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Molecular Modeling Exercises and Experiments
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Mechanisms of Pentacoordinate Pseudorotation. A Molecular Modeling Study of PF5 Craig D. Montgomery Department of Chemistry, Trinity Western University, Langley, BC V2Y 1Y1, Canada;
[email protected] Pentacoordinate phosphorus compounds or phosphoranes are, with few exceptions, trigonal bipyramidal (TBP) in geometry; the exceptions are monocyclic and bicyclic phosphoranes, where ring strain is a factor (1). However, one of the unique properties exhibited by some pentacoordinate compounds that is commonly noted in inorganic chemistry courses and texts is that of pseudorotation, whereby axial and equatorial substituents of the trigonal bipyramid exchange sites without breaking any bonds. Evidence for such pseudorotation comes most often from NMR spectroscopy. A well-known example is PF5, which exhibits one signal, a doublet, in the 19 F NMR above ᎑22 °C (2). Two mechanisms appear possible for the pseudorotation process—the Berry process and the turnstile process, illustrated in Schemes I and II, respectively. In the Berry mechanism, the axial angle (∠DPE in Scheme I) of 180° closes down to 150° at the same time as one of the equatorial bond angles ∠BPC in Scheme I) opens up to 150°; this brings the molecule to the square pyramidal (SP) transition state in the mechanism. Angle DPE then continues to close down until reaching 120°, at which point substituents D and E are in the equatorial positions. Likewise, ∠BPC simultaneously continues to open up until it reaches 180°, at which point B and C have become axial substituents. D A
D
P C B E TBP
A
C
C
P
A
EB SP
Scheme I: Berry pseudorotation mechanism
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D
P BE TBP
In the alternate mechanism, a pair of substituents (A and D in Scheme II), rotates with respect to the remaining three substituents in the manner of a turnstile. (In Scheme II, B rotates toward C, C toward E, and E toward B.) Before this rotation takes place the structure must distort slightly in order to align itself with the turnstile axis; after the rotation it distorts back to a TBP structure. The transition state in the turnstile mechanism is the 30° TR structure and it lies midway through the rotation step; that is, B has rotated halfway toward the position of C, etc. D A
P C B E
D A
A
C B E
D
D P B E C
P
A
P
B E C
Scheme II: turnstile pseudorotation mechanism
Both of these transition states (SP, 30° TR) are illustrated in Scheme III. Holmes et al. (3) have argued in favor of the Berry mechanism on the basis of solid-state structural distortions, although some turnstile-type distortions have also been noted (4 ).
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
Information • Textbooks • Media • Resources 105°
A
D
87°
C
P
150°
Results
D A
P
C B
EB
E
APD, APB, = 105° APC, APE
APD, BPC, = 90° BPE, CPE
DPC, CPE, = 87° BPE, BPD DPE, BPC = 150°
APC, DPE = 155.3° APE, CPD = 84.7° DPB, APB = 114.1°
SP
30° TR
Scheme III: possible transition state geometries for pseudorotation
With the accessibility of desktop molecular modeling software and its application across the chemistry curriculum, including inorganic chemistry (5), it is possible for students to undertake a theoretical study of the fluxional behavior of pentacoordinate molecules. This paper presents such a study using the PF5 molecule as an example. Three types of calculation are applied to determine the most favorable mechanism for pseudorotation. The single point energies of the SP and 30° TR transition states are calculated and compared, a possible transition state is determined by synchronous transit, and the various vibrational modes of trigonal bipyramidal PF5 are determined and considered. Procedure The molecular modeling software that was used in this study was HyperChem 5.1 Professional (6 ), although other modeling software could also be used. The procedure involves the following eight steps. Step 1. A PF5 framework is constructed and converted to a three-dimensional TBP structure by using the “build” command. Step 2. The TBP geometry is optimized with molecular mechanics (MM+ force field).1 Step 3. The TBP geometry is again optimized, this time by semiempirical methods (MNDO).1 Step 4. A single point calculation of the optimized structure is obtained (MNDO). Step 5. An SP PF5 molecule is generated from the TBP structure. This is done by first restraining four F–P–F angles (between one axial fluorine atom and the other four fluorine atoms) as 105°. The geometry is then optimized and a single point calculation is used to determine the energy by repeating steps 3 and 4. Step 6. A 30° TR PF5 molecule is also generated from the TBP structure. Again this is done by first restraining F–P–F angles in the TBP molecule; this time all ten F–P–F angles are restrained according to the values indicated for the 30° TR molecule in Scheme II. The geometry is then optimized and a single point calculation is used to determine the energy by repeating steps 3 and 4. Step 7. An ab initio determination (using 3-21G basis set) of the vibrational spectrum of TBP PF5 is carried out. Step 8. A possible transition state is determined by semiempirical methods (MNDO) using a synchronous transit algorithm.2
For each of the three structures (TBP, SP, 30° TR) it was possible to optimize the geometry and convergence was obtained. The energies calculated for the TBP, SP, and 30° TR structures were ᎑418.8, ᎑414.3, and ᎑403.6 kcal, respectively. This suggests an activation energy of 4.5 kcal for the Berry pseudorotation mechanism (the energy difference between the TBP geometry and the SP transition state), compared with 15.2 kcal for the turnstile mechanism (the energy difference between the TBP geometry and the 30° TR transition state). Consistent with this, other theoretical studies have suggested energy differences of 5–10 kcal between the TBP and SP geometries (1). This suggests that the energy barrier for pseudorotation of a TBP molecule is less via the Berry mechanism than the turnstile mechanism, thus lending support to the Berry mechanism. The vibrational spectral calculations yielded the results shown in Table 1. Of significance to this study is that the ν7 (E′) vibrational mode follows the Berry mechanism, converting the TBP structure to an SP structure. Furthermore, this is the lowest-energy vibrational mode, consistent with the experimental spectrum (7 ). By contrast, there was no vibrational mode that follows the turnstile mechanism. That the lowest-energy vibrational mode leads to the SP transition state is also supportive of the Berry mechanism. The final calculation undertaken was to determine a possible intermediate by the method of synchronous transit.2 In this calculation reactant and product atoms are matched and the transition state is determined by interpolation. This calculation converged to an SP transition state structure (C4v symmetry; P–F bond lengths of 1.555 Å [apical], 1.593 Å [basal]; F–P–F bond angles of 102.9° [apical–basal], 87.1° [basal–basal]). A semiempirical (MNDO) single point calculation yielded approximately the same energy (᎑415.0 kcal) for this transition state as was obtained in the analogous calculation for the SP structure constructed earlier in this study. That the transition state search produced an SP structure rather than a 30° TR structure again supports the Berry mechanism over the turnstile mechanism. The Berry mechanism, shown in this study to be the preferred one for pseudorotation in PF5, is illustrated through a series of still images in Figure 1. Table 1. Vibrational Energies for PF5 ᎑1 Vibrational Vibrational Energy/cm a Mode Experimental Ab Initiob ν1 ( A′1) 817 867
ν2 ( A′1)
640
790
ν3 ( A′′2)
944
1164
ν4 ( A′′2)
575
545
ν5 ( E′)
1026
1180
ν6 ( E′)
532
507
ν7 ( E′)
300
187
ν8 ( E′′)
514
473
aRef
7. bCalculated with a 3-21G basis set.
JChemEd.chem.wisc.edu • Vol. 78 No. 6 June 2001 • Journal of Chemical Education
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Figure 1. The Berry pseudorotation mechanism. Left to right: a PF5 TBP; an intermediate structure with the axial angle closed down to 160° and one equatorial angle opened up to 140°; the SP transition state; an intermediate structure with the axial angle closed down to 140° and one equatorial angle opened up to 160°; a PF5 TBP.
Conclusion This exercise in molecular modeling can easily be undertaken by a student to compare and evaluate the two commonly suggested mechanisms for pseudorotation of pentacoordinate compounds—the Berry and turnstile mechanisms. Evidence from this study, including single point semiempirical energy calculations, vibrational calculations, and transition state searching, all supports the Berry mechanism in the case of PF5. W
Supplemental Material
Supplemental material for this article is available in this issue of JCE Online. Notes 1. Geometry optimizations for both semiempirical and molecular mechanics calculations had a termination condition of less than 0.1 kcal/(Å mol) (decreased to 0.01 before vibrational spectrum calculations) with a Polak–Ribiere algorithm. The setup for semiempirical calculations typically involved a convergence limit of 0.01 kcal/mol, RHF spin pairing, and accelerated convergence. 2. In the synchronous transit method, each atom in the TBP reactant molecule is matched up with an atom in the TBP product
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molecule. The starting point for the transition state search is interpolated as approximately midway between the reactant and product configurations. A vibrational calculation is done, a vibrational eigenvector is chosen and then the search proceeds along that vibrational mode. Here transition-state searches were done by synchronous transit with quadratic interpolation and a termination condition of less than 0.1 kcal/(Å mol).
Literature Cited 1. Corbridge, D. E. C. Phosphorus: An Outline of Its Chemistry, Biochemistry and Technology, 4th ed.; Elsevier: Amsterdam, 1990; pp 994–1007. 2. Gutowsky, H. S.; Hoffman, C. J. J. Chem. Phys. 1951, 19, 1259. 3. Holmes, R. R. Acc. Chem. Res. 1979, 12, 257. 4. Montgomery, C. D. Phosphorus Sulfur Silicon 1993, 84, 23. 5. Lipkowitz, K. B.; Pearl, G. M.; Robertson, D. H.; Schultz, F. A. J. Chem. Educ. 1996, 73, 105. Comba, P.; Zimmer, M. J. Chem. Educ. 1996, 73, 108. Bakalbassis, E. G.; Stiakaki, M. A. D.; Tsipis, A. C.; J. Chem. Educ. 1996, 73, 111. 6. HyperChem Professional, version 5.1; Hypercube, Inc: Gainesville, FL, 1998. 7. Beattie, I. R.; Livingston, K. M. S.; Reynolds, D. J. J. Chem. Phys. 1969, 51, 4269.
Journal of Chemical Education • Vol. 78 No. 6 June 2001 • JChemEd.chem.wisc.edu
