Mechanism of ion exchange in crystalline zirconium phosphates. X

(13) K. Hiroike, N. R. Kestner, S. A.Rice, and J. Jortner, J. Chem. Phys., 43, 2625 (1965). ... M. James and T. A. Keenan, J. Chem. Phys., 31, 12 (195...
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A. Clearfield and L. H. Kullberg

(12) J. Jortner. N. R . Kestner, S. A. Rice, and M. H. Cohen, J. Chem. Phys., 43, 2614 (1965). (13) K. Hiroike, N . R. Kestner. S. A. Rice, and J. Jortner. J. Chem. Phys., 43, 2625 (1965). (14) J. Lekner. Phys. Rev., 158, 130 (1967). (15) M. H. Cohen and J. Lekner. Phys. Rev., 158,305 (1967). (16) B. E. Springett, J. Jortner, and M. H. Cohen. J. Chem. Phys., 48, 2720 (1968). ( 17) H. M. James and T. A. Keenan, J. Chem. Phys., 31, 12 ( 1959). (18) J . A . Pople and R . K. Nesbet, J. Chem. SOC.,22, 571 (1954). (19) J . A. Pople, D. L. Beveridge, and P. A. Dobosh, J. Chem. Phys., 47, 2026 (1967). (20) P . - 0 . Lowdin. Advan. Chem. Phys.. 2,207 (1959). (21) K. F. Berggren and R. F. Wood, Phys. Rev., 130,198 (1963). (22) T. Amos and L. C. Snyder, J. Chem. Phys., 41, 1773 (1964) (23) To three decimal places. (24) This refers to the "corrected stabilization energy" in ref 7. (25) P. G. Fuochi and G. R. Freeman, J. Chem. Phys.. 56, 2333 (1972). (26) W. F. Schmidt and G. Bakale, Chem. Phys. Left., 17, 617 (1972). (27) However, it is to be noticed that the destabilization may be partly attributed to the overestimated charge density of the hydrogen atom of methane in the INDO calculation: for example, according to the ab initio calculation. the charge density of the hydrogen atom of isolated methane is 0.867 with a C-H bond length of 1.094 A (see W. E. Palke and W. N. Lipscomb, J. Amer. Chem. Soc., 88. 2384 ( 1 9 6 6 ) ) ; nevertheless, the INDO calculation with a C-H bond length of 1.090 A gives 1.009 for the value. Therefore, A € was also

(28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39)

recalculated by correcting the electronegativity of the hydrogen atom so that it might give a reasonable charge density for this atom, 0.867. A € consequently obtained is -1.868 eV, which seems to be too low and 16 have errors caused by the collapse of the consistency of parametrization. Hence we will maintain further discussions, keeping in mind that A € will probably be slightly lowered by more accurate calculations. Such a molecular orbital is called 1s MO. H. A. Gillis, N . V. Klassen, G. G. Teather, and K. H. Lokan. Chem. Phys. Lett.. IO, 481 (1971). A. Ekstrom and J. E. Willard, J . Phys. Chem., 72,4599 (1968). K. Tsuji. H. Yoshida, and K. Hayashi, J . Chem. Phys., 46, 810 (19671. K.-Tsuji and T. Williams, J. Amer. Chem. SOC.,89, 1526 (1967). A. F. Kip, C. Kittel, R . A . Levy, and A. M. Portis, Phys. Rev., 91, 1066 (1953). S. Ishimaru, H. Kato. H. Tomita, T. Yamabe, and K. Fukui, Chem. Phys. Lett., in press. According to the results that lp111