Infrared Spectrum and Group Theoretical Analysis of the Vibrational

Therefore undergraduates should acquire a working knowledge of symmetry operations, point groups, and char- acter tables, and these skills should be r...
0 downloads 4 Views 88KB Size
Download PDF
In the Laboratory

Infrared Spectrum and Group Theoretical Analysis of the Vibrational Modes of Carbonyl Sulfide

W

Michael J. Tubergen* and Richard J. Lavrich Department of Chemistry, Kent State University, Kent, OH 44242; *[email protected] James W. McCargar Department of Chemistry, Baldwin-Wallace College, Berea, OH 44017

Undergraduate chemistry majors often receive their first introduction to group theory and its applications in the juniorlevel physical chemistry lecture course. The topic may be explored further in senior-level inorganic chemistry courses and a good background is usually assumed in graduate-level classes. Therefore undergraduates should acquire a working knowledge of symmetry operations, point groups, and character tables, and these skills should be reinforced via laboratory experiments. An experiment assigning the normal modes of a simple polyatomic molecule is a natural way to incorporate group theory into the physical chemistry laboratory. Most physical chemistry laboratory courses include spectroscopic experiments designed to instruct the students in the assignment of normal modes, overtones, and combination bands. CO2 (1), CS2 (2), SO2 (3), HCCH (4 ), and cyclohexane (5) are the most common polyatomic molecules investigated because they are readily available and have relatively simple infrared spectra. With sufficient resolution, the rotational substructure of these small molecules can also be resolved and analyzed. The acetylene experiment (4 ) includes an analysis of the rotational band contours and requires the students to explain the presence or absence of Q branch transitions in terms of the selection rules for parallel and perpendicular transitions. We describe here an undergraduate physical chemistry experiment on the vibrational spectroscopy of carbonyl sulfide (OCS). Like many of the previous experiments, the main purpose of the OCS experiment is to assign fundamental transitions, overtones, and combination bands and to analyze the infrared activity of these transitions using group theory. A second goal is for students to explain the presence or absence of Q branch transitions, as described for acetylene above. The carbonyl sulfide experiment, however, may offer several advantages over the previously published experiments. First, the infrared spectrum of OCS has a larger number of features for students to assign because the fundamental transitions are all infrared active. We have also incorporated semiempirical and ab initio calculations of the normal modes into the experiment so that students can visualize the vibrational motions and make comparisons between theory and experiment. The most interesting feature of the OCS infrared spectrum is the hot-band transition associated with the ν2 fundamental; the relative intensities of the fundamental and hot band are in good agreement with the Boltzmann distribution. This experiment is intended to be performed after both symmetry and vibrational spectroscopy have been covered in the physical chemistry lecture course. Carbonyl sulfide has four normal modes and belongs to the C∞v point group. The fundamental frequencies are ν1 = 859 cm᎑1 (symmetric stretch), ν2 = 521 cm᎑1 (bend, doubly

degenerate), and ν3 = 2062 cm᎑1 (asymmetric stretch), and the irreducible representations of these modes are A1, E1, and A1. Many overtones and combination bands appear in the infrared spectrum (see Fig. 1); our assignment of the spectrum is given in the supplemental material.W We use this experiment to illustrate how irreducible representations are used to label vibrational modes and how direct products are evaluated. The infrared activities of vibrational transitions are derived from the transition dipole moment integral: µz,fi = ᎑ e ∫ ψf* z ψi dτ, and similar integrals for the x and y components of the dipole moment. The direct product of the irreducible representations of ψf, z, and ψ i must span the totally symmetric representation for the integral to be nonzero and the transition to be infrared active. Our students evaluate this direct product for the various fundamentals, overtones, and combination bands of OCS. The effect of symmetry on the number of infrared-active transitions is strikingly illustrated if students also analyze the infrared spectrum of CO2 as part of a prelaboratory assignment. The observation of the second harmonics allows students to estimate anharmonicity constants for modes one and three. The students approximate normal modes as independent anharmonic oscillators, even though cross terms appear in the complete anharmonic-oscillator energy expression for polyatomic molecules (6 ). This approximation is not appropriate for mode two because of the additional level splitting from angular momentum due to the bending motion (labeled with the quantum number ᐉ; see “Additional Information for the Instructor”W). Student evaluation of the complete energy expression, including cross terms, would require solution of simultaneous equations arising from a large data set. The first correction term to the energy of an independent anharmonic oscillator is usually expressed as ᎑hνexe(v + 1⁄2 )2, where ν e is the equilibrium vibrational frequency of the oscillator and xe is the anharmonicity constant. The transition frequency, then, is ν = (v′ – v′′)νe – νexe[(v′ + 1⁄2 )2 – (v′′ + 1⁄2 )2]

(v′′ and v′ are the quantum numbers of the lower and upper vibrational states). Using the frequencies of the fundamental and second harmonic, two equations of this form can be written and solved for the unknowns ν e and xe for each mode. We calculate νe = 866 (4) cm᎑1 and xe = 0.004 (2) for mode one and νe = 2083 (5) cm᎑1 and xe = 0.005 (1) for mode three. The equilibrium frequencies and the anharmonicity constants differ from the literature values (7) (νe = 875.304 (1) cm᎑1 and xe = ᎑ x11/νe = 0.00345 (1) for mode one and νe = 2093.770 (2) cm᎑1 and xe = ᎑ x33/νe = 0.0054724 (5) for mode three) because it is a poor approximation to neglect the anharmonicity cross terms.

JChemEd.chem.wisc.edu • Vol. 77 No. 12 December 2000 • Journal of Chemical Education

1637

In the Laboratory

Figure 1. Infrared survey spectrum of OCS (15 torr) taken with a resolution of 2 cm-1.

Figure 2. Expanded-scale plot of the ν1 fundamental transition in the infrared spectrum of OCS (54 torr).

The rotational substructure of the OCS vibrational transitions is partially resolved, even with 2-cm᎑1 resolution. Most of the transitions in the survey spectrum of Figure 1 appear as “doublets”; when they are plotted on an expanded scale, it is clear that the doublet shape arises from partially resolved P and R branches. Figures 2–4 give expanded-scale plots of the three fundamental transitions. The shape of the band contour depends on the rotational selection rules for parallel and perpendicular transitions. For parallel transitions, the change in the dipole moment during vibration is parallel to the molecular axis. Parallel transitions, such as the ν1 and ν3 fundamentals, have ∆J = ±1 allowed for the rotational transitions and have only P branches (∆J = ᎑1) and R branches (∆J = +1). Perpendicular transitions have the change of dipole moment perpendicular to the molecular axis; the fundamental transition of the bending mode, ν2, is a perpendicular transition. The rotational selection rules for perpendicular transitions are ∆J = 0, ±1. Transitions with ∆J = 0 are called Q branches and appear as a sharp peak near the center of the vibrational band. Before coming to the laboratory, students use one of the semiempirical packages of HyperChem (8) to model the vibrational spectrum of OCS. Alternatively, one could have students

perform a thorough study comparing semiempirical and ab initio calculations with different parametrizations and basis sets. Students will find that the computed frequencies (both ab initio and semiempirical) are in poor agreement with the experimental frequencies; research applications often employ a scaling factor for the computed vibrational frequencies. Nonetheless, students are able to use the predicted frequencies to unambiguously assign the normal modes. The HyperChem modeling is also useful because the animation feature helps students to visualize the motions associated with the normal modes and to explain the band contours using the selection rules given above. The appearance of a second Q branch transition at 526 cm᎑1 associated with the ν2 mode gives students a rare opportunity to assign a hot-band transition and to analyze the relative populations of the v 2 = 0 and v 2 = 1 states. The Boltzmann distribution (at 298 K and including the double degeneracy of the upper state) predicts that N(v 2 = 1)/N(v 2 = 0) = 0.158; the ratio of absorbances, A(hotband)/A(fundamental), should be the same. We find A(hotband)/A(fundamental) = 0.13 (5) for the spectrum shown in Figure 3. The experimental value has a large uncertainty because of the low intensity of the

Figure 3. Expanded-scale plot of the ν2 fundamental transition in the infrared spectrum of OCS (54 torr).

Figure 4. Expanded-scale plot of the ν3 fundamental transition in the infrared spectrum of OCS (15 torr).

1638

Journal of Chemical Education • Vol. 77 No. 12 December 2000 • JChemEd.chem.wisc.edu

In the Laboratory

hot band and the difficulty in separating the intensity of the hot-band Q branch from the underlying R branch (arising from the fundamental).

the instructor fill the storage bulb). The vacuum line should be in a well-ventilated area in case of accidental leakage. Safety goggles must be worn at all times.

Experimental Procedure

W

The spectra shown in Figures 1–4 were obtained using a BioRad FTS 3000MX spectrometer with 2-cm᎑1 resolution. Any infrared spectrometer could be used to record spectra, but resolution of 2 cm᎑1 or better is necessary to clearly separate the hot-band transition at 526 cm᎑1 from the fundamental at 521 cm᎑1. We use a vacuum line to fill a 10-cm sample cell fitted with KBr windows (Wilmad Glass); carbonyl sulfide is available in lecture bottles from Pfaltz & Bauer, Inc., Waterbury, CT. The lecture bottle is used to fill a 2-L glass storage bulb to 300 torr with OCS. The infrared cell is then filled from the storage bulb without danger of over-pressurizing the cell and vacuum line. The survey scan (Fig. 1) and the expandedscale plot of the ν3 fundamental (Fig. 4) were taken with a 15-torr sample of carbonyl sulfide because the ν3 fundamental easily saturates the spectrometer. The expanded-scale plots of the ν1 and ν2 bands (Figs. 2 and 3) were taken with a sample pressure of 54 torr. Further details of the procedure can be found in the laboratory handout.W

The student handout and additional information for instructors are available in this issue of JCE Online.

Hazards Carbonyl sulfide is toxic; use a vacuum line to fill the storage bulb and gas cell. Students must receive training in the proper use of vacuum equipment (we recommend that

Supplemental Material

Acknowledgment This work was supported by a grant from the National Science Foundation (CHE-9700833). Literature Cited 1. Dierenfeldt, K. E. J. Chem. Educ. 1995, 72, 281–283. 2. Mendelsohn, R.; Monse, E. U. J. Chem. Educ. 1981, 58, 582–583. 3. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 6th ed.; McGraw-Hill: New York, 1996; pp 383–388. 4. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Op. cit., pp 404–416. 5. Garcia, M. V.; Redondo, M. I. J. Chem. Educ. 1985, 62, 887–889. 6. Herzberg, G. Molecular Spectra and Molecular Structure, Vol. 2; Van Nostrand: New York, 1945; p 205. 7. Masukidi, L. S.; Lahaye, J. G.; Fayt, A. J. Mol. Spectrosc. 1991, 148, 281–302. 8. HyperChem, release 4; Hypercube: Waterloo, ON, 1994.

JChemEd.chem.wisc.edu • Vol. 77 No. 12 December 2000 • Journal of Chemical Education

1639