R. IKEDA, A. SASANE, D. NAKAMURA, AND M. KUBO
2926
Pure Quadrupole Resonance of Halogens in Some Hexahalorhenates(1V)
by Ryuichi Ikeda, Akinobu Sasane, Daiyu Nakamura, and Masaji Kubo Department of Chemistry, Nagoya University, Chikusa, Nagoya, Japan
(Received March 10, 1966)
The nuclear quadrupole resonance of halogens in various hexahalorhenates(1V) Rz[Rexe] (R = NH4, Rb, Cs; X = C1, Br, I) was observed at various temperatures. The change in the number of observed resonance lines reveals the existence of a phase transition of ammonium hexaiodorhenate(1V) a t 44-46'. From the dependence of resonance frequencies on the kind of cations R, it is concluded that, in addition to the direct electrostatic effect of external charges, a n indirect effect, due to neighboring ions, is significant on the field gradient a t the resonant halogen nucleus. Sternheimer's antishielding accounts for the large field gradient amplification a t least with regard to the sign and the order of magnitude of the indirect effect relative to the direct effect. All these complexes show a positive temperature coefficient of quadrupole resonance frequencies with the single exception of ammonium hexachlororhenate(1V). It is suggested that hydrogen bonding or some electrostatic interaction between hydrogen and chlorine atoms in crystals is responsible for the exceptional behavior of this complex.
Introduction I n a preceding paper,' we have reported that positive temperature coefficients of quadrupole resonance frequencies were found for potassium hexachlororhenate(IV), hexabromorhenate(IV), and hexachlorotungstate(IV). The temperature range was that in which these complexes show a single resonance line, Le., the range in which they form cubic crystals having the potassium hexachloroplatinate(1V) structure. A theoretical explanation was made in terms of the dn-pa bond character of metal-ligand bonds in paramagnetic complexes having one or more vacancies in their de orbitals. However, the field gradient a t the resonant nucleus leading to the positive temperature coefficient does not originate solely from the electron distribution within the complex ion containing the nucleus: charges on other ions should make an appreciable contribution as well. Therefore, we have undertaken a systematic study of the temperature coefficient of quadrupole resonance frequencies of hexachloro-, hexabromo-, and hexaiodorhenates(1V) having ammonium, rubidium, and cesium ions as cations. Potassium hexaiodorhenate(1V) has been already examined,' but it does not crystallize in a cubic structure a t any accessible temperature. No reports have ever been published on the possible formation of lithium and sodium hexahalorhenates(1V). The Journal of Physical Chemistry
Experimental Seetion Apparatus. A Dean-type, self-quenching, superregenerative spectrometer, already described, was used for the observation of quadrupole resonance frequencies of chlorine isotopes. For detecting the resonance absorptions of bromine and iodine isotopes, a self-quenching, superregenerative spectrometer2 equipped with Lecher lines was employed. Resonance frequencies were determined a t room, Dry Ice, and liquid nitrogen temperatures. For ammonium hexaiodorhenate(IV), frequency determination was extended up to about 100" in order to locate a possible phase transition to a cubic structure. For all of the complexes studied, the temperature coefficient of the resonance frequencies was determined between Dry Ice and room temperatures. Materials. When ammonia solution was added to an aqueous solution of rhenium(VI1) heptoxide, Re207, ammonium perrhenate(VII), *(SH4)Re04,separated as a white precipitate. It was dissolved in concentrated hydrochloric acid and reduced with hypophosphorous acid to prepare ammonium hexachlororhenate(1) R.Ikeda, D.Nakamura, and M. Kubo, J . Phys. Chem., 69,2101 (1 965). (2) D. Nakamura, Y. Kurita, K. Ito, and M. Kubo, J . A m . Chem. SOC.,82, 5783 (1960).
PUREQUADRUPOLE RESONANCE OF HALOGENS IN HEXAHALORHENATES (IV)
(IV) . Rubidium and cesium hexachlororhenates(1V) and ammonium, rubidium, and cesium hexabromorhenates(1V) were synthesized in a similar manner from appropriate starting materials (rubidium carbonate and cesium carbonate) using hydrobromic acid in place of hydrochloric acid for obtaining the hexabromo complexes. I n order to identify the samples, each complex was decomposed with a sodium or potassium hydroxide solution and the halogens were determined by Volhard's method. Anat. Calcd for (NH4)ZReCl6: C1, 48.9. Found: C1, 47.3. Calcd for RbzRe(&: C1, 37.3. Found: C1, 37.3. Calcd for Cs2ReC16: C1, 32.0. Found: C1, 31.7. Calcd for (NHS2ReBr6: Br, 68.5. Found: Br, 67.2. Calcd for RbzReBra: Br, 57.3. Found: Br, 55.9. Calcd for Cs2ReBr6: Br, 51.5. Found: Br, 50.7. Ammonium, rubidium, and cesium hexaiodorhenates(IV) were synthesized from the corresponding perrhenates(VI1) in accordance to a method employed by for the preparation of potassium Briscoe, et d.,* hexaiodorhenate(1V) and identified by the analysis of iodine by Volhard's method. Anal. Calcd for (NH4)zReIe: I, 77.4. Found: I, 76.2. Calcd for RbpReI6: I, 68.1. Found: I, 66.3. Calcd for CSZReI6: I, 62.7. Found: I, 61.0. For the rubidium and cesium complexes thus prepared, the resonance signals were barely detectable or undetectable. Therefore, each sample was sealed in a glass tube, heated a t 80-100" for 3-5 hr, and annealed. The signal-to-noise ratio ( S I N ) increased to 2-3 for chlorine and 2-5 for bromine and iodine.
Results All of the hexachloro complexes yielded a single absorption of weak intensity in the whole temperature range studied. The observed resonance frequencies are unequivocally attributable to W I for the following reasons. First, if it is assumed that they were due to 37Cl,those of the more abundant isotope should be observed in a frequency region of high sensitivity of the spectrometer used. This result would have been in contradiction with our observations. Second, the observed frequencies are close to the resonance frequency, 13.9 Mc, of 36Clin potassium hexachlororhenate(IV),l for which the frequencies of both isotopes have been observed. It is quite reasonable to suppose that, in the present study, the resonance frequencies of 37Cl escaped detection because they fell in a frequency region in which the sensitivity of the spectrometer used was relatively low. Another reasonable supposition is that the natural abundance of the 37Clisotope is smaller (about one-third) than that of 35Cl,which showed only a weak signal anyway ( S I N = 2-3).
2927
Each of the three hexabromo complexes showed two weak absorptions (SIN = 3-5). The frequency ratio, 1.197, of the two lines agreed excellently with the known isotopic frequency ratio of bromine. Rubidium and cesium hexaiodorhenates(1V) gave rise to two absorptions of frequency ratio equal to 1 : 2 at room and Dry Ice temperatures as expected for v1 and v2 of 1271. At liquid nitrogen temperature, single lines were observed for both v1 and v2 of the cesium salt, whereas the rubidium salt showed two closely spaced v1 lines of a very weak intensity (SIN < 1.5). It is very likely that the corresponding vZ also is a doublet. However, owing to the low sensitivity of the spectrometer in this frequency range, only a single line was located accurately. Surely, a phase transition takes place a t some temperature between Dry Ice and liquid nitrogen temperatures. The temperature dependence of the resonance frequency of ammonium hexaiodorhenate(1V) is fairly complicated, as shown in Figure 1. At room temperature, two pairs of lines were observed, with a frequency ratio of about 1:2. These lines are attributable to vl and v2, respectively, indicating the existence of two kinds of crystallographically nonequivalent iodine atoms in crystals. The high-frequency doublet component was about twice as intense as the low-frequency component. The frequencies of the doublet lines decreased with increasing temperature. The lines disappeared a t about 46" while a new single line of a stronger intensity and a lower frequency appeared at 44.5" for each of v1 and VZ. Above the transition point, the resonance frequency showed a positive temperature coefficient. Below room temperature, the doublet structure of v1 and v2 persisted down to about - 100". The low-frequency line of each doublet showed a positive temperature coefficient below about -50". At the temperature of liquid nitrogen, triplet lines were observed for both v1 and L ~ ,indicating the existence of three kinds of nonequivalent iodine atoms in the rhenate crystals. Therefore, it is concluded that a phase transition takes place between Dry Ice and liquid nitrogen temperatures. The resonance frequencies of 36Cl, 79Br, and lZ7I, observed a t various temperatures, are listed in Table I. The frequencies of a less abundant isotope, *IBr, are omitted, because they give the correct isotope frequency ratio. The foregoing results indicate that all halogen atoms are equivalent to one another in a crystal of (3) C. L. Rulfs and R. J. Meyer, J . Am. Chem. Soc., 7 7 , 4505 (1955). (4) H.V. A. Briscoe, P. L. Robinson, and A. J. Rudge, J . Chem. SOC.,3218 (1931).
Volume 70, Number 9 September 1966
R. IKEDA, A. SASANE, D. NAKAMURA, AND M. KUBO
2928
Table I: Pure Quadrupole Resonance Frequencies of W1, 7*Br, and 1171 in Some Hexahalorhenates(1V) Temp, OC
Compd
(NH4hReCle
26
RbzReCle
20
Freq, Mc/sec
14.086 f 0.001 14.106f0.001 14.125 f 0.001 14.277f0.001 14.264 f 0.001 14.248 f 0,001 14.611 f 0.001 14.608 f 0,001 14.604f0.001 114.02 f 0 . 0 5 113.98 f 0 . 0 5 113.95 f O . 0 5 116.09 f O . 0 5 115.95 f O . 0 5 115.73 f O . 0 5 118.87 f 0 . 0 5 118.76 f 0 . 0 5 118.41 f 0 . 0 5
-72 Liquid NZ
-66
Liquid NZ Cs2ReCls
18 -66
Liquid N2 (NHdzReBre
27 -71
Liquid NZ Rb~ReBrs
27
- 75
Liquid N2 CszReBrs
26
-73
Liquid NZ Temp, Compd
(NHdzReIs Temp.,
'C
these hexahalo complexes a t room temperature, except for ammonium hexaiodorhenate(1V). This is in agreement with the results of X-ray analysis which show that some of these complexes form cubic crystals of the potassium hexachloroplatinate(1V) type (Fm3m) at room t e m p e r a t ~ r e . ~ ~For ' complexes with no X-ray crystallographic data as yet, Norelco X-ray powder patterns were taken and analyzed to determine the lattice constants. The results are shown in Table 11. The X-ray powder patterns of ammonium hexaiodorhenate(1V) taken at room temperature could not be interpreted as due to a cubic or tetragonal structure. However, those taken a t about 80" indicated that the crystal had the potassium hexachloroplatinate(1V) structure. Accordingly, it is concluded that this compound undergoes a phase transition at 45" from a structure of a lower than tetragonal symmetry to the cubic structure. From the observed frequencies, v1 and v2, of lZ7I in the hexaiodo complexes, the quadrupole coupling constants and the asymmetry parameters were evaluated using Livingston and Zeldes' tables as shown in Table 111. When a multiplet structure appeared as in ammonium hexaiodorhenate(IV), the theoretical The Journal of Physiccrl Chemistry
105 56 18
Figure 1. Temperature dependence of pure quadrupole VI resonance frequencies of 1271 in ammonium hexaiodorhenate (IV).
-67 Liquid NZ RbtReI6
,---Freq,
OC
28
- 73
Mc/secY1
Y2
118.96f0.08
237.7 f 0 . 2 237.3 f O . 3 240.68f0.10 239.54f0.10 241.22 f O . 1 0 239.44f0.10 242.03 f 0.10 241.03 f 0.10 239.42f0.10 244.0 f 0 . 2 243.7 f 0 . 2
119.69 f 0.05 121.20f 0.05 119.74f0.05 122.62 f 0.05 122.10f0.05 119.73 f 0 . 0 5 122.08f 0.05
i
Liquid NZ Cs2ReIa
18 - 74
Liquid Nz
244.8 f 0 . 2 124.91 i 0 . 0 5 124.73 i 0 . 0 5 124.49 i 0.05
249.83 f 0 . 1 0 249.49 f.0.10 2 4 9 . 0 1 f 0.10
requirement, 2v1 1 v2, makes the correspondence between V I and v2 unambiguous, except for the two highfrequency multiplet components of this compound a t liquid nitrogen temperature. Here, it was assumed that the v1 and v2 multiplet components of the highest frequency correspond to each other. The asymmetry parameter is practically zero for complexes of cubic symmetry. (5) B.Aminoff, 2.Kriat., A94, 246 (1936). (6) D. H. Templeton and C. H. Dauben, J. Am. Chem. Soc., 7 3 , 4492 (1961). (7) K.Schwochau, Z.Nuturforsch., 19% 1237 (1964). (8) R. Livingston and H . Zeld!s, "Table of Eigenvalues for Pure Quadrupole Spectra, Spin 5/2, ONRL Report 1913, Oak Ridge National Laboratory, Oak Ridge, Tenn., 1955.
PUREQUADRUPOLE RESONANCE OF HALOGENS IN HEXAHALORHENATES (IV)
Table IF' : Nqr Frequencies of Hexahalorhenates(1V) and Hexahalophtinates(1V) a t 20"
Table 1l : Lattice Constants a of &Re&-%e Crystals a t Room Temperature Compd
2929
a, A
Ref
9.861 =!= 0.003 9.843 =!= 0.002 9.922 f 0.003 9.977 f 0.002 9.950 f 0.007 10.243 f 0.007 10.445 f 0.005 10.387 f 0.002 10.381 f 0.003 10.441f0.003 10.490 f 0.002 10.700 f 0.005 11.27 f O . 0 1 (at 4 0 " ) 11.320 f 0.002 11.409 f 0.005
5
V,
V,
K2ReCl6 (NH&ReCls Rb~ReCl6 CszReCle KzReBr6 (NHdzReBrs RbzReBrs Cs~ReBr6 (NHdzReIe RbzRe16 CszReIs
7
7
6 7
Compd
Mc/sec
Compd
Mc/sec
KzReC16 (NH&ReCls RbtReCls CszReCls
13.887 14.087 14.277 14.611
KzReBre (NH&ReBrs RbzReBre Cs~ReBr6
112.70 114.02 116.08 118.86
KzPtCls (NH4)zPtCle RbzPtCle CsZPtCl6
25.816 26.071 26.29 26.60
KZPtBre (NH4)PPtBre RbzPtBrs CszPtBr6
200.21 202.54 204.38 207.20
7
7
where e& is the quadrupole moment of a halogen cm2, Q 7 9 ~ r= 0.33 nucleus ( Q W I = -0.07894 X X cm2).10s11Now, the field gradient is given by q=
Table 111: Quadrupole Coupling Constants and Asymmetry Parameters of 12'1 in Hexaiodorhenates(1V) Temp, QC
Compd
(NH&ReIe
105 56 18
-67
RbnReIe
28
-73
Liquid NP CSzReI6
18 - 74
Liquid NZ a
EQQ,
Mc/sec
9
792.0 f 1 . 0 791.0 f 1 . 0 802.5 f 0 . 3 1797.9 f 0 . 4 804.6f0.2 798.2 f 0 . 3 811.0f2.0 804.0 f 1 . 0 (796.9 f 0 . 8 813.4 z!= 0 . 5 812.4 f 0 . 6 810.G f 6.0" 832.7 f 0 . 5 831.6 f 0 . 5 829.4 f 0 . 5
0.0 0.0 0.043 =!= 0.007 0.0 0.062f0.004 0.012 f 0.012 0.101f0.003 0,101 f 0.003 0.012 f 0.012 0.0 0.0 0.036 f 0.040 0.0 0.0
Calculated from the mean value of two
YI
0.0
frequencies.
Discussion E$ect of Catiuns on Nqr Frequencies. The resonance frequencies of hexachloro- and hexabromorhenates(IV) increase with increasing ionic radius of cations in the order of potassium, ammonium, rubidium, and cesium (see Table IV). This was already found for hexachloro- and hexabromoplatinates(1V) From the observed resonance frequency v, one can calculate the field gradient q a t the resonant halogen or 7gBr)by nucleus (36Cl
qti
+
qext
(2)
where q t i is the field gradient in an isolated or free complex ion and qext includes all effects due to external ions in a crystal. Since the sign of eQq cannot be determined by nqr spectroscopy, the observed values of q are absolute values. The field gradient qti originating from charges within a free complex ion, except for the resonant halogen nucleus, is positive. This i,s because the halogen atom has partial vacancy in the pp orbital whereas both pz and pv orbitals are filled. It is expected theoretically that the absolute value of qext due to external ions decreases with increasing lattice constant. The aforementioned fact that the observed resonance frequencies increase with increasing lattice constant leads to a conclusion that q e x t is negative and its absolute value is smaller than qti. In principle, one would be able to calculate qfi theoretically if the wave function were known for an isolated complex ion. Since it is hopeless a t the present stage to perform such a calculation, let the difference Aq be taken between complexes having the same kind of complex anions. Then, one has Aq =
(3)
&ext
where Aq is a quantity capable of being determined experimentally. One may presume furt~herthat qext is the sum of two terms.
I
qext
Here,
qdir
=
qdir
+
qind
(4)
stands for the field gradient due to the direct ~
~~
~~~
(9) D. Nakamura and M. Kubo, J . Phys. Chem., 68, 2986 (1964). (10) V. Jaccarino and J. G. King, Phys. Rev., 83, 471 (1951). (11) J. G. King and V. Jaccarino, ibid., 94, 1610 (1954).
Volume 70, Number 9 September 1966
R. IKEDA, A. SASANE, D. NAKAMURA, AND M. KUBO
2930
electrostatic effect of external ions, while qind takes into account the indirect effect, i.e., the distortion or polarization of the complex anion in question caused by external ions. The first term qdir is calculated below for various hexahalorhenates(1V) having alkali metals as cations in order to compare Aqdir with the observed Aq. (We have used Poi and Qni given by Qoi = q t i Qind and q n i = qdir in preceding papers.1~~) The z axis was chosen along an Re-X bond involving the resonant halogen atom X. For a potassium hexachloroplatinate(1V)-type crystal, the principal axes of the field gradient tensor qdir coincide with those of the field gradient originating from charges within the complex anion in question, except for the resonant halogen nucleus. The asymmetry parameter is zero as was confirmed experimentally. Each of the central metal atoms and halogen atoms in complex anions MXS2-, as well as cations R+,was assumed to bear a point charge p. The net charges calculated from the extent of ionic character' of the metal-halogen bonds in these complex anions were used for P M and px, whereas p~ is equal to + e . With this point-charge model, qdz? can be calculated as
+
3212
qdir
=
Ci Pt
is one or two orders of magnitude smaller than In other words, the direct electrostatic effect
Table V: Field Gradient (Idir Calculated for Some Hexahalorhenates(1V)and Hexahaloplatinates(IV)
r16
(5)
10%dir, e.4-8
lo'qdir,
Compd
e A-*
KzReCla - 7.79 RbzReCle - 7 . 5 0 CszReCle -6 . 6 4
Compd
KzReBra Rb~ReBrs CszReBrs
- 6.46 -6.18 - 5.69
10'qdirs
Compd
e A-a
&PtCIa -7.95 RbzPtCle -7.45 CsZPtCl6 6.66
-
of external charges is too small to account for the observed field gradient difference. One is led to conclude that the charge distribution within the complex anion is altered to a certain extent by external ions and that the indirect effect is significant on the field gradient a t a resonant halogen nucleus. Table VI: Contributions of Various Effects to the Field Gradient Difference
- rf2
where zt and ri are, respectively, the z coordinate and the distarice of the ith point charge p i from the origin at the given nucleus with respect to the given z axis, and the sum is over all external ions in the lattice. The lattice constants are tabulated in Table 11. The R e C I and Re-Br bond distances have been determined by X-ray analysis as 2.37 and 2.50 A in potassium he~achlororhenate(1V)~ and potassium hexabromorhenate(IV),6 respectively. It was assumed that these distances are independent of the kind of cations. The calculations of qdir were performed by means of an NEAC digital computer. The summation was extended over all external ions contained in a sphere having its center at the resonant nucleus, the radius being 36, 37, and 38 A for potassium, rubidium, and cesium hexachlororhenates(1V) and 38, 39, and 40 A for potassium, rubidium, and cesium hexabromorhenates(IV), respectively. Similar calculations have also been made for hexachloroplatinates(1V). The results are shown in Table V. Unfortunately, exact X-ray crystal data are not available for the Pt-Br distance of a hexabromoDlatinate(1V) ion. From the Observed frequencies shown in 1' ' by use Of eq '7 &dir was ObAq was v* tained from the Of qdir shown in From these, Aqind can be evaluated using eq 3 and 4. The results are shown in Table VI. It is evident that The Journal of Physical Chemistry
Ahqdir
Aq.
-Field Anion
Cation
ReCh Rb-K
PtC16
ReBra
gradient differences X 103, e A-8-
4ext
{cs-~
28.4 52.7 35 57 58.8 107.2
AQdir
Aqind
0.29 1.15 0.50 1.29 0.28 0.77
28.1 51.5 34.5 55.7 58.5 106.4
Aqextcalod
16.7 66.2 28.8 74.3 28.0 77.0
Sternheimer and other^'^-'^ have shown that, when a spherically symmetric ion is placed in an inhomogeneous electric field, the charge distribution is altered by the field in such a way that an additional field gradient, due to the polarization, acts 011 the nucleus. The effect is approximated quantitatively by introducing Sternheimer's antishielding constant y. qext =
(1 -
?')qdir
(6)
The value of the antishielding constant y is -56.6 for a chlorine ion and -99.0 for a bromine ion as evaluated by Sternheimer and Foley15 and by Wikner and Das,I6 respectively. In other words, the direct electrostatic effect is amplified by an electronic cloud (12) R. Sternheimer, Phys. Rev., 80, 102 (1950). (13) G. Burns and E. G. Wikner, ibid., 121, 155 (1961). (14) R. Bersohn, J. Chem. Phys., 29, 326 (1958). (15) R. Sternheimer and H. 31.FoIey, P h p . Rev., 102, 731 (1956). (16) E.G.Wikner and T.p. Das, ibid., 109, 360 (1958).
PUREQUADRUPOLE RESONANCE OF HALOGENS IN HEXAHALORHENATES(IV)
surrounding the resonant nucleus. Although a halogen nucleus in a hexahalo complex anion has an electronic environment different from that of a simple ion, the amplification of the field gradient must surely be present in complex ions also. Therefore, in order to estimate roughly the extent of field gradient amplification as a check, Aq,,t was calculated from Aqdir by use of eq 6 with y values for simple ions. The results are shown in the last column of Table VI. Comparison of the calculated Aqe.t with the observed Aqext indicates that Sternheimer's antishielding effect accounts for the large indirect effect, at least with regard to the sign and the order of magnitude of qind relative to qdir. Temperature Coeficients of Nqr Frequencies. The temperature dependence of the resonance frequencies of hexachlororhenates(1V) is linear in the temperature range in which the complexes form cubic crystals. The observed temperature coefficients are shown in Table VII. As was anticipated, they are positive regardless of the kind of cations except for ammonium hexachlororhenate(1V). This compound shows a negative temperature coefficient, the absolute value being small compared with those of diamagnetic complexes having a similar structure. We have already explained' the positive temperature coefficients of quadrupole resonance frequencies of hexahalorhenates(1V) and
2931
hexahalotungstates(1V) in terms of the partial dr-pr bond character of the metal-ligand bonds. In view of this theoretical conclusion, it is rather strange bhat a negative temperature coefficient was found for the Table VII: Temperature Coefficient (l/v)dv/dT of Quadrupole Resonance Frequencies of Halogens in Rz[ReX6] Crystals at Room Temperature (l/v)du/dT
x
106
9.4
- 13
10 3.8 22 4.7 7.0 5.2 22 (50-140') 11
15
single exception. Possibly, hydrogen bonding or an electrostatic interation of some sort between hydrogen in ammonium ions and chlorine in the complex anions is responsible for the exceptional behavior of ammonium hexachlororhenate(1V).
