minimization, and screen and hard copy display of calculated structures. One moves easily among the three screens that represent these three functions. Structure input (like most operations) is via a mouse and drawing; correcting errors and aitering previously drawn structures is fast and simple. Students alert to the difficulties associated with locating global minima will wish to use two or more starting geometries for some calculations. The ability, for example, to alter an existing structure in a predictable way by rotation about a particular bond is very useful. During the energy minimization, the screen shows the individual components of the calculated steric energy for the starting geometry, the structure itself (mono or stereo) updated periodically to show changes and the new steric energy after each set of five iterations. Therefore, one sees the quantitative and qualitative slide of the system into a potential energy minimum. When the structure is displayed on the screen following minimization, one can easily tumble i t into the desired position, extract structural parameters (distances between selected atoms, bond angles, dihedral angles), and even throw a second previously minimized structure onto the screen for a visual comparison of shape. Although onemay plot structures from PCMODEL, we use the companion program PCDISPLAY for its ability t o generate PLUTO and ORTEP drawings on the screen and paper via a plotter or laser printer. Students often incorporate reduced copies of these drawings in papers. The power and flexibility of this software clearly exceeds the needs of students a t this level, and one might reasonably focus on the disadvantages of the associated complexity. However, students seem to enjoy wielding a true research tool, accepting, as they do in using our FTNMR spectrometer, that they need not use every feature to use it effectively. Moreover, i t is a pleasure for the instructor to show a new feature to a student that has a prohlem that she recognizes is amenable to a more sophisticated approach. And, students pass that new expertise on with obvious enthusiasm. Finally, the increasingly routine use of structure and energy calculatinns hv chemists is sufficient reason to incorporate them in the undergraduate curriculum. However, from a personal perspective, the central educational benefit here is in giving a chemistry student a sophisticated tool, showing her how to useit togain insight, and then watching her skill andmotivation grow.
where i = 1,2,. . .,Nspecies, C; is the concentration a t time t At, and Ci is the concentration a t time t. For a first-order monoelectronic transfer 0 e a R ( 0 and R being soluble species), current density a t each instant for a semi-infinite linear diffusion process is given by eqs 3 and 4:
+
+
The transformation of eq 4 into two finite-differences equations yields eqs 5 and 6:
The resolution of the system formed by eqs 2 , 3 , 5 , and 6 allows one to calculate the current density a t each instant and the new concentrations a t the electrode surface ( x = 0). For mechanisms where first-order chemical reactions are coupled to the electron transfer, eq 1is transformed into eq 7, and their effect on eq 2 must be considered.
d. l* RWERSE PRINT HOLD SlbRI PROFILESO I - W S PbUSE
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A Voltammetry Experiment by Digital Simulation Gaspar SBnchez, Gulllermo Codlna, and Antonlo Aldaz Universidad de Allcante Aptdo. 99 03080 Allcante. Spain Cyclic voltammetry (17-20)is perhaps the most widely used electrochemical technique for the study of the kinetics of electrodic systems. The technique is based on the variation of the potential of the working electrode in a triangular cyclic form, the resulting current being measured. However, the analytical solution of the differential second-order equations necessary to obtain the voltammetric curves is very difficult if not impossible. Thus, it is not easy for the student to understand the influence on the voltammetric curves either of the different kinetic parameters of the reactions (electrocbemical rate constant, diffusion coefficient, etc.) or of the experimental conditions (scan rate, initial potential, etc.). For these reasons, the aim of this work is to provide a suitable comnuter oromam to be used both for educational . .. purposes and for approximate evaluarion of kinetic parameters. The Droeram developed has been called SIMCLA. he basic equation to solve is the Fick's diffusion equation (eq 1).The model is based upon the transformation of this equation from its differential form into a finite-differences equation using the Cranck-Nicholson's method.
Figure 4. Screen obtained fore simple electron hansfer.
Figure 5. Screen obtained for the ECE mechanism. Volume 68 Number 6 June 1991
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Functlon Keys and Parameters Description of the Function Keys F1: F2: F3: F4: F5: F6: F7:
inverts potential sweep direction. stops potential sweep. A constant potential is maintained shows species concentration profiles. program pause. gets a screen printing. program initialization. exit to DOS.
Input Parameters Range Concentration (0 Electrochemical standard rate constant (@) Chemical rate constant ( k ) Diffusion coefficient (o) Transfer coefficient (8) Standard potential ( P ) Scan rate (v)
10P
