Pentacoordinated phosphorus compounds generally have a trigonal bipyramidal structure. Two geometric isomers are possible for compounds such as PClF₄. In one isomer (C_3v) the chlorine atom occupies an axial site and in the other (C_2v) an equatorial site.

Twelve fundamental frequencies (144, 181, 360, 438, 493, 510, 548, 560, 692, 887, 906, 989 cm^-1) have been identified in the vibrational spectra of PClF₄.^1,2 The ¹⁹F NMR spectrum of PClF₄ in isopentane exhibits one signal (doublet) at 23.5 ppm.³ Apparently, a rapid intramolecular exchange of the axial and equatorial fluorine atoms is responsible for the observed magnetic equivalence of the fluorine atoms. The intramolecular exchange is thought to proceed by the Berry pseudorotation mechanism.⁴ Two of the equatorial atoms move out and the two axial atoms move in to form the basal plane of a square pyramid in the transition state. The third equatorial atom, called the pivotal atom, occupies the vertex of the square pyramid.

Ab initio calculations will be used in this exercise to determine which of the two isomers is present in the gas and liquid states and to explore the Berry pseudorotation mechanism.

Begin the study by constructing a Z-matrix for the PClF₄ isomer (trigonal bipyramid, C_2v) with the chlorine atom in an equatorial position. Use the Restricted Hartree-Fock method with 6-31G* basis set to optimize the geometry, acquire a single point energy, and calculate the vibrational frequencies. Repeat the process for the other PClF₄ isomer (trigonal bipyramid, C_3v) with the chlorine atom in an axial site. Which isomer is the more stable? Compare the calculated vibrational frequencies for each isomer with the spectral data. Which isomer is present in the gas and liquid states?

Next, construct the Z-matrix for the square-pyramidal activated complex with the four fluorine atoms in the basal plane (C_4v). The chlorine atom is at the vertex of the square pyramid. Set the Cl-P-F angles at 103^o. Optimize the transition state geometry (RHF/6-31G*), obtain a single point energy, and calculate the vibrational frequencies. Is one of the calculated frequencies imaginary? Describe the vibrational mode associated with the imaginary frequency. Repeat the process for the square-pyramidal activated complex with the chlorine as a basal atom (C_s). Set the F-P-F and F-P-Cl angles at 105^o. Which activated complex is the more stable? Which activated complex is involved with the isomerization pathway and which complex is associated with the permutation of the fluorine atoms? Construct a diagram that displays the relative Hartree-Fock energies for the isomers and activated complexes. Which pathway is kinetically favored? Is this model consistent with the observed behavior of PClF₄?

The isomer (C_2v) in which the chlorine atom occupies an equatorial site is found to be the more stable. Twelve fundamental frequencies were calculated for this isomer. Only eight fundamental frequencies were obtained for the isomer (C_3v) with the chlorine atom at an axial site (Table I). Four of the eight frequencies are degenerate. Since the number of calculated fundamental frequencies for the isomer with C_2v symmetry is consistent with the spectral data, this isomer is probably the only one present in the gas and liquid states.

Table I. Observed and Calculated* Fundamental Frequencies for PClF4 

Observed  144  181  360  438  493  510  548  560  692  887  906  989	

Cl(eq)    140  171  334  417  461  466  508  554  678  864  938  974

Cl(ax)    146       361  406  485       528       722  854       982
 
*Calculated frequency x 0.89

The frequency calculations yield one imaginary frequency at 146 cm^-1 for the activated complex with the four fluorine atoms in the basal plane (C_4v) and one imaginary frequency at 127 cm^-1 for the activated complex with the chlorine atom in the basal plane (C_s). Both frequencies are associated with a rocking motion in which two basal atoms trans to each other move up while the other two basal atoms move down. The activated complex with C_4v symmetry is the more stable and leads to the exchange of the fluorine atoms between the axial and equatorial sites. The other activated complex (C_s) is associated with the isomerization pathway. A diagram of the differences in Hartree-Fock energies between the isomers and activated complexes is shown below.

The pathway for the permutation of the axial and equatorial fluorine atoms is the more facile. While the HF energies in the diagram probably differ significantly from the true activation energies, the calculations are consistent with experimental observations. Only the left pathway (the more facile) leads to the magnetic equivalence of the fluorine atoms observed in the ¹⁹F NMR spectrum.

Click here to view an animation of the isomerization reaction. Click and hold on the image to rotate the PClF₄ molecule. Chime 2.0 is required for the animation.

(1) Macho, C.; Minkwitz, R.; Rohmann, J.; Steger, B.; Wolfel, V.; 
    Oberhammer. H. Inorg. Chem. 1986, 25, 2828.

(2) Holmes, R. R. J. Chem. Phys. 1967, 46, 3718.

(3) Cater, R. P.; Holmes, R. R. Inorg. Chem. 1965, 4, 738.

(4) Berry, R. S. J. Chem. Phys. 1960, 32, 933.