REINERKOLLRACK
2052
I n conclusion, experiments in heterogeneous media such as those just described should permit a t least qualitative studies of electron capture by liquids, and they may provide means of inducing photochemical reactions which are not observed under homogeneous conditions. Finally, in case where the liquid is absorbent and
photolyzed, the suspended solid particles might be used a t room temperature as a trapping medium for the unstable intermediates produced, whether ions or radicals. Acknowledgment. We are grateful to Drs. Lefort and Bouby for their help in the gas analysis.
Induced Dipole Moments of Inorganic Complex Ions
by Reiner Kollrack Scientific S t a f f , Pratt & Whitney Aircraft Diuision, United Aircraft Corporation, East Hartford, Connecticut (Received October 2, 1963)
The induced dipole moment of a fluorine ion has been calculated for the complex ions [M'VF'6]2-, [>I1'F6l4-, [M"1LF~]2-, [MT11L~F]2+, and trans- [M1"L4F2] using ligand field theory (L = dipole molecule like HzO or "3). The dipole moment of a given Fligand is induced by the inhomogeneous electric field which is caused by the influence of the other ligands and the central ion. +
Introduction During the past 12 years, ligand field theory has been applied to explain properties of inorganic complex compounds.'-13 All ligand field theory calculations, however, lack exact information concerning the two parameters: the distances between the central ion and the ligands and the induced dipole moments of the ligands (the induced dipole moment of the central ion is negligible). Heretofore, the induced dipole moments have always been arbitrarily assigned. In the present paper, the former rough estimations of the induced dipole moments will be replaced by far more accurate calculations. Usually, induced dipole moments of atomic species are calculated or measured only for homogeneous electric fields by determination of the polarizability, as the polarizability is not defined for inhomogeneous fields (Le., it is not unique). In the case of inorganic complex compounds, any given ligand is affected by the inhomogeneous electric field due to the electric charges and/or dipoles of the central ion and the other ligands. The Journal of Physical Chemistry
For a complex ion of the type [n$I'1'F6]3-such an induced dipole moment of a fluorine ligand was first calculated by Hartmann and Kollrack. 14,15 This paper presents the induced dipole moments of fluorine (1) H . Hartmann and F. E. Ilse, 2 . physik. Chem., 6, 768 (1951). (2) H . Hartman and F . E. Ilse, 2 . A'aturforsch., 69, 751 (1951). (3) F. E. Ilse, Thesis, University of Frankfurt, Frankfurt, Germany, 1947. (4) H . Hartmann and H . Fischer-Wasels, 2 . physik. Chem., 4 , 297 (1955). (5) H . Hartmann, "Theorie der chemischen Bindung," Springer Verlag, Berlin, Germany, 1954. (6) C. K . Jergensen, Acta Chem. Scand., 12, 903 (1958). (7) L. E. Orgel, J . Chem. Phys., 23, 1819 (1955). (8) L. E. Orgel, J . Chem. Soc., 4756 (1952). (9) C. J. Ballhausen and C. K . Jergensen, K g l . Danske Videnskab. Selskab. M a t . j u s . Medd., 29, No. 14, 1955. (10) C. K . Jergensen, M o l . Phya., 2 , 96 (1959). (11) C. Furlani and A. Furlani, J . Inorg. Nucl. Chem., 19, 51 (1961). (12) R. E. Hamm, R. Kollrack, G. L. Welch, and R. H. Perkins, J . Am. Chem. Soc., 83, 340 (1961). (13) D. M. Grant and R. Kollrack, J . Inorg. Nucl. Chem., 23, 25 (1962).
2053
IXDUCED DIPOLEMOMENTS OF INORGAN IC COMPLEX IONS
---
2
H,o
=
f $?* H'$oo dr
(3)
where eigenfunction of the perturbed F- ion in the ground state fiOo = eigenfunction of the unperturbed (free) F- ion in the ground state $10 = eigenfunction of the unperturbed F- ion in the lth excited state D = length of the induced dipole Eoo = energy of the unperturbed F- ion in the ground state E ; = energy of the unperturbed F- ion in the lth excited state z = operator corresponding to the coordinate x 2' = summation over all possible 1 values except 1 = 0 H' = perturbation operator representing the electric field $O
Figure 1. Sketch of the complex ion [MFe].
ions in following complex ions: [i\!11VF~]2-, [M11Fe]4-, [M111LFs]2-(only the F- ion in transposition to the dipole ligand L is considered), [M111L5F]2+,and trans[Mr1'L4F2]+. The different values of the resultiiig dipole moments, which depend on the type of complex ion considered, are discussed.
Calculations Basic Model. Lligand field theory considers the central ion aind the ligands as point charges and/or point dipoles. The calculations of the induced dipole moment itself are based on t h e concept that the eleotron cloud of one ,given F- ion is distorted by thle influence of the aforementioned electric field, so that the center of the negative charge of the F- ion no longer coincides with the center of the positive charge. We assume the nucleus to be completely unchanged. Thus, the length of the induced dipole is given by the distance between the nucleus and the center of the electron cloud. Figure 1 shows an octahedral complex ion. The nucleus of the F- ion under consideration is taken as the origin of a Cartesian coordinate system. The other five ligands are either F- ions or "dipole molecules'' such as H2O or S H , as mentioned before. The electron cloud is represented by the proper eigenfunction of the F- ion. From quantum mechanics it follows that G, =
f $O*Z$Odr
(1)
=
Calculations f o r the Free F - Ion. In this section, the atomic states of a free F- ion are determined. For the ground state of a free F- ion and those twelve lowest excited states which are pertinent, the electron configuration and the designation of the resulting atomic states are presented in Table I. Table I
-
2 ~ 5 3 s-P
'S 'P
2P53P
'D 'p
(ls2,2s2)2pG
2p53d
t r ~ n s - [ I I ~ ~ L 4 F>2 ][;\/I"'L6F]2+ ~+ > trans- [iL11"L4F2] +
[M'"F6I3-
>
>
[M1VF6]2-> [i\4111LF5]2->
[MI1L6F]+> trans-[M1'L4F2]O > [h111LF6]3-> [ h f " F ~ ] ~ -
where p~ = 1 a.u., R = 3.5 a.u., R L = 3.5 a.u. I n general, ion ligands show stronger influence than dipole ligands. The aforementioned ratio also determines whether or not there is a maximum for the curves in Fig. 2 ( F as a function of R ) for the considered values of R.
BEHAVIOR O F ALUMINUM
IN
2057
ALKALINE SOLUTIOSS
The dashed curve for [fii111F6]4in Fig. 2 indicates that here the influence of the five ligands dominates a t small ;values of 12. Contrary to the configuration
0xide-Coated Electrodes. 11.
of the dipoles calculated for the other four complex ions, [y111F6]4-here shows the positive pole of the induced dipole of an F- ligand faces the central ion.
Alumiiium in Alkaline Solutions
and the N,ature of the Aluminate Ion'
by Robert C. Plumb and James W. Swaine, Jr. Worcester Polytechnic Institute, Worcester, Massachusetts
(Rewined October 1 , 1963)
An investigation of the electrode potentials of evaporated aluminum films as a function of oxidation time has given the reversible electrode potentials for the aluminum-aluminate ion system. The potentials ha,ve been studied over the pH range from 10.5 to 13.8. Using the observed dependence of electrode potential upon the over-all concentration of aluminum in the solution and the pH, it is shown that the electrode reaction below a pH of 12.4 consists of the addition of aluminum ions from the metal to the aluminzte anion. Above a pH of 12.4 the reaction is directly between hydroxyl ions in solution and the metal ions from the metal. Possible structures for the aluminate anion are discussed. The aluminate ion is shown to be a polymeric anion of composition (OH-)2[A1(OH)4-], in which the Al(OH)4-units are, most likely, linked together by two hydroxyl bridges and each aluminum ion is surrounded by six hydroxyl ions. The chain length is of the order of n = 40 to n = 100.
Introduction A technique for determining the effects of oxide films upon electrode potentials was described in a previous publication.2 'Those studies showed that the electrode potentials of alumin.um in acidic and neutral solutions varied in a systematic way with the period of aiir oxidation. Electrode potentials measured after known and variable periods of air oxidation could be extrapolated to zero oxida,tion time to obtain potentials characteristic of the electrode in particular solutions. Using (1) an assumed electrode reaction and (2) wellestablished free energies of formation and of reaction determined by thermochemical techniques, one can predict a priori thrlee quantities : (1) the standard electrode poten.tia1 far the reaction, (2) the variation. of electrode potential with pH, and (3) the variation of
electrode potential with metal ion concentration in solution. The potentials obtained by extrapolating the experimentally measured potentials to zero oxidation time agree quantitatively with those potentials predicted a priori from thermodynamic data in all three respects showing that the observed potentials are thermodynamic potentials. Accepting the capability of measuring reversible potentials, one can anticipate using these potentials to study the nature of ions in solution. This communication describes our findings on the behavior of the
(1) From a dissertation submitted by J. W. S. in partial fulfillment of the requirements for the degree of Doctor of Philosophy in chemistry.
(2) R.
c. Plumb, J . Phys.
Chem., 66, 866 (1962).
Volume 68, Number 8
August, 1964
