the computer bulletin board
edlted by
RUSSELLH. BATT Kenyon College Gambier,OH 43022
A Graphically Based Program for Carrying Out Hiickel Molecular Orbital Calculations M. P. Sigalas and G. A. Katsoulos Laboratow of Applied Quantum Chemistry Aristotle ~niver'sky 540 06 Thessaloniki, Greece
One of the strengths of the Huckel method ( I ) is that the effects of symmetry and topology on molecular characteristics are easily seen. Moreover, the simplicity of the model makes it a n excellent pedagogical tool for illustrating many quantum chemical concepts, such as bond order, electron densities, and orbital energies. However, many chemistry students experience difficulties relating the numerical quantities to molecular orbital diagrams and drawings of the molecular orbitals. Graphic and Tabular Displays of Computational Results
To overcome such problems, we have written a computer program that takes-advantage of the user-friendly interface and rnaphics of the Macintosh to do Huckel molecular orbital c~lcuiationson a personal computer. I t calculates the energy eigenvalues, eigenvectors, and the bond-order matrix of conjugated and aromatic molecules. To our knowledge, there are two other programs that perform HMO calculations on the Macintosh with the emphasis laid on the graphical presentation of the computational results (2,3). The present program is used as a set of exercises by our chemistry students who, based on the results, proceed to (4)
the prediction of the most pmbahle sites far eleetmphilic or nueleophilie attacks the estimation of bond lengths t h e application of the perturbation method
I
Name o f the molecule: Olphenylmethyi - Anion
charge: - 3
Figure 2. Energy-level diagram generated by the program for the diphenylmethyl anion. User-Friendly Entry The program supports the mouse-based, interactive user interface of the Macintosh for entering the structure of a molecule. The user specifies the structure of the target molecule by simply clicking the corresponding nodes of a hexagonal grid, as shown in Figure 1. Then the program displays the molecule on the screen as a ball and stick model and automatically calculates the number of n electrons. A click on a n alreadv defined atom (carbon bv default) deselects it and erases all its neighboring bond; The user is also able to add heteroatoms to the structure using the "Heteroatoms" menu. A wmplete set of perturbation parameten (5)for all the common heternatoms are built in the program. Displays in a Series of Windows
I
From the supplied structure the program constructs the secular determinant and computes the eigenvecton and eigenvalues by the Jacobi diagonalization method. A series of windows displays the results of the calculations in both graphic and tabular form: the energy levels the eigenvalues the charge densities the bond orders
Figure 1. The drawing window of the program.
For example. the "n-Enerm Levels" window (see Fin. 2) displays thk ca.lculated en&-level diagram scale2 in units of the resonance internal. D. The electrons occupying .- the orbitals are shown as up &d down arrows in a manner consistent with the degeneracy of the system. The calculated eigenvalues are also displayed to the right of the diamam - in a tabular form. The Window menu becomes active after a calculation has been carried out, allowinn the user to choose among the various graphic &splays. Any item chosen from this menu affects only the appearance of the structure shown on the screen. In the display of the eigenvectors (see Fig. 3) the (Continued on next page) A255
Volume 70 Number 10 October 1993
the comnuter bulletin board t
Molecule
llrlrio&m\
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Results
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We provide the measured heat capacity C, data for solid
Window
Ag as a function of the temperature T (7). From their first
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n - molecular oroltal no. 2 with energy 2.000 p
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courses in general chemistry they know that C, = 3R for solid substances a t room temperature and above (the Doulong and Petit law), but the picture is very different a t low temperature. We asked them to plot those data using MathCad,'which allows them to write a s in their notebooks. Two vectors-2, a n d T-are defined, and the data is read and plotted. Of course they do not obtain a straight line but a graph, a s shown i n Figure 1, where C, approaches zero with temperature, a surprising thing for a "classical man". The second step is to extract more information to build a theory and, as many researchers do, to fit the data applying a least-squares analysis to a polynomial expression, such as
Figure 3. The eigenvectors window displaying the second eigenvector of the diphenylmethyl anion.
gray circles indicate positive coefficients, and the diameter of a circle is proportional to the square of the coefficient of the particular atom in each MO. The coefficients presented to the right of the diagram help the students understand the relation between the numerical results and their graphic representation. When the user clicks on either button in the bottom of the window, the program sequentially displays all the eigenvedors of the system. When the "Charpe Densities" menu item is selected, a window is presented that, apart from the numerical values of the calculated n-charge densities, displays the moleculc with a number of homocentric circles located on each atom. The number i f circles on each atom is proportional to the calculated charge. I n the "Bond Orders" window the program draws a n ellipse for each bond filled with a gray pattern. The principal axis of each ellipse is the particular bond, and the minor axis is proportional to the calculated bond order. Finally, the "Results" menu allows the user to print both the contents of the foremost window and the numerical results in tabular form. It saves them in a text file a s well. The program is a stand-alone application that was writI t runs on any Macinten with the ZBasic 5.0 compiler (6). tosh computer with a t least 512K RAM. Copies of the program are available from the authors by sending $10 to cover the cost of the disk and postage.
With the aid of MathCAD's MINERR function, they find the parameters A, B, and C. As shown in Figure 1the results are poor, so we suggest that they fit only the low-temperature values of C, (from about 0.001 K to 20 K). Now the weight of the polynomial fit is only in the parameter, and the students now have two clues for their work: the null value of C , a t near-zero T and a cubic temperature law approaching this value (see Fig. 1). '~uthorto whom correspondence should be sent. 'Mathcad, Version 2.0; MathSofl Inc.,Cambridge, MA, 1987
Using MathCad in Physical Chemistry G. P. Brizuela and A. ~ u a n '
Depto. de Fisica Universidad Nacional del Sur 8000 Bahia Blanca, Argentina Because the students cannot see a vibrating molecule a s they see the spring of their car suspension, they do not have everyday experience with quantum phenomena. Due to this and the mathematical obstacle always involved, the students very oRen do not get the basicconcepts. To solve this problem we have developed a computer laboratory exercise. A256
Journal of Chemical Education
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T3 FIT EXPERIMENTAL DATA
- POLYNOMIAL
FIT
Figure 1 . Experimental and polynomial fit of the heat capacity of solid Ag. (Continued on page 4.258)
