A Spreadsheet Approach to Determining the Degree of Distortion in Five-Coordinate Compounds
Absorbance vs. Relative Concentration 640 nrn
Craig D. Montgomery Trinity Western University 7600 Glover Rd. Langiey, B.C., Canada, V3A6H4
Relative Concentration (Green Solution) 0 CdS + Spectronic 20 Figure 14. Beer's Law plots for green foodcoloring 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 effect 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 photometer for educational laboratories that gives reasonable absorption measurements over three wavelength ranges. The awxiated LlMS~ortsoftware allows control from a latus 12-3 spreadsheet k t h automatic display of results in spreadsheet 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.
The stereochemistry of five-coordinate compounds, of both main gmup and transition metal elements, is of considerable 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 complexes, 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 phosphoranes 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 mechanism, 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 chemistry course, it is often stressed that there exists a delicate balance of energetic factors that results in the favoring of either the TBP and S P structure over the other. Typically [Ni(CN)51&is referred to since both structures are observed 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 interplay 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 coordinates 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 pyramidal geometry (RP), for structures of spirobicyclic compounds having two five-membered rings.For these struc-
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 53.1 53.1
76.9
76.9 0.0 76.9
BC AC
0.0 76.9
TBP ldealized trigonal bipyramidal (TBP) and square pyramidal geometries Volume 71 Number 10 October 1994
885
tures the internal ring angle at the phosphorus is approximately 90". One may define the dihedral angles by the two substituents lying along the edge between two triangular faces. For example, dihedral angle BC refers to the dihedral angle between faces BCE and BCD. Table 1 gives the dihedral angles for the idealized TBP, SP, and RP structures. The method used by Holmes for determining the distortion of structure X alone the Berm coordinate. involves calculating 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 &(structureX) - &(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&(structure 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,(stmctureXI - S,(TBP)l11217.7 x 100ri. Spreadsheet Method
The author used the Microsoft Works Version 2.00e spreadsheet program on a Macintosh I1 computer. Individuals desiring a copy of the spreadsheet template can write to the author, enclosing a 3 %-in. disk. Calculating the planes and ultimately the dihedral angles is rather difficult for a structure in an noncubic, nontetragonal or nonorthorhombic space group. However, if the five bond distances and 10 bond angles about the central atom are known then, one can determine relative atomic positions. The spreadsheet operator first inputs the five bond distances, 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 structure, that is, angle B-P-C has opened up to a value greater than 120". The first step in the spreadsheet calculations is to determine 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:
Having calculated relative atomic positions for the six atoms, the next step is to generate the equations describing the six triangular faces. These equations are of the form: Kr+Ly+Mz+N=O
S i m three points in each plane are known, then by arbitrarily setting the value of N equal to 1in 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 1and 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 1indicates, angles AB, AC, and BC remain acute across the Berry coordinate. Angles BD, BE, CD and CE remain obtuse across the coordinate and therefore 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 determine whether to assign an acute angle or the obtuse compliment to AD and AE. For each angle the difference between the value for We structure under investieation and the value for an idealized TBP is calculated.These differences are then summed uo eivine XJ - S,(TBP) . Likewise Xlh(struc- ZG,(structure .. 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: -
u
-
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 understanding the various factors affecting the stereochemistry of five-coordinate compounds. If it is deemed beneficial, the student may be required to consult one paper, otherwise, 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 distortion from a TBP arrangement as seen by comparing compounds 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 X Y RP structure. Likewise that the effect of havP( 0 , 0. 0) ing like, a s opposed to unlike, doA( PA, 0, 0) nor atoms in each of the rines of a B( PB cos (APB). PB sin (APB), O) spirobicyclic compound, is to inC( 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 - (XC- %d2- (M: - JO) 1 + a) be seen by comparing compounds sin(APg 6 and 7. Unlike atoms more readily occupy the axial and equatorial PD2-m2-J02) sites ofa TBP due to the electmne D( PD Cos (APD). PD[ws (BPD)- cos (APE)cos (APD)] sin(APQ gativity difference. Comparing compounds 6 and 8 P E ~ rr2 E2) E( PEcos(APE), PE[cos (BPE)- cos (APB) cos (APD)] shows the effectof increasing the sin(APQ degree of unsaturation in the
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666
Journal of Chemical Education
Table 2. Example of Spreadsheet Calculation for ( C ~ H ~ O Z ) Z P ( C(6). ~H~)
Table 3. Possible Series of Phosphoranes to be Considered
Bond Distances andAngles P-A 1.775 APB 108.5 DPC 89.9
P-B 1.65 BPC 145.4 EPA 100.0
Compound P-C
1.655 APC 106.1 EPB 90.0
P-D 1.691 DPA 100.0 EPC 84.2
% Distottion from TBP
Ref,
P-E 1.682 DPB 84.0 DPE 160.0
OPh PhO.,, I P , -OPh PhO I OPh
1
15
(7)
Atomic Coordinates
DihedralAngles Cosine AB BC AC BD CD AD BE CE AE
a(") 70.227 13.652 71.485 114.545 111.865 84.009 112.886 113.329 83.942
I&(structureX) &(TBP)I
17.127 39.448 18.385 13.045 10.365 17.491 11.386 11.829 17.658 156.635 %Deviation from TBP = 71.95
0.338 0.972 0.318 0.415 0.372 0.104 0.389 0.396 0.106
I&(structureX) &(RP)I
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
