Particle in a Disk: A Spectroscopic and Computational Laboratory

Laboratory Experiment pubs.acs.org/jchemeduc

Particle in a Disk: A Spectroscopic and Computational Laboratory Exercise Studying the Polycyclic Aromatic Hydrocarbon Corannulene E. Ramsey Frey,† Andrzej Sygula,‡ and Nathan I. Hammer*,† †

Department of Chemistry and Biochemistry, University of Mississippi, University, Mississippi 38677, United States Department of Chemistry, Mississippi State University, Mississippi State, Mississippi 39762, United States

‡

S Supporting Information *

ABSTRACT: This laboratory exercise introduces undergraduate chemistry majors to the spectroscopic and theoretical study of the polycyclic aromatic hydrocarbon (PAH), corannulene. Students explore the spectroscopic properties of corannulene using UV−vis and Raman vibrational spectroscopies. They compare their experimental results to simulated vibrational spectra and the molecular structure obtained from computational chemistry to other PAHs, including C60. The delocalized electron in corannulene is also conceptually explored using the particle in a disk model. This laboratory exercise allows students to explore multiple physical chemistry concepts in one, 3 h laboratory exercise centered around one theme.

KEYWORDS: Upper-Division Undergraduate, Physical Chemistry, Hands-On Learning/Manipulatives, UV−vis Spectroscopy, Raman Spectroscopy, Computational Chemistry, Nanotechnology, Laboratory Instruction

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INTRODUCTION The physical chemistry laboratory course in many chemistry departments has been scaled back from the traditional twosemester period to just one with the number of hours also reduced to a single credit hour.1 This reduction has a variety of origins, including the reduction of the number of hours in liberal arts majors and the introduction of new specialty courses such as environmental and forensic chemistry. A challenge, therefore, is the ability to provide students with enough laboratory experience that covers all of the important areas of physical chemistry including thermodynamics, kinetics, spectroscopy, and quantum chemistry in a one credit hour course in a single semester. Here, we show that the study of the nanomaterial building block corannulene (see Figure 1) offers instructors the opportunity to cover a variety of concepts in a single physical chemistry laboratory meeting. These include the study of nanomaterials, quantum chemistry, vibrational spectroscopy, UV−vis absorption spectroscopy, and a confined particle problemthe particle in a disk.2 By studying corannulene’s physical properties both experimentally and theoretically, students are introduced to not only the use of spectroscopic techniques such as UV−vis and Raman spectroscopies in the study of nanomaterials but also computational chemistry and modeling in the laboratory setting. Corannulene is a polycyclic aromatic hydrocarbon (PAH), meaning it is composed of fused aromatic rings that contain only carbon and hydrogen. It belongs to the novel subclass of the curved-surface PAHs known as “buckybowls” or “fullerene fragments.”3−7 It was first isolated in 1966 by a multistep © XXXX American Chemical Society and Division of Chemical Education, Inc.

Figure 1. Molecular models of the popular polycyclic aromatic hydrocarbon nanomolecular building blocks. A, Pyrene; B, perylene; C, corannulene (head-on); D, corannulene (rotated to show curvature); and E, buckminsterfullerene (C60).

organic synthesis,3 and now multiple pathways exist for the synthesis of corannulene, even on the kilogram scale.8 With a molecular formula of C20H10, corannulene is composed of one cyclopentane ring fused with five benzene rings and can be thought of as one-third of the important molecule buckminsterfullerene, C60.9 The aromaticity that corannulene and other PAHs possess is an advantageous chemical property in which a conjugated ring of unsaturated bonds and empty orbitals exhibits a stabilization stronger than that which would be expected by the stabilization of conjugation alone.10

A

dx.doi.org/10.1021/ed4005062 | J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Laboratory Experiment

student handout. The energy levels of the electron in the disk are given by

PAHs such as corannulene, as well as fullerenes, generally absorb light in the ultraviolet and visible regions of the electromagnetic spectrum and also strongly fluoresce because of the π-electron conjugated systems. This makes them very useful molecular electronic building blocks11,12 for light harvesting13−15 and photoemission applications.16−18 PAHs in general, and corannulene in particular, are thus good models to illustrate the photophysical properties of electronically active nanomaterials for students.19,20 The absorption and emission ranges of PAHs vary due to a number of factors including the substituent group, conjugation length and branching, and molecular symmetry. Because corannulene is an organic molecule, it also dissolves well in organic solvents such as toluene, cyclohexane, methylcyclohexane, isopentane, and dichloromethane.21 The availability of corannulene on a large scale allowed for the synthesis of its several derivatives5−7an important feature for applications that use nanomolecular building blocks with designer properties. Because of the growth in research in the field of nanotechnology and the desire to engineer materials with tunable photophysical properties, the study of molecular building blocks such as corannulene and other PAHs continues to rapidly accelerate. For example, complementarity of the concave surfaces of corannulene and other buckybowls with the convex surfaces of fullerenes brings about a possibility to construct molecular clips and tweezers with the potential for the formation of supramolecular assemblies with fullerenes.22 Although corannulene has only been available commercially for a short time, a number of experimental and theoretical studies have explored its photophysical properties. In 2006, Yamaji et al. reported on absorption and fluorescence spectra of corannulene in cyclohexane at 295 K.21 Absorption peaks were observed around 260 and 290 nm in an absorption range of about 220−300 nm. The fluorescence spectrum for corannulene reveals a broad peak around 450 nm. In 2008, Rouillé et al. reported on the infrared and Raman spectra of corannulene grains embedded in polyethylene or CsI pellets.23 The illustration of the particle in a box model in the undergraduate physical chemistry laboratory, using the absorption spectra of linear-conjugated dye molecules, is a favorite experiment in many chemistry departments.24,25 In the classic experiment, the absorption spectra of three cyanine dyes are recorded, and the lengths of the conjugated π orbitals are determined from the measured absorption maxima. Confined particle problems that possess distinctive geometries and boundary conditions offer physical chemistry students unique challenges, and many variations have appeared in this journal. Examples include the one-dimensional particle in a box,24−26 two-dimensional particle in a box,27 particle in a onedimensional champagne bottle,28,29 particle in an isoceles right triangle,30 particle in an equilateral triangle,31 particle in a sphere,2,32 and particle in a disk2 models. As in the case of the cyanine dye experiment, the electronic energy levels of C60 (see Figure 1) can be described by the particle in a sphere model,2,32 and the allowed transitions can be compared to the experimental absorption spectra of C60 in hexane.33 The present laboratory exercise is offered not as a replacement to the traditional cyanine dyes experiment but rather as an additional option for instructors who wish to combine multiple concepts into one laboratory exercise. Newhouse and McGill previously derived the particle in a disk model in this journal,2 and a brief summary of their derivation is included in the

Em , n =

αm2 , nℏ2 2μrb2

(1)

where μ is the mass of the electron, rb is the radius of the disk, and αm,n is the nth root to the mth order Bessel function. The αm,n values are thus the quantum numbers of interest, although a direct correlation to the molecular orbitals in corannulene is not possible as is the case in the linear cyanine dyes experiment and in the case of C60. Students, however, can determine rb for corannulene using the results from the electronic structure calculations and measuring the diameter (across terminal carbon atoms). The diameter of corannulene, optimized using the B3LYP/6-31+G* level of theory, is 6.5 Å, which means rb = 3.25 Å.

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EXPERIMENTAL DETAILS This laboratory exercise was performed for two semesters in a 3 h physical chemistry laboratory class. Corannulene was obtained from two different sources. It was synthesized by one of the authors (A.S.) and was purified by recrystallization using ethanol. Corannulene was also purchased from TCI America (Portland, Oregon), and C60 was purchased from Aldrich. Perylene bisimide (PBI, a perylene derivative) and pyrene were synthesized by co-workers at the University of Mississippi. The UV−vis absorption spectra of corannulene, C60, pyrene, and PBI were obtained in cyclohexane using a Cary 100 Bio UV−vis spectrophotometer. The Raman spectrum of corannulene was recorded using the 514.5 nm laser line from an Ar+ laser and microRaman spectrometer, as described earlier.34 Theoretical calculations that used the Gaussian software package35 were performed prior to data acquisition so that the students could visualize the geometry and normal modes of corannulene. The GaussView36 software program was employed to construct corannulene, although other graphical drawing packages could be employed. Using GaussView, students can start with the built-in geometry of C60 and delete atoms until only C20 remains. Ten hydrogen atoms are then added to the outer benzene rings to complete the structure. The symmetry of corannulene should be constrained to the C5v point group. An optimization and frequency calculation with Raman intensities was performed using either the HF method or the B3LYP density functional method and the 6-31+G* basis set, depending on the speed of the computers to be used for the laboratory exercise. Instructors may wish to have their students compare their results using other methods such as semiempirical or the MP2 method and also examine the effects of changing the size of the basis set. After the calculations are completed, students construct simulated Raman spectra from the vibrational frequencies and Raman intensities by summing the Lorentzian functions of each normal mode.1 Alternately, if a Raman spectrometer is not available, students could obtain an infrared absorption spectrum in a salt pellet or by using an attenuated total reflection Fourier transform infrared spectrometer (ATR-FTIR) and then compare their experimental results to the simulated infrared spectra. The derivation of the particle in a disk model can be introduced to the students as an extension to the particle in a box model in the prelaboratory lecture. A variation of this laboratory exercise involves the modeling of the vibrational frequencies of C60 and the B




Figure 3 compares the experimental and theoretical Raman spectra from 150−1650 cm−1 for solid state corannulene. The

calculation of the excited states of both corannulene and C60 using the ZINDO semiempirical method or the B3LYP timedependent density functional theory (TDDFT) method as demonstrated by Rouillé et al.23 Although the results of the ZINDO method will be much quicker, the TDDFT results match better with the experiment. These additional computational chemistry exercises (including calculations that use larger basis sets and the MP2 method) will likely require more time than allotted for one class meeting and may require students to start their calculations and then return for the results at a later time. Further details are provided in the Supporting Information.

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RESULTS AND DISCUSSION Seven students performed this laboratory exercise at the University of Mississippi in 2012, and eight students performed it in 2014. After a brief 15 min prelaboratory discussion about the particle in a disk model and nanomaterial building blocks in general, students in pairs constructed corannulane using GaussView software starting from C60 as a basis and then started the combined optimization and frequency calculations using Gaussian 09. As a group, the students then acquired the UV−vis spectra of the four PAHs and studied the differences between them. The students then acquired the Raman spectrum of corannulene as a group. After data acquisition, the students explored the location in wavenumbers of normal modes using GaussView and compared the simulated spectrum in GaussView to the experimental spectrum they had just acquired. The students also animated the normal modes in GaussView in order to visualize which ones yielded the strongest experimental intensities. Figure 2 shows the UV−vis absorption spectra of corannulene compared to those of C60, pyrene, and PBI. PBI

Figure 3. A, Comparison of theoretical and experimental Raman spectrum of corannulene; B, normal mode displacements of the most intense Raman active mode at 1430 cm−1.

agreement between the experiment and theory is very good and illustrates to students the usefulness of modeling the properties of new materials theoretically. This is especially true in the design of new materials where the properties can be simulated prior to synthesis. Students can visualize the atom displacements of the different normal modes using a program such as GaussView,36 Molekel,37 Molden,38 Jmol,39 or Vibalizer.40 Shown in Figure 3, panel B is a representation of the motion of the atoms in the most intense normal mode at 1430 cm−1 (ring breathing mode). In this mode, the central pentagon expands and contracts while carbon−carbon bonds in the surrounding hexagons also stretch. The surrounding hydrogen atoms also bend. After the laboratory period, the students can construct their own simulated Raman spectra from the computed vibrational frequencies and Raman intensities by summing Lorentzian functions for each normal mode.1 The 2014 physical chemistry laboratory class participated in a survey about the exercise. The survey consisted of five questions: (1) Did you find the study of nanomolecular building blocks and in particular, corannulene, interesting and useful? (2) Did you learn about the use of electronic (UV−visible absorption) and vibrational spectroscopy and in particular, Raman spectroscopy, to study nanomaterials? (3) Did you learn about the use of quantum chemistry to study the optimized molecular structure, vibrational energy levels, and motions of different normal modes in corannulene? (4) Did you find it useful and enlightening to compare the experimental vibrational spectroscopy results to the theoretical simulations? (5) Did you find the particle in a disk model interesting? The participants were asked to respond on a four-point scale where 0 represented “strongly disagree”, 1 represented “disagree”, 2 represented “neutral”, 3 represented “agree”, and

Figure 2. Comparison of the UV−vis absorption spectra of the PAHs corannulene (C20H10), buckminsterfullerene (C60), perylenebisimide (PBI), and pyrene.

exhibits the lowest energy absorption spectrum, while pyrene, C60, and corannulene have features at much higher energies. Corannulene’s high symmetry (C5v) results in a number of forbidden electronic transitions and thus fluoresces in the blue. Despite its high symmetry, C60 displays many available electronic transitions in the visible region of the spectrum and exhibits absorption peaks from 200−700 nm.33 The most dominant transitions, however, lie below 400 nm. C



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4 represented “strongly agree”. The average responses are indicated in Table 1. All of the average responses were at least

Average Responsea (N = 8)

1 2 3 4 5

3.4 3.2 3.6 3.8 3.0

a

Scale used ranged from 0 (“strongly disagree”) to 4 (“strongly agree”).

3.0, which indicates that the students agreed that components of the laboratory exercise were interesting and useful and that they also learned about the use of UV−vis and vibrational spectroscopies and quantum chemistry to study nanomaterials. Interestingly, students agreed most with the statement that the comparison of the experimental vibrational spectroscopy results to the theoretical simulations was useful and enlightening.

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CONCLUSIONS This laboratory exercise offers students the opportunity to study both experimentally and theoretically the properties of the unique nanomolecular building block corannulene and compare its properties to other PAHs in one laboratory setting. Students learn how to employ computational chemistry to predict the physical properties of such building blocks and are also introduced to the particle in a disk model. When surveyed, students indicated that they found the comparison of the experimental vibrational spectroscopy results to the theoretical simulations very useful and enlightening.

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ASSOCIATED CONTENT

S Supporting Information *

Instructor notes and a sample student handout. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

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Table 1. Distribution of Student Responses to Survey Regarding the Laboratory Exercise Question


AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS N.I.H. would like to acknowledge support from the U.S. National Science Foundation EPS-0903787 and NSF-0955550 as well as the University of Mississippi College of Liberal Arts, Department of Chemistry and Biochemistry, Office of Research and Sponsored Programs, the Sally McDonnell Barksdale Honors College, and the NSF-funded Ole Miss Physical Chemistry Summer Research Program REU (CHE-1156713). A.S. thanks the Office of Science, U.S. Department of Energy for the support through Grant No. DE-FG02-04ER15514. The authors would also like to acknowledge Kristina Cuellar, Louis McNamara, Samantha Reilly, John Kelly, and Debra Jo Scardino Sage for their contributions to the development of this laboratory exercise and Daniell Mattern and Jared Delcamp for the synthesis of PBI and pyrene, respectively. D




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Particle in a Disk: A Spectroscopic and Computational Laboratory

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