Absorbance vs. Relative Concentration 640 nrn

Relative Concentration (Green Solution) 0 CdS + Spectronic 20

Figure 14. Beer's Law plots for green food coloring solution measured with the Spectronic 20 at 640 nm, either with the standard detector or a CdS photocell.

Phot~transistors'~ with verv fast remonse times mav be substituted for the photocells; and they are available with either flat or convex lenses. There is a dramatic d~fference in phototransistor resistance when the rubber stopper mount is rotated from measurement to measurement for the same sample, or when the cuvette is rotated, due to the small active area of the phototransistor, and focussing ef- fect of round cuvettes. This may be obviated to some extent by choosing phototransistors integral wide-angle lenses, or by using two or more phototransistors in parallel or series as the detector. Silicon photodiodes may provide the ideal combination of large active area and fast response, but they are current1 quite expensive unless purchased from surplus dealers. I? Concluslons

The Pipetronic is an easily wnstruded, inexpensive pho- tometer for educational laboratories that gives reasonable absorption measurements over three wavelength ranges. The awxiated LlMS~ort software allows control from a latus 1- 2-3 spreadsheet k t h automatic display of results in spread- sheet cells in a wlor that refleets the incident light color. The CdS detector assembly from the Pipetronic can be used easily in a Spectronic 20, and LIMSport soRware can be used to acquire data from the modified instrument. To obtain a Lotus 1-2-3 spreadsheet tutorial for wnstructmg the Pipetronic, and wpies of the macros used to control it, send a blank disk and prepaid mailer to the author.

Literature Cited 1. W z . E.: Reinhard. S. J. C h . Edue. 1885.70.245. 2. Wz; E.J. Cham. Educ. 1992,6!3,744 3. Re. E. J. C h . Edue. 1885, 70.63. 4. Re, E.; Reinhard, S. J. Cham. Edue. 1885,70,758-761. 5.Wz.E.;Betta, T A. ZIMSportuersuspHDataAcq~ition: AoInerpensiveRobeand

Calibration SoRware,'J Cham. Edue., in press. 6. Berkka, L. H.: Clark, W. J.; White, D. C. J. Ckem Edue.. 19% 69,691. 7. Nagel, EdgarH. J Cham. Edue. 1880,67,A75.

Table 1. Dihedral Angles for Idealized TBP, SP and RP Structures (1).

Dihedral Angle. Si TBP SP RP

AB 53.1 76.9 76.9 BC 53.1 0.0 0.0 AC 53.1 76.9 76.9

A Spreadsheet Approach to Determining the Degree of Distortion

in Five-Coordinate Compounds Craig D. Montgomery Trinity Western University 7600 Glover Rd. Langiey, B.C., Canada, V3A6H4

The stereochemistry of five-coordinate compounds, of both main gmup and transition metal elements, is of con- siderable interest because of the wide range of geometries observed. Although a trigonal bipyramidal (TBP) geometry would be predicted if consideration was given only to VSEPR arguments, other factors such as incompletely filled d subshells, in the case of transition metal com- plexes, and ring strain can result in distortion.

Holmes (1, 2) has quantified the degree of distortion from an idealized TBP geometry for a series of phosphora- nes in the solid state by considering dihedral angles and found that the distorted structures tend to lie along the Berry coordinate (3). That is, the distortion is towards a square or rectangular pyramidal structure (SP, RP). This has been used to support the Berry pseudorotation mecha- nism, as opposed to the turnstile mechanism (41, as the means by which these phosphoranes exchange sites in a TBP arrangement.

When considering five-coordinate stereochemistry in either a main group or transition metal inorganic chemis- try course, it is often stressed that there exists a delicate balance of energetic factors that results in the favoring of either the TBP and SP structure over the other. Typically [Ni(CN)51& is referred to since both structures are ob- served in a single crystal (5). Therefore it would be a useful exercise for students to calculate the degree of distortion for a series of compounds and thereby see the subtle inter- play of factors affecting pentacoordinate stereochemistry. Furthermore, because these two Idealized structures are related by the Berry pseudorotation mechanism, such an exercise could illustrate the adherence of such structures to the Berry coordinate versus the turnstile coordinate.

However, calculating the distortion using Holmes' method of dihedral angles, given fractional atomic coordi- nates can be rather difficult for a crystal system that is not tetragonal, cubic, or orthorhombic. This paper illustrates how Holmes' method may he adapted to a spreadsheet, given only the five bond distances and ten bond angles around the central atom.

Dihedral Angles and Distortion The idealized TBP and SP geometries are shown in the

figure. In addition, Holmes alsn refers to a rectangular py- ramidal geometry (RP), for structures of spirobicyclic com- pounds having two five-membered rings.For these struc-

TBP

ldealized trigonal bipyramidal (TBP) and square pyramidal geome- tries

Volume 71 Number 10 October 1994 885

tures the internal ring angle at the phosphorus is approxi- mately 90".

One may define the dihedral angles by the two substi- tuents lying along the edge between two triangular faces. For example, dihedral angle BC refers to the dihedral an- gle between faces BCE and BCD. Table 1 gives the dihe- dral angles for the idealized TBP, SP, and RP structures.

The method used by Holmes for determining the distor- tion of structure X alone the Berm coordinate. involves cal- culating the absolute dkerence Getween the "slue of each dihedral angle 6, for structure X, and the corresponding value for the idealized TBP geometry. These differences are then summed giving Z I &(structure X) - &(TBP) I . The value of q&(SP) -&(TBP) I is 217.9", that is, the sum of the changes in the dihedral angles between the TBP and SP geometries is 217.9". The value of g&(RP) - S,(TBP) I is 217.7".

Therefore, if a strucure X lies along the Berry coordinate somewhere between the TBP and RP structures, then ZISi(structure X) - &(TBP) I will equal 217.7 - q&(struc- ture X) - Si(RP) I . As mentioned earlier, this was found to be the case for a series of cyclic phosphorane structures, thus lending support to the Berry exchange mechanism. The deeree of distortion for such a structure alone the Berry &ordinate may then be quantified as a percen'iage, ZG,(stmcture XI - S,(TBP)l 11217.7 x 100ri.

Spreadsheet Method The author used the Microsoft Works Version 2.00e

spreadsheet program on a Macintosh I1 computer. Indi- viduals desiring a copy of the spreadsheet template can write to the author, enclosing a 3 %-in. disk.

Calculating the planes and ultimately the dihedral an- gles is rather difficult for a structure in an noncubic, non- tetragonal or nonorthorhombic space group. However, if the five bond distances and 10 bond angles about the cen- tral atom are known then, one can determine relative atomic positions.

The spreadsheet operator first inputs the five bond dis- tances, PA through PE, and the 10 bond angles about the central atom, APB through DPE. This should be done so that the substituent labels match those in the figure. This means that if viewing the molecule as a TBP, substituents A, B, and C are in the equatorial positions while D and E are axial. Of the three equatorial substituents, A appears the most like the apical substituent in an SP or RP struc- ture, that is, angle B-P-C has opened up to a value greater than 120".

The first step in the spreadsheet calculations is to deter- mine relative atomic positions. To do this the origin is set at atom P, the x-axis is taken as collinear with the PA bond and the q plane is defined by atoms P, A, B. Therefore the relative atomic positions of the six atoms (XA, y ~ , ZA etc.) are as follows:

X Y

P( 0 , 0.

A( PA, 0, 0)

Having calculated relative atomic positions for the six atoms, the next step is to generate the equations describ- ing the six triangular faces. These equations are of the form:

K r + L y + M z + N = O

S i m three points in each plane are known, then by arbitrar- ily setting the value of N equal to 1 in each case, it is possible to solve a system of three equations for K, L and M.

In order to calculate the dihedral angle, between planes 1 and 2 for example, the following equation is used:

Since the above equation involves the absolute value of cos 0, care must be taken as to whether the dihedral angle is acute or obtuse, when converting the cosine values to angles. As Table 1 indicates, angles AB, AC, and BC re- main acute across the Berry coordinate. Angles BD, BE, CD and CE remain obtuse across the coordinate and there- fore the above equation needs to be modified to give the obtuse compliment. Only angles AD andAE go from obtuse to acute and this occurs when angle BC is approximately 28'. Therefore an "if' statement may be employed to deter- mine whether to assign an acute angle or the obtuse com- pliment to AD and AE.

For each angle the difference between the value for We structure under investieation and the value for an ideal- ized TBP is calculated. These differences are then summed uo eivine ZG,(structure XJ - S,(TBP) . Likewise Xlh(struc- - u - . .

ture X) - Si(RP) I is calculated. The two values s h h d add UD to 217.7". if indeed the structure lies alone the Bern - coordinate. '

Finally, the percent de+iation is obtained simply as:

An example of such a spreadsheet is shown in Table 2, for the compound (CsH,02~2P(C6H5) (6).

Application of Spreadsheet The spreadsheet may be used, along with a series of

phosphoranes such as that in Table 3, as an aid in under- standing the various factors affecting the stereochemistry of five-coordinate compounds. If it is deemed beneficial, the student may be required to consult one paper, other- wise, the relevant data from these papers may be supplied to the student.

The effect of introducing one, then two, five-membered rings into an acyclic phosporane is to increase the distor- tion from a TBP arrangement as seen by comparing com- pounds 1.2, and 3 from Table 3. This is clearly due to the increased ring strain as a five-membered ring is imposed on axial and equatorial sites of a TBP, as opposed to the

more favorable basal sites of an z RP structure.

0) Likewise that the effect of hav- ing like, as opposed to unlike, do- nor atoms in each of the rines of a

B( PB cos (APB). PB sin (APB), - O) spirobicyclic compound, is to in-

C( PC cos (APC), PC[cos (BPC) - cos (APB) cos (APQ -[PD' - P C ~ - 2(PC)(PD) c?s,,LCPD) crease distortion from a TBP, an sin(APg - (XC- %d2 - (M: - JO) 1 + a) be seen by comparing compounds

6 and 7. Unlike atoms more read-

D( PD Cos (APD). PD[ws (BPD) - cos (APE) cos (APD)] sin(APQ

ily occupy the axial and equatorial PD2-m2- J02) sites ofa TBP due to the electmne

gativity difference. E( PEcos(APE), PE[cos (BPE) - cos (APB) cos (APD)] P E ~ - rr2 - E2) Comparing compounds 6 and 8

sin(APQ shows the effect of increasing the degree of unsaturation in the

666 Journal of Chemical Education

Table 2. Example of Spreadsheet Calculation for (C~H~OZ)ZP(C~H~) (6).

Bond Distances and Angles

P-A P-B P-C P-D P-E

1.775 1.65 1.655 1.691 1.682

APB BPC APC D PA DPB

108.5 145.4 106.1 100.0 84.0

DPC EPA EPB EPC DPE

89.9 100.0 90.0 84.2 160.0

Atomic Coordinates

Dihedral Angles

Cosine a(") I&(structure X) - I&(structure X) - &(TBP)I &(RP)I

AB 0.338 70.227 17.127 6.673

BC 0.972 13.652 39.448 13.652

AC 0.318 71.485 18.385 5.415

BD 0.415 114.545 13.045 3.055

CD 0.372 111.865 10.365 7.435

AD 0.104 84.009 17.491 7.109

BE 0.389 112.886 11.386 6.414

CE 0.396 113.329 11.829 4.271

AE 0.106 83.942 17.658 7.042

156.635 61.065

%Deviation from TBP = 71.95 % Deviation from RP = 28.05

rings. This too can be related to differences i n r i ng strain. Fmallv the effect o f the electronegativity and steric bulk

of the f i k h substituent may be se& be comparing com- pounds 4,6, and 6.

The student may be given the bond distances and angles for a series of compounds as shown in Table 3 and be asked to determine the factors which favour a n RP arrangement and supply explanations as to why this is the case.

Literature Cited 1. Holmes, R. R; Deiters, J. A. J Am C h . Soc. 1977.99,331&3326 2. Holmea, R. RAm. Chem. &s. 1879,IZ, 257-275. R Re- R. S . I . Chem. Phva. lsBO.32.933438. .~ ~~ ~ ~ ~

4. Ramtrez, F.; Ugi, I . Bul<Chim. SCG k~ 1974,453-470. 5. Raymond, K N.; Corfreld, P W. R.; Ibera, J. A Inorg C h . lsBs,7,13621372.

Table 3. Possible Series of Phosphoranes to be Considered

Compound % Distottion Ref, from TBP

OPh PhO.,, I

,P-OPh PhO I

1 OPh 15 (7)

3 R = OPh 88

6 . B m m , R. K: Holmea, R. R J Am. Chem Soc Is??, 99,33263331. 7 . S m s . R;Ramirez, F.;MeKeever,B.;Mamk, J. E: Lee.6. J A m . Chrm. S a . l S l 6 ,

98.581587. 8. Sprafley, R. D.; Hamiltan, W. C.; Ladell, J. J. Am. C h . S a . 1887,89,2272-2278. 9. Sama, R.; Ramire., F.; Mara.ek,J. I? J. Org Chem. 1976,41.413479.

10. Wunderlich, H A - Clysfdlogr, S e l . B 1974,30,93W345. 11. Wunderlich, H.: M&, D. Acts Crystallogr. Sect. B 1874,30,935-939. 12, Day,R. 0.; Sau,A.C.;Holmea,R.R. J A m C h m . Soe 1978,101,379&3801. 13. B m m , R. K: Day, R. 0.: Huaebye, S.; Holmee, R. R. I n o g Chem 1976.17,3216.

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