This relationship is accurate to any desired degree of approximation.

To summarize, the cumulant method establishes a general relationship between diffraction intensity and cumulant averages defined with regard to the Pij(r) or Pij(r)/r functions. By inserting equation 2 into equation 1, one obtains The γn values are sensitive functions of the molecular force field and vibrational distribution. It is useful to consider the dimensionless cumulant coefficients, γn, which are defined (15) by The latter can be assigned a clear meaning in terms of properties determining the vibrational probability density function: =re + is the mean position, c≈lg2 is the dispersion, c is the skew, and c is the excess, respectively, of the probability density. One can adjust the equilibrium internuclear distances re and cumulants c with n=1~4. Where (omitting the subscripts ij for simplicity)Įquation 1 provides a basis for least-squares model refinement from GED data. One can get reduced molecular intensities with cumulant average and the vibrational probability density function as follows11-14 10 Displacements of the nuclear positions with respect to their equilibrium positions are expanded in terms of the normal coordinates and vibrational averages taken then, the average over random orientations of the molecule is obtained. There exist alternative methods for calculating Imol(s) by making the vibrational and rotational averages. The temperature dependent vibrational amplitudes la of C-F and F…F were obtained with five different force fields. By using CA method, various temperature dependent parameters of CF4 were calculated in a straight forward manner such as mean internuclear distances ra, and vibrational amplitudes la as well as cumulant coefficients γn. The equilibrium distances (re) for C-F are presented by using various force fields. The parameters of CF4 from CA are compared with those from SCA method and tradition method. The CA method was applied to analyze the GED/RT data of CF4 using five different anharmonic force fields as well as SCA method and traditional method. In this paper, the cumulant analysis method has been expanded to include the direct evaluation of equilibrium geometries of tetrahedrally symmetric (Td) molecules such as CF4.

A simplified-cumulant analysis procedure9 was developed recently to allow for data refinements without the need for extraneous information from spectroscopy. The method applies to both equilibrium and non-equilibrium molecular ensembles. The effects of anharmonicity on the molecular scattering and probability density function have been considered previously by using perturbation7 or variational8 approaches. The anharmonic part of the potential function contributes significantly to the apparent molecular geometry, and thus can not simply be ignored in a precise treatment of equilibrium structures. In conjunction with cumulant analysis,4-6 the method determines not only the vibrational average structures, but also the equilibrium molecular geometries. GED/RT has been applied to discriminate among various molecular force fields as derived from high-resolution spectroscopy. GED/RT2-3 instrument was constructed with a multichannel photodiode array (PDA) detector, and is thus an online technique. The technique of direct electron counting with a photomultiplier system was reported in 19791. The photographic measurements have insurmountable problem of inaccuracy because of irregularities of photographic emulsion and chemical processes of development. CF 4 has a Tetrahedral molecular structure and shape with bond angles of 109.5 °.The hybridization of the CF 4 is given by sp 3.In its most stable state, the Carbon atom forms covalent atoms with the Fluorine atoms.CF 4 comprises a Carbon atom surrounded by four Fluorine atoms.Let’s quickly summarize the salient features of Carbon Tetrafluoride Since there are no lone pairs, the electron geometry is Tetrahedral as well. Therefore, the molecular geometry of CF 4 is Tetrahedral. From the A-X-N table below, we can determine the molecular geometry. We can ignore ‘N’ since there are no lone pairs. Therefore, that would give us AX 4 for the CF 4 molecule. ‘N’ represents the number of lone pairs attached to the central atom. In this case, there are four Fluorine atoms bonded to the central Carbon atom. ‘X’ represents the number of atoms bonded to the central atom. This can also be determined by using the steric number or the A-X-N method. This results in a Tetrahedral molecular geometry, as shown.

Cf4 molecular geometry