Feasibility Study of the Gaussian Curve Resolution Technique for the Analysis of Transition Metal Visible Absorption Spectra H. A. Kuska, D. H. Beebe, and F. L. Urbach Department of Chemistry, The University of Akron, Akron, Ohio 44325 and Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44 106
As discussed by Perone ( I ) , digital electronics for data acquisition appear destined to dominate the designs of future laboratory instruments. In addition to an increase of a t least ten in the accuracy of most digital data taking over the corresponding analog form, having the data in digital form allows the utilization of data refinement programs which can: apply base-line corrections, digital smoothing, line sharpening, curve fitting, time averaging, line following, area determinations, peak locations, and/or Fourier transforms. Programs to carry out these operations are available (for example) through the Perkin-Elmer program exchange library, (131 Danbury Rd., Wilton, Conn. 06897), the Packard Instrument Company exchange library, (2200 Warrenville Rd., Downers Grove, Ill. 60515), and/or the National Research Council of Canada Bulletins 11, 12, and 13 (1968-69, National Research Council of Canada, Ottawa, Canada). The use of data refinement programs is still in its infancy and many scientists are skeptical of data “generated” by these techniques. It, therefore, appears that feasibility studies of systems that have been well defined by other methods are in order. Of particular interest to us has been the use of Gaussian analysis techniques to increase the resolution of the visible absorption spectra of transition metal complexes. The technique has been a popular one; however, as mentioned above, it has not been universally accepted. Two techniques which are generally considered superior to solution absorption spectroscopy as far as their resolution capabilities are concerned are the polarized single crystal technique and the circular dichroism (CD) technique. I t is the purpose of the present paper to determine to what extent the use of Gaussian curve resolution techniques on visible absorption spectra can duplicate the results obtained by the above two “superior” methods.
EXPERIMENTAL A series of three square-planar copper(I1) complexes, N,N‘-bis(wlicy1idene)-(R)-(-)-propane-l,2-diaminocopper(II)(Cu(sal)n(-)pn), and chelates derived from o- hydroxyacetophenone (H-’i-Mesal), and 2,4-pentanedione (Hacac) with @)-(-)-propane. 1,2-diamine ((-)pn) were chosen for this study since their circular dichroism spectra have previously been reported (2) and they are very similar optically to the corresponding ethylenediamine complexes, some of which have been studied by polarized single crystal methods. The Gaussian analysis program used is the one by Cavell (3).I t has the capability of fitting the spectrum to either a symmetrical Gaussian or an asymmetric bi-Gaussian set of peaks. The asymmetric bi-Gaussian function should consist of a larger peak width Gaussian on the higher energy side of the peak than on the lower energy side; however, the program in the version used does not restrict the bi-Gaussians as to their relative half widths. Theoretically, the exact shape of the peak depends on the mechanism involved in the absorption but practically this shape generally lies somewhere between the Gaussian and the higher energy skewed bi-Gaussian extremes. The spectra were recorded on a (I! S.P. Perone, J. Chem. Educ.,47, 105 (1970). S.Downing and F. L. Urbach. J. Amer. Chem. Soc., 91, 5977 (1969). G.Cavell, W. Byers. and E. D. Day, Inorg. Chem., 10,2710 (1971).
(2) R. (3) R.
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Cary I7 spectrophotometer modified for paper tape output (experimental details will be supplied on request). Spectroquality chloroform was used as the solvent so that results would be directly comparable with the earlier CD studies. A computer fit was attempted for 3 through 8 peaks for each spectrum. One of the peaks will always be for the UV tail so that the number of effective peaks was 2 through 7. The experimental spectra of the three compounds are given in Figure 1. As can be seen from these spectra, the compounds provide a series of spectra that range from semi-resolved peaks to an apparent single peak.
RESULTS AND DISCUSSION The bi-Gaussian runs usually were unsatisfactory for one or more of the following reasons: 1) The program would often converge with the higher energy half-line width smaller then the lower energy half-line width contrary to theory as discussed earlier. 2) The final right half-line width sometimes would be widely different than the left half-line width-only small differences are expected, 3) Although the two methods generally found the same approximate centers for the peaks, the bi-Gaussian method often “took” considerable intensity from the medium intensity peaks and “gave” it to the high intensity peaks (relative to the intensities found by the Gaussian method). This would place peaks that were known to exist and have appreciable intensities from the single crystal and/or CD studies in the low intensity questionable category. The bi-Gaussian option has proved useful in spectra where the overlap between peaks is small such as is often found in the UV region. In these cases, a bi-Gaussian fit gives a better determination of the actual intensity of the absorption. The complete results of the Gaussian analysis runs for the two extreme cases are given in Tables I and 11. In general, the predominant bands tended to remain as the program attempted to fit the spectrum with a higher number of bands. Since the UV end of the spectrum has most of the intensity, the least squares fit normally put a large number of bands in that region before finding additional weak bands a t the IR end of the spectrum. In only a very few cases did the program split one band into two nearly symmetrical bands of the type predicted by Perram ( 4 ) .As can be seen from the multiple run cases, to rely on the analysis of a single run can be misleading. In general, it appears that one can be very confident in the highest intensity bands that appear from run to run (except for the UV tail band). Medium intensity bands that have line widths similar to the highest intensity bands and recur from run t o run are also very probable. The above two cases, in general, cover the bands located by single crystal and CD studies so that one could be optimistic and report that the Gaussian analysis method is comparable to the other two. However, there is one major problem in the utilization of a Gaussian analysis. Where do the medium intensity probable band assignments stop and low intensity spurious band assignments start? In the present investigation, this question appears again and again as the single crystal and/or CD studies did (4) J. W.
NO. 14, DECEMBER 1974
Perram, J. Chem. Phys., 49, 4245 (1968).
Table I. Gaussian Analysis of Cu(acac)z (-)pn No. of peaks in 10-24 klC region
_ _ I _ _ _ _ _
18.34 (31.9)g 23.67 (17.6)
18. 55 (35.3) 22.62 (6.81)
18.45 (33. 1) 23. 56 (13. 2)
15.87 (1.39) 18.43 (26.0)
15.88 (1. 56) 18.45 (26.7) 21.42 (2.60)
15.86 (2.41)' 18.32 (26.2)
16.21 (5.40) 18.24 (17.6) 19.65 (9.86)
16.21 18.28 19. 76 21.20 16.32 18.56 21.47 23. 1 2
(5.31) (20.1) (6.09) (1.39) (6.16) (25. 1) (8.41) (0. 75) 15.89 18.42 20.84 23. 53
16.22 18.28 19.65 21. 19 16.32 18.56 21.48 23.27 (3.26) (26.9) (4.94) (8. 11)
15.89 18.26 18.71 19.92
(1.691 (21.8) (0.44) (6.04)
(5.39) (19. 7) (3.82) (8. 72) (6.19) (25.1) (8.67) (1. 37)
15.12 15.91 18.45 20.86 23. 53
(0.90) (1.98) (28.4) (2. 77) (10.9) 15.88 18.39 18. 72 20.39 21.46
15.12 15.91 18.45 20.85 23.52 (1. 50) (25.2) (1.02) (0.45) (3.20)
(0.85) (2.00) (28.4) (2.08) (11.9)
Transitions are in units of 1000 c m - l ( k K ) . The values in parentheses are the oscillator strengths x 104. " NC means that the program did not converge for that number of peaks in the 10-24 kK region. More t h a n one set of data can appear in a column. For example, the attempted fits for 7 and 8 peaks may both yield only 5 peaks in the 10-24 kK region and 2 or 3 peaks above 24 k K .
not find all of the four expected d-d transitions for a Cu(1I) with an x s ground state, x 2 - y 2 +xy, z 2 - x ) , xz *xs, and J Z +xy Thus, the additional low intensity Gaussian bands found may or may not be real. With this limitation in mind, we will discuss the compounds individually. Cu(acac),(-)pn. From our published ( 5 ) and unpublished electron spin resonance work and from the literature optical studies (2, 5, 61, it appears that this compound has bonding properties virtually identical to those for Cu(acac)een so we will assume that the studies on Cu(acac)zen are also applicable to Cu(acac),( -)pn. The polarized single crystal spectrum for Cu(acac12en has been reported by Olson, Basu, and Belford (6). They were able to resolve bands a t 16.4 kK, 18.4 kK, and 22.5 kK. They assigned the 18.4 kK band to the z * -* x y transition and the 16.4 kK band to the x 2 - y 2 x y transition. The 22.5-kK band was thought not to be of d-d origin. Downing and Urbach (21, using CD, reported bands a t 15.95 kK, 18.15 kK, and 21.69 kK, in qualitative agreement with the single crystal work (CD peak centers are difficult to determine to any quantitative degree). Thus, the superior methods definitely give three bands in the area of interest with the possibility of one or two additional bands that could not be resolved. The peak5 expected a t 16 kK and 18 kK appear consistently in the four Gaussian analysis runs; the peak expected near 22 k K is not as well behaved, runs 1, 2, and 4 place it between 20 and 21.5 kK, run 3 locates a relatively intense band a t 23.5 kK and a band of about the correct intensity at 21 kK. Cu(7-Mesal)2(-)pn. This compound was expected to be more of a test for the Gaussian analysis than was the Cu(acac)z(-)pn since the optical spectra, see Figure 1, did not reveal any obvious shoulders. The CD spectrum revealed peaks a t 16.03 kK, 18.35 kK, 20.58 kK, and 21.98 kK ( 2 ) . The Gaussian analysis results are in good agreement with the (3D work as far as the number and positions of the prin-
(5) H A. Kuska, M. F. Farona. P. P. Pappas, and Chem. 1. 259 11971).
Figure 1. Observed experimental visible spectra. (--) Cu(AcAc)2(-)pn. (- - -) Cu(Sal)z(-)pn (C~(7-Mesal)~(-)pn m
cipal bands. Unfortunately, one cannot compare circular dichroism intensities with optical absorption intensities. Cu(Sal)z(-)pn. Ferguson ( 7 ) studied the polarized single crystal spectra of the similar Cu(sa1)zen and found a band a t 17.9 kK and a shoulder a t 20.8 kK. The CD results gave peaks a t 16.95 kK and 20.7 kK. The Gaussian analysis of the optical spectrum gave predominant peaks at, 17.8 kK (68. 0) and 21.7 kK (11.5). Lower intensity peaks were found a t 12.2 kK (0.3), 15.3 kK (4.0), and 20.4 kK (5.0). The values in the parent,heses are the oscillator strengths. Computer Generated Spectrum. As a check on the ability of the program to find only the actual peaks present in a spectrum, a synthetic spectrum was generated with peaks a t 100, 200, 300, and 400 units, relative intensities of 0.3, 1.0, 0.6, and 0.3 and half-widths of 50 units. The computer determined the following values 100.7, 0.306, 46.1; 197.8, 1.00, 47.8; 299.1, 0.64, 53.6; and 404.3, 0.279, 44.9 for the positions, relative intensities, and half-line widths, respectively. A convergence for three peaks w a s obtained also, but one of the half-line widths was 100 units. The important point from the standpoint of the problem of spurious peaks is that the program did not converge for t,rials
S. Potterton, J. Coord. (7) J. Fewuson, J. Chem. Phys., 34, 2206 (1961).
ANALYTICAL CHEMISTRY, VOL. 46, NO. 1 4 , DECEMBER 1974
Table 11. Gaussian Analysis of Cu(i’-Mesal)z(-)pn No. of peaks in 10-23 kK region RlUl
18.17 (62. 3)a 22. 70 (46. 7)
15.54 (2.99) 18. 14 (55.4) 22.70 (53.9)
18.25 (61.4) 21. 51 (10.1)
18.27 (65.8) 21.66 (14.8)
18.35 (67.4) 21. 79 (14,7)
15. 71 (3.92) 18.35 (60.0) 21.79 (21.9)
18.29 (66.1) 21.63 (12.9)
15. 72 (4.05) 18.28 (58.1) 21.64 (21. 5)
18.23 (60.4) 21. 56 (13. 1)
15. 55 18.11 18.38 22. 71 15.65 18.26 20.53 21.55
(3.14) (44.8) (10.9) (53.3) (3.24) (55.4) (2.12) (10.5)
15.69 18.28 20. 55 21.69
(3. 70) (58.9) (1. 64) (17.8)
15. 73 (4.24) 18.36 (59. 7) 20.61 (2.69) 21.78 (14.2) NC
12.91 15,64 18.26 20.54 21. 54 14.69 15.70 18.27 20.56 21.68
(0.47) (2. 71) (56.2) (1.51) (11.4) (0.50) (2.18) (60.6) (1.48) (16.3)
14.12 (0.12) 15.72 (3.61) 18.29 (59.1) 20.48 (2.35) 21.62 (12.8) NC
a Transitions are in units of 1000 cm-1 (kK). The values in parentheses are the oscillator strengths x 104. b NC means that the program did not converge for that number of peaks in the 10-23 kK region.
that asked for more than four peaks in the fit. When the same synthetic curve was resolved with bi-Gaussians, the program did successfully converge for four peaks; however, it also converged for five peaks with values 147.8, 0.50, 32.9, 71.5: 203.9, 1.00, 30.1, 34.1; 252.0. 0.59, 22.3, 25.2; 294.0, 0.63, 32.0, 24.0, and 353.1, 0.40, 82.6, 35.0 for the positions, relative intensities, left half-line widths and right half-line widths. The large difference in the left and right line widths can be used to rule out such a convergence.
ter approximation than the unconstrained bi-Gaussian. The use of the Gaussian form does introduce one difficulty. Although multiple runs may eliminate low intensity peaks due to noise, impurities, etc., they will have no effect on low intensity “peaks” which are actually the asymmetric components of higher intensity peaks.
ACKNOWLEDGMENT We thank R. G. Cavell, University of Alberta, and J. R. Wasson, University of Kentucky, for providing us with Fortran copies of the program used.
The use of multiple runs is recommended even for medium and high intensity peaks as seemingly similar spectra sometimes would have quite different convergence properties. See for example Run 6 of Table 11. For closely overlapped peaks, the Gaussian form of fit appears to be a bet-
RECEIVEDfor review July 12, 1973. Resubmitted January 25, 1974. Accepted July 22, 1974. This research was supported at Akron University by NSF Grant GP-9485 and a t Case Western Reserve University by NSF Grant GP-33834.
ANALYTICAL CHEMISTRY, VOL. 46, NO. 14, DECEMBER 1974