Jay S.Merriam and Jayarama R. Perumareddi
142
(IO)B. Grabe, "Almquist and Wiksells Boktryckeri AB," Uppsala, 1960. (11)J. Fritzsche, J. Prakt. Chem., 73,288 (1958). (12)F. Geiss and S. Sandroni, Rapp. Euratom, Eur, 87 (1962). (13)P. D. Eley and H. Inokuchi, "Proceedings of the Third Biennial Conference on Carbon," Pergamon Press, New York, N.Y., 1959. (14)S. D. Ross and I. Kuntz, J. Amer. Chem. SOC., 76, 3000 (1954). (15) J. Higuchi and R. No, Theor. Chim. Acta, 22, 61 (1971). (16)R. S.Mulliken and W. B. Person, "Molecular Complexes," Wiley, New York, N.Y., 1969. (17)M. J. S. Dewar and A. R. Lepley, J. Amer. Chem. SOC., 83, 4560 (1961). (18) R. L. Flurry, Jr., J. Phys. Chem., 6S, 1927 (1965). (19)J. N. Murrell, M. Randic, and D. R. Williams, Proc. Roy SOC., Ser. A, 284, 1865 (1965). (20) D. B. Chesnut and R. W. Moseley, Theor. Chim. Acta, 13, 230 (1969). (21)0.B. Nagy and J. 8. Nagy, ind. Chim. Be@., 36, 829 (1971). (22)J. L. Lippert, M. W. Hanna, and P. J. Trotter, J. Amer. Chem. SOC., 91,
4035 (1969). (23)W. C. Herndon and J. Feuer, J. Amer. Chem. Soc., SO, 5914 (1968). (24)H. Tsuchiya, F. Marumo, and Y. Saito, Acta Crystalogr., Sect. 19, 29, 659 (1973). (25)J. C. A. Boeyerns and F. H.Herbstein, J. Phys. Chem., 6S, 2153 (1965). (26)I. Ikemoto, K. Chlkaishi, K. Yakushi, and H. Kuroda, Acta Crystalogr., Sect. B, 28, 3503 (1972). (27)Z.Yoshida and T. Kobayashi, Theor. Chim. Acta, 23,67(1971). (28)D. B. Chesnut and P. E. S. Wormer, Theor. Chim. Acta, 20, 250 (1971). (29)P. Markov, C. R. Acad. Bulg. Sci., 22, 419 (1969). (30) B. Nelander, Theor. Chim. Acta, 25, 382 (1972). (31)M. J. S. Dewar and C. C. Thompson, Tetrahedron Suppl., No. 7, 97 (1966). (32)R. G. Jesaitis and A. Streitwieser, Jr., Theor. Chim. Acta, 17, 165 (1970). (33)R. S.Mulliken, J. Chem. Phys., 61, 20 (1964). (34)R. S.Mulliken, J. Amer. Chem. Soc.. 74, 811 (1952).
Polarized Electronic Spectra and Electronic Energy Levels of Some Tetragonal Nickel(l1) Complexes',* Jay S. Merriam and Jayarama R. Perumareddi" Department of Chemistry, Fiorida Atlantic University, Boca Raton, Florida 33432 (Received April 11, 7974)
Single crystal electronic spectra of quadrate nickel(I1) complexes, [Ni(py)cBrz], [Ni(py)&12], and [Ni(py)4(H20)2]12,where py is pyridine, and [Ni(im)4(H20)2]Br2,where im is imidazole, have been measured with polarized light a t liquid N2 temperature. The tetragonally split components of the first and second spin-allowed cubic bands in the pyridine complexes show definite polarization characteristics and are assigned on the basis of a comparison of the observed polarization pattern with that predicted for D4h vibronic intensity mechanism and the knowledge that the lower energy component of the first cubic band is 3E, in tetragonal complexes when the substituting axial ligands are of weaker field than the equatorial ligands of the parent octahedral system. No distinct polarization of the bands was observed in the spectrum of the tetraimidazole complex, and thus the quadrate components of the second cubic band were assigned assuming the same order of levels as in the corresponding tetrapyridine system. Only one component of the highest energy spin-allowed cubic band has been uncovered at -27 kK in all the systems. The assignment of this band and the spin-forbidden bands is based on fitting the observed band maxima with the calculated transition energies using d8 quadrate energy levels without and with spin-orbit perturbation and full configuration interaction. The importance of full configuration interaction has been underscored in arriving at the assignments by energy level fitting. It has been shown further that the differences in the bonding nature of ligands in the quadrate complexes in general can be understood in terms of ligand field parameters without recourse to the other kinds of parameters.
Introduction Although it is necessary to make use of complete crystal structure data for a definitive interpretation of assignments of the observed polarized bands in the polarized electronic spectra of a single crystal, it is still possible to obtain meaningful spectral data by measuring the polarized spectra along the extinction directions on a well-defined face of the single crystal. We use all accessible well-defined faces of the crystal for this purpose and only when we observe distinct polarized bands, will we be able to verify the predicted polarization pattern for a certain intensity mechanism and make assignments. All the polarized spectral data available on the quadrate chromium(II1) complexes, for instance, have been obtained by this p r ~ c e d u r e We .~ have obtained such polarized spectral data on four quadrate nickel(I1) systems. The assignments of the observed The Journal of Physical Chemistry, Vol. 79,No. 2, 1975
spectral bands and the derivation of electronic energy levels of these systems form the subject of this report. The complexes studied are [Ni(py)4Brz], [Ni(py)&lz], [Ni(py)4(H20)2]12,and [Ni(im)dHzO)~]Br~, all trans disubstituted derivative^.^^^ The spectra of dibromo- and dichlorotetrapyridine systems have been studied previously in the mull form6 and in the diffuse reflectance form.7 The diaquotetrapyridine system had been characterizeds although no spectral data had been reported. The [Ni(im)4(HzO)z]Brp system is new. We have synthesized it in this work and characterized it by elemental analysis and ascertained the trans structure from its electronic spectrum. Experimental Techniques Preparation of Complexes and Growth of Single Crystals. [Ni(py)4Brz] and [Ni(~y)~C12] were prepared by the
Polarized Electronic Spectra of Tetragonal Ni(llI Complexes
method of Rowley and Drago.6 The complexes were bluegreen and light blue in color, respectively. Since the unpo larized spectra of the crystals were identical with the mull spectra (with the exception of appearance of another spinforbidden band at high energy), no elemental analyses were performed on these systems. Single crystals of both complexes were grown by dissolving the solids in a 50-50 mixture of ethanol and pyridine and allowing the solutions to evaporate very slowly. The evaporation took place over a period of 3 to 6 weeks in a vacuum desiccator under normal house vacuum. Even after this length of time, the single crystals were small (diameter, 2-3 mm). The crystals of [Ni(py)4Br2] were almost green and the [Ni(py)&l2] crystals were light blue in color. [Ni(py)4(H20)2]Iz was prepared from the yellow complex [Ni(py)&] which was made by the same method used in the case of dichloro and dibromo complexes. After several weeks of slow evaporation of ethanol-pyridine solution of [Ni(py)&], the solution was removed from the vacuum desiccator and allowed to evaporate in air. After several days, the solution had slowly aquated and dark blue crystals of [Ni(py)4(H20)& were formed. The [Ni(im)4(HzO)z]Brz complex was prepared from [Ni(irn)dBrz] complex which was made by the method described for the corresponding pyridine complex. The [Ni(im)lBrz] was dissolved in isopropyl alcohol and allowed to evaporate in air. After two days, blue, single crystals formed. An elemental analysis of these crystals gave the following results. Calcd for [Ni(im)4(HzO)2]Brz: C, 27.35; N, 21.27; H, 3.80; Br, 30.35. Found: C, 27.89; N, 23.17; H, 3.63; Br, 30.05. (The CHN analysis was performed by PAR Alexander Laboratories in South Daytona, Fla, and the Br was determined gravimetrically as AgBr.) Spectral Measurements. All spectra were obtained on a Cary 14 spectrophotometer. The crystals were mounted on a cold-fingered dewar3 and spectra taken a t liquid N2 temperature. A t this temperature, the bands are better defined than at room temperature where rapid decomposition occurs. The crystals, generally of 1 mm thickness, were mounted over an aperture 0.040 or 0.065 in. in diameter. The exact thickness and the density of the crystals were not determined. The extinction directions of the mounted crystal were determined using a polarizing microscope. All crystals showed extinctions at 90" under polarizing microscope. The shapes of the crystals and the directions of the observed extinctions are shown in Figures 1 and 2. The light beam in the Cary 14 was polarized to coincide with the observed extinction directions by using a Glan-Taylor polarizing prism inserted in the sample beam of the instrument. Further details can be found in ref 3.
Results and Discussion
Intensity Mechanism and Polarization Selection Rules. The polarized spectra of tetrapyridine systems measured along the directions shown in Figures 1 and 2 are displayed in Figures 3-6. The directions 21, 2 2 and Y1, Y2 labeled on these diagrams are arbitrary and are not meant to be taken as equivalent to molecular z (tetragonal) or y axis. No distinct polarization pattern was uncovered in the polarized spectra of the diaquotetraimidazole complex, hence only the unpolarized spectrum is given for this system in Figure 7. The spectra of each compound had been reproduced by making the measurements on different crystals of
143
Figure 1. Crystal hablt and the extinction directions of trans-[Ni(pykBr2] and frans-[Ni(py)4(H20)2]l2 single crystals.
Figure 2. Crystal habit and the extinction directions of trans-[Ni(py)&12] and trans- [Ni(im)4(H20)2]Br2 single crystals.
[N I (PY)4 Br2 1 POLARIZED ALONG
2,
_ _ _ _ _ _ _ _ _ _ P O L A R I Z E D ALONG
Zz
14-
v , kK
Figure 3. Polarized electronic spectra of trans- [Ni(py)&r2] at liquid N2 temperature.
one preparation and also on crystals grown from a second preparation. The theory of electronic energy levels of d8 configuration in quadrate ligand fields had been described elsewhereg and will not be repeated here. The symmetry of all of the complexes studied in this report is D4h. Assuming that the transitions in these systems are electric dipole in origin, the polarization selection rules for the vibronic intensity mechanism are given in Table I. In the limit of zero spin-orbit perturbation, the only spin-allowed transitions allowed in both perpendicular (x,y ) and parallel ( 2 )polarizations are The Journal of Physical Chemistry, Vol. 79, No. 2, 1975
144
Jay S.Merriam and Jayarama R. Perumareddi
241
TABLE I: Vibronic Selection Rules for d8 Electronic Configuration in D4h Symmetry
~NI(PY),(H,O)~I l2 .______POLARIZED
ALONG 2 ,
POLARIZED ALONG Z I
2 0
Figure 6. Polarized electronic spectra of trans- [N i ( ~ y ) ~ ( H ~ I20at) ~ ] liquid N2 temperature.
20
-
[ N l ( ~ ~ l e CIl z
UNPOLARIZED SPECTRUM
0 E .
POLARIZED ALONG 2 ,
l
_ _ _ _ _ _ _ _ _ _ P O L A R I Z E D ALONG 22
16-
15
20 Y,
kK
25
Figure 7. Unpolarized electronic spectrum (im)4(H20)2]Br2 at liquid N2 temperature.
2).
[Nlipy),CIzl
20
POLARIZED ALONG Y I I
l
,
16
%
_____._..._ POLARIZED ALONG Y2
\
I
12 O D 0 8
0 4
00
, 1
IO
1
1
15
1
20
1
1
Y ,
25
1
~
30
'
'
35
1
kK
Figure 5. Polarized electronic spectra of trans- [Ni(py)&12] at liquid N2 temperature measured on the Y plane of the crystal (see Figure 2).
-
the three 3B1g 3Egtransitions. The other three spin-allowed transitions 3B1, 3B2g,23A2g,are allowed in the x, y polarization only. Thus we expect all six tetragonal components to appear in the x, y polarization and only the three components in the z polarization. The vibronic selection rules become somewhat complicated and not as clear cut -+
The Journal of Physical Chemistry, Vol. 79, No. 2, 1975
35
30
of
trans- [Ni-
when spin-orbit perturbation is included. The complication arises due to the fact that the ground state 3B1, yields two spin-orbital states, r4 and I'5, and in order to be able to use the selection rules, it is necessary to know which of these is the ground state in these systems. If r5 is the ground state, transition to every excited state is allowed in both polarizations resulting in no definitive polarization pattern. On the other hand with r4 as the ground state, only transitions to rz, I'd, and r 5 are allowed in both polarizations while the transitions to rl and r3 are allowed in the x, y polarization only. This means that although all the five spin-orbital states of 3Eg are now allowed in the x, y polarization, only three of these are allowed in the z polarization. Among the 3Bzgand 3Azgtransitions although the r5 spin-orbital state of each of these is allowed in both polarizations the other spin-orbital states, r3 of 3B2, and rl of 3A2g,are allowed in the x , y polarization only. Thus, with the I'd ground state, vibronic selection rules remain essentially the same as in the limit of zero spin-orbit perturbation with the exception that (1)the transitions to 3B2gand 3Azgmay not be completely wiped out in the z polarization and instead perhaps appear with reduced intensity and (2) the transition to 3E, may also be reduced in intensity in the z polarization although may not be to the same extent as the 3Bzgand SAzgtransitions. Since the bands are polarized in all the polarized spectra, we shall take r4 as the ground state in these systems. As we will see later, it turns out that r4 is the calculated ground state in every system studied
Polarized Electronic Spectra of Tetragonal N i ( I I ) Complexes here consistent with the set of parameters derived for each complex. The inference of polarizations then in our polarized spectra as being predominantly z or x, y was based on a comparison of the observed polarization pattern with the predicted as above and also on the observation that the lower energy tetragonal component of the first cubic band, 3T2,, is 3E, when the axial ligands are of weaker field than the equatorial ligands just as in the case of quadrate chromium(II1) complexes.3a Parent Octahedral Systems. An understanding of the electronic transitions in the spectra of parent octahedral systems aids in the interpretation of the observed bands in the spectra of their tetragonal derivatives. The solution absorption spectrum of [Ni(py)6](NO& in ethanol-pyridine solvent shows band maxima a t 9.7, 13.1, 16.0, and 26.3 kK. In addition, a sharp peak appears at 8.8 kK which had been attributed to a pyridine overtone by others6 and also by us. This overtone appears a t the same frequency in dichloroand dibromotetrapyridine complexes and at 8.9 kK in the spectrum of diaquotetrapyridine complex. The spectrum of pyridine itself shows overtone structure at 8.787 (very strong), 8.68 (strong), 11.494 (very weak), and 11.325 kK (very very weak). The band a t 13.1 kK is the spin-forbidden transition 3A2g lE, and the other three bands in increasing energy, respectively, are the transitions to 3T2g, 3Tlg1,and 3T1,2.It should be noted that the bands usually are displaced a few hundred wave numbers toward the higher energy side in a crystal spectrum as compared with the solution spectrum of the same complex. Our attempts to obtain a good reproducible single crystal spectrum of hexapyridine complex have not been successful. The crystal spectrum of [Ni(im)~](N03)2shows band maxima at 10.3, 13.09, 17.6, and 28.15 kK, the one a t 13.09 kK being the spin-forbidden transition and the other three successively are the 3T2g,3Tlg1, and 3T1g2transitions. An additional sharp peak a t 10.15 kK has been observed in this system which is probably a spin-orbit component of 3T2g transition rather than an overtone of imidazole because imidazole overtone appears a t 9.15 and 9.05 kK, respectively, in the spectra of diaquotetraimidazole complex and pure imidazole. The fitting of the observed data with the assigned transitions is given in Table I1 (see paragraph at end of text regarding miniprint material). The fitting procedure for octahedral nickel(I1) complexes is well known.1° Since the observed bands in all the systems studied are broad with no spin-orbit fine structure, we have used a constant f value of -550 cm-l (83% of the free-ion value)g for all the systems in fitting the levels with the inclusion of spin-orbit interaction. The fitting is such that the spread of the spinorbit components of a band envelops the breadth of the band maximum. It should be remembered while comparing the parameters for various systems that the parameters of the hexapyridine complex will be different for a crystal spectrum from those evaluated here for the solution spectrum. In particular the Dq value could be higher by a few hundred wave numbers. Fitting of the Observed Band Maxima i n the Quadrate Derivatives. The process of fitting the band maxima with the predicted transitions in the spectra of quadrate nickel(11) complexes is exactly same as that used in the case of quadrate chromium(II1) complexe~.~Jl The procedure is briefly as follows. The position of 3B2 is directly lODq including configuration interaction and the first estimate of Dt is obtained by fitting the 3E component of the first
-
145
cubic band. Both Dt and Ds (or K = Ds/Dt ) fix the splitting of the second cubic band although the actual positions of the two quadrate components is decided upon by the B value. Once the first estimates of Ds and B are obtained, then the Dt, Ds, and B are varied to take into account the configuration i n t e r a ~ t i o nThus, .~ with the four parameters, Dq, Dt, Ds, and B, the four components of the first two cubic bands can be fitted exactly. These parameters then predict the positions of the two components of the third cubic band. The parameters are in turn used along with a value of C to fit the lowest energy singlets, lA1, and lBlg, the quadrate components of the intraconfigurational cubic singlet, lE,. The higher energy spin-forbidden transitions are predicted with derived values of the parameters and compared with those uncovered. As pointed above, we have used a canstant value of the spin-orbit coupling parameter (f = -550 cm-l) for all the systems to calculate the transition energies of spin-orbital levels. trans- [Ni (py)4Br2].Figure 3 shows the polarized spectra of dibromo system. It is obvious that Z1 and 2 2 directions correspond, respectively, to predominantly the (x,y ) and z polarizations although it is not clear as to why the intensity of the lowest energy 3E is actually greater in the Zz polarization. This feature is common to all the three pyridine systems studied in this report. The bands at 8.432 and 11.547 kK are certainly the 3E and 3Bz components of the first cubic band, respectively. Since there is a greater reduction in intensity in the 14.104-kK band than that in the 16.367-kK band in the z- polarized spectrum, these are assigned, respectively, as the 3A2 and 3E components of the second cubic band. The 25.907-kK band then is assigned by calculation to be the 3E component of the third cubic band. The spectra also show low-intensity transitions, a sharp doublet at 12.315 and 12.453 kK (although the resolution in the parallel spectrum is not as clear cut, with 12.453-kK maximum having disappeared), and somewhat broad maxima at 19.305 and 20.964 kK. It should be noted that since all the spin-forbidden transitions appear usually as shoulders on the spin-allowed bands, the intensity changes of the spin-forbidden bands from one polarization to the other are not clearly discernible. The sharp doublet, which appears in all the pyridine systems, is split by 140 cm-1 in the dibromo spectrum, whereas the calculated splitting is 1655 cm-l including spin-orbit interaction and 1382 cm-l without spin-orbit interaction. Considering these bands being sharp and there can be no uncertainty in the estimation of their maxima, this is a large disagreement. Thus, it is not possible to assign the double peaked maxima to the quadrate components of lE,. Hence we assign only one of the observed components, that being the one that seems to decrease in intensity in the z polarization, the 12.453-kK maximum. This band has been assigned as the lB1, transition so that the calculated position of the lAlg transition which is always lower in energy than the lB1, falls in the 3B2genergy region and is not resolved. The other band is left unassigned at present. The alternatives for the assignment of this band are as follows. (1)It may be another pyridine overtone. (2) It may be a spin-orbit component of 'B2,. In this case it should be noted that although the spinorbit splitting of %& is only 300 cm-l the 11.547-kK estimation of the 3Bzg maximum may not be exact because of the broad nature of the band. (3) It may be a vibrational component of lB1,. (4) Finally, the six parameter theory we are using here may not be adequate. Further experimental and theoretical studies are needed to resolve this problem. The Journai of Physical Chemistry, Voi. 79, No. 2, 1975
146
The C value obtained by fitting the lB1, level predicts the two higher energy spin-forbidden bands as the 1E,(1T2g) and lAlg(lAlg)transitions. The assignments and the calculated transition energies for this system are summarized in Table 111. trans- [Ni( ~ y ) ~ C 1 2The ] . polarized spectra measured along the extinction directions on two different planes are shown in Figures 4 and 5 . The polarization pattern is clearly definitive in the spectra of the Y plane, Y2 being predominantly the x, y polarization. The 8.993- and 11.682-kK bands definitely are the 3Eg and 3Bzg components, respectively, of the 3Tzgcubic band. Since the 15.267-kK maximum is reduced in intensity in the Y1 polarization more than that of the 16.807-kK band, these peaks are assigned, respectively, the 3A2g and 3E, components of the second cubic band, 3Tlg1.The parameters evaluated by the fitting of these four bands predict the positions of the 3A2gand 3E, components of the third cubic band, 3T1g2,at 25.8 and The Journal of Physical Chemistry, Vol. 79, No. 2 , 1975
Jay S.Merriarn and Jayararna R. Perurnareddi
26.7 kK, respectively. Although no band maximum could be resolved at this energy region in the polarized spectra of this system because of large intensity of absorption, a band a t 27.174 kK was uncovered in the unpolarized spectrum of a different (thin) crystal which we assign to the 3E, component. The low-intensity transitions appear at 12.642 and 12.804 kK as a sharp doublet and a t 21.834 and 23.923 kK as a broad maximum and a shoulder on increasing absorption, respectively. The 12.642-kK component of the doublet peak is assigned as the 1B1, transition leaving the other component unassigned as before. Such a fitting gives rise to the assignment that the 21.834-kK band is the lAIg(1Alg) transition and the 23.923-kK band is the IBzg(lTzg) transition. The calculated position of the lEg(1Tzg) transition comes at 21.0 kM, within 800 cm-l from the observed maximum for the lAlg(lAlg) transition so that it is possible that this maximum contains also the
147
Polarized Electronic Spectra of Tetragonal Ni(l I ) Complexes
lEg(ITzg)transition. The assignments and a comparison of the observed maxima with the calculated energies for the dichloro system are summarized in Table IV. trans- [Ni(py)4(Hz0)2]12.The polarized spectra of the diaquo system are displayed in Figure 6. The 21 direction is obviously the x, y predominant polarization. The 9.75and 11.78-kK bands are the 3Eg and 3B2gcomponents of the first cubic band. The 15.76-kK band is actually a shoulder with an undefined maximum. However, this shoulder is almost eliminated in the 2 2 polarization so that it can be identified as the 3A2, component of the second cubic band which means that the clearly defined maximum a t 17.39 kK becomes the 3Eg component. Only one band has been uncovered a t 28.00 kK (because of steep rise in intensity of the absorption at this energy in the Z1 polarization, it is not shown in the figure) where the third band components are predicted to appear by an energy separation of about 600-800 cm-l. Thus, this barid has been assigned as the higher energy component, 3Eg,of the third cubic band. Once again a sharp doublet appears at 13.16 and 13.39 kK the lower energy peak disappearing in the z polarization. This peak is assigned as the lB1, by the same reasoning as in the dichloro and dibromo systems. Thus the 13.39-kK peak is unassigned. Only one spin-forbidden band is uncovered in the diaquo system a t higher energy at 22.1 kK which is within 280 cm-l from the average of the predicted maxima for the lE,(lT2,) and the lAIg(lAlg) transitions and hence is assigned as due to these two transitions as in the dichloro complex. The data for this system are tabulated in Table V. trans- [Ni( i m ) 4 ( H z 0 ) 2 ] B r z .The unpolarized spectrum of the tetraimidazolediaquo complex is shown in Figure 7 as the polarized spectra showed no differences in peak intensities perhaps due to unfavorable molecular orientation in the single crystals of this complex. The tetragonally split peaks are very distinct including the appearance of a spinforbidden shoulder a t 13.99 kK although not split as in the pyridine systems. The band assignments were made assuming the peaks follow the same order of splitting as in the pyridine complexes. It should be noted that the assignment of the first cubic band components, namely, that the 9.34 and 11.83 kK are the 3Eg and 3B2gtransitions, is definite. Since the Dq of the hexaimidazole complex is greater than that of the hexaaquo complex, D t is expected to be negative as in the pyridine systems, and hence the 3Egshould be placed lower in energy than the 3B2, component. It is only the assignment of the quadrate components of the second cubic band based on the pyridine spectra is tentative and should be verified. It should be pointed out that although it is not evident in the figure the experimental spectrum shows distinct splitting at 14.62 and 14.815 kK which fit nicely with the spin-orbit components of the SAzg transition of the second cubic band. An interesting feature of the spectrum of the tetraimidazolediaquo system is the appearance of a shoulder a t about 32.5 kK which has not been observed in any of the systems we have studied so far. Although this band can be construed as the second component of the third cubic band, the 28.3-kK peak being the other component, since the calculated splitting of the third band is only about 1000 cm-l, it is not possible to assign the 32.5-k~Kband as being the spin-allowed component. It may be argued that a reversal of the 3A2g,3Eg assignments of the second cubic band, resulting in Ds negative of Dt, could give rise to a large splitting of the third cubic band since the 3Eg-3Azg energy dif-
ference is given by (3Ds - 5Dt).gb In order to verify this reasoning, we have constructed an energy diagram (see Figure 8) in the limit of zero spin-orbit interaction varying K , keeping all other parameters constant. The configuration interaction is such that the splitting is less than 1900 cm-l even when K is -7, whereas the energy separation of the 28.3 kK and 32.5-kK maxima is 4200 cm-l. Hence we eliminate the possibility that it is a component of the third spinallowed cubic band. The only alternative left is that it is a high-energy spin-forbidden band. The C value obtained by fitting the 13.99-kK band as the IB1, transition predicts two spin-forbidden transitions, lEg(lT1,) a t 29.5 kK and lA$Eg) a t 35.6 kK and none at 32.5 kK. We tentatively assign the 32.5-kK band maximum as being these two transitions although the agreement is not good even considering that the 32.5-kK maximum is uncertain perhaps by about 1250 cm-l because of the broad nature of the shoulder. It should be noted that much better agreement can be obtained (lEg(lTig)a t 31.579 kK) by assigning the 13.99kK band as the lAlg(lEg) rather than as the lB1g(lEg) which will now be calculated to be positioned at 15.846 kK. (Actually there is considerable mixing of eigenvectors when the C parameter is altered to achieve this assignment. A band calculated to be at 13.979 kK has 39.9% r1(3A2g) + 43.4% rl(lA1,) and the other a t 15.278 kK has 41.9% rl(lA1,) + 34.4% while the r5 of 3A2gcalculated to be at 14.704 kK is 77.5% pure.) We do not favor this alternative, however, since such an assignment requires a C value of 5036 cm-l, much greater than the free-ion C value of 4060 cm-l. No other spin-forbidden bands have been uncovered in this system. We have summarized these assignments along with the calculated transition energies for the tetraimidazole system in Table VI. Analysis of the Parameters. The ligand field and the electron correlation parameters evaluated for all the nickel(11) complexes in this study are collected in Table VII. As pointed already the Dq for the octahedral hexapyridine system should be greater for a crystal spectrum than that given in the table which is from the solution spectrum. I t could be as much as 1030 cm-l, similar to the hexaimidazole system. The B and C values are all within the free-ion values which for Ni(I1) are 1042 and 4060 cm-l, respectivel ~No. other ~ definite trend of these parameters could be infered for the tetragonal complexes. Although the Dq in the parent octahedral systems is about 1030 cm-1, Dq in their tetragonal derivatives is almost constant a t 1180 cm-l, i.e., 150 cm-l higher. The Dq value is expected to be same in both the parent octahedral complex and its tetragonal derivatives provided no change takes place in the metal-ligand bonding in going from the octahedral complex to the same metal-ligand bonding in the quadrate complex. The increase in Dq in the quadrate systems implies that there is a change in the metal-ligand bonding and in particular the nickel-pyridine and nickel-imidazole bond distances in the quadrate systems are perhaps shorter than those in the cubic systems. The trend in D t for the tetrapyridine systems is as expected. Since the Dq of the octahedral hexabromo, hexachloro, and the hexaaquo increase in that order, dibromo has the highest Dt, followed by dichloro, and then diaquo. Using octahedral Dq values of bromo,12 chloro,12 and aquoLoaligands and assuming that these values do not change in the tetragonal complexes, the D t values for the dibromo-, dichloro-, and diaquotetrapyridine systems, respectively, are calculatedl3 as -295, -275, and -190 cm-I and for the diaquotetraimidaThe Journal of Physical Chemistry, Vol. 79,
No. 2, 1975
148
Jay S. Merriam and Jayarama R.. Perumareddi
TABLE VII: Electronic Spectral Parameters for Some Nickel(11) Complexes Complex
B, ern-'"
C,
ern-'*
Dq, cm-'
Dt, cm-'
Ds, cm-I
K
CIB
0 0 -342 -299 -221 -254
0 0 -535 -336 -384 -706
0 0 1.5643 1.1237 1.7376 2.7795
4.0417 3.3696 4.6335 3.7295 4.4962 5.2208
970 Ni(PY ),](NO,),C 840 3395 1030 920 3100 Ni(im)~] (NO,), 1171 N i (PYl4Br21 723 3350 1176 Ni(py )4CIz1 828 3088 1183 Ni (PY)4(H20)2112 7 84 3525 770 4020 1187 Ni (im)a(H20)&r2 a Bo = 1042 c m - l . * CO= 4060 cm-l. From solution spectrum.
.
1
6
k? - o I b
________-----
-+
Flgure 9. One-electron molecular energy levels of some tetragonal nickel(l1)complexes.
Flgure 8. Electronic energy levels of a quadrate nickel(l1)system a s , a function of K in the limit of zero spin-orbit interaction. Other parameters are those of the diaquotetraimidazole complex: Dq = 1187 cm-', Dt = -254 cm-l, B = 770 cm-', and C = 4020 cm-'. Only spin-triplets are shown. zole system -193 cm-l, all within 24-61 cm-l. Since the Dq value of the axial ligand in a tetragonal system could be different from the Dq of that ligand in its octahedral complex, as is the case with the equatorial pyridine ligand, such a discrepancy is expected. It is interesting to note that the observed Dt values are greater in all the systems implying that the metal-axial ligand bond distances are perhaps longer in the tetragonal systems than in the corresponding octahedral systems. The significance of the Ds parameter can be understood by calculating the one-electron molecular energy levels of the quadrate systems which are shown in Figure 9. The bl(drz-yz) being greater in energy than al(d,n) in all the systems implies that the equatorial ligands, Le., pyridine and imidazole, are more a antibonding than the aquo, chloro, and bromo ligands. The u antibonding trend among H20, C1-, and Br- is decreasing in that order and is the same trend found in the quadrate chromium(II1) complexes.3 Although the bz(d,,) level is lower in energy than the e(dyz,d,,) level in the dichloro and the dibromo complexes both are at about the same energy in the diaquo complex, which implies that both chloro and bromo ligands are more a antibonding than pyridine, while there is not much difference in the x antibonding nature of pyridine and water. In the case of tetraimidazole complex, however, since E'2 lies above e, the equatorial imidazole ligand is The Journal ot Physical Chemistry, Vol. 79, No. 2, 1975
more x antibonding than the axial H20. This result, of course, is tentative until the assignments of the second cubic band in the tetraimidazole system are verified. I t should be pointed out that the above conclusions in terms of the bonding nature of the ligands are arrived at by considering the one-electron energy level diagram without recourse to translating our ligand field parameters to the semiempirical molecular orbital parameters,14 60- and 67. It is not necessary to express the ligand field parameters in terms of semiempirical molecular orbital parameters since the energy splittings of the one-electron cubic eg and t z g levels are directly proportional to the 6a and 6 x parameters. Thus, the 6a (aaxial- aequatorial) is simply 3/8 of the splitting of eg(al - bl) and the 6 x (aaxial - requatorial) is 1/2 of the splitting of tzg(e - b2).15The redundancy of the semiempirical molecular orbital parameters or of parameters other than the ligand field in the analysis of the electronic energy levels of quadrate complexes in general will be elaborated in a future communication.
Miniprint Material Available. Full-sized photocopies of the miniprinted material from this paper only (Tables IIVI) or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the miniprinted and supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-75-142.
Mossbauer Study of
Equilibrium
Constants of Solvates
149
References and Notes (1) Taken in part from a thesis submitted by J. S. Merriam to the Department of Chemistry of Florida Atlantic University in partial fulfillment of the requirements for the M.S. degree, Aug 1972. (2) Presented in part before the Division of Inorganic Chemistry at the 166th National Meeting of the American Chemical Society, Chicago, Ill., Aug 26-31, 1973. (3) (a) R. L. Klein, Jr., N. C. Miller, and J. R. Perumareddi, Inorg. Chim. Acta, 7, 685 (1973), and references cited therein; (b) R. L. Klein, Jr., M.S. Thesis, Florida Atlantic University, Aug 1971. (4) (a) py and im stand for pyridine and imidazole, respectively. In the case of imidazole, the coordination site of the ligand was suggested to be the pyridine nitrogen. See for a discussion on this J. Reedijk, R e d Trav. Chim. Pays-Bas, 88, 1451 (1969), and references cited there in. (b) Preliminary crystal structure data on the dihalotetrapyridine systems has been reported by M. A. Paraj-Kojic, A. S. Antzishkina, L. M. Dickareva, and E. K. Jukhnov, Acta CrystaIIogr., I O , 784 (1957). (5) See for polarized spectral studies on other quadrate Ni(ll) complexes,
(a) N. S. Hush and R. J. M. Hobbs, frogr. Inorg. Chem., I O , 259 (1968); see also (b) C. W. Reimann, J. Phys. Chem., 74, 561 (1970); (c) M. A. Hitchman, Inorg. Chem., 11, 2387 (1972). (6) D. A. Rowley and R. S. Drago, Inorg. Chem., 6, 1092 (1967). (7) D. M. L. Goodgame, M. Goodgame, M. A. Hitchman, and M. J. Weeks, J. Chem. SOC.A, 1769 (1966). (8) W. E. Bull and L. E. Moore, J. horg. Nuci. Chem., 27, 1341 (1965). (9) (a) J. R. Perumareddl, 2.Naturforsch. A, 27, 1820 (1972); (b) J. R. Perumareddi, ,/. Phys. Chem., 76, 3401 (1972). (10) (a) J. R. Perumareddi, 2.Nafurforsch. B, 22, 908 (1967); (b) J. Reedijk, P. W. N. M. Van Leeuwen, and W. L. Groeneveld, R e d Trav. Chim., fays-Bas, 87, 129 (1968). (11) R. K. Lowry, Jr., and J. R. Perumareddi, J. Phys. Chem., 74, 1371 (1970). (12) G. L. McPherson and G. D. Stucky, J. Chem. Phys., 57,3780 (1972). (13) J. R. Perumareddi, Coord. Chem. Rev., 4, 73 (1969). (14) (a) H. Yamatera, BuII. Chem. SOC. Jap., 31, 95 (1958); (b) D. S. McClure in "Advances in the Chemistry of Coordination Compounds," S. Kirschner, Ed., Macmillan, New York, N.Y., 1961, p 498. (15) J. R. Perumareddi, Phys. Status SoIidi, B 59, K127 (1973).
Mossbauer Study of Equilibrium Constants of Solvates. 1. Determination of Equilibrium Constants of Tetraiodotin-Trimethylisopropoxysilane and Tetrabromotin-Acetic Anhydride Solvates Attila Vertes,' Sandor Nagy, Ilona CzakbNagy, and Eva Cshkvary Depatfment of Physical Chemistry and RadioIogy, L. Eotvos University, 1088 Budapest, Hungary (ReceivedFebruary 27, 1974; Revised Manuscript Received September 23, 1974)
The equilibrium constants of solvate formation in CC14 and benzene as indifferent solvents has been determined by means of Mossbauer spectroscopy: SnX4 2D + SnX4D2, where X = I or Br, D is the donor solvent trimethylisopropoxysilane, (CH&CHOSi(CH3)3, or acetic anhydride. For the solution containing SnI4, trimethylisopropoxysilane and cc14 K = (1.4 f 0.3) X lo2 [mol(kg of CC14)-1]-2, and for SnBr4, acetic anhydride, and benzene K = 3.15 f 1.05 [mol(kg of benzene)-1]-2.
+
Mossbauer (MB) spectroscopic and thermoanalytic studies of frozen solutions (published recently) suggest that the composition of the first ligand sphere of MB atoms and the chemical bonds between MB atoms and their ligands remain unchanged during rapid freezing.l-ll Assuming, that the Mossbauer-Lamb factors of different species of tin are equal or very similar in the same solution (as was proved earlier12 for another system of solutions of tin compounds) it is possible (in some cases) to calculate by MB measurements the equilibrium or stability constants of solvates and complexes formed by the solvation of compounds with MB atoms.13 The purpose of this paper is to demonstrate the determination of equilibrium constant of the SnX4 2D +SnX4D2 reaction in indifferent solvent, where D is the donor solvent.
+
Determination of Concentration from Mossbauer Spectra As it is well known, the area of the Mossbauer lines is, e.g.,
where cy is a constant; q(u ) is the magnitude of the effect; u = Doppler velocity; t = f'nao; f and f' are the recoil-free fractions for the source and absorber, respectively; n is the number of Mossbauer atoms belonging to the given line in 1 cm2 of absorber; a0 = resonance cross section; Io and I 1 are the Bessel functions of zero and first order. Using a thin absorber
exp{-ft}
+
[I&)
Il($t)]
=1
(2)
and so S is proportional to t
s " afrt
(3)
(e.g., in the case t = 0.2 the application of eq 3 results a relative error of -5%.) When using of a thicker absorber is unavoidable, the calThe Journal of Physical Chemistry, Voi. 79, No. 2, 1975
