M. Kilner and
J. M. Smith' University of Durham Durham City, England
d'
Energy Level Diagram
A n experiment for advanced students
Lectures on theories of bonding in transition metal complexes are playing an ever increasing role in the teaching of transition metal chemistry to undergraduates. For example, the concepts of crystal and ligand field theory are used in discussions of the spectral and magnetic properties of complexes, and students are expected to have some understanding of energy level diagrams and how these are used to interpret spectra and spectral changes brought about by variations of the central metal ion and ligands. I n order to provide practical experience in the use of energy level diagrams, an experiment was devised and has been in use here for two years as part of the third year (final) honors inorganic chemistry course. A r e cent paper (I), based on the spectra of Cr(II1) complexes, is concerned primarily with the spectrochemical series. Students prepare samples of three complexes, measure the spectra and (since the low energy transition gives a direct measure of A, the crystal field splitting energy) arrange the ligands in order of increasing A (the spectrochemical series). We have used a different approach in designing the present experiment. The spectra of six complexes, samples of which are provided, are recorded, and the results used to plot an energy level diagram. The experimental work is followed by a series of questions, based upon the derived diagram, which do not require additional information beyond that obtained by the student himself. The aim of the questions is to give the student experience in the use of energy level diagrams, and to illustrate some fundamental points of transition metal spectra. The list of supplementary questions is not normally used as it involves knowledge of topics not at present covered in the lecture course. However it illustrates the amount of information which may be obtained from the basic experiment. The experiment is designed for a specialist course in transition metal chemistry, either at a final undergraduate level, or preferably at a graduate level when the supplementary questions could be used to advantage. Throughout the experiment students are expected to consult their lecture notes and textbooks (9, 3,) for background information, to read review articles (4-6), original papers of direct interest (7-9), and more advanced hooks (10,II). The Experiment
The script given to the students is reproduced below. The introductory section contains sufficient theory to enable the student to conduct the experiment with LPresent address: Durham, England.
Sunderland Technical College, County
94 / Journctl of Chemical Educofion
understanding and saves recourse to lecture notes in t.his first instance. The Script Introduction
Because of the differing symmetry properties of d orbitals, their initial degeneracy is removed when they are brought under the influence of external fields other than a uniform spherically symmetrical one. Similarly, the Russell-Saunders states associated with the various d orbital configurations are also split. I n the case of an electronic configuration dl, the 2D state is split by the octahedral (Oh)field into %T2and 2E states (Fig. 1). This also applies to the d8 configuration case, which by application of the "hole formalism" we may write as the inverse of the d' diagram (Fig. 1). (Note that both d' and d ghave ground states.)
Figure 1.
Energy level diagram ford' and d Qconfigurations.
Other multi-electron systems are more complicated because the interaction of several electrons gives rise to a series of Russell-Saunders states, D, F , P, G etc., which are affected differently by the Oh field. For example, the dZ configuration gives rise t o 3F, 'D,3P, '0, and ' S states (see ref. (5)), which are split by the ligand field according to Figure 2. Now for d8, the relative energies of the RussellSaunders terms in the free ion are also 3F, ID,3P, etc. (in order of increasing energy), hut the splitting of the individual terms will be the inverse of those for the d2 energy diagram (Fig. 2).
d8
ing the various states. Alternatively, given that the free ion T - -P separation is 15,836 cm-I (1.9) and that the energy of the aA2ground state varies with A according to
OCt.
construct the Orgel diagram for Ni(I1). Care should be taken in assigning transitions to the various absorption maxima. The shoulders observed on absorption peaks for several complexes can he ignored in this treatment of the spectra. However, it is most important not to confuse a shoulder which is part of the "fine structure" of a given transition with an absorption due to a transition between different states (e.g., in some spectra, there is a shoulder on the side of the 3Az 3T1(F) transition which should not be confused with the 3A, absorption which may be found at much lower frequencies). Difficulties of this type will occur in complex 1 in the 800 mF region, and in complexes 4 and 6 in the 700 mp region.
- -
Figure 2.
Energy level di0gr.m.
for d2 and d B configuroiionr
Origin of Spectra
When an electron undergoes a transition from the ground state to an excited state, thc molecule must absorb energy. I n the case of the d-d transitions the absorption bands occur in the near uv, visible, and the near ir. To a first approximation, the observed d d transitions are forbidden, but more refined theory allows them to occur to give weak absorptions, as the Laporte selection rule is broken down. The spin selection rule may also be overcome, and when it is we observe very weak bands ~vithan intensity of about that ohserved for spin allowed transitions. The absorption bands expected in the spectra of d8complexes are
---
Jll? a.42
-
Questions 1. Give assignmeuts lo the two bauds in the spectrom of eompomd 5, and estimate the freqlrency of the missing hand. 2. Estimate Lhe frequency of the ahsorption maximum far the qA.3T,(P) trarrsition in complex 1. Why is i t not possible to get this directly from the spectrum? 3. Predict the posit,ion of the absorption maxima fur Ni(ophen).804.01120 (16)and KNiFa (14, 17) and with the aid of Figure 3, dedilce t,he color of these compo~ulds. KNiFa in the solid state has the perovskite structure with the Ni(I1) iurm oetahedrally surrounded by fluoride ions.
-
1 1 1 1 1 1
Near InfraredRed Orange Yellow Green Rlue Violet cm.-' 13,300 15,400 17,000 19,000 20,400 23,800 25,600
(F)
=T,(P)
and possibly some spin forbidden triplet-singlet bands. The transition energy for the lowest energy absorption (3A2 3T2)for the d8 case gives the value of A directly for the complex under investigation. It is therefore possible to derive an energy level diagram for the various states, based upon the ground state 3A2as the energy zero for all values of A. If, however, the variation in energy of the 3A2ground state with A is known, an Orgel diagram may be constructed. A knowledge of the 3F- BPfree ion separation enables a more precise diagram to be constructed as it avoids the need for extrapolation to A = 0. Object of the Experiment
To construct the energy level diagram for Ni(I1) (within the limits dictated by the various A values for the ligands) from the spectra obtained for the series of complexes, and to use this to derive spectral and other information on nickel complexes in general. Method
Weigh sufficient material to prepare 10 ml of a M/20 solution of each complex listed in the table, and record its spectrum in the region 30&1000 mF. Plot the energy level diagram E versus A based upon the ground state 3Az as the energy zero for all values of A (E and A in units of cm-') for the complexes 1-4, clearly label-
Figure 3.
The visible region of h e spectrum.
Arrange the various ligands in the spectroehemical series in order of increasing A. 5 . Suggest an explanation for the presence of the shoulder on the low frequency side of the $A2 ST,(F) transition in complex 4. 6. Discuss the differences in the spectra of the complex6 when in acet,one and aqueous KNCS. A diffuse reflectance soectmm of solid KaNi(NCSh.4H,O eave the followine @A;I T , ( P ) ) 15,95i ibbsorption maxima: -25,800 ITl). G ~ v e em-' (=Aa >T,(F)) and 9600 ern-' (8A1 reasons for the differences between the spectra when determined in aqmous KNCS and in the solid state. 7. Calculate extind.ion coefficients for the absorption peaks in one spectrum. Comment upon the difference between these
4.
-
-
-
Complexa
Solvent and Blank
Concentration
Wnter 20% en Aqueous N131 Water U.M.S.0. Acetone IOM KNCS in water
M/400 and M/1600
nr/zo
bipy = 2,2'-bipyridyl, en = ethylenedismine, D.M.S.O. = dimethylsdfoxide. Volume 45, Number 2, February 1968
/
95
COMPLEX
-= 1 ..... = 2
SEE TEXT
.----.-r.
=
4
SOLVENTS
WAVELENGTH Figure 4.
Absorption rpectro of the compiexe, in the region 300-1.000 m p
values and those for d-d transitions in tetrahedral con>plexes, e.g., NiCL1- (t = 200) and for charge transfer traositions (C = lo4 - lo5) e.g., iUnO+-.
Supplementary Questions
8. Use eqn. (1) to constmot the Orgel diagram. 9. Using eqn. (l),determine the mean energy (E) (Fig. 2) of the T state, relative to the aAA.ground state, for com~ l e x e 2-6. s Use the diffuse reflectance data for com~lex6.
Calculate the energy (aT,(P) - E) for each value of A ; this gives E.,, of eqn. (2). 10. Substitute for E., in the following equstion and obtain P for each complex.
This equation (18) relates the energy of the T, terms l o the crystal field splitting A, and the =F- -'P term separation, P. Assuming that the 3F - IP separation in the complexes is the same as in the free ion, the equation can he solved for values of E, far a. given A. The Lwo solutions refer to the energ* of t.he aTI(F) and STI(,P)states. Thus using eqns. (I), (2), and the energy relatranship
11.
12. 13. 14.
in the 300-700 mfi region using a Unicam SPSOO spectrophotometer and the region 700-1000 mfi is scanned manually using an SP600 instrument. A sample spectrum of the absorption at 1175 mfifor [Ni(HpO)6]SOa is given to the student. Xormally, the results (Fig. 4) are used to plot an energy level diagram based upon the ground state 3A2as the energy zero (Fig. 5) and the student then proceeds with the questions 1-7. Alternatively, using eqn. (I), the Orgel diagram (Fig. 6) may be obtained.
Notes o n the Script and Experiment
Of the many possible transition metal ions which could have been chosen for the experiment, the trivial d'/d9 cases were not considered, nor the d4, d5, d6 cases where there is the possibility of a change in ground state terms for different complexes (although such cases would make an excellent experiment in conjunction with magnetic measurements). Ni(1I) was considered to be a good choice from the remaining possibilities as there are many octahedral Ni(I1) complexes affording a wide range of A values. Furthermore, the spectral properties of Ni(I1) complexes have been extensively studied so that such information is readily available (7, 9-12) as are preparative details (8, 12, 17). The spectral results from this system are very suitable for interpretation by students because A values are obtained directly from the spectra (3A2 3T2) and complications due to spin orbital interactions are kept to a minimum. For the spectral determinations, we found it necessary
-
the Orgel diagram can be constructed from theoretical principles. Since complexes deviate from the paint charge electrostatic model, and orbital interaction between the metal and ligands occurs, the experimental energies of the various states differ from those calculated. Alt,ernat,ively, b> snbstituting one experimental value (for STI(F) or 3T1(P)) in eqn. (Z),a calculated value of P, the aF - 3Pterm separation in the complex, can be obtained. Obtain the Racah parameter. B, for each ligand. The Racsh parameter, B, - 3P term separation in complex t aF- JPterm separation in the free ion) gives ameastre of the orbital interaction between the metal and the ligands. Far the gaseous Nix+ion, the 3F - =Pterm separation is 15,836 em-' (19). Arrange the ligands in order of their decreasing B values. This gives the nephelauxetic series. Comment upon differences in order between the nepbelauxetic and spectrochemical series. Explain why the energy versus A correlations for SZ't(P) and ST,(F) deviate from linearity.
Practical Details
Students are not required t o prepare the complexes, but from given samples, they m k e up solutions to the specified concentrations. The spectra are determined 96 / Journal of Chemical Education
Figure 5. Energy level diagrorn obtained from the measurements, taking the ground state % 03 the energy zero for all valuer of A.
tion in complex 1 means that, for the student who is not aware that bipyridyl is a strong ligand, some thought must be given to the assignment of the two frequencies available. It is, however, rather diicult to assign complex 5 to other than a weak field position on the diagrams. I n attempting an answer to question 5 , most students discuss effects of lowering of symmetry on the absorption hands before arriving at an explana'E transitions. Few students tion in terms of 'Az without direction have discussed the ideas of Ballhausen and co-workers (11) with regard to the appearance of a double peak in the region under discussion. Question 6 is designed to bring the students' attention to the problem of changes in ligand coordination and stereochemistry upon dissolution of complexes. The spectrum of KNi(NCS)Beven in 10M KNCS is very different from that for the solid complex and in aqueous solution without added KNCS it is similar to that for Ni(H20)s2+. Although the supplementary questions have been written so that a student can work through them unaided, nevertheless it is intended that some discussion of Racah parameters and interelectronic repulsions be undertaken with the student at the time these questions are attempted.
-
Figure 6.
EIW
Orgel d i a g r a m obtained from tho measurements assuming
= - 665
a.
Literature Cited
to use 2 cm cells as the Unicam SP800 instrument gives a display which is linear in absorbance units (G2.0) (Fig. 4). For many complexes, it was not possible to obtain a sufficiently concentrated solution, using 1 cm cells, to give a satisfactory display of the spectra on the paper. However, if results are presented in per cent transmission, 1 cm cells may be used, or alternatively 2 cm cells with reduced concentrations. The latter reduces the amount of sample used and facilitates dissolution of the complexes. The basic experiment involves the construction of an energy level diagram with the ground state 3Az as the energy zero for all values of A. This diagram (Fig. 5) is quite sufficient for the student to carry out questions 1-7 without any further information being supplied. However, the - 3Pseparation energy may be incorporated on this diagram when the curvature of the 3T1(P) term becomes more apparent. Alternatively, one may extrapolate the 3T1(P)level to A = 0 to obtain a rough estimate of the 3F- 3Pterm separation which is found to he between 14,000 and 17,000 cm-' (Fig. 5 ) . For questions 8-14 the given 3F-3Pterm separation should be used in conjunction with eqn. (1) to obtain the Orgel diagram (Fig. 6). If students first plot the data for complexes 2 , 3 , 4 for which all the information is available, it is possible to deduce the missing bands in complexes 1 and 5 simply by attempting to fit the available points onto the graph already obtained. The curvature of the a T ~ ( F plot, ) giving a value of 19,200 om-' for 3Az 3T1(F) transi-
-
(1) DUNNE,T. G., J. CHEM.Enuc., 44, 101 (1967). G., "Advanced Inorganic (2) COTTON,F. A,, AND WILKINSON, Chemistry" (2nd Ed), John Wiley & Sons, Inc., New York, 1966. $ AND WILKINS,R., Editors, "Modern Co-ordina(3) L E ~ J., tion Chemistry," Interscience Publishers, London, 1960. (4) COTTVN,F. A,, J. CHEM.EDUC.,41,466 (1964). (5) S U ~ NL., E., J. CHEM.EDUC.,37,498 (1960). W. C., J. CHEM.EDUC.,38, (6) MANCH,W., AND FERNELIUS, D. W., DRAGO, R. S., AND PIPER,T. S., Inorg. Chem.,
(9) FORSTER, D.,'ANDG O O D ~ MD.~ M. , L., Imrg. Chem., 4 , 8 2 3 1196.5). ~ ~, (10) J#RGENSEN, C. K., "Absorption, Spectra and Chemical
Bonding in Complexes,'' Pergamon Press, Inc., New York, 1067
(11) BALLHAUSEN, C. J., "Introduction to Ligand Field Theory," McGraw-Hill, London, 1962. G. T., AND BURSTALL, F. H., J. Chem. Soc., 2213 (12) MORGAN, (1931). (13) ~ o ' c e o wE. , G., Editor, "InorganicSyntheses," 6,200(1960). (14) PALMER,W. G., "Experimental Inorganic Chemistry," Cambridge University Press, 1959, p. 564-7. (15) "Gmelin Handhuch der Anorganischen Chemie," Verlag Chemie, 57, 1058 (1966). P., AND NAKATSUKA, Y., Ber., 66, 415 (1933). (16) PFEIFFEH, J. B., "Advanced Practical (17) ADAMS,D. M., AND RAYNOR, Inorganic Chemistry," Wiley, London, 1965, p. 57. R. S., "Physical Methods in Inorganic Chemistry," (18) DRAGO, Reinhold Publishing Corp., New York, 1965, p. 168 and din
(19) MOORE, c.E., "Atomic Energy Levels," National Bureau of Standards, No. 467.
+
Volume 45, Number 2, February 1968
/
97
