R. H. WOODAND L. A. D’ORAZIO
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Thermodynamics of the Higher Oxides. 11. Lattice Energies of the Alkali and Alkaline Earth Peroxides and the Double Electron Affinity of the Oxygen Molecule’
by R. H. Wood and L. A. D’Orazio Department of Chemistry, University of Delaware, Newark, Delaware
(Received January 13, 1966)
The Madelung constants for the alkali metal peroxides and the van der Waals sums for both the alkali and alkaline earth peroxides have been calculated. The results are used to evaluate the lattice energies of the peroxides and the double electron affinity of the oxygen molecule, E(Oz-t OZF2)= - 145 f 15 kcal./mole. The covalent bond energy in the peroxide ion (D = -95 kcal./mole) is discussed.
During the past 15 years there have been four separate calculations of the double electron affinity of molecular oxygen. Evans and Uri2&using an approximate Madelung constant for the alkaline earth peroxides, found the value E(Oz -t O Z - ~ )= - 112 f 8 kcal./mole. Vedeneev, et aZ.,2busing an accurate Madelung constant for the alkaline earth peroxides, found E(Oz + 02-2)= -175 f 15 kcal./mole. More recently, Yatsimirskii3 applied the Kapustinskii approximation to the alkali metal peroxides and obtained E(Oz + 02-2)= -120 kcal./mole. Tuck4 applied the Kapustinskii approximation to barium peroxide and found E(Oz + 02-2)= -121 kcal./mole. He pointed out that the recent determinations of the crystal structures of the alkali metal peroxides5-7 would allow rigorous calculations of the lattice energies of these salts. All of the previous workers have failed to assess the importance of higher pole interactions and their conclusions rest on the assumption that the peroxide ion can be adequately represented by a point charge. This paper reports the results of a more rigorous calculation of the lattice energies of the alkali metal and alkaline earth peroxides and the double electron affinity of molecular oxygen. As in the first paper in this series8 (hereafter referred to as part I) the van der Waals interactions and the effects of the charge distribution in the anion are assessed. The Journul of Physical Chemistry
Calculations of Madelung Constants The Madelung constants of the alkali metal peroxides were calculated by the method of W00d,9110 which involves the direct calculation of the interaction of a molecule with successive shells composed of unit cells. The results are given in Table I for two different charge distributions; case I, a - 1charge on each oxygen atom, and case 11, a -2 charge at the center of the peroxide ion (the “point charge approximation”). Case I was used in the calculation of the lattice energy. This case should be closer to the actual charge distribution since molecular oxygen has a very low quadrupole moment11112and two antibonding electrons are added (1) This study was supported by Air Force Office of Scientific Research Grant No. AF-AFOSR325-63. (2) (a) M. G. Evans and N. Uri, Trans. Faraday Soc., 45, 224 (1949); (b) A. V. Vedeneev, L. I. Kazamovskaya, and I. A. Kazarnovskii, Zh. Fiz. Khim., 26, 1808 (1952). (3) K. B. Yatsimirskii, Khim. i. Khim. Telcnol., 4, 480 (1959). (4) D. G. Tuck, J . Inorg. Nucl. Chem., 26, 1525 (1964). (5) H. Foppl, 2.amrg. allgem. Chem., 291, 12 (1957). (6) R. Tailman, J. L. Margrave, and S. W. Bailey, J . Am. Chem. SOC., 79, 2979 (1957). (7) F. Feher, I. V. Wilucki, and G. Dost, Chem. Ber., 86, 1429 (1953). (8) L. A. D’Orazio and R. H. Wood, J . Phys. C h a . , 69, 2550 (1965). (9) R. H. Wood, J . Chem. Phys., 32, 1690 (1960). (10) A Fortran listing and a set of directions can be obtained by writing to R. H. Wood.
THERMODYNAMICS OF THE HIGHEROXIDES
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Table I : Madelung Constants of the Alkali Metal Peroxides Madelung constantb Compound
Liz02
NazOz
M6(MzOd
Structurea
M6(Mz[Oz])
M6(MZ [Ozl) point charge
V’/S X 108 cm.
P6 (Cgh’), a = 3.142, c = 7.650 Li-a, Li-d, Li-i (z = I/d) 0-g ( Z = 0.401), 0-h ( Z = 0.099)
5.0057 *
