition of an electron to the ground state of the atom and, hence, may correspond to a negative orhital energy (or electron affinity). In contrast, both types of core-excited states require that a t least one of the original electrons undergo an excitation. In the article by Chen and Wentworth ( 4 ) ,the electron affinities of the Group IIA atoms, Be, Mg, and Ca, were reported to be -2.5, -2.4, and -1.62 eV, respectively. These energies are for the formation of the 4P metastable anion states and
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Journal of Chemical Education
Electron Affinities of Group II Atoms and Their Associated Lowest Unoccupied Orbitals
Electron Atom Group IIA
Group llB
Affinit~'.~
Orbital
Be M!3 Ca
Z" Cd Ha
.heV. 'croup IIA valuer are horn Ref. ( 13 and croup 116 values horn Ref. (91.
correspond to a core-excited type of resonance. As noted nreviouslv. these are not the Droner values for the electron affinitieswhich may he associate'd with the energies of the lowest unoccupied orbitals. Recent experimental (8-10) and theoretical (11, 12) studies have been performed on these Groun IIA atoms. Thev have shown that both Be and Me possess 2P single-particie shape resonances a t about 0.20 e ~ y These neeative ion states are the lowest such states and. therefore,correspond to the negative electron affinities foi addition of an electron to the LUMO (a p orhital). For Ca there are two identifiable shape resonances: 2P and ZD. The lowest in enerw is the 2P resonance at 0.1 eV and corresponds to addition ofan electron to the lowest unoccupied orbital of Ca, the 4p orbital. In addition, the 2D resonance a t 0.8 eV indicates the position of the next unoccupied orbital of Ca, the 3d orbital. The shape resonances of the Group IIB atoms Zn, Cd, and Hg have also been studied experimentally (9),and values for the electron affinities of both groups are given in the table. Also shown are the lowest unoccupied orbitals whose energies can be associated with these affinities. Another set of elements that do not have nositive electron affinities is the Group 0 (rare gas) elements. ?;hey are different from the Groun IIA and IIB elements in that thev do not seem to have any 10;-energy shape resonances (6). Foiexample, the lowest enerev resonance of He- is the ls2s2 state. a coreexcited-typestate. This leads one to couclude for these atoms that either there are no low-lvine shane resonances or their lifetimes are too short to be disc&nible. In either case, it is impossible to obtain unambiguous values that correspond to the unbound orbital energies. Onlv the negative electron affinities of atomic systems have been discussedso far. There are also molecular systems which do not have positive electron affinities, for example Np and ethylene. The study and assignment of resonances in these systems is very different from the atomic systems due to the new integral degrees of freedom. ~owever[onecan still find low-energy shape resonances which correspond to LUMO energies. An excellent example of the type of information that can be obtained about unbound molecular orbitals was given by Jordan and Burrow (13). They used electron transmission spectroscopy to study the temporary anion states of several unsaturated hvdrocarhons. In conclusi&, I would like to emphasize that values for unbound orhital energies used by many theories can indeed
be obtained from certain negative electron affinities. These quantities can be obtained both experimentally and theoretically, and the results can then be used to explain or predict chemical processes. Literature Clted (1) Koopmans. T.. Physieo. 1,104 (1934). NY, (2) Baker. A. D., and Bettoridge. D.. "Photaledmn Spednxwpy." Pc'gamo'gamh. 1972.
(3) HO~OP, H., and ~ i ~W. c., ~J phys b them ~ R& ~ &to, , 4.539 (19'1s). (0 Chm. E. C. M.,and Wentworth, W. E., J. CHEM.EDUC., 52,486 (1975). (5) ~ m hD., w.. ~ e y e r sE . A,. sici~io, and ~ e a r i n pJ., c..J. CHEM.EDUC..50.487 11973).
(6) (7) (8) (9)
Schu1z.G. J..Reu. Mod. Phys,45,378,(1973). Taylor.H.S..Adu. Chem. Phys.XVIIl.91 (1970). Burrow, P. D.,and Comer, J., J. Phys. B: Atom. Molec. Phys., 8, L92 (1975). Burrow, P. D..Miehejda, J. A.,and Comer,J., J Phys. &Atom. Moloe. Phya.,9.3225
(1976). (10) Johnston, A. R..and Bumow, P. D., Bull. Amen Phys. Soc., 24,1189 (1979). (11) Ku*, H.A., and Ohm, Y.,Phys. Re". A, 19.43 (1979). 112) Kurtr, H. A,, and Jordan, K. D., J Phya. B:Alam. Moler. Phyr.. 14,4361 11981). (13) Jodan.K.D.,andBunow,P. D.,Aecf. Chem Res., 11.341 (1978).
Volume 61
Number 7
July 1964
581
