in this issue Modeling at the Molecular Level We humans are all macroscopic in scale and receive our data through the senses of vision, touch, smell, hearing, and taste. Therefore, when we have to understand things, such as chemical reactions, that happen on the submicroscopic scale, we have to devise a way of simulating this activity. Two very divergent routes have been taken-one concrete operational ana one a b s t r a c t i n representing a world we cannot see. The most immediate and accessible way to represent the world that is unobsewable is to make a physical model that is on our own scale and that uses familiar forms. Hence, we have produced-depending on our theoretical model of the unseen-images of mds and spirits, tiny versions of the solar system to represent atoms, and sticks and pieces of plastic foam to represent molecules. The more sophisticated approach is to create a mathematical model based on the phenomenon that is observable: enerev. From the data collected bvindirect observation of howk-isible particles absorb ahd give off heat and light and using theoretical assumptions, we have generated equations that describe electronic levels in atoms, the changes in a molecule's enerev when it reads with another, and the rates of these reactions. Agroup of articles in this issue reflect new ways to use both mathematical a n d physical models to explore t h e theoretical underpinings of molecules and their chemical reactions. Emphasizing mathematical models is a n article by Harbola and Sabni (page 920), who investigate "Theories of Electronic Structure in the Pauli-Correlated Approximation", showing how they have extended Slater's ideas to achieve closer approximations of ground state energies. Others investigating the equations describing the electronic structure of the atom are Pisani, And&, And& and Clementi (page 894), who study relativistic effects in the LCAO a~oroach:Bendazzoli (oaee 912). eives .. who " some simple*~xampl& to illustrate the variational principle to students; and Veguilla-Berdecia (page 9281, who offers a simple method for solving the Schroedinger equation for a particle moving in a double well. Wiseman and Rice (page 914) explore a theoretical model for gas-phase reactions and offermodifications (page 914). However, even those relying on mathematical equations to represent the unseen world need some ohvsical manifestation of their algebraic expressions to get their ideas
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Journal of Chemical Education
across and make them seem "real" to their audience. Basically the graph was developed for this purpose. A graph can just be a two-dimensional plot of two variables, but if it is has three variables and these are the coordinates of three-dimensional space, it is possible to simulate physically the system being described mathematically. For the chemist, such a graph can give a picture of how energy is dispersed around a n atom, the probabilitv of fmding an electron around the nucleus, or the positions of atoms-in a crystal. The graphs then become the basis for the physically three-dimesional models such as ball-and-stick molecules and crystal lattices and the old favorite Styrofoam shapes representing electronic orbitals. These familiar models are considered necessam to teach the introductory portions of theoretical chemistry; no teacher can expect students to look a t an equation andunderstand the elaborate physical interactions it represents. Nevertheless, they are not easy to build; since its early years, this Journal has published reader's suggestions for constructing atomic and molecular models using everything from cast latex in molds to business euvelo~es.The a d v k t of the affordable personal computer has >hanged the kind of effort we must exoend to oroduce ohvsical models from abstract expressio&. ~ o w ' t h eeq;ations can be entered into a promam that will oroduce the eraohed model on the s&een. Parameters can be changes tdproduce representations of different molecules and the form the representation takes can be varied as well. Calculations that used to require months of human effort or hours oftimeon the old mainframe computers (and whoseoutput was a string of numbers or a fuaey dotmatrix printout,can now be assigned as homework to undergrad&tes. The state-of-the-art in this computer modeling is represented on this month's cover in which each step of a reaction is modelled using personal computer software and output inn diferent forn~at,eachin color. Casanova (page 904,. in his artcle on comouter-based molecular modeline. reviews the latest softwaie that can be used in the undergraduate curriculum to unite calculations with visual models. Further, the new issue of Journal of Chemical Education: SoRware abstracted in this issue (oaee 902) offers its subscribers a program that uses ~ a t h c i ro d bridge the gap between the formalism of quantum theory and its various computational methods, allowing them to calculate and graph quantum equations in a Windows environment.
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