Naphthalene and Azulene I: Semimicro Bomb Calorimetry and

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Naphthalene and Azulene I: Semimicro Bomb Calorimetry and Quantum Mechanical Calculations Carl Salter Department of Chemistry, Moravian College, Bethlehem, PA 18018 James B. Foresman Physical Sciences Department, York College of Pennsylvania, York, PA 17405

At its best, any physical chemistry laboratory experiment should be an investigation of molecular structure and its effect on physical properties. When experimental data are collected, they should be analyzed with the molecular level in mind. The most effective way to achieve this is to complement the experimental work with theoretical calculations. In the past, when electronic calculations were included in lab experiments, the theoretical methods were usually crude and approximate. The best example of this is probably the classic experiment on the UV–visible absorption spectra of a series of carbocyanine dyes, in which the π electrons are treated using the particle-in-a-box model (1): the agreement between theory and experiment is no better than qualitative. With the advent of more powerful desktop computers and the availability of computational chemistry software for these platforms, it is now reasonable to expect undergraduate chemistry students to perform sophisticated quantum mechanical calculations that yield quantitative agreement with traditional lab experiments. An excellent example has recently appeared in this Journal, in which the measurement of the rotation– vibration IR absorption spectrum of HCl is accompanied by detailed quantum mechanical calculations (2). One effective way to introduce students to the importance of quantum mechanical effects is to compare the properties of two molecules that superficially appear to be similar. In this series of papers we will describe laboratory exercises that perform detailed experimental and theoretical comparisons of two geometric isomers of C10H8: naphthalene and azulene. The logical place to begin such a comparison is with total energies: Which isomer is more stable and why? Since the molecules are isomers, a direct measure of their relative stability can be made using the difference between their heats of combustion. This difference, while not large, can be measured by an apparatus that is common in the undergraduate physical chemistry lab: the bomb calorimeter. Although simple theories involving aromatic stabilization can correctly predict which isomer is more stable, calculating an accurate energy difference demands the use of a high level of theory. The goal of this experiment is to compare the heats of combustion of azulene and naphthalene and to relate the observed difference to theoretically computed differences in the energy of the two molecules. Background Naphthalene and azulene are both aromatic hydrocarbons and have the same molecular formula, C10H8, but they differ geometrically.

naphthalene

azulene

For both naphthalene and azulene, valence bond structures can be drawn that contain five C–C single bonds, five C–C double bonds, and eight C–H bonds. A simple bond energy calculation would naively predict that the two molecules have equal heats of combustion. Both naphthalene and azulene are aromatic. Most students assume that naphthalene is more stable because more resonance structures can be draw for it than for azulene (3 vs 2) and because its bond angles should be closer to 120° for pure sp2 bonding. The properties of azulene suggest that it has significant contribution from a structure in which the seven-membered ring has donated a π electron to the fivemembered ring.

This structure accounts for azulene’s large dipole moment, its intense charge-transfer absorption in the visible region, and its tendency to undergo electrophilic aromatic substitution at the five-membered ring. The electron transfer allows both rings to be aromatic, but the charge separation requires energy; so the net effect is that azulene’s π system is more energetic than naphthalene’s. Simple theories of resonance predict that azulene, as a nonalternant hydrocarbon, does not gain as much stability by resonance as does naphthalene; more sophisticated theories of aromaticity also support this conclusion (3). For students the experiment can be explained as an attempt to measure the difference in resonance energies of the two aromatic molecules. We know of only one other undergraduate experiment involving the measurement of resonance energy (4). Since the two molecules are isomers, they have the same combustion reaction: C10H8(s) + 12 O2(g) → 10 CO2(g) + 4 H2O(l) The difference in heats of combustion immediately reflects the difference in the energies of the two molecules. The heat of combustion of crystalline naphthalene is ᎑1232.4 kcal/mol and that of crystalline azulene is ᎑1264.5 kcal/mol. Azulene has the larger (more negative) heat of combustion and is therefore the higher-energy (less stable) isomer (5). The difference in heats of combustion, ᎑32.1 kcal/mol, could be thought of as the enthalpy change for the isomerization of solid azulene to solid naphthalene. Notice that the relative difference in enthalpies of combustion is only 2.5%. A new semimicro bomb calorimeter makes the measurement of this rather small energy difference possible in the undergraduate laboratory; recent developments in electronic structure theory permit accurate calculation of this energy difference on fast, affordable microcomputers.

JChemEd.chem.wisc.edu • Vol. 75 No. 10 October 1998 • Journal of Chemical Education

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Experimental Bomb Calorimetry The Parr 1425 Semimicro Calorimeter, introduced about six years ago, uses the 1107 (22-mL) oxygen bomb. (With a conversion kit sold by Parr, this bomb can be used inside the well-known Parr solution calorimeter.) The bomb’s small size makes it safer and easier to handle than the traditional 1108 “bucket” (342-mL) bomb. In addition, the 1107 bomb handles samples of 200 mg or less, about one-tenth the sample size required by the 1108 bomb. The smaller sample size opens up the possibility of experiments on materials that are either too expensive or too energetic for the larger bomb. We exploit this feature to measure the heat of combustion of azulene. Azulene’s current price is $97 per gram (Aldrich 1995) and it is sold in 1-g amounts only. Since the sample size in a 1108 bomb is 1–2 g, azulene is too expensive for the usual undergraduate bomb. The semimicro bomb permits determinations using just 100 mg of azulene; thus the “price per burn” drops to $10, and 1 g of material will serve for roughly ten trials. (As an alternative to purchasing azulene, it can be synthesized using a procedure previously published in this Journal [6 ]. This preparation is suitable for undergraduate students.) Standardization trials using benzoic acid pellets should be performed as described in the Parr manual to determine the heat capacity of the calorimeter. The mass of water in the Dewar should be the same from one trial to the next. With 450 g of water in the Dewar the heat capacity of the semimicro calorimeter will be about 530 cal/°C (2220 J/°C); under these conditions burning the benzoic acid pellets will produce a 2.5 °C temperature rise. Avoid the common “organic lab”-grade 98% naphthalene; it produces inconsistent results. We used 99% naphthalene and 99% azulene from Aldrich without further purification. Pellets of naphthalene and azulene can be made using the pellet press and small die sold by Parr. The mass of the pellets should be at least 100 mg but should never exceed 120 mg. Pellet masses must be measured on the highest-resolution balance available: 0.01 mg resolution is strongly recommended. The bomb should be filled with 25 atm of oxygen to avoid sooty burns. (The nichrome fuse wire provided by Parr will burn and produce small beads of oxide. This is perfectly normal and should not be taken as evidence of incomplete combustion.) Burning these pellets will produce a temperature rise of 1.7–1.9 °C. Table 1 presents results obtained by Moravian College students during 1997. It shows that students can obtain excellent results. The trials can be corrected for the combustion of the fuse wire: each cm of wire releases 2.3 cal of heat. This correction, if made, should be applied to the standardizations with benzoic acid as well as to the trials with azulene and naphthalene. The heat released by combustion of the fuse wire will be about 10–13 cal/trial, typically about 1% of the total heat liberated. (For nichrome wire there is no correction for electrical heating.) Table 1 shows that the wire correction improves the accuracy of the individual heats of combustion but is not crucial for obtaining a good difference in the heats of combustion. The calibration trials using benzoic acid and the experimental trials on naphthalene and azulene were also corrected for constant-volume combustion. This correction is ∆H = ∆U + ∆ngRT, where ∆ng is the change in the number of moles of gas due to the combustion reaction. 1342

Table 1. Experimental Enthalpy of Combustion, ⌬ H/ kcal mol –1 C10H8 Isomer

W/O Wire Correction

Naphthalene

᎑1236.8 (4.7)

᎑1232.3 (4.4)

᎑1232.4

Azulene

᎑1270.1 (5.4)

᎑1266.5 (5.4)

᎑1264.5

᎑33.3 (7.2)

᎑34.2 (7.0)

᎑32.1

Difference

W/ Wire Correctiona

Literatureb

NOTE: Values are the average of three student trials, corrected for constant-volume combustion. Standard deviation is in parentheses. aAssuming an average wire burn of 5 cm at 2.3 cal/cm. Applied to benzoic acid calibration trials and trials on naphthalene and azulene. bValue for crystal ( 5).

Table 2. Calculated Electronic and Thermal Energies for Gas Phase at 300 K, kcal/mol C10H8 Isomer

Eelec

Etrans

Erot

Evib

Naphthalene

᎑242149.95

0.89

0.89

93.25

᎑242054.91

Azulene

᎑242115.94

0.89

0.89

91.36

᎑242022.79

᎑34.00

0.00

0.00

᎑1.89

᎑32.11

∆E

Etotal

NOTE: B3LYP/6-31G(D)//RHF/6-31G(D) model of theory described in text.

For benzoic acid ∆ng = ᎑1/2, so the correction is only ᎑0.3 kcal/mole at 25 °C; for naphthalene and azulene ∆ng = ᎑2 and the correction is ᎑1.2 kcal/mole. Although they are small, it is pedagogically desirable to make these corrections. Standard deviations in the heat of combustion and the energy difference are reported to indicate the reproducibility of the experiment. The errors in the mean values as measured by either the standard deviation of the mean (standard error) or 95% confidence limits are slightly smaller and could be made smaller still by increasing the number of trials. When t tests are applied to the data, with or without the wire correction, results indicate a >99% chance that the means of the two sets of data are different. With minimal effort and minimal amounts of azulene, good experimental agreement with the literature can be obtained by students using the semimicro bomb. Our experience indicates that consistent results depend on consistently filling the bomb to a presure of 25 atm. Underfilling occasionally leads to sooty burns, which must be rejected, and a sooty azulene burn is an economic tragedy. Parr has engineered a simple and clever solution to filling this palmsized bomb, but its mechanism is not obvious to undergraduates who have had no experience with O-ring seals. We have found it helpful to have each student perform a “dry run”, assembling and sealing the bomb without wire or pellet, pressurizing it to 25 atm, releasing the pressure, and taking it apart. This lessens their anxiety about filling the bomb with oxygen, lets them see how the O-rings make seals, and gives the instructor an opportunity to impress on them the importance of filling to the right pressure. Electronic Structure Calculations Using Gaussian 94 Solving Schrödinger’s equation for molecules the size of naphthalene and azulene has always been a difficult task. Typically the Hückel approximation is used to treat large aromatic molecules, but this approach limits the calculation to a description of the π structure of the molecule and invokes some

Journal of Chemical Education • Vol. 75 No. 10 October 1998 • JChemEd.chem.wisc.edu


serious assumptions about the resonance and overlap integrals among the interacting π orbitals. Most students and instructors will view the Hückel method as a gross oversimplification, but it is still a useful point of departure for discussing naphthalene and azulene. Simple Hückel calculations yield the following energies for the π-electronic structure of naphthalene and azulene (7 ): Naphthalene Azulene

Eπ = 10α + 13.6832β Eπ = 10α + 13.3635β ∆ Eπ = 0.3197β

Using a β value of ᎑32 kcal/mole, the difference in energy between the two isomers is ᎑11 kcal/mol. Hückel theory yields a correct qualitative result, but clearly a more sophisticated model will be needed to accurately reproduce the experimental energy difference. Complete-electron calculations treating both the σ and π structure of these molecules are more satisfying, and such calculations are now possible on 486 or Pentium microcomputers. We will use Gaussian 94 (8), available for PC Windows or Unix workstations, to compute the energies of naphthalene and azulene. The theoretical models available in Gaussian 94 are still not exact solutions to the equations of quantum mechanics, but their accuracy is sufficient to reproduce many experimental heats of reaction. Comparisons of the results for these models with known thermodynamic data show that they are reliable predictive tools. For an overview of these models, their approximations and successes, consult references 9–11. Reference 11 is especially aimed at the beginner, while 9 and 10 provide more detail. Based on its success in predicting accurate enthalpy changes for reactions (see ref 9), the following ab initio model is recommended for the calculation of the energy difference. First, the geometry of each molecule is optimized at the RHF/6-31G(D) level, and the frequencies of vibration of each molecule (required for the computation of the thermal energy at 300 K) should be determined at this level. To accurately compute the electronic energy difference between naphthalene and azulene, our model must include some electron correlation: the Becke3LYP model (hereafter abbreviated B3LYP), a hybrid form of density functional theory, serves this purpose. It is possible, but not necessary, to perform the geometry optimizations and frequency calculations at the B3LYP/6-31G(D) level. Instead, a second calculation using the B3LYP/6-31G(D) model on the RHF/6-31G(D) optimized structures will yield adequate results. This type of calculation is called a “singlepoint calculation” because it is invoked on a fixed structure without further geometry optimization. The electronic energies found from the B3LYP/6-31G(D) single-point calculations are then added to the thermal energies computed from the RHF/6-31G(D) frequencies. The results are the total energies of naphthalene and azulene at 300 K. Results using this theoretical model are presented in Table 2. Gaussian input files for the required calculations on naphthalene and azulene are listed in the Appendix. Note the excellent agreement of the theoretical energy difference with the experimental difference found by bomb calorimetry. Actually, it is fortuitous that the theoretical energy difference matches the literature value of ᎑32.1 kcal/mole— the electronic structure calculations actually predict the gasphase energy difference, not the energy difference of the crystal

Table 3. Energies Calculated Using Various Theoretical Models at 300 K, kcal/mol Model [ref]

Naphthalene

∆H

Azulene

140.31

182.70

᎑42.40

HF/6-31G(D)

᎑240463.89

᎑240420.69

᎑43.20

B3LYP/6-31G(D)

᎑242056.02

᎑242022.36

᎑33.65

B3LYP/6-311++G(D,P)

᎑242116.42

᎑242083.27

᎑33.15

AM1

CBS-4/CBS-Q [12]

–

–

᎑35.2± 1.0

Experimental [13, 14]

–

–

᎑35.3± 2.2

NOTE: Energies include both the electronic and thermal energy. Geometries were obtained by energy minimization at the stated level of theory.

phase. Nonetheless, students should be very pleased with the superb quantitative agreement between theory and experiment. The contributions of different types of energy to the overall energy difference can be determined directly from the Gaussian output files. It is a valuable exercise for students to summarize the results of the theoretical calculations in a table like Table 2. Students can see that energy difference between the isomers is dominated by the electronic component, but also that the difference in the vibrational energy between the two isomers does account for 6% of the computed energy difference. They can also see that the translational and rotational components of thermal energy are equal for both isomers, and they can verify that these correspond to the classical value given by 1.5 RT. The time required for these calculations is reasonable. The calculation on azulene requires about 9 hours on a Silicon Graphics Indy R5000 workstation. The naphthalene job is a bit shorter (5.5 h) because of symmetry. A Pentium 90 processor would take 4–5 times longer. This means the jobs could not be run during a lab period, but each job could be finished by leaving a microcomputer running over a weekend. In the meantime, students can perform both semiempirical and other ab initio molecular orbital calculations to see how the theoretical results compare from one level of theory to the next and to determine what level of theory is needed to obtain the accuracy of the calorimeter. The results of such a study are summarized in Table 3. For each theoretical model shown in Table 3 a complete geometry optimization has been performed on the two molecules. The AM1 model has been parameterized by matching heats of formation for standard organic molecules, so it is close to the correct value but is a little high owing to the unusual bonding characteristics of azulene. Hartree–Fock (HF) theory using a 6-31G(D) basis set is not much of an improvement because it still neglects electron correlation. Density functional theory is the closest to experiment, since it corrects for some of the effects of electron correlation. We can see that the theory has converged with respect to basis set, since the larger 6-311++G(D,P) basis set leads to an answer that is not significantly different from the one obtained at 6-31G(D). Optimizing the geometry at the B3LYP/6-31G(D) level improves the results slightly over the single-point method used in Table 2, but it may not be worth the increase in computational time. Also listed in Table 3 are the results from a family of highly accurate models that use the complete basis set method (CBS) (12). These are presented with error bars because there is a range of results depending on which variant of the method


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one chooses. These models have extremely good agreement with experiment. The experimental value listed in Table 3 is for the gas phase enthalpy difference between the two isomers at 300 K (13, 14); note that this difference is slightly higher than the crystal difference given above. (The crystal structure of azulene actually stabilizes azulene slightly with respect to naphthalene, presumably because the dipole moment of azulene yields a higher lattice energy.) It is remarkable that theory has achieved a level of accuracy rivaling experimental determinations of these quantities.

Discussion Students should realize that the energy difference between the ground states of naphthalene and azulene can be accurately measured and, with a sufficient level of theory, accurately calculated. The calculated energy difference using the recommended theoretical model falls inside the error limits of the difference measured by bomb calorimetry. In the end, the calculations available to students through Gaussian are more accurate than the Parr calorimeter.

Gaussian Input Files for Naphthalene and Azulene Using the B3LYP/6-31G(D)//HF/6-31G(D) Model Chemistry Gaussian Input File for Naphthalene %Chk=naphthalene #p HF 6-31G(D) FOPT FREQ =ReadIsotopes Naphthalene 01 C C C C C C C C C C H H H H H H H H

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

300

1.0

0.9135

0 0 2.4 1.2 ᎑2.4 ᎑1.2

0.7 ᎑0.7 ᎑0.7 ᎑1.4 ᎑0.7 ᎑1.4

1.2 2.4 ᎑1.2 ᎑2.4 3.4 1.2 ᎑3.4 ᎑1.2

1.4 0.7 1.4 0.7 ᎑1.2 ᎑2.5 ᎑1.2 ᎑2.5

3.4 1.2 ᎑1.2 ᎑3.4

1.2 2.5 2.5 1.2

12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1 —link1— %Chk=naphthalene #p B3LYP 6-31G(D) Geom =Checkpoint Naphthalene 01

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Explanation checkpoint filename route section title charge and multiplicity specification of atomic coordinates in Angstroms

Temp Pressure Scale Isotope of atom 1 Isotope of atom 2 etc.

Second Job Marker checkpoint filename route section title charge and multiplicity

Gaussian Input File for Azulene %Chk=azulene #p HF 6-31G(D) FOPT FREQ =ReadIsotopes Azulene 01 C C C C C C C C C C H H H H H H H H

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 ᎑1.2 1.2 ᎑0.7 0.7 ᎑1.6 1.6 ᎑1.3 1.3 0 0 ᎑2.2 2.2 ᎑2.7 2.7 ᎑2.1 2.1

2.7 ᎑2.5 1.9 1.9 0.5 0.5 ᎑-0.5 ᎑0.5 ᎑1.9 ᎑1.9

—link1— %Chk=azulene #p B3LYP 6-31G(D) Geom =Checkpoint

1

title charge and multiplicity specification of atomic coordinates in Angstroms

2.2 2.2 ᎑0.3 ᎑0.3 ᎑2.6 ᎑2.6

12 12 12 12 12 12 12 12 12 12 1 1 1 1 1 1 1 1

0

checkpoint filename route section

3.8 ᎑3.6

300 1.0 0.9135

Azulene

Explanation

Temp Pressure Scale Isotope of atom 1 Isotope of atom 2 etc.

Second Job Marker checkpoint filename route section title charge and multiplicity

Journal of Chemical Education • Vol. 75 No. 10 October 1998 • JChemEd.chem.wisc.edu


An interesting way to implement the experiment in a traditional two-semester physical chemistry sequence is to carry out the bomb calorimetry experiments in the first semester when thermodynamics is discussed and then revisit the problem during the second semester, when quantum chemistry is usually covered. In this way the experiment provides a context for launching into the realm of ab initio molecular orbital theory, the level of theory needed to understand the difference observed in the first semester experiment. As an extension of the experiment students can compute other isomers of C10H8 and predict heats of combustion for these molecules. A prediction of the properties of guaiazulene, a natural product containing the azulene system, is another possible extension. Finally, although we recommend this experiment for the physical chemistry lab, its application is not limited to physical chemistry. It would be a logical extension to the synthesis of azulene in an advanced synthesis laboratory or advanced organic chemistry course. Other properties of naphthalene and azulene could be the subject of experimental and theoretical comparison. In subsequent papers we plan to outline lab exercises on the IR, UV–vis, and 13C NMR spectra of the two compounds as well as a study on the site of electrophilic aromatic substitution. Acknowledgments We would like to thank Gaussian, Inc., for its generous support of this work. CS would like to thank Tom Tingle of the Parr Instrument Company for helpful discussions. Literature Cited 1. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 6th ed.; McGraw-Hill: New York, 1996; p 378. Bahnick, D. A. J. Chem. Educ. 1994, 71, 171. 2. Williams, D. L.; Minarik, P. R.; Nibler, J. W. J. Chem. Educ. 1996, 73, 608. 3. Schaad, L. J.; Hess, B. A. J. Chem. Educ. 1974, 51, 640. 4. Sime, R. J.; Physical Chemistry: Methods, Techniques, and Experiments; Saunders: Philadelphia, 1990; p 440. Pickering, M. J. Chem. Educ. 1982, 59, 318. 5. CRC Handbook, 73rd ed.; Lide, D. R., Ed.; CRC: Boca Raton, 1992–93; p 5-90. 6. Lemal, D. M.; Goldman, G. D. J. Chem. Educ. 1988, 65, 923. For a microscale version of this synthesis, see Brieger, G. J. Chem. Educ. 1992, 69, A262. 7. Lowe, J. P. Quantum Chemistry; Academic: Boston, 1993.

8. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Bomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Rev. D.3; Gaussian, Inc: Pittsburgh, PA, 1995. 9. Foresman, J. B.; Frisch, A. E. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian, Inc.: Pittsburgh, PA, 1996. 10. Hehre, W. J.; Radom, L; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. 11. Foresman, J. B. In What Every Chemist Should Know About Computers; Swift, M. L., Zielinski, T. J., Eds.; ACS Books: Washington, DC, 1997; Chapter 14. 12. Ochterski, J. W.; Petersson, G. A.; Montgomery, J. A., Jr. J. Chem. Phys. 1996, 104, 2598. 13. Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17(Suppl. 1). 14. Cox, J. D.; Pilcher, G. Thermochemistry of Organic and Organometallic Compounds, Academic: New York, 1970.

Appendix Gaussian Input Files for Naphthalene and Azulene Using the B3LYP/6-31G(D)//HF/6-31G(D) Model Chemistry The input files on page 1344 will perform a geometry optimization and vibrational analysis at RHF/6-31G(D) and then automatically perform a single-point energy calculation at B3LYP/631G(D) using the RHF/6-31G(D) optimized structure. Thus it will perform the two required Gaussian calculations as a single task. The required input files can be created using any standard molecular sketching program (such as HyperChem or PCModel) by making the graphics program output a file containing the Cartesian coordinates of the atoms. Then the other job information can be entered by using an ASCII text editor. The scale factor of 0.9135 appears in the input because this is the recommended value to account for systematic errors in the theory at this level (determined by comparing to a wide variety of experimental thermal energies). It should be noted that the input file for azulene forces the molecule to have C 2ν symmetry. Some molecular sketching programs may not provide the same symmetry; computational results may be slightly different if the molecule relaxes to a lower symmetry. In fact, this relaxation will happen at the level of theory used here (indicated by the presence of one imaginary frequency in the output file). This distortion is an artifact of the theory and results in only a minor difference in computed energies.


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Naphthalene and Azulene I: Semimicro Bomb Calorimetry and

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