Teaching Computational Chemistry Using Computers

KOLUMNE 77

CHIMIA 49 (1995) Nr. J (Miirzl

COMPUTATIONAL

CHEMISTRY Column Editors: Prof. Dr. J. Weber, University of Geneva COLUMN Prof. Dr. H. Huber, University of Basel ______Dr. H. P. Weber, Sandoz AG, Basel

Chimia 49 (]995) 77-83 ical information and theoretical chemis- © Neue Schweizerische Chemische Gesellschaft try. Whereas the first one is obviously ]SSN 0009-4293 related to data acquisition and processing in chemical experimentation, the second one deals with all possible applications concerned with chemical data bases. The Teaching Computational third one, the classical area ofCC, encom- passes all modeling applications, per- Chemistry Using Computers formed using either computational quantum or classical mechanics, molecular dynamics and Monte Carlo simulations, Jacques Weber* and Pierre-Yves Morgantini reaction dynamics and molecular graphics. In this Column, we are going to con- centrate on teaching applications of CC related to this vast third subfield. Indeed, Introduction In this Column, we would like to present structure elucidation and analysis is a rath- and illustrate by examples the various er specialized topic which is not frequent- This title is not as paradoxical as it tools we use in Geneva to teach CC using ly taught in first- or second-cycle univer- seems in a first sight, since it is only a computers. In all cases, the presentation sity lectures, whereas it is relatively easy recent fact that computational chemistry will cover teaching applications devel- to introduce students to the management (CC) can be efficiently taught using com- oped for both auditori urn lectures and prac- of chemical information at an elementary puters, both in the auditorium (plenary tical exercises in the laboratory. level which enables them to perform their lectures) and in the laboratory (practical own simple Chemical Abstracts Service exercises). This is undoubtedly a great (CAS) on-line searches, for example [2]. progress to the equal profit of students and Scope of the Applications As to more sophisticated and specialized instructors. Indeed, lectures devoted to 3D-database searches such as 'database chemical information retrieval or to mo- Before looking at applications devoted mining' and 'electronic screening' [3], lecular modeling, to take simple exam- to CC teaching, it is probably worthwhile these new CC applications are just emerg- ples, can be vividly illustrated by perform- to define again computational chemistry, ing and they can be adequately taught only ing on-line computer demonstrations so as to better circumscribe the scope of in highly specialized lectures or seminars. which are conveniently projected on a the present Column. We have previously The most general part of CC teaching is, large screen using a videodata equipment. stated that 'CC, synonymous with compu- therefore, undoubtedly that devoted to This has been made possible only recently ter-assisted chemistry, consists of all the computational theoretical chemistry, as it through spectacular progresses both of areas of chemistry which benefitfrom the is part of the physical chemistry curricu- hardware (powerful PCs, workstations, use of computers' [1]. Subsequent discus- lum in all Swiss Universities and Institutes videodata projectors, networking, etc.), sions with colleagues have convinced us of Technology. concomitant of falling costs, and of soft- that this definition is too broad, as practi- In this Column, the use of computers in ware (user friendly program packages with cally all the areas of chemistry benefit the following CC lectures, which are all graphical user interfaces). Of course, all today from the use of computers, which part of the chemistry diploma curriculum the topics of the broad field which consti- leads to the nonsense that CC would actu- of the University of Geneva, will be pre- tutes CC cannot equally benefit from these ally be nothing else than chemistry itself! sented: new facilities, and it is difficult, e.g., to Rather, we prefer the following definition: - introduction to quantum chemistry teach the basic theories underlying several CC consists of all the areas of chemistry (IQC), part of the general physical areas of CC using computers, but their where the computer. is the essential piece chemistry I course (36 h of lectures + applications are again good candidates for of instrumentation. This means that all the 24 h of exercises, altogether, 4th se- computer-aided teaching. traditional fields of chemistry, namely mester); synthesis, analysis, spectroscopy, etc., are - introduction to group theory (IGT), de facto excluded from CC since, even part of the general physical chemistry though they may be somewhat computer- II course (12 h of lectures + 4 h of ized, computers cannot be regarded as exercises, altogether, 5th semester); *Correspondence: Prof. 1. Weber being the essential part oftheir equipment. Department of Physical Chemistry - molecular modeling and simulation University of Geneva It is generally accepted that CC is made (MMS), optional course (60 h of lec- 30 quai Ernest-Ansermet of the following subfields: structure eluci- tures + 40 h of exercises, altogether, CH-1211 Geneva 4 dation and analysis, management of chem- 7th and 8th semesters). KOLUMNE 78 CHI MIA 4\1(1995) Nr. 3 (Miirzl

Hardware and Software Available PC or the workstation to the Ethemet net- students and ... instructors have some work allows the instructor to use any pro- knowledge of Maple (or of any other sim- Auditorium Lectures gram installed on another host system. ilar computer algebra system). In the Sciences II building, which hosts These facilities enable instructors to viv- In addition to the standard packages our Chemistry Section, one finds several idly illustrate, using interactive program HyperChem [4] and Gaussian 92 [5] men- auditoriums among them the 100 seats A- operations, virtually any topic of compu- tioned above, we use in our CC teaching 100 is conveniently equipped with audio- tational theoretical chemistry. In addition, applications some other commercial pro- visual material for computer-aided teach- the merging of video images and motion grams such as Spartan [9] and Macromod- ing(Fig.l). Indeed, in addition toa486/33 sequences, stored, e.g. on a videodisk, el [10], and the Molekel program as well PCunderWindowswithVGA(1024 x 768) with instructional computer programs of- which has been developed in our laborato- graphics connected to the Ethernet net- fers the possibility to present multimedia ry [II]. Whereas HyperChem is a general work of the University, it is possible to use CC courses, which have undoubtedly a purpose molecular modeling program en- a Sony VPH 1270videodataprojectorwith great potential in future chemistry teach- abling the user to perform molecular me- a resolution of 1100 x 970 pixels and a ing [6]. chanics, dynamics and semi-empirical projected image dimension of 3 m. In As far as software is concerned, we quantum chemistry calculations, Macro- addition to being able to project multi- incline to think that, with the advent of model exhibits similar features but it is norm videotapes, this system has a direct computer algebra systems such as Maple restricted to molecular mechanics and RGB connection to the PC, and built-in [7], it is not indispensable that first- and dynamics. Both packages offer the possi- interfaces as well for RGB connections to second-cycle students in chemistry are bility to build interactively molecularstruc- Macintosh computers and standard work- literate in a true scientific programming tures. Gaussian 92 and Spartan are well- stations (Sun, SGI etc.) which can be eas- language, such as PASCAL or FORTRAN, known quantum chemistry programs in- ily installed in the auditorium. A second to take CC lectures or exercises. The situ- cluding semi-empirical and ab initio meth- classroom with a similar equipment is ation in this respect is somewhat different ods, the characteristic of Spartan being its available in the building. from that which prevailed three years ago graphical user interface. Finally, Molekel Using these equipments, the instructor [8], which may be attributed to the factthat is a molecular graphics package allowing is able to project in real time the screen of Maple and similar systems recently high-quality visualization of chemical sys- the PC, or of any workstation if more emerged as powerful tools to perform sym- tems and properties. compute power or better quality graphics bolic, numeric and graphical computa- is needed. He is thus in a position to tions involved in mathematical problem Practical Exercies interactively display and comment any solving. To a very large extent, they may Sessions of practical exercises take step in usingCC software packages, would thus serve as substitutes for scientific pro- place in a new PC room which is equipped they be education oriented such as Hyper- gramming languages, but this statement with 8 DX41100 diskless machines con- Chern [4], or research oriented such as does of course not apply to graduate stu- nected through Ethernet to a Novell net- Gaussian [5]. Of course such a distinction dents preparing a Ph.D. in CC as they must work with the central PC of the Section of is somewhat arbitrary and one may find be able to carry out some programming Chemistry library as a server (Fig. 2). The abundant examples demonstrating that developments in FORTRAN. We assume choice of diskless PCs has been dictated most CC packages can be used for both therefore that, for the applications in CC by financial, practical, and safety reasons. purposes. In addition, connection of the teaching presented in this Column, both Extension of this facility to 16 PCs is planned for J 995. To reduce computation times and to allow students to perform the maximum number of calculations within a given time, the HyperChem jobs may run on the PCs or remotely on an Indy R4600 SGI workstation (16 Mflops) server. Sim- ilarly, all the molecular mechanics, dynamics, and quantum chemistry programs used by the students in their exercises sessions run on SGI workstations of the Department of Physical Chemistry. The CC software which is available to the students for their exercises is the same as that used for auditorium lectures.

CC Teaching Applications

'Course Introduction to Quantum Chemistry' The course content is devoted to the following topics: - basic quantum theory; Fig. I. A computational chemistry lecture in the A-IOO auditorium of the Chemistry Section of the - applications to simple systems (parti- University of Geneva, with the videodata projector (top right) displaying all the screen a space-filling cle in a box, harmonic and anharmonic model of the butane molecule generated on the PC by HyperChem oscillator); KOLUMNE 79

CHIMIA 4~ (19')} Nr. J (M:in.)

- atomic structure; - molecular electronic structure: diatomics, small molecules, Huckel molecular orbital (HMO). Practically all the auditorium lectures Central University Network can be enriched by an appropriate use of the Maple software on the PC together with real-time projection of the PC display. Similar applications have been re- Fiber-optic link cently reported by Rioux using the Math- Noven Serv.r cad system [12]. Actually, Maple enables Compaq Prolinea the user to combine, into the same docu- MT 4166 ment, text, data, mathematics and graph- Sciences ics, which leads to the maximum flexibil- Network ity. For example, in the context of these lQC lectures, mathematical computations such as differentiation and integration are used in the following applications: - illustration of the Heisenberg princi- ple using test functions f(x), that is calculation of the commutator [x, pJ applied to f(x) in order to demonstrate that this expression is proportional to f(x). Simple f(x) functions such as Indy R4600 PC exp(-x), cosx, etc., are appropriate. - Calculation of the normalization fac- tors of the eigenfunctions of the particle in a box for various values of the quantum number n to show that they are not n dependent. Novell Network - Calculation of the average radius of the J s orbital in the H-atom. 8 Compaq All these applications have been adapt- Prollnea 4/100 ed to Maple from a software distributed by the American Chemical Society [13]. Several other topics of the course are also taught with the assistance of both mathematical computations and graphics facilities offered by Maple: - 2D and 3D representation of the solutions of the Schrodinger equation of the following systems: particle in aID Fig. 2. Block diagram of the computer hardware available at the Chemistry Section of the Universi~)' and 20 box (Fig. 3), harmonic oscilla- of Geneva to teach computational chemistry tor, hydrogenic atom (radial wavefunctions and polar plots of the angular ones, both as surfaces in 3D space and topics which are designed so as to fit to 2 sions on Maple, but this is a good invest- as contour levels in selected planes). h sessions. Control of the students' work is ment for the students as they are then able - Potential energy curves of diatomics fairly easy as they have to print out at the to use this system for many other applica- calculated in the LCAO approxima- end of the session the Maple file corre- tions. tion and corresponding MOs. sponding to the live document they have - HMO wavefunctions and energies cal- been preparing to solve the problem. In Course 'Introduction to Group Theory' culated for simple systems; correla- general, the subjects of these exercises The application of group theory to tions (linear regressions) between se- have been chosen such as the students molecular symmetry is an important topic lected properties (e.g. oxidation po- have to combine mathematical calcula- as it has practical consequences in all tentials) and HMO results (e.g. HOMO tions and graphics in the same session. A fields of chemistry [14]. This subject de- energies). good example is provided by the calcula- serves, therefore, undoubtedly its place in - Numerical solutions of the Schrodin- tion of the potential energy curves of the the chemistry curriculum, but, for the av- gerequation in the case of the harmon- HCI and HBr molecules in the Morse erage student, its mathematical aspects ic osci lIator and comparison with the approximation and their graphical repre- should be reduced to a minimum and em- analytical ones, which allows the stu- sentation together with the first anhar- phasis should be placed on the symmetry dent to understand the role of quantum monic vibrational energy levels. Of course, of molecules as an intrinsic property due numbers. such a conception of the exercises of a to their shape. Furthermore, we are of the The exercises of this course consist of quantum chemistry course requires to or- opinion that this course represents an ideal a series of Maple applications of these ganize in the beginning some tutorial ses- application field of molecular graphics KOLUMNE 80

CHIMIA 49(1995) NT. 3 (Mtin) packages such as Molekel. Our choice of perposed to molecular models; ii) real- We have, therefore, achieved several Molekel as the basic program to teach this time 3D interactive manipulation of mo- teaching developments in this direction course is motivated by two reasons: i) it is lecular models and of corresponding sym- and the auditorium lectures of the ICT essential to have access to the source code metry elements is essential and this can course make the maximum use of video of such a program so as to implement the only be performed using a package run- projections of the display of the SGI work- representation of symmetry elements su- ning on a graphics workstation. station running the Molekel program. This equipment is used to display the following applications: - visualization ofthe CIIsymmetry axes,

O'mirror planes, and 511 improper rotation axes superposed to the molecular model of any compound belonging to any point group (Figs. 4 and 5). - For the CJlaxes, it is possible todynam- ically represent the 3600ln rotation of > phi:=subs(iP'1,b"1,phi); the molecular skeleton around the ax is, ~ .••2 sm(/IX n %) sm("Y ny) in order to check that the operation > fct:=slJbs(nx0:2,phl); leaves the molecule unchanged. Jet = 2 sm( 2 11 %) Slll( 10' 11y) - These two features of Molekel are also > fc:t:-subs(nV"'2,fct)~ applicable to 3D models of Mas, which fet = 2 sm(211 x) sm(211y) > plot3d(fct.x=O ..1,y=O ..1); is a valuable tool to determine their symmetry type, i.e., the irreducible representation to which they belong. It is well known that this information is essential to apply electric dipole selection rules, for instance. Similarly, Molekel allows the instructor to dynamically display the normal modes of vibration of any molecule, after their calculation has been performed using a suitable program, e.g. Gaussian 92. Their symmetry species Fig. 3. Window of the Maple V system with the workspace used by a student to display the can than be determined using the same eigenfunctions of the Schrodinger equation of the particle in a 2D box tools, which is important to interpret IR and Raman spectra. The subjects of exercises of this course consist of determining the point groups to which a series of molecules belong, visualizing the corresponding symmetry operations, finding the symmetry type of Mas and normal modes of vibration, and apply- ing the selection rules to electronic and vibrational transitions and of Raman activity as well. As these exercises are carried out by the students using the Molekel package running on SGI workstations, they take place in our laboratory which hosts seven such machines.

Course Molecular Modeling and Simulation

This is the typical CC course which is intended to teach modeling and simulation techniques and to train students to perform by their own some applications relevant to various fields of chemistry .It is taken each year by 15-20 students who are in general highly motivated and conscious of the fact that computational chemistry is part of modern physical chemistry research. The content of the course is devot- Fig. 4. Molekel representation of all the Cn symmetry axes and Sn improper rotation axes for a metal ed to the following topics: cluster made of an octahedron inscribed in a cube and belonging to the point group Oh - basic features of the Maple system; KOLUMNE 81

CHIMIA 49 (1995) Nr. 3 (Miirz)

- introduction to computer graphics; advantage of the real-time projection fa- - the various force fields of molecular cility of a HyperChem application. In- mechanics; optimization techniques; deed, in addition to visualizing the trajec- elements of molecular graphics, intro- tories of atoms generated by a MD simu- duction to the HyperChem package; lation of any type, it is possible to display - molecular dynamics simulations; the energy components and the value of - quantum chemistry: derivation of the structural parameters as a function oftime, Hartree-Fock equations; electron cor- which allows to follow conformational relation; ab initio and semi-empirical changes as the simulation proceeds. A techniques. good example is provided by a teaching Most of the lectures devoted to these application of the simulated annealing tech- topics make use of live projections of nique [15] we have developed recently applications of the HyperChem and Gaus- [16]. sian 92 program packages, which allows Indeed, an interesting feature of MD the instructor to vividly illustrate any par- techniques lies in the fact that, when sam- ticular aspect of modeling techniques. For pling the configuration space, the kinetic example, it is possible to present and dis- energy of the system allows it to surmount cuss the form of the various potentials of energy barriers of the order of kT per the four different force fields implement- degree of freedom. It is, therefore, possi- ed in HyperChem and to emphasize their ble to artificially raise the temperature to specificities by optimizing the geometry search larger portions of the configuration of selected compounds using all of these space or, alternatively, to cool down the methods. One may also demonstrate the system to reach minima on the Born-Op- importance of the el ectrostatic component penheimer energy surface, that is to re- of the steric energy by switching it on and move kinetic energy from the system, off in MM+ calculations, for instance, and which is known as simulated annealing by using then various sets of atomic charg- [15]. es to investigate their influence. As an example, Fig. 6 summarizes the Fig. 5. Molekel representation of a dihedral Molecular dynamics (MD) is another results of a MD calculation performed for vertical mirror plane ad for the adamantane topic for which the instructor can take a single molecule of butane (CHrCH2- molecule belonging to point group Tct

500.0 360.0 ,...... , en ,...... ,400.0 ~ 300.0 :lc:: .... •...... • 0'1 CI.l CI.l •...... •~ 240.0 ; 300.0 .•... CI.l o •... 0'1 180.0 CI.l c a. 200.0 « E c 120.0 CI.l .Q I- en 100.0 •... ~ 60.0

0.0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Time [ps] Time [ps]

Fig. 6. Summary of the MD simulation of butane performed using the simulated annealing technique as implemented in HyperChem. Top left: initial gauche structure, top right: final anti form. The diagrams in the lower part of the figure display the evolution of temperature (left) and of torsion angle OJ (right) as a function of time. KOLUMNE 82 C'HIMIA 49 (1995) Nr. 3tMlirz)

CHrCH3) so as to generate a simulated a) annealing. The butane molecule was chosen as it is a standard hydrocarbon exhib- iting several conformational isomers with different C-C-C-C torsion angles (OJ, Fig. 7). The anti conformer (OJ = 180°) is known to be the most stable one, with an energy roughly 1 kcal/mollower than the two gauche forms (OJ = 60° and 240°), whereas the barrier height for the molecule to rotate from the gauche to the anti form is 3 kcallmol [17]. The purpose of the H MD study of butane was to determine the capability of the simulated annealing tech- b) nique to rearrange the molecular conformation from the gauche to the anti form. 7 Examination of Fig. 6 shows that this is indeed the case: the simulation starts at a 6 K with butane in a gauche conformation (OJ=600) and temperature is raised rapidly ~ "0 5 up to 300 Kin 0.1 ps, the time step being E ::::, 0.0005 ps. Then, after a short equilibration ro 0 4 period ofOA ps, the system is cooled down ~ to 0 K in 3 ps. It is seen that, shortly after w 3 the beginning of the simulation, the torsion angle OJ changes abruptly to a value 2 fluctuating around 180°, i.e., the butane molecule has overcome the energy barrier 1 separating the gauche and anti forms to end up in the latter conformation. This 0 example illustrates both the efficiency of 0 60 120 180 240 300 360 the simulated annealing technique and the importance of graphics to visualize con- Fig. 7. a) Newman projection of the butane molecule with definition of the torsion angle w; b) potential formational changes. In addition, it repre- energy curve calculated for butane as afunction of W using the MM+ force field of HyperChem sents for students a typical application of MD simulations and of the important role they play today in computational chemis- MIcrosoft e-I- TP!i.XlS try. DIe [dlt )'lew 1nscf1 FJIrIlllIt IDOls Yillndow It is of course impossible to report here Iwss".s.m Wfil all the teaching applications of the Hyper- chent and Gaussian programs we use in quantum chemistry lectures. Let us just _r ,.- B D mention that computational quantum 411 S40 5.816525 O.2llO731 1.336379 1.liS31i38 chemistry techniques, at a semi-empiri- SO 350 6.S87393 02HI!l29 lA37732 2D87625 51 3IlD 6.S0223lI 0.221_ l.A52253 2.317111 cal, ab initio and density functional level, liZ are conveniently illustrated by taking ex- sa n-bulan •• MM+ Sot amples based on simple molecules such as li6 (NH 0H). 511 , . hydroxylamine 2 In the case of !51 ,. this compound, for which many experi- 51 6 \ i mental data are available to estimate the III• C'jD ~ \ / l' reliability of the theory, we systematically 81 . \ ,,/ "\, 1!2 '. t .l use all the semiempirical models availa- a .~ 3 \ 14 ble in HyperChem and perform many ab e5 ..c 2 initio and density functional calculations II with the Gaussian program so as to: i) fI7 o • o 180 360 optimize the geometry; ii) determine the ••10 electronic structure and atomic charges; 71 12 • iii) display the frontier and most relevant •• 4 .. • MOs; iv) evaluate the electrostatic poten- r .. + tial and the relative basicities of the N vs. sites; v) compute the corresponding Fig. 8. Windows of the HyperChem and Excel systems with the workingspaces used by a student to o investigate the C-C-C-C torsional potential function of butane. The left window displays the proton affinities and the geometries of the decomposition of the potential function into its various MM+ components, whereas the right windows protonation sites; vi) determine the vibra- depict some molecular models of butane. tional frequences and display the normal KOLUMNE 83 CHIMIA 49 (1995) Nr. 3 (Mii17.)

modes of vibration using the Molekelpack- 8. Conformational analysis offi-alanine research and education are often intimately con- age. In all the cases, the emphasis is placed in gas phase and aqueous solution nected, some of the these teaching developments on the comparison with experimental val- using the BIO+ force field of Hyper- have benetitted form investigations carried out in the context of the Project 203613 1.92 of the Swiss ues, so as to estimate the quality/cost ratio Chem. National Science Foundation. of the various models, and on the rele- 9. Geometry optimization of small or- vance of performing such calculations in ganic molecules and of malonalde- chemistry. Although it is far from being hyde using the MNDO, AMI, and Received: February 2, 1995 exhaustive, this list shows that several PM3 semi-empirical methods imple- important concepts of computational quan- mented in HyperChem. [1] J. Weber, H. Huber, H.P. Weber, Chimia tum chemistry can be taught interactively 10. Potential energy surface of the HCN 1992, 46, 84. using live projections of computer dis- ~ HNC isomerization reaction using [2] E. Zass, Chimia 1994, 48,109. plays, which actually represents a signifi- the AMI and PM3 methods. [3] H.P. Weber, Chimia 1994, 48, I 12. cant progress in chemical education. I]. AMI molecular electrostatic poten- [4] HyperChem4.0, HypercubeInc.,419Phil- lips Street, Waterloo, Ontario, CanadaN2L The exercises in the PCs room consti- tials of organic compounds: hydroxyl- 3X2,1994. tute on important component of this MMS amine, formamide, pyrrole, pyrrolid- [5] Gaussian 92, Revision A, M.J. Frisch, G.W. course, as they allow the students, under ine and adenine; correlation with Trucks, M. Head-Gordon, P.M.W. Gill, the supervision of assistants, to have their HOMO localization and gas phase M.W. Wong, J.B. Foresman, B.G. John- hands on computer keyboards so as to proton affinity. son, H.B. Schlegel, M.A. Robb, B.S. Re- prepare datafiles and to run the calcula- 12. Ab initio geometry optimization of plogle, R. Gomperts, J.L. Andres, K. Ra- ghavachari, 1.S. Binkley, C. Gonzalez, R.L. tions, and, a key point in CC, to perform a ethylene, fluoroethylene and propene Martin, D.1. Fox, D.J. Defrees, 1. Baker, proper interpretation of the results. We at various levels of theory usingGaus- J.J.P. Stewart, 1.A. Pople, Gaussian Inc., particularly insist on this latter point, as it sian 92. Pittsburgh PA, USA, 1992. is useless to carry out (time-consuming or 13. Calculation of the vibrational frequen- [6] L.L. Jones, S.G. Smith, Pure Appl. Chem. not!) calculations without a deep under- cies of acetaldehyde using the ab ini- 1993, 65, 245. standing of the meaning of the results. The tio method (Gaussian 92) and visual- [7] B.W. Char, K.O. Geddes, G.H. Gonnet, subjects of the exercises have been mostly ization of the normal modes of vibra- B.L. Leong, M.B. Monagan, S.M. Watt, 'Maple V Language Reference Manual', developed by our own group, but some of tion using Molekel. Springer, New York, 1991. them have been taken from the monograph 14. Geometry optimization of transition [8J 1. Weber, H. Huber, H.P. Weber, Chimia of Foresman and Frisch [18]. They are states using the ab initio method. Ap- 1992,46, 224. listed below: plication to HCN, vinyl alcohol, and [9] Spartan 3.1, Wavefunction Inc., 18401 Von I. General case of least-squares fitting formamide. Karman # 210, Irvine, CA 92715, USA, of a linear combination of M basis 15. Calculation of the geometry of the 1994. functions to N data points using Maple water dimer and of the dimerization [IOJ Macromodel 3.1, Columbia University, New York NY 10027, USA, 1991. [ 19]. enthalpy of water using the ab initio [11J P.P. Fluekiger, Ph.D. thesis No. 2561. Uni- 2. Optimization by simulated annealing method. versity of Geneva, 1992. theory: minimization of functions of Practically all these exercises cannot [12] F. Rioux, i. Chem. Educ. 1992, 69, A240. several variables using Maple [20]. be considered as simple ('presse-bouton') [13J F. Rioux, 'Enriching Quantum Chemistry 3. Geometry optimization of the various applications of the CC programs used. with Mathcad', lCE: Software, Department con figurati on s (chai r, boat, twi st-boat) They require agood understanding of both of Chemistry, University of Wisconsin, 1101 University Avenue, Madison, WI of cyclohexane using the force fields theoretical chemistry concepts and pro- 53706-1396, USA. of HyperChem. gram packages functionalities. However, [14] F.A. Cotton, 'Chemical Applications of 4. Geometry optimization of the various in most of the cases, students are able to GroupTheory', 3rdedn., Wiley, New York, configurations of piperidine, N-meth- succeed in doing them with a limited help ]990. ylpiperidine, piperazine, and tetrahy- from the assistants. In addition, the use of [15] S. Kirkpatrick C.D. Gelatti, M.P. Vecchi, dropyran using the force fields of Hy- the graphical user interfaces available for Science 1983, 220, 671. perChem. both input and output has been found to be [16J 1. Weber, A. Deloff, P.F. Fluekiger, Spee- dup 1994, 8, 63. 5. Investigation of the C-C-C-C tor- effective in the various steps of the exer- [17J N.L. Allinger, S. Profeta,i. Comput. Chem. sional potential functions of butane cises. 1980, J, 18l. and 2,3-dichlorobutane using the force As compared with the situation which [18J 1.B. Foresman, A. Frisch, 'ExploringChem- fields of HyperChem (Fig. 8). prevailed 5-10 years ago, it is, therefore, istry with Electronic Structure Methods: A 6. Structure-activity relationships stud- no overstatement to assert that computa- Guide to Using Gaussian', Gaussian Inc., ies of morphine and mescal in deriva- tional chemistry can be taught to a large Pittsburgh, 1993. tives using molecular mechanics (Hy- extent using computers. [19] W.H. Press, B.P. Flannery, S.A. Teukol- sky, W.T. Vetterling, 'Numerical Recipes. perChem) and graphics (Molekel). The authors are grateful to all theircoworkers The Art of Scientific Computing', Cam- 7. Gas phase conformational analysis and students who were patient and persevering bridge University Press, Cambridge, 1986, (Ramachandran plots) of glycine us- enough in the various phases of the development p.509. ing the force fields of HyperChem. and tuning of these teaching applications. As [20] M.A. Curtis, i.Chem. Educ. 1994, 7J, 775.