W. Gale Rhodesl Richard Smock and Lynn Brown Maryville College Maryville. Tennessee 37801
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Ever-More Sophisticated Lies about Bonding A minicourse in HMO theory utilizing small computers
During t h e past three years, as part of a senior course entitled Chemical Bonding, we have taught a module in Huckel molecular orbital (HMO) theory of extended *-systems. This self-contained minicourse, which requires approximately 12 class hours, would be appropriate for any upper-level chemistry student who is acquainted with the schrodinger equation and some of its 8,classical,, applications, such as the particle in a the principles and the hydrogen molecule' The in Our a mitment to HMO theory a t the undergraduate level. A special feature of the module is the availability of a group of computer oroerams in the BASIC laneuaee, . . . . which allows calculation of energy lewls, w;tvt~lttt~ctitmi, and 19ther dt:rivrrl paramerrrs tirr systems contnininr! -up . tu I0 atomic orbitals, using .. a digital computer of 8K memory. W e set a s t h e primary goals of this module t h e building of a sound foundation in zeroth-order H M O theory and calculation, the development of a n appreciation of some of t h e applications of the theory t o organic chemistry, a n d a familiarization with t h e convenience a n d power of t h e small computer in HMO calculation. In terms of performance objectives, we felt that the student successfully completing the module should be able t o carry out the following operations 1) Set up the secular equation for a system of atomic orbitals 2) Solve the secular equation for the electronicenergy levels of the system 3) Calculate from the results of 2) the total z energy, the delaealizatian energy and excitation energy
4) Solve the secular equation for the wavefunctions of the system atom in the system 6) Carry out the above operations for systems containing heteroatoms and thme in which inductive effeds of nearby groups can be taken into account 7) Apply the resuk of HMO calculations in prediction of chemical reactivity of organic compounds 8) Use HMO theory to distinguish aromatic and nonaromatic systems
A variety of available textbooks makes these goals accessible t o t h e undergraduate student. We have used Roberts2 as our primary source a n d Liherles," now out of print, a s a reserve source. T h e latter has many examples of each type of basic calculation, a n d its systematic and repetitive approach gives it somewhat t h e character of a programmed learning guide. We recommend, a n d will likely use, S m i t h q n some capacity in t h e future. Excellent supplements are Streitwieserhnd Zimmerman.6 In order to olace in the students'hands the caoacitv . " t o carrv out all necessary calculations, we have collected and devised a set of comouter oroerams in t h e Basic laneuaee. Followine" a r e brief descript&nsof each MATCOEFII. This program computes from the secular determi"ant the coefficients of the secular equation in its polynomial form. The program is a modification of a routine for obtaining the eharaetermtic pd\ncmtnld ,drtcrm~nnnr. Rt,l~Tf.~Il, 3 41ghtl) mmlltlrd pnrgrnm t n m the Hrulcrt-l'ocknrd r I , t i I 1 I the s e n I! l
method. Forcertainsystems, this process fails toconvergeand we have two slower hackup programs, NEWROOT, which applies Newton's method, and POKEY ROOTER, which simply evaluates the polymenial and prints results "ear Y = 0. HMOCOEFFIII computes coefficients of the HMO wavefunetions. The program involves a modification of a routine for solving simultaneous equations with a normalization routine added. We are eurrently developing a new program which utilizes the cofactor method. In bath programs, the user inputs the set of simultaneous equations and all the system energylevels.The program orders the energy leveis from lowest to highest and computesand prints the coefficients of all nondegenerate wavefunctians. Degenerate wavefunctions must be hand-calculated from the secular equation and the orthoeonalitv requirement. HMOPARAM III receives the outout from HMOCOEFF 111 and wquc.ts of the ~ l i r the r numl,er 01 rlrrln.n; In the byitrm, r h t u prim, an energy Ir\rl nlaerdm, f d l w r d Iby tile rlrrtnm,chargr.md Foku~ irmtipr elv:tnr dtw4irr at rarh atom B y the time the student reaches this module, which a t Maryville College is one'of the chemistry major's last course experiences, he or she has utilized a variety of half-truths about bonding, with increasing completeness as more detailed models have been needed t o cope with more complex phenomena. Where t h e most modern mvths have been needed. , find this they have been largely taken on f a i t h . ~ h u sstudents module verv satisfvine and often sav t h a t manv things fall into place during this three-week period. While thky often see this module as the culmination of a grand procession of evermore-sophisticated lies about bonding, we take pains t o remind them t h a t thev have merely come t o the threshold of some of science's most powerfui and beautiful models. for rendering comprehensible the chaos of chemical structure and along with a module syllabus, are available from t h e au: thor.
ALL PROGRAMS: Basic, transportability not certified; studentrun, time-shared mode (110 = teletype terminal); execution for up to 10 atomic orbitals requires up to 8K (HP2114, 8K, 16 bit words); no line printer plots or graphics; minimal written documentation for bath faculty and students; no flow chart; several sample executions. Copies of listing, documentation, and sample executions are available ($2.00
This paper was presented tothe Fourth Biennial Conference on Chemical Education, University of Wisconsin, August, 1976. 'To whom all requests should be addressed st.: Department. 'Roberts, J. D., "Notes on Molecular Orbital Calculations," W. A. Benjamin, Inc., New York, 1961. :'Librrles, Amo, "Introduction to Molecular Orbital Theory," Holt, Rinehart & Winston, Inc., New Yark, 1966. 'Smith, W. B., "Molecular Orbital Methods in Organic Chemistry HMO & PMO," Marcel Dekker, Inc., New York, 1974. Streitwieser. Andrew. "Molecular Orbital Theorv for ~ r e n n i r ' Chem~.ti,'' h,hn \Vilry & S t m a . in
