Figure 3, when it is viewed on the monitor. The geometries corresponding to A, B, C, and D on Figure 3 are in Figure 4. The PES shows most of the features anyone would encounter in computational chemistry. There is a saddle point at A connectiIlg a local minimum at B with a deeper, apparent global minimum at C. A particularly instructive feature is that the saddle point is actually canted so the path from B to C is not a direct one. Often this is a feature of transition states (saddle oointsl that is comoletelv lost in the undergraduate cdculuk. ~ccasionailya Groad plane, where many loosely coupled motions can occur, is found in computational chemistry. This fact also is illustrated. Finally, a hilltop, at D, illustrates situations where gradient searches in such programs as MOPAC 6.0 would give two negative eigenvalues for Hessian matrix diagonalization. This occurs often when locating saddle points with SIGMA or NLLSQ in MOPAC. It is diagnosed by running a FORCE calculation to obtain two or more negative eigenvalues. We also have experienced this problem with the newer routine eigenvector following (Keyword TS in MOPAC). Seeing this feature alerts students to the meaning of two or more negative Hessian eigenvalues. The use of this lab experiment has given students insight into molecular mechanics, and later, the vagaries of transition state computations with MO packages. Such visual connection of the rotational angles q and m in 1with the energies in casting the data into a 3-D representation opens up entirely new prospects for students accustomed to 2-D transition state representations in textbooks.
Acknowledgment We thank the Petroleum Research Fund, administered by the American Chemical Soeiety, for support of this research.
Chemical Checkers on the Computer Y. G. Orlik, P. V. Glyakov, and R. M. Varova
Byelorussian University Minsk 220050, Byelarus The ~ l e ofs a well-known game served as a basis for the computer program "Chemical Checkers", implemented for the IBM personal computer and available from Project SERAPHIM. The program "Chemical Checkers" is intended for mastering the following inorganic chemistry topics: "Chemical properties of the main classes of inorganic compounds", "Chemical Properties of Metals", and Chemical Properties of Acids, Bases, and Salts". The program enables the students to organize and sum up their knowledge of the topics given above. Feedback is a necessarv condition for effective leamine. This im~lies monitoring acquisition of the material s t h i e d and'disolavinr information about the results achieved. This function i'implemented in the learning mode during the course of the game. The rules defining the set of possible moves constitute the basis of any game. The rules of the game "Chemical Checkers" include one characteristic feature-chemical compounds are checker pieces: acids, salts, oxides, metals, water. Their formulas are displayed on the screen. According to the rules, the checker piece can be removed only
C Figure 4. The geometries corresponding to A, B, C, and D in Figure 3 Volume 70 Number 4 A~ril1993
297
Reaction equation: 2HC1
+
Ce(OH)2
-
Ca012
+
2H20
Soluble acids r e a c t t o salts i n t h e change reactions
Figure 5. Jumping the piece,
Figure 6. Error in jumping the piece.
when substances read with one another. This property is referred to as the main rule of the game. Some minor rule limitations also were introduced, aimed at facilitating the shorthand notation of the move. These can be excluded in other variants of the game. Learning occurs during the course of the student's game with the computer. The pieces are displayed on the screen. The partners are equal, so the student records his move first. The position change is highlighted on the screen. Then the computer makes its move and comments on it. The next position is displayed and the student has to make his move. The following situations are possible while recording the move.
Removing the Pieces
Piece Movements
The student has recorded a move that implies moving the piece one position ahead. An ordinary checkersman can move only diagonally forward to the vacant position while the king can move diagonally both forward and backward. As a result of the move by the student, the computer highlights the change of the position and makes its move. Erroneous Move Record
This situation is possible when the student did notmaster the rules ofthe game of checkers and moves incorrectly. The computer points out the error made and suggests that the student should make a new move. Error in Removing the Pieces
The student has recorded the move, implying removing his opponent's piece and violating the main rule of the game. This situation arises when the student does not know the properties of some substances. The computer highlights the substances which, according to the student, will enter into the reaction and comments on the rules or properties the student does not know. Then the computer suggests that the student should make a new move. Violation of the Rules of "Battle"
This situation can arise when there was a possibility to remove a niece but the student did not notice it and recorded the'move mentioned in point 1.It also arises when the student has removed several nieces hut did not notice that he could remove some more. The computer assumes that the student does not know the properties of the substances or the rules of their reaction, removes the pieces itself, and highlights the corresponding equations for the chemical reactions. 298
Journal of Chemical Education
The move leading to removing the opponent's pieces has been recorded. The pieces are removed in turn in the direction implied by the move. A corresponding equation of a chemical reaction is highlighted. Information support of the game is represented by two sets of chemical substances. These sets of chemicals cover the topic studied. One set represents the computer's checker pieces; the other, the pieces of the student. The following lists of chemical compounds serve as an example of the set related to the topic "Chemical properties of the main classes of inorganic compounds": HC1, HzS, KOH, CU(OH)Z,HzO, K2C03,CuC12, COz, CaO, KzO, Fe, H2C03 and NaOH, Ca(OHI2,HN03, HzS04,AgN03, MgS04, HzO, MgO, S03, Pz05, Mg, Mg(OH)z. Let's consider the game situation for these chemical compounds. Two computer checkersmen c5 (MgSOJ and e5 (C~(OH)Z) are under the attack of the student checkersman d4 (HC1). In order to determine which checkersman to attack, the student must know the main properties of chemical compounds and the rules of their reaction. Figure 5 represents the situation on the screen when the student makes the right move, and Figure 6 represents the situation when the student has violated the main rule of the game. In the first case, the student will score one point and in the second case will lose a point. The arrangement of chemical compounds on the checkers board is given by the random number generator, so the probability of occurrence of two similar arrangements of compounds is small and is even less after the beginning of the game. In practice this means that each student works with a different arrangement of checkers pieces and chemical compounds. Moreover, if the student plays several games with the computer, each time he will get a new arrangement on the board. Thus, the possibility of rapid conquest in the game is eliminated. The student is eager to play with the computer and win.What is most important is that the student masters his knowledge of chemistry. At the beginning of the computer game the student gets familiar with the rules of the game of checkers and with the rules for recording moves. Then he acquaints himself with the main rules of chemical reactions. He must read the information displayed on the screen attentively. The rate of turning the pages is determined by the student him- or herself with the help of the ENTER key. Conventional notation is chosen for recording moves; for example, c3-d4, b6-a5, d2:f4, d6:b4. The game ends when the opponent has no pieces left or when there are some pieces left hut there is no possibility
of another move. Sometimes it is advisable to finish the game by the end of a certain time interval, say in 15-20 min. In anv case. statistical information summarizine the game is diiplayed at the end of the game: the score, the total number of i u m ~ e d~ieces.the total number of mistakes made and the num6er of mistakes on each rule, and the grade (from 2 to 5). The criteria for determining the grade can be changed or under some circumstances, it may be desirable not to eive a made at all. As a rule, the made is given according tithe points won. The teache;can aetermine what material is most difficult. The authors would like to thank W. Torop (West Chester University) for revising this article. Literature Cited
Ruekelshaw ,W. D.Issups hS&m and Zkhnologv 1986.1 (3),19-38. Kaapemon, R. E.R i s k A d y ~ b1988,6(31,276281. Mmalcy. S.; Plough, A. E n u i m m n t d HmanZe Communicating Risks a m Social Phcess;AvbumHouae: Ihwr, MA,1988. Sharlin, H. I.Ri*AnolyJis 1986.6 (11,6168. C o d o , V T;AUen, F, W Sewn C o r d i d R u k of Risk Cammunleotion; EP.A.: Waahmgtan, DC, 1988. Whiwant, D. M. J Ckem Ed=. 1984,61(71,627426. HiU. R. BCTC termoaoer. . . 1988. l a I l p k o w v . K H J Lhem Kduc 1998.66.615;b Slmpon. J. U.J. C h , , WLC 1989 66.406. e Bislr. S E .I Chem Edur ISM. 67. 10'!3 d l Aduldd!n. S Ak1tu.r. P. Flrld P Nu& P . OSulltuan. k:. 0'('mnor. K . H x t h a r s y . H J J (')urn Mur 1991.M.5'6 c Box Y O S . J Ckem Ed=. 1USl.66.662 f Jarrcr. R M : S m , N J Chen. Educ IBB0.67.lS~ (a) Gilliom. R. D. J. Ckem. Ed=. 1989,66,41;(bl Little, T. S.: andYeager, K,J. Ckem Ed-. 1989,66,675;(4Colwell, S. M.; and Handy, N. C. J Chem Edur 1988,65.21. Butcher, P G.; Mortimer, M.:Whatley, B. G. J Ckem. Edvc 1987,M, 495. Burke- U.;Allinger, N. I.; ACS Monograeh Series, no. 175;American Chemical Societ~Washington, DC, 1982. Cajewski, J . J.; Gilbert, K E.; McKeIvey, J. Aduonws in Mdpeular Mdzling; D. Irotta. Ed.,Val. 2,p 85,(19901,JAI Resa, h e . , Greenwich, CT.
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