Parameter method in the calculation of force constants - application to e' species force field of phosphorous pentafluoride

Abstract

A parameter method is developed for mapping all the mathematically possible force fields fitting the experimental data on the vibration frequencies and Coriolis coupling constants in the case of vibrational species of order three. The method is applied to the E' vibrations of phosphorous pentafluoride and all the possible force fields fitting the frequencies and Coriolis data, for both assignments viz. v(equatorial in-plane bending) > v(axial bending) and vice versa, are mapped. The vibrational amplitudes l(P-F eq) corresponding to these various force fields are also plotted. Comparison of the plot with the electron diffraction result conclusively settles the assignment in favour of v(axial bending) > v(equatorial in-plane bending). Comparison of the vibrational amplitudes l(P-F eq) and l(F eqβF ax), for the remaining sets of force fields, with the electron diffraction results leads to a remarkable restriction of the ranges of parameters involved. The final results yield a mapping for the force constants in the range F 11( E')=4.18 to 5.79 mdyn Å −1, F 22( E')=0.23 to 0.57 mdyn Å, F 33( E')=4.77 to 2.33 mdyn Å, F 12( E')=−0.37 to 0.57 mdyn, F 13( E')=−0.51 to 1.42 mdyn and F 23( E')=0 to −0.44 mdyn Å. The result is discussed in the light of the various force fields suggested for the molecule by different authors.