Theoretical Study of the Vibrational-Rotational Spectra of Diatomic Molecules A Quantum Chemistry Experiment Jose M. Lucas, Fernando Mota, and Juan J. Novoa Universidad de Barcelona, Av. Diagonal 647, 0802&Barcelona, Spain One of the most common problems in an introductory course onquantum chemistry is the lack of aphysical insight of the theoretical methods introduced in it. Some students find it too hard to extract the ~ h v s i c ainformation l behind the mathematical language employed, a problem that is particularly troublesome to those students who look a t quantum chemistry as a tool to interpret experimental fact'. The resolution of this problem is not an easy task. Usually textbooks' try to find the answer through the use of model systems on which i t is possible to apply the methods directly onlv allows examnles in an analvtical fashion. This annroach .. that either are simple and use overaimplitied models (particle in a box) or, it the problem is treated more realisticallv. make use of l&ge and tedious mathematical developmenis: Alternatively, one can make use of the increasinelv ~owerful computing facilities and try a numerical approaeh to resolve a real problem. Following this, the student chooses the theoretical method toresolve the problem andusesa computer to perform the mathematical operations. This means the use of a previously written program capable of treating with numerical calculus all the possible methods that the student can select. In this way, it is possible to find applications that are closer to students' fields of interest, more realistic, and in the methodoloeical line normallv used in ouantum chemistry, where the computer is used as a numerical tool. One ran also eo a little further and heain to familiarize the student with-the numerical methods-normally used in quantum chemistry. Following the ideas exposed above, the problem selected was the theoretical study of the vibrational-rotational spectra of the diatomic molecules. There are many reasons for this selection: i t is a topic very well covered in most chemical curricula, it allows the interaction with experimental data obtainable by the same student (as a part of the proposed work for this experience or another one), and, finally i t allows the application of most of the quantum chemical methods introduced in the theoretical lectures. Therefore, one can test these methods by their power to reproduce the experimental results.
the experimental rotational-vibrational gas phase spectrum using any infrared apparatus equipped with a gas cell (we use a low-cost Pye Unicam SPlOOO Infrared Spectrophotom-
General Development The theoretical study of the vibrational-rotational spectrum of any given molecule can only be achieved once the form of its potential energy curve for the nuclear motion is known. This implies that we must compute the total energy for the moleculeat areasonable number of different internuclear distances, using any of the available quantum chemical Droerams. These results can be fitted to a model ~ o t e n t i a l an& from it, the spectroscopic data can be obtained. In our denartment. we have desiened a theoretical exneriment in order to compute the vibr&ional-rotational spectra of diatomic molecules. Usually we take, as a first example, the HCI molecule because it is easy for the student to obtain
' Levine, I. N. "Molecular Spectroscopy"; Wiley: New York, 1975.
Computed and experimental vibrational-rotational spectrum of me HCI molebansition asrociated to
cule in gas phase at 298.15 K. The wavelength and each line are given far the computed specbum.
Volume 63 Number 10 October 1986
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Expwlmental and Computed Spectrorcoplc Constants lor the HCI Moleculea Methoda
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eter). Hieher resolution data can he found. if needed. in spectroscopic data handbook^.^ Once the experimental spectrum has been obtained by the students, the theoretical spectrum has to he computed. T o do this, we assien a microcom~utert o a m o u of ~ about four students. ~ a c h k o u pcomputes the toti1 en& of the selected molecule for one or two uoints of the potential curve using a MIN1)OIR semiempirich program." The next step is to fit the points to a model potential, i.e., harmonic, anh&monic, or Morse potential, and then to calculate the main spectroscopical parameters within each model. We have developed a Fortran program (called SPECTRA4) that allows the students to carry out these calculations in an interactive wav bv introducine the ~reviouslv calculated points and sele"cting the suitacle ophons. hi final result is a theoretical prediction of the spectrum of the selected molecule. The program can also produce a bar diaaram - representation of the rotational structure of the spectrum. This information can be used in two main ways:
One can compare the differences between the theoretical methods and the experiment. (2) One can predict the spectra not easily available eaperimentalIY.
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ist. As a deener insieht. students can he introduced to the theoretical dackgro&din the program used, and its practical imolementation. Furthermore. if is is desired. more sophisticated quantum chemical, methods (such as CI, MCSCF, MP/2, etc.) can he used and their results contrasted with the experimental information. Thus, a wide view of the utilitv of the semiempirical. "ah initio" Hartree-Fock and post:~artree-~ockmethods can be reached in a way easy for the student. Our previous experience shows that the students find i t very interesting to he able to predict an experimentalspectrum, and, with alittle help, have no prohlems in using the computer programs involved. Mnowledgment Financial support from the Spanish ministry of Science and Education throueh a mant CAICYT-0657181 is fullv acknowledged. Use ofcom&tational facilities provided h i the Universitv of Barcelona Computer Center is also acknowledged.
(1)
Typical results for the HCl molecule are given in the figure and the table, where a comparison between the computed and experimental data is also done. Flnal Remarks The methodology outlined ahove can illustrate the way in which quantum chemistry can help the experimental chem-
920
Journal of Chemical Education
Herzberg. G. "Molecular Spectra and Molecular Structure": Van Nostrand: Princeton. NJ. 1950: vols I. 11. 111. Bingham R. C.; Dewar M. J. S.; Lo D. H. J. Amer. Chem. Soc. 1975,97, 1285. The SPECTRA program as well as a detailed explanation of the program structure, methodology employed, and inputloutput description is available as QCMPOO8from the Quantum Chemislw. Proaram Exchange in their sect on for personal-computer-orlentedprograms More tnformatnon about the program and development 01 the experlence IS avallable from the authors upon request.
