In any university, computers are crucial tools for the teaching of chemistry. There is widespread agreement that computers can perform a vital role in developing student understanding, but less universal agreement on what that role should be. At one extreme, computers may be used as fast calculators, or to run spreadsheet macros or Basic programs. At the other extreme, they may drive complex, interactive simulations, perhaps taking advantage of multimedia or the Internet.
The versatility of the computer permits a wide range of uses. For example, their speed makes them ideal tools in the acquisition and analysis of experimental data; their memory makes make them powerful bibliographic search engines. However, one can argue that in neither role does the computer actually do much to help students understand the underlying chemistry. Instead, it amplifies and illustrates whatever understanding the student already possesses. Spreadsheets may help in the assessment of chemical data - and this is undoubtedly a valuable role - but, when using them, students' data massaging skills may develop at a faster rate than their chemical understanding.
As the power of computers increases, the range and complexity of chemical systems that can be simulated increases in proportion. It is now possible to routinely simulate in real time the interactions among several hundred (small!) molecules in the gaseous or condensed phases. Such simulations intrigue and stimulate students, and, if carefully designed, are effective teaching tools also. The recent dramatic growth of Internet applications employing Java provides new opportunities for chemists to provide such simulations to their students. Those chemists who might previously have been reluctant to face the trials of working with X and Motif, can now develop professional-looking, effective simulations and make them available, through the net, to a wide
audience.
As a consequence both of the increase in computer power and of the development of Java, chemical simulations and graphical applications of all types are appearing at a considerable rate. However, allowing
students to simulate a chemical process does not guarantee enhanced student learning.
This paper argues that simulations in which a mathematical description of natural phenomena can be derived from the behaviour of a physical system have notable advantages over those in which the
mathematical description is the basis for the simulation itself. We shall discuss simulations of both the "mathematics-rich" and "mathematics-lean" variety, and consider the advantages each may offer.
Suitable on-line links are provided.
Computers are somewhat cheaper than most scientific instruments and considerably cheaper than a professor. It is not surprising then that they are in widespread use (Table 1).
Table 1. Typical computer use in university chemistry departments.
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The contribution which computers make varies from one department to another, depending on the machines available, local expertise, and the teaching philosophy of the department. Consequently, their impact on student learning is far from uniform.
Where the computer is used primarily as an administrative tool, for example to store student records, there is little direct benefit to the student. Similarly, when students have ready access, but the computer is used just to word process laboratory reports or assignments, it does not contribute a great deal to scientific understanding. Students' keyboard and computer skills improve, but the computer is not helping them to understand "why things are the way they are".
Even when employed scientifically, if computers are used to help students to balance equations or follow VSEPR rules, the software may just be a disguised "programmed learning" text. The application of rules to determine molecular shapes or balance equations is, in a sense, a mechanical operation which can be carried out without knowledge of the underlying science.
The primary aim of a chemistry course must be to develop in students an appreciation of how the material world behaves, and this requires that the computer play an active, positive role in learning. The key to this is the simulation. Simulations have long been a part of chemistry, and although longevity is not in itself a persuasive argument for their use, they find a place in most courses. We argue in this paper that one of the most valuable uses of the computer in a chemistry course is to run simulations which develop understanding of the molecular world.
Detailed simulations of scientific phenomena can provide an insight which transcends a mathematical description, and an understanding of how materials behave is at least as important as being able to express that behaviour in algebraic terms. By interacting with a computer model students can develop an understanding that - at its best - becomes almost intuitive.
2. The place of simulation in the undergraduate course
The level of detail may be limited by the facilities available, (it is a common observation that, no matter how much computer power is available to a chemist, it is never enough). Nevertheless, sophisticated simulation is not always necessary; a detailed view might conceal important generalisations, and thus be counterproductive. Consequently, both molecular level simulations and their coarser counterparts, in which behaviour in the bulk is simulated, have a role to play in a chemistry course. It is important to realise, though, that they are not equivalent. Visualisation of equations, which is essentially what most bulk-level simulations involve, is one step removed from the "real" world of atoms and molecules; we shall argue that in some ways this lessens their value and their impact in teaching.
Computer visualisation can be introduced almost anywhere in a chemistry course, but grapeshot firing of simulation into it is rarely desirable. A simulation must justify its place no less rigorously than a lecture or practical experiment. (Equally, lectures and experiments should be able to justify their existence against the competition provided by simulations). To do this, the simulation must teach concepts more efficiently, or give students a special insight into a topic, or perhaps link together disparate areas of the subject. It must not be a soft financial option whose raison d'etre is to allow administration to replace professors, or keep students quiet when there are not enough spectrometers to go around.
Variety is beneficial in learning, so a mixed diet of simulation, lecture, experiment and discussion will do much to stimulate students' appetite for chemistry.
3. Categories of Simulation
Fig. 1. The spectrum calculated by a "Black Box" NMR instrument. This display is created by a Java applet [1]. Full size version of this figure.
Black Box simulations can also be used to provide remote Internet access to real equipment. The Black Box element then consists of software which allows the student to control equipment in a user-friendly fashion (Fig. 2).
Fig. 2. Data from an on-line optical rig, gathered remotely and displayed using Java applets [2]. Full size version of this figure.
Most of the earliest simulations in chemistry were built around the interpretation of equations describing bulk behaviour. For example, the P-V-T behaviour of an ideal gas can be understood by investigating how the volume of a gas trapped by a moveable piston changes as the pressure or temperature of the gas is adjusted. Such a simulation is independent of the behaviour of individual molecules. Indeed, even the presence of molecules is not acknowledged, since it is the behaviour of an equation which is simulated (in this case, PV=nRT ), rather than the behaviour of an aggregation of molecules.
While this paper argues that simulation of equations is not always the most productive way to proceed, sometimes such an approach is unavoidable. Fig 3 illustrates a simulation of the Belousov reaction, in which calculation at the molecular level is very involved, so that bulk calculation is the only realistic way to proceed.
Fig 3. The development of concentric rings of concentration minima in the Belousov reaction [3]. Full size version of this figure.
Simulations need not be correct to be useful. From the Bohr planetary model onwards, students meet chemical models which are idealisations or approximations. On occasion it is helpful to isolate for inspection one aspect of molecular behaviour which, in a real system, cannot actually be isolated.
Molecular vibration provides an example. Even molecules of modest size have many modes of vibration (according to the 3n-5 rule for linear molecules, or 3n-6 for non-linear molecules, where n is the number of atoms in the molecule). The vibrational motion which results is complex, even in quite simple molecules (Fig. 4).
Fig. 4. A vibrating molecule displayed by a Java applet. [4] Full size version of this figure.
When students meet normal modes and characteristic frequencies, it is helpful to discuss the vibrations of functional groups as though a group were capable of vibrating in isolation from the rest of the molecule. This can be illustrated using an idealised model in which only one mode is active. This qualitative picture - though unrealistic - both clarifies the concept of characteristic functional group frequencies, and can be used to show how one specific vibration affects the symmetry of the molecule, thus leading into selection rules. What is essentially a scientifically unjustifiable simulation can in this way be of value.
Such simulations are computationally demanding, and represent the practical limit of simulations at present, since a further dissection into the movement of electrons and nuclei leads to intractable calculations. As an example of such a simulation, Fig 5 shows the establishment of a concentration gradient for argon atoms above a solid surface under the influence of (very strong!) gravity.
Fig. 5. Simulation of the movement of gas phase argon atoms above a solid surface. [5] Full size version of this figure.
There are various advantages to such a simulation, which we shall shortly consider. We can note immediately that minimal assumptions are made in the calculation: we assume only that
Complex behaviour (such as the Maxwell-Boltzmann distribution of molecular speeds, or the Boltzmann variation of density with height) emerges readily from the simulation, and it is the way in which detailed physical behaviour can be shown to be the result of simple physical interactions that represents one of the most potent features of molecular-level simulation
Fig. 6. The radiation field around a group of moving point charges [6]. Full size version of this figure.
Fig. 7. The potential energy well for reaction between a hydrogen molecule and a fluorine atom [11]. Full size version of this figure.
Interactivity is also a powerful argument in favour of simulation. Users quickly become bored if they are just passive consumers of information. They learn better when they need to respond frequently to, and have control over computer software.
It should be appreciated, though, that interactivity carries with it some dangers. A conventional program which channels all users along a pre-defined track depends on that track being chosen with care, and on it being suitable for almost every user. Interactive software by contrast presents the user with many facilities and numerous choices. This flexibility may remove from the user any sense of direction, so that they become lost within the software package. The academic objectives of the work may become unclear, and the user may wander inefficiently through attractive but meaningless exercises. Interactive software must therefore be sufficiently structured that users do not lose sight of the educational target.
The use of html wrappers and embedded Java applets can provide this essential structure, though there are of course other equally effective ways of ensuring that users are not submerged in a complex, multi-faceted simulation.
Fig. 8. A frictionless hinged beam falling under gravity. [6] Full size version of this figure.
Let us allow the beam to fall; how will it strike the floor? There are three options:
Which of these possibilities is correct? The equation which describes the behaviour of a such a beam of connected masses would tell us, but doubtless this equation is complex, and it would be no simple matter to determine from it how the shape of the beam varies. It is simpler to run a simulation, the results of which are shown in figures 9a to 9e below.
Fig 9a. The initial configuration of the beam. Full size version of this figure.
Fig. 9b. Considerable curvature is apparent shortly after the beam begins to fall. Full size version of this figure.
Fig. 9c. The combination of gravity and the unequal stretching of the sides of the beam, shown in figure 9b, are forcing it to straighten. Full size version of this figure.
Fig. 9d. The curvature of the beam has been over-corrected, and the beam is now nearly horizontal. Full size version of this figure.
Fig. 9e. At the point of impact, crushing of the right-hand end of the beam is apparent. Full size version of this figure.
Fig. 10. The development of fractal growth at electrodes arising from the movement of copper ions in solution [7]. Full size version of this figure.
Fig 11. A display of a cold gas about to condense to a liquid; pairs of molecules have already begun to form [8]. Full size version of this figure.
The Clausius-Clapeyron equation expresses the dependence of vapour pressure of a volatile solid or liquid on temperature. It contains differentials (or logs in the integrated form). It is an important equation in thermodynamics, but though it is not particularly complex, it still presents students with difficulties, and they may not appreciate that vapour pressure rises approximately exponentially with temperature. A simulation of a collection of molecules, assuming a simple interaction potential, will allow students quickly to investigate the dependence of vapour pressure on temperature.
The experimental behaviour is not "built-into" the simulation - indeed thermodynamic properties are defined only for bulk systems, and the simulation is of individual molecules. Nevertheless, with a sufficiently large number of molecules, the user can measure vapour pressure and investigate P/T relationships.
In a two phase (gas/solid) system, one can illustrate the principles of Langmuir or BET behaviour using again simple interaction potentials. (Fig 12).
Fig. 12 Simulation of argon above a charcoal surface. The movement of the argon atoms is illustrated by the tracks. [5]. Full size version of this figure.
This leads us to a further point of crucial importance:- molecular simulations also simulate what we do not see.
This sounds like nonsense. What can it mean? Although the primary role of the simulation shown in Fig 12 might be to allow students to study adsorption on solids, further physical phenomena may be investigated using the same model. For example, the molecular tracks in Fig 12 hint that the molecules adsorbed on the surface are not actually stationary, but move around a little. This behaviour is not "what we are looking for" if we are using the simulation to study Langmuir adsorption; indeed, this movement across the surface could not be observed if the simulation was based solely on the Langmuir equation. In this sense then, the molecular level simulation may include within it behaviour we are not looking for (and may not even notice). The sudden discovery by a student of quite unexpected phenomena, such as movement of adsorbed molecules, is both a stimulant to learning, and often a source of delight to the student.
Fig. 13 A simple simulation of gas molecules confined to a small container. [9]. Full size version of this figure.
5.5 Revelation of complex behaviour from simple equations
Fig. 14. Fractal growth resulting from a small centro-symmetric field applied to an electrode in a dilute solution of copper ions [7]. Full size version of this figure.
Fig. 15. Fractal growth by deposition of ions released from a point source. Full size version of this figure.
Fig 16 shows a fractal that results when we assume that the central electrode provides a potential concentrated along the Cartesian axes. The resulting 4-fold symmetry is striking.
Fig. 16. A fractal growth generated by an electrode which provides a field aligned along the x-y axes. Full size version of this figure.
A chemist who understands only equations is really a mathematician. A chemist who has a feel for the way in which molecules behave, and who thinks that he or she knows what moleculeswant to do is a scientist.
Readers who share this interest may like to know that CoLoS is offering prizes for innovative scientific software available through the Internet. First prize is one thousand dollars, travel from anywhere in the world to a CoLoS conference, and day-to-day expenses for attendance at the conference.
The closing date for applications is expected to be February 1st 1998.
1. Taken from an experiment in NMR spectroscopy under development in the Physical and Theoretical Chemistry Laboratory at Oxford University.
2. Taken from an on-line experiment in error analysis under development in the Physical and Theoretical Chemistry Laboratory at Oxford University. Data are generated by connecting to an optical rig through the Internet.
3. Data from Computer simulation of the Belousov-Zhabotinsky reaction, Chi Ho Lam, Chemistry Part II thesis, Oxford, 1996
4. A java applet showing a vibrating molecule: http://www.pc.chemie.th-darmstadt.de/java/
5. Screen shot from a simulation written using X, C and Motif. Pete Bennett, Mathematical modelling and computer simulation of aspects of surface science, Chemistry Part II thesis, Oxford University, date.
6. An experiment under the control of the CoLoS program xyzet, developed at Kiel University, Germany.
7. Screen shot from an experimental CoLoS program on fractal growth, developed at Oxford University.
8. A screen shot from a CoLoS demonstration program on the thermodynamics of simple liquids. Andy Armstrong, Computational modelling and simulation of molecular phase dynamics. Chemistry Part II thesis, Oxford University, June 1995.
9. A screen shot for a simple simulation of gas-phase molecules.
10. The virtual lab in Oxford is at http://neon.chemistry.ox.ac.uk
11. An interactive computer simulation of collisional potential surfaces, Russell Strevens, Chemistry Part II thesis, Oxford University, England, 1995