kc? discoverer: a computer program for descriptive inorganic chemistry

6
edited by JAMES P. BiRK A Computer Program for Descriptive Inorganic Chemistry John C. Kotz State University of New York, College at Oneonta, Oneonta, NY 13820 The teachine of descrintive inoreanic chemistw is cur- rently the top; of considerable di&ssion (14) since the recent American Chemical Societv curricular aidelines re- quire more emphasis on this topi; before the &a], junior- level course in phvsical chemistry.' Proiect SERAPHIM has recently deve~&~ed a tool for teaching some aspects of de- scriptive inorganic chemistry, a computer program called "KC? Discoverer: Exploring the Periodic Table" (7L2s3 This program is an interactive data base of chemical information, a "CRC Handbook on disk", and it bas been used successful- ly for several years in a new sophomore-level course, De- scriptive Inorganic Chemistry, at the State University of New York at One~nta.~ Although an early version of the nroeram was oreviouslv discussed in a brief note in this >o&nal (9), t i e intentbf the present article is to describe the functions of the final version of KC? Discoverer in more detail and to indicate how they can assist in teaching de- scriptive inorganic chemistry. The data base for KC? Discoverer contains 49 different nieces of information for each of the first 103 elements (Fig. 1). The computer presents the information for each element in a series of three screens. The first of these, as illustrated for carbon in Fieure 2a. consists of macrosconic ~ r o ~ e r t i e s ... such as melting ioint, hardness, and condu~tivity.~ Further- more, this screen lists some useful information on reactivity: Descriptive inorganic chemistry was the subject of two recant symposia, one at the Southwest Regional American Chemical Soci- ety meeting. Little Rock. Arkansas. November 1987. and another at the Biennial Conference on Chemical Education, Purdue University. Lafayette. Indiana. July 31-August 4. 1988. Aspects of this paper were presented in each of these symposia. The name of the program comes from its original conception as a "knowledgeable counseior", in which the user would be assisted in answering questions to "discover" new concepts and correlations. The version of the program now available does not contain this function,but this capability is currently under development. The computer program is now supplemented with a 30-min video- disc from Project SERAPHIM that includes pictures of the elements; motion sequences of the reactions (if any) of each element with air. water. acids, and bases; and still pictures of some uses of each element (4. %t present, the course has two one-hour lectures per week with occasional iaboratorv work. Thus far it has focused on the chemistry -~~~~ of the elements. ari&arilv those of the main orouos. No newtheoreti- ~, cai concepts are introduced beyond those appropriatefor the usual freshman-level course. in addition to chemistry majors, the course has anracted some geology and biology ma;ors interested in a minor in chemistry. SThe figures in this paper were printed using the (shift) (print screen) function available on IBMcompatibie computer systems. FIND You can search "ithi" my Of the foliowing olltqorie.: .tmir nwber aisswarea (year, atmis *eight no. ,sotogs density 1st ionlrat<on cnevy hardness ,*on.1 2nd ionirarion anew xdting point 3rd ionization enem electron affi"ih *"nd. emrih cant ionic nldi"S (I* ion1 coat(pure, ionic radius ,I+ ion1 coat(bulk1 ionic radius (I+ ion1 wax. s m oxidation no. nuu. ban oxidation no. .I". scnnxn 0xid.ti.n no. .in. born oxidation no. Figure 1. KC? Discoverer enables UM user to search for any of 49 different piem d information fw each of the first 103 known elements. This listing is me first acreen of infmtlon ghm when using the FIND function. the results of reactine the elements with air, water, or com- mon acids and bases. The second screenful of information for each element (Fig. 2b) consists of atomic-level properties, and the formulas of the hvdrides, oxides, and chlorides formed by the element are given. ina all^, the third information screen for an ele- ment (Fig. 2c) illustrates the solid state structure of the element. . -. -. -- The program is menu-driven so that students can learn to use KC? Discoverer with a minimum of instruction. For example, after starting the program the first screen of in- structions asks if the user wishes to: 1. FIND the element(s) that has (have)as~ecified ranee of values 2. GRAPH one numeric property against another. 3. LIST the name, symbol, aMmie number, and up to four other properties for all elements or for a selected group of elements, &Aged in order of increasing atomic number. 4. SORT elements in increasing alphabetic or numeric order for one property. 5. use the oeriodicTABLE to eraoh or sort informstion r e e d i n g ". a property within a group or period. 6. ask for HELP with any of the functionsofthe programs. Help is always available from within the program simply by typing '..," The HELP function is useful for two reasons. First, the user can learn about each of the functions of the program 750 Journal of Chemical Education

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Page 1: KC? Discoverer: A computer program for descriptive inorganic chemistry

edited by JAMES P. BiRK

A Computer Program for Descriptive Inorganic Chemistry

John C. Kotz State University of New York, College at Oneonta, Oneonta, NY 13820

The teachine of descrintive inoreanic chemistw is cur- rently the top; of considerable di&ssion ( 1 4 ) since the recent American Chemical Societv curricular aidelines re- quire more emphasis on this topi; before the &a], junior- level course in phvsical chemistry.' Proiect SERAPHIM has recently d e v e ~ & ~ e d a tool for teaching some aspects of de- scriptive inorganic chemistry, a computer program called "KC? Discoverer: Exploring the Periodic Table" ( 7 L 2 s 3 This program is an interactive data base of chemical information, a "CRC Handbook on disk", and i t bas been used successful- ly for several years in a new sophomore-level course, De- scriptive Inorganic Chemistry, a t the State University of New York a t O n e ~ n t a . ~ Although an early version of the nroeram was oreviouslv discussed in a brief note in this >o&nal (9), t i e intentbf the present article is to describe the functions of the final version of KC? Discoverer in more detail and to indicate how they can assist in teaching de- scriptive inorganic chemistry.

The data base for KC? Discoverer contains 49 different nieces of information for each of the first 103 elements (Fig. 1). The computer presents the information for each element in a series of three screens. The first of these, as illustrated for carbon in Fieure 2a. consists of macrosconic ~ r o ~ e r t i e s ~ ~~ . . . such as melting ioint, hardness, and condu~tivity.~ Further- more, this screen lists some useful information on reactivity:

Descriptive inorganic chemistry was the subject of two recant symposia, one at the Southwest Regional American Chemical Soci- ety meeting. Little Rock. Arkansas. November 1987. and another at the Biennial Conference on Chemical Education, Purdue University. Lafayette. Indiana. July 31-August 4. 1988. Aspects of this paper were presented in each of these symposia.

The name of the program comes from its original conception as a "knowledgeable counseior", in which the user would be assisted in answering questions to "discover" new concepts and correlations. The version of the program now available does not contain this function, but this capability is currently under development.

The computer program is now supplemented with a 30-min video- disc from Project SERAPHIM that includes pictures of the elements; motion sequences of the reactions (if any) of each element with air. water. acids, and bases; and still pictures of some uses of each element (4.

%t present, the course has two one-hour lectures per week with occasional iaboratorv work. Thus far it has focused on the chemistry -~~~~

of the elements. ari&arilv those of the main orouos. No newtheoreti- ~, cai concepts are introduced beyond those appropriate for the usual freshman-level course. in addition to chemistry majors, the course has anracted some geology and biology ma;ors interested in a minor in chemistry.

SThe figures in this paper were printed using the (shift) (print screen) function available on IBMcompatibie computer systems.

FIND

You can search "ithi" m y Of the foliowing olltqorie.:

.tmir nwber aisswarea (year, atmis *eight no. ,sotogs density 1st ionlrat<on cnevy hardness ,*on.1 2nd ionirarion a n e w xdt ing point 3rd ionization enem

electron affi"ih

*"nd. emrih c a n t ionic nldi"S (I* ion1 coat(pure, ionic radius , I+ ion1 coat(bulk1 ionic radius (I+ ion1 wax. s m oxidation no. nuu. ban oxidation no. .I". scnnxn 0xid.ti.n no. .in. born oxidation no.

Figure 1. KC? Discoverer enables UM user to search for any of 49 different piem d information fw each of the first 103 known elements. This listing is me first acreen of infmtlon g h m when using the FIND function.

the results of reactine the elements with air, water, or com- mon acids and bases.

The second screenful of information for each element (Fig. 2b) consists of atomic-level properties, and the formulas of the hvdrides, oxides, and chlorides formed by the element are given. ina all^, the third information screen for an ele- ment (Fig. 2c) illustrates the solid state structure of the element. . -. -. --

The program is menu-driven so that students can learn to use KC? Discoverer with a minimum of instruction. For ~~ ~ ~

example, after starting the program the first screen of in- structions asks if the user wishes to:

1. FIND the element(s) that has (have) as~ecified ranee of values

2. GRAPH one numeric property against another. 3. LIST the name, symbol, aMmie number, and up to four other

properties for all elements or for a selected group of elements, &Aged in order of increasing atomic number.

4. SORT elements in increasing alphabetic or numeric order for one property.

5. use the oeriodicTABLE to eraoh or sort informstion reeding ~ ~~ " . a property within a group or period.

6. ask for HELP with any of the functions ofthe programs. Help is always available from within the program simply by typing '..,"

The HELP function is useful for two reasons. First, the user can learn about each of the functions of the program

750 Journal of Chemical Education

Page 2: KC? Discoverer: A computer program for descriptive inorganic chemistry

Carbon 6.0

C 12.01 2.2660 0.8

NO data. no

black 3 2 "

and how they can he used. And second, one can obtain background information on each type of data in the data base. The user is first given a definition of the tern, some discnssion concerning the meaning of the information, and, in some cases, how such values are obtained experimentallv. Following this the program indicates the sourEe of the data in the chemical literature. Our students find this function to be quite useful, not only because it reminds them of the correct definition of terms, hut also because it is important for them to know the source of the data in order to assess its accuracy.

The FIND function allows you to search for all the ele- ments having a particular property or attribute. If you choose a numerical property the program allows you to spec- ify a range of values within which to search. Figure 3 shows the result of requesting all the elements with a melting point less than 373 K. As seen at the bottom of the screen, three

PERIODIC lGBlE OF THE ElWMS

FIND: nltinr pt: 11.8 - 313.8 X - rrms s data auailablc

(E) Eltant rcwnr (F) Find again: d ing pt (Esc) bin rrnu

NAME: Carbon lTOMIC NO: 6 STRUCTURE: hexagonal layem

Figure 3. The FlND hmctlon in the pmgram oan be used, for example, to locate d l elements having a menlng point lower than 373 K. See Flgure 1 for a list of Other properties h t may be searched wlth FIND.

PERIODIC TABLE OF THE ElWMS

FIND: 1511 HHW: ui~mur -

(E) Elennt rcntns (F) Find wain: 1511 HHW {kc) kin rrnu

{P p) ( P g M fo r nope infomation about th i s elellent {C ff fo r next elellent found {Esd to quit

C

Figure 2. An i l l m i o n of thee weens of information available for each element. Cabon is used as an example here. (a) Manoscopic properties. (b) Atomlc-level propnies. (c) The solid-state sbuchrre of h element.

Flgve 4. In addition to searching for numerical infwmation, the FlND function can be usad to locate all elements having a particular reactivity. See Figure 1 lor a list of other properties that may be searched with FIND.

Volume 66 Number 9 September 1989 75 1

Page 3: KC? Discoverer: A computer program for descriptive inorganic chemistry

PWIODIC rim OF ruB maws FIND: some: sulfide OF sulfate om - -

means no data available

[XI nms data ~ o c k Na lk

(1) Blelrnt scnens (F) rind again: some (kc) hin nnu

F@M 5. me FIND tuncllon can be used, twexample. to expiwe lhs sourm of me elemsnts. See Figwe 1 fw a llst of other pmperties mat m y be searched wih FIND.

0 ) Pisplay X, Y values (E) Enlur~e (kc) to win rwnu

Figve 6. An exampls ofmd GRAPH function. Densnies of lhs elements have been pinned against ammic number.

ontions are now available: (1) The data screens for one or -.~ ~-~~ ~ ~ ~

more of the elements found in'this search may be viewed. (2) The user can search the data base again for the same infor- mation in a different range. (3) onecan return to the main menu. (The single line through the block for some elements indicates that there is no data on that property for that element. A crossed pair of lines indicates that that piece of data for that element has been "blocked" or hidden from view. The "blockina" option is descrihed below.)

When searching For "onnumerical information, the user is prompted to choose from a list of characteristics for a given property. For example, one may find all the elements having a certain color or a particular type of solid state structure. Alternatively, the user can seatch for all the elements having agiven reaction withair, water, 6 MHC1,15 M HN08, or 6 M NaOH. In the case of reactions, furthermore, it is also possi- ble to find elements that have no reaction, a mild reaction, or a vigorous reaction (see Fig. 4).

Sy X-axis Y-axis density (g/cMmO) 11, Sc 21.8 3.8

Ti 22.8 4.5 U 23.8 6,1 Cr 24.8 7,l

8.8,

6.6'

1,4. Rs 33,8 5.8 Se 34.8 4.3 Br 35.8 3.1 KF 36.8 8,E I

atomic no 8.8 4.8 9.6 14 19 24 29 34

TYR tk s y M ol tk tlennt or wss (CR) to wit.

Fl@m 7. An enlargemem of F i w e 6 using h e "(E) Enlarga" tunction wihin GRAPH.

e.eJ.l i I

I hiling pt E,E 189,l 1519.5 2369,2 3158,9 3948.1 4138,4 5528.1 (X)

(D) Pisplay X, Y values (1) h l w {kc) to win wnu

Figure 8. A plot of h e hem ot vaporIration of me elemem againsl heir boiling points using me ORAPH hmction.

An interesting attribute that one may explore, and one that is useful in a descriptive inorganic chemistry course, is the source of elements. For instance, the student can ask what elements are found as sulfide or sulfate ores (Fig. 51, phosphates, oxides, or those that come from water, air, or natural gas.

GRAPH is one of the most useful options available in KC? Discoverer. Figures 6-9 illustrate at least two ways the func- tion may be used. In Figure 6 the densities of the elements were plotted (on the ordinate) against atomic number (on the abscissa). Notice that the bottom of the screen asks if you wish to display the x and y values, enlarge the graph, or return to the menu. We have chosen in Figure 7 to enlarge the graph and then list values for a few elements.

Although plots of some numerical quantity against atomic number are useful, it is possible that a plot using some parameter other than atomic number on the ordinate would be informative. As an example, Figure 8 shows a plot of heat

752 Journal of Chemical Education

Page 4: KC? Discoverer: A computer program for descriptive inorganic chemistry

I atomic no BOB 14 21 U 55 69 82 96

Flgum 9. llm GRAPH functlon allows the u ~ e r M plat me sum, dlttersnce. product, or qunlemoftwo numeric properties on me wdlnete. In mla case me quotient ot Me sewnd and first lonlrstlon energies of the elemems has been plonedagainst momlcnumber. This plot Is lmerestlngforthr88reasons: (a)the pominence of Me alkali metals, which Is evidence tw me quantlzatlan of electrmic shells: (b) the prominence, albeit minor, of the grwp 13 elements; and (c) tha relative wnstancy of Me ionization energy quotlent tw the vast majwm, of elemento outside of the alkali metals.

of vaporization against boiling point and illustrates the es- sential validitvof Trouton's rule (that awide ranee of liauids have an entropy of vaporization of about 85 J I K ~ O I ) . -

Finallv, an im~ortant wav to use GRAPH is to d o t some numerica parameter on the 1: axis against a c o m b h i o n of parameters on they axis. For example, in Figure 9 we have plotted the quotient of the second and first ionization ener- gies of the elements versus atomic number, and the alkali metals are predictably prominent.

The GRAPH function is especially useful in the class- room. Graphs may be viewed in class on a large-screen moni- tor or by means of a computer projector device. Alternative- ly, a printed copy can be made into a transparency on a copy machine. Overhead transparencies have been used in the lectures on Deriodic ~ r o ~ e r t i e s in our so~homore-level de- scriptive inorganic cl;emkry course, anda computer is also available in the classroom. After showing: the class a series of graphs illustrating various periodic trends, the students are asked if they wish to try new relationships or to ask "what- if' questions using the computer. For example, what do we expect to see if electron affinity is plotted against the first ionization energy for the first 36 elements, or what is the relation between the expected cost of the element and its abundance in the Earth's crust?

The LIST and SORT commands are similar in that hoth provide a list of values of pro~erties for a selected list of k~ements. With LIST the user can, for example, list all the elements, in order of increasing atomic number, that have melting points somewhere between room temperature, say 20 "C, and 100°C (Na, K, Rb, Cs, Fr, P,and Ga). Atthe same time, up to three other properties of each element can be listed (such as boiling point, ionization energy, and electron affinity). With SORT, on the other hand, the program will list all elements having a value within a range of values, the list beine ananeed in order of ascendine value for the vrov- erty of &teres< In addition, the user may ask to have one other property of the element listed (see the table).

E 1 2 3 4 5 6 7 0 9 18 I1 12 13 14 I5 16 17 18 goup no.

( 6 ) Paph m o t h (CR) to m e e d

F i w e 10. L h l c g b T A W function. the pmpertles of the elsmems in a given g q Or period msy bs plotted against atomic number. The dinsrance b e Ween GQAPH funnlon lhslf and the graphing tunction wwin TABLE !a that, w M me latter, one can superimpose plats to m e directly compare elemental propeniea.

The periodic TABLE function is as useful as GRAPH, but it offers other possibilities. With TABLE you are shown a periodic table on the screen and given the option to SORT or GRAPH numerical information. These functions work as

~~~

described above, except that one has the option of sorting or graphing by group or by period. The particular advantage of the GRAPH function here, however, is that the graph for one group or period may be superimposed on another, thus mak- ing direct comparisons possible (Fig. 10).

"Blocking" of data is a potentially useful function of KC? Discoverer. The instructor can, if desired, "block" certain pieces of information from access. For example, suppose the instructor wishes to test the ability of the students to esti- mate the melting point, density, or even reactivity of eka- silicon (germanium) based on periodic trends in group 14. It is possible to "block this information on these or other proverties for eermanium on the disks eiven to the students. j3y studying tce periodic trends for gr&p 14 using GRAPH or SORT in the TABLE o ~ t i o n the students can arrive at some reasonable answers.

Each student in our descriptive inorganic chemistry course is given a copy of KC? Discoverer that can be used on the IBM-compatible computers in the campus computer

An Example o( the SORT Function*

COST (PURE) ABUND CRUST Nams SYM. NO. ($1100 g) (log)

Pallsdl~m Pd 46 1280.00 -2.0 Europium Eu 83 1876.00 0.1 ~hulium Tm 89 2288.00 -0.3 lrldlum lr 77 3300.00 -3.0 Gold Au 79 3332.00 -2.4 Platinum F'l 78 3398.00 -2.3 Lutetium Lu 71 3744.00 -0.3 Osmium 0s 78 8500.00 -2.8 Rhodium Rh 45 8100.00 -3.0 Scandium Sc 21 8300.00 1.3

'lM elements rrae mod aomrdlng m mst, and me ten d expensive elemnh were li~ted in ascanding ada M -1, lM log of me abundance M me element In me W 8 CmS1 I- dY) l l W .

Volume 66 Number 9 September 1989 753

Page 5: KC? Discoverer: A computer program for descriptive inorganic chemistry

center. All homework assignments and the take-home ex- aminations require them to use the program to locate infor- mation.

To teach the students how t o use the program the first homework assignments involve such questions as:

1. Find the 10 mast expensive elements. Which is the moat expensive?

2. What group 14 element has the lowest melting point, and which one has the highest melting point? (Other groups could be chosen, or the same question could be asked of a period. Different students can he given different assignments.)

3. What elements that are solid at room temperature can he melted by placing them in atest tube in a boiling water bath?

4. What elements are Listed as being orange in color? (Each student can be given a different calor.)

5. What elements were discovered between 1850 and 19W? (Each student can be given a different time period.)

6. What allotropes are possihle for oxygen and sulfur? What is the structure of the common allotrope of S?

7. What elements are used in any way as a fuel or in fuels? 8. What elements are used as lubricants or in lubricants? 9. What nonmetals react with water? 10. What elements have a chain structure, and what are their

uses? 11. What elements are considered poisonous? 12. Name the five elements that have the highest electrical con-

ductivity. Briefly compare and contrast this with the thermal conductivity of these elements.

13. What was the Last naturally occurring element found and in what year?

14. Given some list of elements (say Li, Be, B, C, N, the group 13 elements, or elements from different groups and periods), place them in order of increasing covalent radius, ionization energy, or electronegativity. Check the predictions against the information in KC? Discoverer.

As the students understand how to use the program, and as the course Droeresses, the questions become more in- volved. For elrampie, the studenis can he asked to calculate Avowdro's number based on the density, atomic radius, and solid state structure for some element, gold for example, given in KC? Discoverer. Yet another question involves the calculation of the enthalpy of a reaction such as Mg(s) + %02(g) - MgO. Here the data necessary to calculate the lattice enerw of Me0 are in the oroeram. as are the heats of atomizationl'bf ~ & d 0 2 , and iheuioniiation energies and electron affinitv of Me and 0. res~ed ive lv .~ - . -

There are of course numerous periodic trend questions that can he Dosed. (Here the instructor could make the necessary or obtain the required data and attach it to the homework or examination.) One examination question we have used is to ask the students t o plot the heats of atomization for the elements of groups 15 and 16 (Fig. 11) and to give a complete explanation ofthe trends ohse&ed.

Students havealways been interested indiscussionsof the origin of the elements. Thus, a good homework or examina-. tion question after such a series of lectures is to ask for an explanation of the plot of cosmic abundance versus atomic number of a selected period (Fig. 12).

On a take-home examination the students were asked to imagine that they were chemists working for a company interested in new materials. They were to find an element that has only a mild reaction with acid and hase but no reaction with water, an electrical conductivity of a t least 150 (mohm-em)-', and a cost less than $2 per 100 g. The easiest search strategy to find the element was to use the GRAPH option and to plot electrical conductivity against cost. In this way the options narrow quickly to Cu, Zn, Mg, and Al, and the other requirements mean that Al is the proper choice.

The students need to be told that MgO is facecentered cubic. so the Madelung constant can be found in any textbook of inorganic chemistry. Alternatively, the lanice energy can be estimated using the Kapustinskii equation.

754 Journal of Chemical Education

After this, the students were asked a series of questions concerning the element of their choice. For example, they indicated the productofreactionwithNaOH orair,ind they identified the source of the element. In addition, beginning with the density of the element in the program, &d the known geometry of the unit cell, they calculated the radius of the atom and compared i t with the experimental value of the atomic radius of the element in KC? Discoverer.

After several years of using KC? Discoverer in the class- room, we believe the program has proven its worth. The advantage of the program, over many others available, is that is truly open-ended. That is, the student or instructor asks the auestion and then the data hase is used to explore possible answers: the program does not prompt the question, tutor the user on finding the answer, or provide the answer directly. (Indeed, the prigram often invokes the most desir- able possible response from students and instructors alike:

8,E 8 1 2 3 4 5 6 7 p e r i o d n o ,

(D) Display X, Y values (CR) to pmceed

Figure 11. The graphing capabllily wlthin h TABLE function was ussd to graph me heats of ammiration against the period number for groups 14-17.

{Dl Display X, Y values (CR) to pmceed

Flgwe 12. The GRAPH function was used to prepare a plot of the awmlc abundances of elements 55-71 in the sixih period.

Page 6: KC? Discoverer: A computer program for descriptive inorganic chemistry

"Gee, whiz! I didn't realize that that periodic correlation was and Engineering Education and grant number GOO-8642147 possible or that element had those properties.") And finally, from the U.S. Department of Education Fund for the Im- as instructors, we find that it is ofwn much more convenient provement of Postsecondary Education. Initiation of J . to use KC? Discoverer on a computer disk instead of search- Chem. Educ.: Software was supported by the Camille and ing through printed data bases.

Acknowleagment

Henry Dreyfus ~bundation. Opinions expressed here are not necessarily those of the sponsoring organizations.

I am grateful to the American Chemical Society for a Lnerature travel grant to attend the 9th International Conference on Chemical Education (July 1987) in Sao Paulo, Brazil, where ~ ~ ~ ~ ~ ~ & w ~ $ ~ j ~ ~ ~ $ ~ ~ ~ l ~ ~ ~ ; 6 9 , ,o12. this work was first nresented. I also wish to express mv 3. zuckerman, J. J. J . Chcrn.Educ. 1386.63.829.

appreciation for the k s t a n c e and cooperation of the stak : ~,f,";;~iH;~;~";;",~;8':,"~;,M~$2,,, of Proiect SERAPHIM. particularlv J. W. Moore. Proiect fi nd,,. F c h r r n . ~ ~ . .weus ISR%I.I~IY 1 ) . 2

SERAPHIM, now locar&j at the university of wiscons&, is 7 F c w A . M ~ ~ ~ . . I . W . E I ~ ~ ~ . W ; ~ & h s n . ~ . J . C h e r n Edur. Soltworr 1588.IRI11. 21-11.

supported by g r a m MDR-8400351 and MDR-8751262 from 8 ~..k, A J J c ~ P ~ . E ~ ~ . 1 0 ~ 5 . ~ . 19 the National Science Foundation, Directorate for Science 9 Fena.A:Mmre, . l .W J Chem Edw.1984h9.327.

Volume 66 Number 9 September 1989 755