Wilson FG-matrix

Solutions of the vibrational secular equation for [XeF] [IrF5] were carried out using the Wilson FG-Matrix Method for several sets of force constants to test the consistency of the observed spectrum with the postulated structure and to seek an explanation for the doublet at ca. 600 cm. attributed to Xe F stretching. 

In the Wilson FG-matrix method, the problem is framed in internal coordinates rather than in... 

IR absorption spectra of oxypentafluoroniobates are discussed in several publications [115, 157, 167, 185, 186], but only Surandra et al. [187] performed a complete assignment of the spectra. Force constants were defined in the modified Urey-Bradley field using Wilson s FG matrix method. Based on data by Gorbunova et al. [188], the point group of the NbOF52 ion was defined as C4V. Fifteen normal modes are identified for this group, as follows ... 

In this case, analytic formulas can also be obtained for the second derivatives that govern the harmonic vibrations [10]. Table 2 lists the vibrational force constants and normal mode frequencies determined [10, 12] using Wilson s FG matrix treatment, the procedure standard for molecular vibrations [14]. The radial displacements from the minimum are combined in the usual way to form symmetry coordinates,... 

Given the molecular geometry and a set of force constants for a polyatomic molecule, it is a routine matter to calculate the normal coordinates, a procedure known as normal coordinate analysis. Suites of computer programs are readily available that will calculate vibrational frequencies and the internal coordinate composition of each normal vibration. Most of the early calculation of vibration frequencies were made by Wilson s FG-matrix method, which is briefly summarized below. Today, a number of alternative techniques based on semiempirical methods, molecular mechanics, or density functional theory are also available, in convenient commercial software packages. 

A normal coordinate analysis (NCA) for hexazacyclophane Cu(II) complex was performed by using the Wilson s force field geometrical matrix (FG) method . An INDO/1 optimized molecular geometry was used to build the G matrix . The CuN distance is 1.84 A for the copper atom in the macrocycle plane this bond length is relatively short in comparison to that reported for the non-macrocycle tris-(l,10-phenantroline)Cu(II) (2.1 A) the planar macrocycles copper porphin (2.031 and tetraazacyclotetradecane Cu(II) derivatives (2.08... 

The geometrical factors needed to set up Wilson s G-matrix have already been prescribed. With F- as found above and the bending and stretching force constants derived above, the F-matrix is also complete. The straightforward solution of FG —EA = 0 gives the imaginary frequency v as well as the real frequencies v. From these frequencies the terms F in Eq. (4) can easily be evaluated. 

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