Crystal Field Spectra
Charles Trapp and Richard Johnson
Illinois Institute of Technology Chicago, Illinois 60616
I
of Transition Metal Ions A physical chemistry experiment
I t has been a decade or more since most undergraduate chemistry curricula have reflected the view that quantum mechanics, statistical mechanics, and spectroscopy should constitute a major portion of physical chemistry courses. For example ( I ) , at Illinois Institute of Technology we have a four-semester physical chemistry sequence, the last two semesters of which cover the above-mentioned topics in a fairly rigorous manner. Each of these courses is associated with a 4-hr laboratory period once per week. One of the most difficult aspects of such a course is the development of nowtrivial experiment.^ to illustrate the lecture material. Most modern spectroscopic experiments require t h e use of sophisticat.ed and expensive equipment which usually canuot be made available to the students. Another difficulty is that the student may not have sufficient hckgronud to understand the complex instrumentation involved in such equipment, even if it were available. One solution to these problems is, simply, not to offer a laboratory course in these areas. Another is to present. t,he student. with spectra which have been previously run and t,hen ask him just to do t h e interpretation. We hare adopted the view that a concurrent laboratorv which illustrates the lecture material is the best approach. One of t,he more successful of our new experiments is the one described here. This experiment which we call "Crystal Field Spectra" is concerned with the spectrophotomet,ric determination of crystal field splittings for various t.ra~~sition metal ions in various complex ions in solution. The experiment clearly indicates the principles of crystal field theory or ligand field theory. The latt,er name indicates, of course, that a purely iouic model is not sufficient to explain all the data. The basic ideas of crystal field theory are developed in the lecture p r t of our course in a fairly rigorous fashion similar t,o the treatment in chapter 2 of the book on ligand field theory by B. N. k'iggis (3). The fact t,hat crystal field theory cau be taught successfully to undergraduat,es is attested to by the large number of articles which have appeared in the past six years in this JOURNAL which have either stated this explicitly or implied it. Refereuces to some of these articles are given in the bibliography (5). The problem in the laboratory part of t,he course is to find an experiment which illustrates cryst,al field theory in a meaningful manner and which can he performed without too much difficulty by third year undergraduates. The experiment described here has the advantages that it requires only relatively simple and inexpensive equipment, is easy to perform, and gives results in very good agreement with the puhlishcd spectra. A similar but different experiment I I I I Cr" conlplexes using more
sophisticated equipment for use in an inorganic chemistry course has been described by T. G. Dunne
(4). Theory
We perform the crystal field calculations assuming that the ligands can be represented by an octahedral arrangement of point charges. The form of the crystal field potential is obtained as a solution of LaPlace's equation PI'
=
0
giving
where the Aim'sare constants determined by the particular arrangement of ligands being considered and the YLm'sare the surface spherical harmonics. In order to determine the effect of V(T,@,@) on the d wave functions we use the h e a r variation method rather than perturbation theory since perturbation theory is not developed in the course. We choose as our trial wave function where u, = 3d,,, uz = 3d,,, ua = 3d,,, ur = 3d,. and us = 3dz2-,2. Here we are, of course, restricting the calculation to the configuration 3d1 such as occurs in Ti3+ion. The integrals t,hatwe must evaluate are
The u i s are solutions of XOu*= Eouc where X0 is the unperturbed Hamiltoniau. When we are considering only the above wavefunctions V may be expressed as
where q' is the charge of the ligands and a is the metal to ligand distance. A constant D is defined as
and a constant q as
Volume 44, Number 9, September 1967
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527
The Experiment
Dropping the term 6q1/afrom Tr(1.,9,4),since it is a constant, and setting Eo= 0, we get for our integrals
[Y**
+ (&)"*(1;' + Y , - a ) ]
d j sin a da dm
where di represents the angular part of u i = 3dr = Ra2di. Fortunately, because of our choice of basis functions, all off-diagonal terms in the secular determinant are zero. The X < ,are evaluat,ed as X n = G2= M133 = -4 Dq and Xln = X66= 6 Dq. Thus det I Xu Eat, 1 = 0 becomes
Solving for the energies we get El = Ean,, = Es = Eady2 = El = ExdZl= - 4 Dq and El = E8a,z= Ea = E3nzz-uz = 6Dq. Thus we get the results depicted in Figure 1 where E, represents the orbitals with energy GDq and Tzorepresents the orbitals with energy -4Dq. We may extend our treatment without much difficulty to the case of 3de (Cu2+)by considering the configuration 3ds to be equivalent to a single hole outside a closed shell of electrons. In this case me must evaluate the integrals
Absorption of radiation in the waveleugt,l~mnge 34g950 nip by rarinus solutions of transition metal salts was examined with a simple spectrophotomctcr such as the Bauseh and 1,omb "Spectronic 20." T l ~ c sample cell consisted of an ordinary 12-mm Pyres test tube. Matched t,cst t,ubes provided by various manufacturers can also be used, but we have found this rcfinement to be unnecessary as the student can usually find two ordinary test tubes that match without too much difficulty. Fortunately, most of the d-d transitions for ions of the 3d met,als lie within the wavelrngth range of our instrumcnt. In the following paragmphs and figures the results of one of our students are prcsented. The resuks irhtained by other students are not significantly different. TiCla in water. 111ivat,er solution the comples ion Ti(H20)s3+ is formed. The ligand arrangement is approximately octahedral. 10 Dq may he evaluated from the posit,ion of the single peak observed. Sec Figure 2 and the table. We have found that solutions of about 1% by weight concentration give the nicest looking spectra. At this concentration signs of the double peak presmmhly due to a Jahn-Teller distortion of the excited 2Eg level are observed. In Figure 2 the curve for 0.5% ci~nccntratinnof TiCb is also presented.
which clearly gives an energy level diagram which is inverted with respect t,o 3d'. This situation is also depicted in Figure 1.
Figure 2.
Absorption curves for Tint ion in voter solution.
It can be seen that 13ccr's law holds approximatcl?. for these concentrations. The solutions are prepared simply by diluting :L conlmercially available 20% Ticlasolution.
DCTMEDRIL
Flu Figure 1.
Crystal fleld rplittings for TiaC,Cu2+, and N i l t ions.
Finally we indicate how the above treatment can be extended to other transition metal ions such as 3d2, 3d3, . . . , 3d?. A proper treatment of these cases is considerably more complicated so we content ourselves with a very brief discussion. For the case of 3rP(NiZ+) we get the diagram on the right in Figure 1. Here we may have transitions from the lowest level to both of the excited states. The lowest energy band gives 10 Dq and the next higher band gives 18 Dq approximately. 528 / Journal o f Chemical Education
. wat.er solution the conlplcx Cu(NO& in ~ o a t ~ r 111 ion C U ( H ~ O )is~ ~formed. + The results are shown in Figure 3 and the tahle. Once again 10 Dq may be evaluated from the single peak observed. We have used a solution which has a cnncentration of Cu(NO& of about 0.01 M and a conccntrat,ion of NHcN03of about 2 d l . The NH4N03serves as a buffer in the next part of the experiment when onc, two, three, and four equivalents of NHa are added to the solution. The results of the stepwise addition of NH3 are shown in Figure 3 also. The fifth and sixth positions are more difficult to coordinate and a large excess of NH1 must be added. We have not done this in our course since bhe status of the pentammine and hexammine in aqueous solution does
10
12
Figure 3. dutionr.
I t
16
X IO'CM-'
18
20
22
Absorption curves for Cult ion in xoter and aqueous ommonio
not seem to be ~et,tled,but it could be done without mnch difficulty. One should then observe a shift of the peak toward lower wave numbers. Cu(NO& in wafer. This part of the experiment is similar to what was described in the preceding par* g a p h except that here we have added ethylenediamine (m) st,epwiserather than ammonia. Ethylenediamine Abrorption Maxima for Complexes Studied*
l/Ama*
X 10' CM-' Figure 4.
Absorption for Cue
tin
water and mqueous ethylenediomine
sol~ii~n~
the spectrum only two of which are within the wavelength range of our instrument. The peak at 14,000 cm-' corresponds to the transition from the A%,ground state to the TI, excited state (see Fig. 1). Thus we may set this equal to 18 Dq. This band is in reality a double band with the second peak occurring at about 15,400 cm-'. The splitting is probably due to a spin-orbit coupling effect (5). The second peak in Figure 5 for Ni(H20)6Z+ is due to a transition from the ground state to a TI,state arising from the first excited aP term. The solution used in Figure 5 for the Ni(HIO)aZ+curve is a 0.5 M Ni(NO& in water solution.
Complex
Bendn which appem ss B dislrwtion of mother stronger band are written irr pwenthesea.
is a chelating agent and is a somewhat stronger ligand than ammonia. The results are presented in Figure 4 and the table. The addition of one equivalent of cthylenediamine causes a more pronounced shift to higher wave numbers than the addition of two equive le~itsof ammonia. The starting solntion for this part of the experiment was 0.01 M C U ( K O ~and ) ~ 1 M KNOa in water. In order to get the third ethylenediamine molecule to coordinate we added a larger excess of ethylenediamine so that the fund concentration of ethylenediamine in solution was 12 11. The third ligand may coordinate only in one position on the molerule rather than two. This causes a splitting of the :~bsorption band as shown by the asymmetry of the rurve in Figure 4. Ni(NO& tn water. The results are presented in Figure 5 and the table. In water solution the complex ion Si(Ha0)62+is formed. There are three bands in
X 10' CM4 Abrorption curves for Ni" tin water, excess aqueous ammonio, and excess aqueous ethylenodiomine rolutbnr Figure 5.
The curve for Ni(KH3)e2+in Figure 5 was obtained from a 0.2 M Ni(NO3)%solution in 10 M aqueous ammonia. We see that the band that was at 14,000 cm-' has now shifted to 17,400 cm-' and that a new band at the far left (10,600 cm-') has appeared. This hand is due to the transition from the ground state to the excited Tz,state and gives us 10Dq directly. The curve for Ni(en)2+ in Figure 5 was obtained from a 0.2 M N'I(NO~)~ solution in 1 Ili ethylenediamine. The curve obtained is interpreted in the same manner as the curve for Ni(NH&?+. The peaks are shifted to somewhat higher wave numbers indicating once again that ethylenediamine is a stronger ligand than ammonia. Volume 44, Number
9, Sepfember 1967
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529
Results and Discussion
From the positions of the peaks the students may calculate 10 Dq for each ion and ligand. The best way to plot the results is to plot absorption versus reciprocal wavelength (i.e., wavenumbers) as there is some evidence that the bands should then be symmetrical (6). By comparing Dq values the effect of replacing one ligand by another is easily demonstrated. The student may work out his own (partial) spectrochemical series. Beer's law may also be verified, approximately, by successive dilutions of almost any solution. A glance at the data presented in the table shows that the absorption maxima obtained with the "Spectronic 20" are in a11 cases within 3% of the maxima reported in the literature. I n our course we devote two 4-hr laboratory periods to this experiment. This is not time enough to run all the complexes listed in the table. About six complexes can be done in the eight hours available by two students working together. The results presented here were all obtained by one student, who spent additional time on the experiment. The instructor may assign different complexes to different groups of students and the data may be combined at the end of the period. Additional ligands may he used such as ethylenediaminetetraacetate, o-phenanthroline, and others giving a more complete spectrochemical series. Ions other than the
530
/
Journol of Chemical
Education
ones describcd here may :dso he used. For example, the complexes Cr(HzO)B3+and Cr(en)2+, which are described in the experituent. devised by Dunne (4), could also be studied satisfactorily with the Spectronic 20. Literature Cited (1) MARTELL, A. E., J. CHEII.I:I)uc., 43, 117 (1966). (2) Froc~s,D. N., "Iotrodoction to Ligand Fields." Interseienee Publishers, division of John Wiley & Sons, New York, 1966. (3) SUTTON, L. E., J. CHEDI. E I I I : ~37, . , 498 (1960). P E A R ~ R. ~ NG., , J. CEEM.I
