In the Classroom
Molecular Modeling Exercises and Experiments
Using a Molecular Modeling Program to Calculate Electron Paramagnetic Resonance Hyperfine Couplings in Semiquinone Anion Radicals
W
Alice Haddy Department of Chemistry and Biochemistry, UNC-Greensboro, Greensboro, NC 27402;
[email protected] The availability of computers and software for modeling molecular properties now enables students to perform sophisticated and accurate calculations of chemical properties. A common application of molecular modeling is in the calculation of molecular orbitals and their correlation with spectroscopic properties. Experience with such techniques familiarizes students with some of the approximation methods used for modeling molecular orbitals and prepares them for application of these methods after graduation. In a well-established experiment for the physical chemistry laboratory, described in Experiments in Physical Chemistry by Shoemaker, Garland, and Nibler (1), students produce electron paramagnetic resonance spectra of semiquinone anions by base-catalyzed air oxidation of hydroquinones (Scheme I). O
OH
-0.5
OH −, O2
OH −, O2
O -0.5
OH p-hydroquinone
O
p-semiquinone
O p-benzoquinone
Scheme I The base-catalyzed air oxidation of p-hydroquinone to p-benzoquinone. The EPR-visible form is the semiquinone intermediate, represented with a split charge to reflect the electron delocalization.
In the traditional version of the experiment, hyperfine couplings to the ring hydrogens are estimated from carbon atom electron populations given by Hückel theory. This method is limited in its accuracy and can be carried out by hand for only the unsubstituted semiquinone anion. In the modification presented here, hydrogen hyperfine couplings are based on hydrogen atom electron populations, which are calculated by semiempirical molecular orbital methods using HyperChem or another molecular modeling program. The exercise can be used in conjunction with the EPR spectroscopy lab experiment, in which the student observes several semiquinone spectra, or it can be used as a stand-alone computational exercise. Experimental Procedure
Background Computer-based molecular orbital calculations were first established in the 1960s with the methods worked out by Pople and coworkers (2, 3). For this monumental work, Pople shared the 1998 Nobel Prize in Chemistry. The earliest semiempirical methods developed were CNDO (complete neglect of differential overlap) and INDO (intermediate neglect of 1206
differential overlap), upon which numerous other modifications were based. The INDO method allowed separation of the electron pairs into α and β states, so that spin densities could be calculated. EPR measurements of organic radicals provided one way to experimentally check the INDO calculations. While the INDO method proved to be quite accurate for many simple organic radicals, it did not work well for semiquinones. Further refinements of the basic method greatly improved the results. Quinones are of continuing interest to researchers because of their importance as electron acceptors in the electron transport chains of all living systems. Recent computational studies have employed density functional methods for molecular orbital calculations of quinones in all oxidation states (4–6 ). Although generally less favored for research in recent years, semiempirical methods are widely available and reasonably accurate and therefore provide an excellent demonstration of the principles of computer-based MO calculations for students.
General Method The calculation of orbital electron populations in an organic molecule is carried out in two major steps: construction and geometry optimization of the molecule, and a single point molecular orbital calculation using the optimized structure. During the single point calculation, a log file is used to record the parameters resulting from the calculation, including the electron population at each atom in the molecule. The electron populations are then used to calculate spin densities and the hyperfine coupling constants. Because this laboratory exercise makes an in-depth use of the molecular modeling program, the students should have enough experience with the program to be comfortable with the typical manipulations and molecular orbital calculation for simple molecules. Prior assignments should be made in either the physical chemistry lecture or laboratory setting. In addition to the tutorials provided by the program vendor, a molecular orbital calculation of the NO molecule is suggested.W This ties in well with the lecture course discussion of diatomic molecular orbitals and demonstrates the use of the program for molecules with unpaired electrons. Guiding the Students The principles behind the calculation methods should be discussed with the students (see Supplemental MaterialsW). For example, semiempirical methods make use of spectroscopic or other physical (i.e., empirical) data to estimate values of many of the integrals used for the calculation. Hartree– Fock self-consistent field approximation is also used during the semiempirical calculation. A distinction needs to be made
Journal of Chemical Education • Vol. 78 No. 9 September 2001 • JChemEd.chem.wisc.edu
In the Classroom
between restricted and unrestricted Hartree–Fock approximations, since the restricted approximation is not appropriate for the calculation of electron spin densities. Students should clearly understand that a geometry optimization of the molecule needs to be carried out before the final molecular orbital electron populations are recorded in the log file. Separate geometry optimization exercises, in which bond lengths and angles are analyzed, can be assigned to reinforce this idea. For this computational exercise, geometry optimizations are best carried out using the same semiempirical method as will be used for the final calculation, but the instructor has the option of assigning a molecular force field for this step. Students can often understand the idea behind the molecular force field approach, since it is based on classical concepts. The substituted semiquinones chosen for this exercise should not include molecules that will require consideration of more than one conformer; that is, the molecules should have no rotating side-groups. For this reason, results presented in the Supplemental MaterialsW are mainly for unsubstituted and chloro-substituted semiquinones. A particularly ambitious student may be able to carry out the calculation for the methylp-semiquinone, for which two conformers must be considered. Once the electron populations have been found, the calculation of the hydrogen atom hyperfine coupling constants is fairly simple. First spin densities are calculated by taking the difference between the α and β electron populations for each hydrogen 1s orbital. Then the spin densities are converted to hyperfine constants, in gauss, by comparison with the theoretical hyperfine constant for a lone hydrogen atom (which has a spin density of 1). Students should gain an understanding of how delocalization of the electron in a molecule reduces the pure hyperfine constant.
12). An example of the results expected are shown in Table 1. The INDO method generally provides the worst prediction of the experimental results, whereas AM1 usually provides the best; MNDO often gives the next best prediction. Students should be asked to consider some of the following questions:
Discussion
I would like to thank Surya Satapathy for assistance during the early stages of this project and Dennis Burnes for implementing this experiment in the UNCG Physical Chemistry Laboratory course. I also thank the JCE feature editor Ronald Starkey for a helpful addition to the semiquinone calculation. This work was supported by a grant from the National Science Foundation.
For each semiquinone considered, students should carry out the calculation using at least two semiempirical methods to gain an appreciation for their relative accuracies. Students can compare their calculations either with their own experimental results or with literature values. While the calculation gives the sign of the hyperfine coupling constant, the sign is not apparent from an experimental continuous wave spectrum. Some literature resources can be provided to the students (7– Table 1. Calculations for the p-Semiquinone Anion Radical Using Various Semiempirical Methods Semiempirical Method
Electron Population a
Hyperfine Constant/ Gauss b
α
β
Spin Density (α – β)
INDO
0.533012
0.534903
᎑0.001891
᎑0.959
MINDO3
0.511481
0.519480
᎑0.007999
᎑4.055
MNDO
0.482192
0.487547
᎑0.005355
᎑2.714
AM1
0.446240
0.451830
᎑0.005590
᎑2.834
PM3
0.454454
0.462362
᎑0.007908
᎑4.009
Exptl
—
—
—
2.37c
a Calculated
using HyperChem version 5.11 (Hypercube, Inc.). using 506.9 gauss as the theoretical hyperfine constant for a lone hydrogen atom. c From refs 7 and 8 (sign not given). bCalculated
1. How do the various methods compare with the experimental results? 2. Which semiempirical methods are the most accurate? 3. What differences between the semiempirical methods could account for the variation in their accuracy? 4. How important is the geometry optimization step? 5. How does the electron spin density plot compare with the observed couplings? 6. What is the theory behind the “pure” hyperfine coupling in a lone hydrogen atom? How reliable is the factor used?
We have used this computational lab experiment in conjunction with the traditional EPR spectroscopy lab experiment in our physical chemistry laboratory course. Although our students have generally found this to be a challenging laboratory exercise, it is an excellent conclusion to the time invested in learning to use the molecular modeling program HyperChem. We often ask students to work through the tutorials and carry out various exercises without providing them with a real-life example of how the results of molecular orbital calculations can be used. This laboratory assignment ties together a classic spectroscopic experience with a modern computational method. Students will thereby gain an in-depth understanding of what computational methods are capable of. Acknowledgments
W
Supplemental Material
The supplemental material for this article available in this issue of JCE Online provides student handouts for an introductory exercise (MO calculation of the NO molecule), and detailed instructions for carrying out the exercise described in this paper, and notes for the instructor. Literature Cited 1. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry, 6th ed.; McGraw-Hill: New York, 1996. 2. Pople, J. A.; Beveridge, D. L. Approximate Molecular Orbital Theory; McGraw-Hill: New York, 1970. 3. Pople, J. A.; Beveridge, D. L.; Dobosh, P. A. J. Am. Chem. Soc. 1968, 90, 4201. 4. Nonella, M.; Brandli, C. J. Phys. Chem. 1996, 100, 14549. 5. Nonella, M. J. Phys. Chem. A 1999, 103, 7069. 6. Wheeler, D. E.; Rodriquez, J. H.; McCusker, J. K. J. Phys.
JChemEd.chem.wisc.edu • Vol. 78 No. 9 September 2001 • Journal of Chemical Education
1207
In the Classroom Chem. A 1999, 103, 4101. 7. Pedersen, J. A. CRC Handbook of EPR Spectra from Quinones and Quinols; CRC Press: Boca Raton, FL, 1985. 8. Hellwege, K. H. Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology; Springer: Berlin, 1965; Group II, Vol. 1.
1208
9. Venkataraman, B; Segal, B. G.; Fraenkel, G. K. J. Chem. Phys. 1959, 30, 1006. 10. Vincow, G.; Fraenkel, G. K. J. Chem. Phys. 1961, 34, 1333. 11. Bersohn, R. J. Chem. Phys. 1956, 24, 1066. 12. Trapp, C.; Tyson, C. A.; Giacometti, G. J. Am. Chem. Soc. 1968, 90, 1394.
Journal of Chemical Education • Vol. 78 No. 9 September 2001 • JChemEd.chem.wisc.edu
