In the Classroom edited by
Advanced Chemistry Classroom and Laboratory
Joseph J. BelBruno Dartmouth College Hanover, NH 03755
Undergraduate Lectures on Infrared Spectroscopy in the Solid State E. A. Secco* Chemistry Department, St. Francis Xavier University, P.O. Box 5000, Antigonish, NS B2G 2W5, Canada
For about the past 20 years I have incorporated some aspects of materials science or solid state chemistry into the 3rd-year physical chemistry lectures and experiments. The intent was to offer students an aperitif for what I consider an important branch of chemistry that is not given its due in the undergraduate curriculum. It is interesting to note in an issue of Chemistry in Britain (1) the opening sentence highlighting the topic of solid state chemistry: “Few people, even professional chemists, appreciate the immense importance of solid state chemistry and physics.” Of the 5 solid state experiments we do, one involves IR spectroscopy. In the course of lectures on vibrational spectroscopy, the fundamentals of symmetry elements, symmetry operations, and point groups and their classification along with character tables are presented. The topics are introduced with simple diatomic molecules and progress to polyatomic molecules with higher symmetry as described in physical chemistry textbooks (2–4 ) and supporting texts (5–7). After identifying the species/modes A1, A2, B1, B2, E, etc., the number of each species/mode type is calculated for the given molecule point group. The next step is to consult the character table for that molecular point group to identify the IR-active and -inactive modes. In our case, attention is focused on two molecular point groups, D3h and Td , represented by NO3{ and SO42{, respectively. The character table for D3h indicates that all modes are IR and Raman active except A′1, which is Raman active only, and also that the 2E ′ modes are doubly degenerate in both IR and Raman. In the case of Td the character table shows only the 2F2(T2) modes are IR active and all modes (viz., A1 + E + 2F2) are Raman active. The question is, can we activate the inactive IR modes and separate the doubly (E ) and triply (F ) degenerate modes? To answer this question there must be a reduction or descent in symmetry for the given molecular/polyatomic species. One can illustrate this descent in symmetry for SO42{ (Td ) in solution with 2 active modes followed by SO3F { (C3ν) with 6 active modes and then SO2F2 (C2ν) with 8 active modes. One is confronted with the challenge that, while the tetrahedral configuration may be retained, the chemical species is different in each case and the 9th mode as required remains unobserved. One then proceeds to illustrate the steps of symmetry reduction for SO4 in crystalline environments with Na2SO4 (Td ) → KNaSO4 (C3ν) → [Co2(NH3)8NH2SO4]3+ (C2ν) → Li 2SO4(C1). The readily available Li2SO4 can be used as the compound, but I have chosen the compounds Cu4(OH)6SO4 (8) and Cu4(OH)6(NO3)2 (9) for the student experiment because of *Presented at 78th CSCCE, 1995, in Guelph, ON. Email:
[email protected].
their many instructive aspects and their availability from our research studies (an attempt also to provide students with an insight to research). Each compound is used in alternate years. This experimental exercise in solid state IR uses the Halford– Hornig site group or correlation method (7) to illustrate the reduction in symmetry without altering the chemical species NO3{ or SO42{. The Halford–Hornig (H–H) method takes into account the symmetry properties inherent in the crystal lattice. In a crystal, if one defines translation that takes a point in one unit cell to an equivalent point in the neighboring unit cell as the identity, one defines a finite group called a “factor group” of the space group. The molecules located at particular positions in the unit cell of the lattice can only be located on one of the symmetry elements of the factor group that remains invariant under the operation independent of translation. The point has fewer symmetry elements than the parent factor group and belongs to a so-called “site group”, which is a subgroup of the factor group. In summary, the H–H method relates the factor group and the site group to the molecular point group. Table 1. Correlation Table for NO3– in Ag2ClNO3 Molecular Point Group D3h
Site Group Cs (σxz )
1 A'1
Factor Group 16 D 2h 4 Ag
(Rz) 0 A'2
4 A'
4 B2g (Ry) 4 B1u (Tz) 4 B3u (Tx)
(Tx,Ty) 2 E'
2 B1g (Rz)
0 A''1 (Tz) 1 A''2 (Rx,Ry) 0 E''
2 A''
2 B3g (Rx) 2 Au 2 B2u (Ty)
Table 2. Correlation Table for SO 42– in Cu4(OH)6SO4 Molecular Point Group Td ν1
A1
ν2
E
ν3,ν4
2F2(T2)
Site Group C1
Factor Group 5 C 2h
Ag A
Bg Au Bu
JChemEd.chem.wisc.edu • Vol. 76 No. 3 March 1999 • Journal of Chemical Education
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Transmittance (AU)
In the Classroom
Frequency / cm {1
Figure 2. IR spectrum in active region of Cu 4(OH)6SO4.
Transmittance (AU)
Transmittance (AU)
Figure 1. Unit cell diagram of Cu4(OH)6SO4 crystal with various OH… OSO3 distances.
Frequency / cm {1
Figure 3. Higher-resolution IR spectrum portions in active region of Cu4(OH)6SO4.
To illustrate the H–H method the compound Ag2ClNO3 16 is considered. The molecule belongs to the space group D2h (no. 62), containing four molecules per (crystallographic) unit cell (10). As stated above, the acceptable site group for NO3{ must be a subgroup of both its space/factor group and its 16 molecular point group, D3h . The site symmetries for D 2h are given as 2Ci(4), Cs(4), C1(8) (7). The correlation tables (7 ) show the possible subgroups for D3h are C3h, D3, C3ν , C2ν, C3, 16 C2, Cs. Therefore, only Cs is common to D 2h and D3h to give { the correlation table for NO 3 (Table 1). In the case of Cu4(OH)6SO4, the student is given the unit cell diagram of 5 Cu4(OH)6SO4 (Fig. 1), with its space group C 2h (no. 14). Students are required to calculate the number of molecules in the cell—there are four. They then follow the procedure described above for NO3{ to construct the correlation table for SO42{ (Table 2). For a n-particle system with 3n modes of freedom and with Z′ = 4 molecules per unit cell, the number of SO42{ modes is 60 (3 × 5 × 4), of which Γint = 4(15 – 6) = 36, of which 18 are IR active (viz., Au’s and Bu’s). We see that all the fundamental vibrations of SO42{ are predicted to be IR active with all the degeneracies removed and where splittings for E and F2 occur. 374
Frequency / cm {1
Figure 4. IR spectrum of Cu4(OH)6SO4 in OH stretch region.
Experimental Procedure The IR transmission spectra were recorded with a PerkinElmer 180 spectrophotometer using both the standard compressed KBr disc sample and the Nujol mull sample between polyethylene windows. This instrument is capable of scanning from 4000 to 32 cm{1. The globar source and TGS (triglycine sulfate) detector were used to scan from 500 to 100 cm{1 with good signal-to-noise ratio. Under ideal purging and optimal instrument conditions one can scan from 125 to 50 cm{1 using Hg source and TGS detector with good signal-to-noise ratio. The laboratory exercise was limited to the scanning regions 4000–3000 and 1200–200 cm{1. The portion of the spectrum in the region 225–50 cm{1 was provided for the student. Results and Discussion The recorded spectrum for Cu4(OH)6SO4 in the SO4 vibrational region is shown in Figure 2 and at higher resolution in Figure 3, to resolve the E and F2 splittings. The spectrum provides many additional features, such as SO4 external optic modes, 172–112 cm{1, and Cu–O stretching and bending frequencies, 338–230 cm{1.
Journal of Chemical Education • Vol. 76 No. 3 March 1999 • JChemEd.chem.wisc.edu
In the Classroom
An added bonus of this exercise and one of the reasons for choosing Cu4(OH) 6SO4 and Cu 4(OH)6(NO 3) 2 for the student touches on the OH group/species. That is the frequency dependence on H-bonding and dependence of Hbonding strength on O–H… O distance. Examination of the Cu 4(OH) 6SO4 unit cell (Fig. 1) reveals 3 types of OH group environments and H…O distances, namely, O5H…O9 (2.96 Å) and O6H…O7 (3.16 Å); O2H…O8, O3H… O10, O4H…O9 (2.86 and 2.87 Å); and O1H… O8 (2.65 Å). The three types are confirmed in the spectrum, Figure 4. The two largest H… O separations, 3.16 and 2.96 Å, are identified with 3596 and 3572 cm{1 peaks for free non-H-bonded OH, whereas the shortest separation at 2.65 Å is associated with strong H-bonding at 3272 cm{1. The slightly broader band, 3412–3388 cm{1, is correlated with the different degrees of H-bridging or medium H-bonding. This experiment in solid state infrared spectroscopy is an effort to expose the student to a little something extra. The exposure provides an insight into and better appreciation of vibrational dynamics in response to different potential energy environments. Also, the interrelationship between space
group and molecular point group symmetry elements suggests that with a single crystal one can in principle determine the crystal structure from IR and/or Raman spectroscopy. Literature Cited 1. Blunt, R. Chem. Br. 1995, 31, 371. 2. Atkins, P. W. Physical Chemistry, 4th ed.; Freeman: New York, 1990. 3. Moore, Walter J. Physical Chemistry; Prentice-Hall: Englewood Cliffs, NJ, 1983. 4. Alberty, R. A.; Selbey, R. J. Physical Chemistry; Wiley: New York, 1992. 5. Cotton, F. A. Chemical Applications of Group Theory; Wiley: New York, 1971. 6. Hollas, J. M. Modern Spectroscopy; Wiley: Englewood Cliffs, NJ, 1987. 7. Ferraro, J. R.; Ziomek, J. S. Introductory Group Theory, 2nd ed.; Plenum: New York, 1975. 8. Secco, E. A. Can J. Chem. 1988, 66, 329, 337. 9. Secco, E. A.; Worth, G. G. Can. J. Chem. 1987, 65, 2504. 10. Natarajan, M.; Secco, E. A. J. Solid State Chem. 1984, 54, 213.
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