THERELATIVE STABILITIES OF PERCHLORATE, PERRROMATE, AND PERIODATE IONS
627
The Relative Stabilities of Perchlorate, Perbromate, and Periodate Ions by Margaret M. Cox and John W. Moore Contribution N o . 1761 from the Department of Chemistry,Indiana University, Bloomington, Indiana 47401 (Received August 14, 1969)
Several explanations of the instability of perbromate salts and perbromic acid have been examined using Hartree-Fock-Slater atomic wave functions and self-consistent charge and configuration (extended Huckel) MO calculations. It is concluded that perbromates should be similar to perchlorates and periodates in stability. The molecular orbital treatment, although highly approximate, corresponds well with observed properties of Br04- and in the case of Clod- is in agreement with previous calculations.
The synthesis of perbromates and the mass spectrum of perbromic acid1 indicate that these compounds are not extremely unstable, despite many unsuccessful attempts to prepare them.2 Prior to the reports by Appleman and Studier we had begun a study of a number of “explanations” of the absence of perbromates. Thc results are reported here. There have been at least four different rationalizations of the difficulty of preparation of perbromates. Hug& suggested that the normal trend would be a decrease in stability in the order clod- > BrO4- > IOd-, but that periodate was unusually stable because f orbitals were available for bonding. The f orbitals should be contracted by increasing charge on iodine and would therefore stabilize higher oxidation states. Nyholm showed4 that s + p promotion energies for arsenic are larger than those for phosphorus or antimony. He argued that the general instability of the highest oxidation states of representative elements in the fourth period is due to this effect. Because of the difficulty of unpairing the s electrons, spahybridized bromine should be less stable than sp3chlorine or iodine. Urchs argued that the promotion energy problem could be overcome provided that strong ?r bonds were formed using vacant d orbitals on the central atom. Using hydrogenic functions for the bromine d orbitals, Urch showed that a radial node might occur in the bonding region, making d,-p, overlap very small. Ferreirae*found that d,-p, overlap between Kr and 0 was not noticably smaller than between Ar and 0, which would appear to invalidate Urch’s argument. In order to explain the absence of perbromate Ferreira used Pitzer’s inner shell repulsionseb and suggested that the electronegativities of I and 0 differ enough so that coulombic attractions overcome the electron repulsions in IO4-. It appeared to us that the difference in stabilities of Clod-, Br04-, and 104- should be a result of differences in atomic properties of the halogens. Atomic energy levels and radial behavior of atomic wave func-
tions constitute the basis of all of the arguments listed above. Since numerical Hartree-Fock-Slater atomic wave functions7can be obtained for most atoms and ions without excessive computation, we decided to examine explanations of the nonexistence of perbromate in terms of the results obtained from the Herman-Skillman Hartree-Fock-Slater formalism.
Atomic Wave Functions and Orbital Energies Numerical radial wave functions were obtained using the Fortran program of Herman and Skillman’ modified for use on the Control Data 3400-3600 System of the Indiana University Research Computing Center. Radial functions were calculated for mono- and dipositive ions as well as for neutral halogen atoms, and were approximated by a sum of Slater-type orbitals using a least-squares procedure.* Oxygen 2s and 2p functions were obtained from the paper by Clementi,9 and halogen-oxygen overlaps were evaluated in the usual way.8 Bond lengths were obtained from Wellslo for C1-0 and 1-0. A Br-0 length of 1.62 was obtained by interpolation, using the relative lengths of C103-, Br03-, and 1 0 3 - as a guide. Table I gives positions of radial (1) E. H.Appelman, J. Amer. Chem. SOC.,90, 1900 (1968); M, H. Studier, ibid., 90, 1901 (1968). (2) See, for example, W. F. DeCoursey, “Preparation of Perbromates,” Doctoral Dissertation. State College of Iowa. Cedar Falls. Iowa. 1953; G. M. Bancroft and H. D. Gesser, J. Inorg.-NucL Chem., 27, 1545 (1965). (3) 2 2. Hugus, Jr., J. Amer. Chem. Soc., 74, 1076 (1952). (4) R. 8. Nyholm, Proc. Chem. Soc., 273 (1961). (5) D. S. Urch, J.Inorg. Nucl. Chem., 25,771 (1963). (6) (a) R. Ferreira, An. Acad. Bresileira de Ciencias, 38, 407 (1966); (b) K. S. Pitzer, J. Amer. Chem. Soc., 70,2140 (1948). (7) F. Herman and S. Skillman, “Atomic Structure Calculations,” Prentice-Hall, Inc., Englewood Cliffs, N. J., 1963. (8) H.Johansen, “Algol Programs for Molecular Calculations,” H. C . srsted Institute, University of Copenhagen, Denmark, 1965. (9) E. Clementi, C. C. J. Roothaan, and M. Yoshimine, Phys. Rev., 127,1618 (1962). (10) A. F.Wells, “Structural Inorganic Chemistry,” 3rd ed, Oxford University Press, London, 1962,p 334.
Volume 74, Number 3 February 6 , 1070
MARGARET A t . Cox AND JOHN W. NIOORE
628
Discussion
Table I: Atomic Wave Functions and Overlap Integrals Distance to
outermost radial
Function
node, A
c14s Cl+ 4s C13d C1+ 3d Br 5s Br+ 5s Br 4d Br+ 4d 16s I + 6s 15d I+ 5d I 4f I + 4f 15d(4f1) If5d(4f1)
0.944 0.843
...
...
1.06 1.11 0.40 0.39 1.22 1.18 0.59 0.59
...
... 0.59 0.58
Bond leneth.
d
’
1.43 1.43 1.43 1.43 1.62“ 1.62“ 1.62” 1.62a 1.79 1.79 1.79 1.79 1.79 1.79 1.79 1.79
---Magnitude of Overlau02su
02po
0.182 0.254 0.284 0.408 0.178 0.242 0.262 0.432 0.146 0.203 0.322 0.429 0.046 0.267 0.433 0.430
0.076 0,059 0.048 0.051 0.062 0.044 0,058 0.051 0.069 0.061 0.033 0.064 0.021 0.037 0.067 0.077
0 2 p 7l I . ,
... 0.260 0.354
... ...
0.218 0.341
... ...
0.244 0.313 0.048 0.264 0.315 0.313
Obtained by interpolation (see text).
nodes and magnitudes of overlap integrals for neutral and monopositive halogen functions. Using orbital energies derived from the HFS treatment it is possible to estimate s --+ p, s + d, and s + f promotion energies. This has been done for neutral halogens and monopositive ions. The results appear in Table 11. Higher charges were not considered because it is unlikely that the charge on the central halogen in XO4- will exceed unity (vide infra). Although not all of the required terms in the atomic spectra” have been observed, it is possible to estimate empirical promotion energies by extrapolation along isoelectronic series. The empirical values are about 15% below the HFS resuits in all cases where comparisons have been made, but the trends in HFS values follow the trends in empirical promotion energies.
Extended Hiickel Calculations In order to translate the atomic properties of the halogens into more readily understandable chemical terms we have carried out self-consistent charge and configuration calculations as described by Ballhausen and Gray.12 The corrections to group overlap formulas noted by Bishopla were applied. Calculations were performed initially using basis functions for the neutral halogens. Since charges on all of the halogens were between +0.6 and +0.9 the final results were obtained by interpolation of overlaps between those obtained for univalent and zerovalent halogen functions. The final calculation, therefore, is a function of VSIE’s and overlaps which are appropriate to the charges and configurations of the atoms involved. Pertinent results are shown in Table 111. The Journal of Physical Chemistry
From the data reported in Table I, it is clear that radial nodes in the bromine 4d and iodine 5d functions do not have an adverse effect on d,-p, overlap relative to the nodeless chlorine 3d. While d,-p, overlap for neutral bromine is smaller than for chlorine or iodine, this may be due partly to inaccuracy in fitting a sum of Slater functions to the numerical HFS results. The situation is reversed for C1+, Br+ and, I+where d,-p, overlap decreases in the order C1+ > Br+ > I+. Since the results of extended Hiickel calculations often underestimate the positive charge on the central atom,I4 overlaps for the unipositive halogens should be more appropriate than for the neutral atoms. Urch’s suggestion that poor d,-p, overlap makes perbromate unstable is incorrect . Several interest’ingfacts about the behavior of atomic wave functions are implicit in the results in Table I. First of all, an increase in nuclear charge can cause a drastic contraction of diffuseatomic orbitals. The most striking case is shown in Figure 1 where f orbitals for Io and I+ are compared. This contraction causes an increase of about a factor of ten in overlap of the 4f orbital with oxygen functions at an appropriate distance. A second very interesting result is that if f orbitals are occupied they tend to make the d functions much more suitable for bonding. Because the f electron has a high probability of being far from the nucleus it tends to contract the d function beneath it as shown in Figure 2. Together with the rather high energy of the f orbital this effect guarantees that, d orbital bonding will be more important than f orbital bonding in periodate. Although Hugus’ suggestion that utilization of f orbitals should stabilize higher valence states for iodine was based correctly on the fact that these orbitals are greatly contracted by increasing charge, our results indicate that f orbitals will not be nearly as efficacious as d orbitals in stabilizing IO4-. The HFS results in Table I1 indicate that s -+ p promotion energies for Bro and Br+ are 4% larger than for Cl0 and Cl+ and 15% larger than for Io and I+. This places the bromine s --+ p promotion energy 10% above the value to be expected on the basis of a linear periodic trend. Based on the empirical promotion energies the difference is only about 5%. In the case of s d promotion energies the bromine value is only 7% above a linear interpolation. These figures can be compared with promotion energies for Se (s p 12T0,s d 9% high) and As (s --t p 13%, s + d 10% high). Difficulty of s 4 p and s + d promotion relative to other members --+
-
--+
(11) C. E. Moore, “Atomio Energy Levels,” National Bureau of Standards Circular 467, U. 5. Government Printing Office, Washington, D. C., 1955. (12) C. J. Ballhausen and H. B. Gray, “Molecular Orbital Theory,” Benjamin, New York, N. Y . ,1964. (13) D. M. Bishop, Theoret. Chim. Acta, 8 , 2 8 5 (1967). (14) R. F. Fenske,Inorg. Chem., 4 , 3 3 (1965).
THERELATIVE STABILITIES OF PERCHLORATE, PERBROMATE, AND PERIODATE IONS
629
Table I1 : Promotion Energies Type of promotion
-
ns-np
ns ----f nd ns (n 0
-
HFSa EmpiricaF HFSo l)f HFSa
ClO
CI +
101 85 233
105 93 249
...
-
Energy, 108 om-' Bro Br +
106 87 229
110 95 250
...
...
I+
IO
91 79 193 229
...
95 78 210 257
Obtained from atomic spectra (ref 11, see text).
Obtained from Herman-Skillman program (ref 7).
Table 111: Self-consistent Charge and Configuration Calculations for XOd-
X
Charge
ns
np
c1
0.64 0.72 0.81 0.83 0.57 0.65 0.75
1.42 1.54 1.48 1.46 1.41 1.52 1.46
3.56 3.53 3.37 3.37 3.62 3.62 3.41
Br I Ib Clc Brc I C
a
Electron populations Atomic nd (n
1.38 1.22 1.34 1.39 1.14 1.01 1.22
- 1)f ...
(n
*..
.*. -0.05
... *.. ...
-Overlap-
+ 1)s ... ... ... ...
0.26 0.19 0.15
Energy of lowest fully allowed electronic transition (1Tz(t1W)C - lAi(ti6)).
Orbital energies, 10s om-'
U
?r
Aa
Z€i
0.65 0.53 0.53 0.47 0.68 0.57 0.54
0.43 0.41 0.43 0.44 0.37 0.37 0.42
73.6 73.3 80.1 68.1 77.1 67.9 65.4
- 5315 - 5295 -5218 - 5237 - 5346 - 5355 - 5226
Including (n
+ 1)s orbital.
Including 4f orbitals.
6
An estimation of the contribution of inner shell repulsionssb to the instability of the perhalate ions can be made. One would expect inner shell repulsions to increase as the radius of the inner shell increases. The distance from the nucleus to the outermost radial maximum of the highest energy closed shell orbitals of each halogen is given in Table IV. If anything, the bromine
m ?'
Table IV Atoni
C1 (n = 3) Br (n = 4) I (n = 5)
a C'
m.
5.0
10.0
, . . . .
15.0
I
.
.
.
Distance t o outermost radial maximum, A (n - l ) b (iz - 1)p (n - l)d
0.19 0.26 0.37
0.16 0.25 0.38
... 0.22 0.41
.
20.0
7
Figure 1. Plots of ampjitude of radial wave function us. distance from nucleus (A) for If [Kr]4d1°4.f15s25pa(upper) and Io [Kr]4d14df15s25p*(lower). Italicized orbital is plotted.
of a periodic group decreases in the order As > Se > Br. Since selenates and arsenates have been well characterized for some time, it would appear that these relatively small differences are not sufficient to preclude formation of a stable tetrahedral ion.
radii are smaller than would be expected on the basis of a linear interpolation between C1 and I. Unusually large inner shell repulsions do not appear to be a viable explanation for the difficulty of preparation of perbromates. An estimation of the stabilization of XO1- anions by partial ionic character in the bonds can be made by calculating coulombic attractions and repulsions assuming point charges in a tetrahedral array with the X-0 distances in Table I. The stabilizations are 27.0 X lo3cm-', 32.2 X lo3em-', and 39.9 X lo3ern-', respectively, for C104-, BrOd-, and IOd-, using charges generated by the extended Huckel calculation including (n 1)s orbitals. Using the radii in Table IV as a
+
Volume 74, Number 9 February 6 , 1070
MARGARET M. Cox AND JOHN W. MOORE
630
Figure 2. Plots of ampiitude of radial wave functions us. distance from nucleus (A) for In[Xi]4d105s26p46d1 (upper), IO[Kr]4dln4fl5~25pS5d’(middle), and I + [Kr]4d~05s%pa5cP (lower). Italicized orbital is plotted.
guide, inner shell repulsions should be in the ratio 1:1.4:1.9,whichisofthesameorderastheratio (1,:l.Z: 1.5) of ionic stabilizations for c104-, BrOd-, and I04-, respectively. From these ratios it would appear that Br04- is neither stabilized nor destabilized by the combination of effects. Using the results of the extended Huclrel calculations, a number of predictions can be made regarding the properties of the perhalates. Further discussion is based on the calculations involving (n 1)s orbitals. From Table I11 it can be seen that the energies of the first fully allowed transitions (‘Tz(tI6tz1)+- ’A1(tle) in all cases) decrease in the order A a > AB^ > AI. This is in accord with the ultraviolet spectra of the ions.
+
The Journal of Phgsical Chemistry
Perchlorate does not absorb significantly below 56,000 em-’, perbromate has a peak a t 53,200 cm-’,I6 a,nd periodate has a maximum absorbance at 46,000cm-l. The observed trend is reflected by the A values, although they are somewhat too large because of overof off-diagonal matrix elements involving e~timation’~ the low-lying s orbitals on halogen and oxygen by the geometric mean approximation. If these functions are removed from the basis set, the lowest virtual orbitals of tz and a1 symmetry become much more stable. The effect on the a1 level is so large that it drops below the highest filled level, producing a paramagnetic ground state. Obviously the ns orbitals on halogens and oxygen must be included in the basis set, but their effect is probably not as great as our results iadicate. An estimate of the Br-0 stretching frequency can be made by assuming a linear relation between force constant and bond order and using the equation dcrived by Gillespie and Robinson. l6 Since total overlap populations should be proportional to bond orders, l7 extrapolation on a plot of force constant us. total overlap population for clod- and 104- was used to obtain a force constant of 5.40 >( lo6 dyn em-’ for tho Er-Q sLretch.l* This corresponds to a weighted average frequency of 829 cm-I for the symmetric and antisymmetric shretching vibrations, which can be compared with the weighted average of 862 cm-’ for the observed V I and ~ 3 . l These Br-0 frequencies give a force constant of 5.83 X 106 dyn cm-I, nearly the same as the 1-0 force const,ant of 5.87 X lo” dyn em-’, but much smaller than the C1-0 value of 7.45 X lo5 dyn cm-’. Despite the absence of any major discontinuity in the atomic properties of C1, Br, and I, our calculation predicts a slightly weaker Br-0 bond than is actually obwrved. The smsLller overlap population and force constant calculated for Br04- suggest that the bond distance might be slightly larger than the average of C1-0 and 1-0. Calculation of overlap integrals as a function of X-0 distance indicates that Er-0 overlaps are less dependent on this parameter than C1-0 or 1-0. Should the experiniental b2nd distance prove to be slightly different from 1.62 A our results would probably not be grossly different. The results reported here may be compared with previous work in the case of perchlorate. WagnerLghas treated a series of chlorine oxyanions using a molecular orbital method. By using a somewhat arbitrary choice of the off-diagonal matrix element for d,-p, bonding he obtained a final charge of 0.44on chlorine and a n-bond (15) E. €1.Appelman, Inorg. Chem., 8, 223 (1969). (16) R. J. Gillespie and E. A. Robinson, Can. J . Chem., 41, 2074 (1963). (17) R. S. Mulliken, J . Chcm. Phys., 23, 1833 (1955). (18) K. Nakamotjo, “Infrared Spectra of Inorganic and Coordination Compounds,” John Wiley and Sons, Inc., New York, N. Y.,1963, pp 103-110. (19) E. L.Wagner, J . Chem. Phys., 37,751 (1962).
~
THE!RELATIVE STABILITIES OF PERCHLORATE, PERBROMATE, AND PERIODATE IONS order of 0.21. Our results indicate that this choice of & L - p may be somewhat high. ManneZ0has applied an approximate LCAO-&TO-SCF calculational scheme to sulfur and chlorine oxyanions, but d orbitals on the central atoms were not included. This results in a considerably higher residual charge on chlorine (-+2.1) than we obtain. However, it is interesting to note that if the population analysis in our calculation were confined to 3s and 3p orbitals, the charge on chlorine would be +2.02 (not including (n 1)s) or +2.03 (including (n 1)s). Thus the difference is accounted for almost exactly by the amount of charge transferred from the oxygens to chlorine orbitals not included in Manne's calculation. The same ordering of the one-electron levels (except for the additional virtual orbitals produced by expansion of the basis set) is obtained from both calculations. We do not claim to know the extent of d-orbital participation in bonding in the perhalates. There are two indications that we may have overestimated d-orbital bonding. First, as Fenske14 has pointed out, the geometric mean approximiLtion for off-diagonal matrix elements is poor when large diagonal terms are involved. Second, we have underestimated the force constant for bromine-oxygen stretching. Since all overlaps except those involving d orbitals are in the order C1:Br:I for both zero- and univalent ions, the discrepancy may be due to an overemphasis on d-orbital bonding. Nevertheless, the rapid increase in d,-p, overlap with increasing charge on the halogen indicates that some charge neutrttlization via T bonding should occur before the charge reaches +2. The answer probably lies between our results and Manne's. A more rigorous
+
+
631
calculational scheme involving atomic basis functions appropriate to the atoms in the molecule or ion will be necessary in order to decide this issue. We have been unable to find any reasonable explanation for the difficulty of preparation of perbromates nor have we been able to confirm previous suggest i o n ~ . ~ While -~ our results indicate that perbromate may be slightly less stable than periodate or perchlorate, the differences are small. We suggest that unfavorable reaction rates, rather than the intrinsic instability of perbromate, may account for the facts. Heating of bromates has probably not worked because the perbromate formed decomposes rapidly at high temperatures, and oxidation of bromine by perchlorate or periodate is an unlikely method because both of the latter are slightly more stable than perbromate. Our conclusions are supported by the successful isolation of perbromate at a low t,emperature and the apparent stability of perbromic acid in the mass spectrometer,' and we are in agreement with those reached by Appelman.l5
Aclcnowledgment. We wish to thank R4r. John Kindsvater for his interest in this problem and several helpful discussions. Formulas for f orbital overlap integrals were derived by Mr. Douglas Shepard. The help of Mr. Charles Flowers of the Indiana University Research Computing Center in modifying the HermanSkillman program is gratefully acknowledged. This work was supported in part by a Frederick Gardnor Cottrell grant-in-aid from the Research Corporation. (20)
R.Manne, J . Chem. Phys., 46,4645 (1667).
Volume 74, Number I February 6, 1970
