Revised Mulliken Electronegativities I. Calculation and Conversion to Pauling Units Steven G. Bratxh The University of Texas, Austin, TX 78712 One of the best known and conceptually simplest electronegativity scales is that proposed by Mulliken (1.2):
where IPv and EAv are the valence-state ionization potential and electroti affinitv. resoectivelv. The theoretical basis of the Mulliken electrohega&ity sche has received considerable attention. bv Mulliken himself in a valence-bond treatment (2) and amolecular-orbital treatment (3). and by manv others (4-18. I9a). he valence state concept is an attempt to describe the condition of an atom as it exists in combination with other atoms. In general, the valence state of an atom is not a stationary spectroscopic state nor even a nonstationary state, but a statistical average of stationary states, chosen so as to duplicate in the isolated atom the electronic interactions obtained when the atom is bonded to other atoms (10). Moffitt (4, 7) has expressed the belief that specification of the valence state is necessarv and sufficient for the entire electronegativity concept. he valence state concept bas been investieated and discussed bv Mulliken (I). Moffitt (4. 5, 7), skinner and Pritchard (6, 8j,Hinze, whitehead, and Jaffe (10-12), Ponec (18), and Huheey (19a-c). The most widely used currently available set of Mulliken electroneeativities is that of Hinze, Whitehead, and Jaffe (10-12). which considers 29 elements. However, their set is largely bawd on inaccurate electron affinities and is derived from a method of valence-state promotion energy calculation which is not well suited for teaching purposes. Revision of the Mulliken electroneeativitv scale is ao~ronriatea t this time because accurate, egperimmtal electron kfinities are now available for many elements (201, which in turn allow the estimation of the electron affinities of the remaining elements with greater confidence (21). In addition, the considerable progress in electronegativity theory over the past 25 years gives a new perspective to the significance and utility of the Mulliken scale. The results of this two-part series include: 1. A revision and extension of the MuUiken electronegativity scale to consider 50 elements.
2. The application of Mulliken electronegativities to topics in chemical education. -
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3. The identification of problems within the Mulliken system; sug-
gestions far their solution where possible. 4. Recommendations for future research.
The elements considered in this work are those in the main groups of the Periodic Table, and the copper and zinc suberouos. As in nrevious maior cornoilations (6.8.10-12). t h e ~ u l i i k e ne~ecirone~ativitfes consLdered in this work entail onlv valence states involvine s and D orbitals. Hinee and .Jane (22)have tabulated very u&rtain'~ulliken electronegativities for elements of the firgt transition series. includine" many valence states involving d orbitals; these are considered to be too poorly known to be included in the present work. Following a suggestion of Pritchard and Skinner (8). Hinze and Jaffe (10) have interpreted the Mulliken electro34
Journal of Chemical Education
negativity as an orbital property, asserting that "electronegativity can only be defined for bonding orbitals". However, Ponec (18) and Reed (23) have pointed out that differentiation of energies of nonequivalent orbitals is unavoidably arbitrary and ambiguous for atoms in molecules and have recommended the retention of the "dobal" atomic electronegativity concept. The renewed interest in electronegativity as the chemical potential of Density Functional Theory (17. 24-26) treats electroneeativitv as an atomic. not an orbital, prdperty. Ferreira (I;), callkg the ~ u l l i k e n m e t h o d "the basic definition of atomic electronegativity", has stated that the concept of electronegativity is in conformity with the approximate theories of chemical bonding (Valence Bond Theory and Molecular Orbital Theory) in "preservinp"the conceDt of atoms in molecules. Finallv, i t should be mentioned that the method of partial ionic charge calculation currently applied to the Mulliken system is ultimately derived from the Iczkowski-Margrave atomic charge-energy which holds approximately for multiple ionizafunction (9), tions. In this work, therefore, electronegativity is treated as a "global" atomic property that is determined by the valence state. Calculallon of Valence-Slate Promoilon Enersles Valence-state promotion energies (P) are calculated in this work by the method of Pritchard and Skinner (81, based on the formulas of Moffitt (7). This is a pedagogically simple and direct approach to valence-state promotion energies, consistent with the method of linear combination of atomic orbitals (6,8,19b,19c). Contributions of spectroscopic terms to valence-state nromotion enereies are iresented-in Table 1.Terms with multiple J values (J = total angular momentum auantum number. L-S coualine) are weiehted in the ratio bf lowest 2highe$t J = l:i(7,8). This refinement is significant for heavy elements which exhibit large J splitting~. Valence-state promotion energies are listed in Table 2, using atomic energy levels from Moore's tables (27). Pvalues derived in this manner are given to three decimal places, although more significant figures are possible in most cases.
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Table 1. ConMbutions of Spectroscopic Term to Valence-State Promotion Energiesd Confiauratians
Terms
Weiahts
Eight spectroscopic values in Table 2 are taken from Pritchard and Skinner (8) and are tabulated to twodecimal places. Moffitt's formulas (7)give results whose reliabilities are limited only by the spectroscopic measurements, which are usuallv known co ereat accuracy. This method of calculation fails, however, iflnot all con
