Fundamental frequencies force, constants from

It is customary in applying normal coordinate theory to use the experimentally observed fundamental frequencies as the basis of the calculation of the quadratic force constants. From a strict viewpoint this is not justifiable inasmuch as the observed fundamental frequencies do not have the same values as they would if the anharmonic terms were zero. In order to calculate the quadratic force constants accurately, it is necessary to use the so-called mechanical frequencies of vibration, which are the frequencies which the molecule would exhibit if the anharmonic terms in V were all zero. When an empirical formula of the type given in (3) has been obtained, the mechanical frequencies can be calculated from the relations... 

The linear structure of 93 was derived from experiments with labeled precursor molecules and by correlation of vibrational frequencies calculated from estimated force constants with the recorded IR absorptions. The three fundamentals were observed as well as the UV/VIS spectrum,131 which was resolved and analyzed by gas phase measurements.132 The predicted triplet ground state was confirmed by recording the ESR spectrum of 93 isolated in various matrices.131... 

Infrared Spectrum. The infrared spectrum of gaseous SiF 2 has been recorded from 1050 to 400 cm"1 63 Two absorption bands, centered at 855 and 872 cm 1, were assigned to the symmetric (v j) and antisymmetric (V3) stretching modes, respectively. The assignment was rendered difficult because of the considerable overlap of the two bands. The fundamental bending frequency occurs below the instrumental range of the study, but a value of 345 cm 1 can be determined from the ultraviolet study. The vibrational frequencies were combined with data from a refined microwave study 641 and utilized to calculate force constants and revised thermodynamic functions. 

The six fundamental vibrational frequencies for SeF and TeFe are given in Table XII (21,37,38,103). Force constants for SeFs, calculated with the frequencies from vapor-phase Raman spectra (21) and using isotope shifts and Coriolis coupling constants as additional data (103), are listed in Table XIII in comparison to TeFg (1,24,104,125,139). 

SCF, SCF-MI and MCSCF-MI level. Frequencies co were calculated directly from the force constants K by applying the harmonic approximation or by means of the Noumerov method [45,46]. In the latter case, frequencies were evaluated from the energy difference AE between the fundamental and the first excited states by applying Plank s law. This technique is undoubtedly more accurate than the harmonic approximation. 

In mass-weighted coordinates, the hessian matrix becomes the harmonic force constant matrix, from which a normal coordinate analysis may be carried out to yield harmonic frequencies and normal modes, essentially a prediction of the fundamental IR transition... 

Here kb is the force constant or bond strength and r0 is the ideal or unstrained bond length. A first approximation to the force constant can be calculated from the fundamental vibration frequency, v, of the X-Y bond, taken from the infrared spectrum of a representative compound by using Eq. 15.2,... 

The lower vibrational levels have been studied by infrared (IR) and Raman spectroscopies [16]. Normal coordinate analyses based on force constants transferred from other molecules (Urey-Bradley type) or from ab initio HF calculations have played a part in the construction of the vibrational assignments [17]. The observed fundamental frequencies are given in Table 2.3. 

On the other hand, we were concerned with consistency within our calculations. Thus, we used the same values for atomic masses throughout the calculations. (For Cl and Br, the masses of the most abundant isotopes were used.) Therefore, some of our calculated frequencies do not agree exactly with previously published data. Further, again for consistency, the force fields used were based exclusively on fundamental frequencies even though, in a few cases, data for zero-order frequencies are available. In order to permit replication of our results, the force constants actually used in the calculations are reported to as many as nine significant figures, which is, of course, far beyond the precision justified from present spectroscopic methods. 

The first step was to obtain approximate force-constants for [IrFg]" (Oh) which could be transferred in this approximation to the XeF,IrF0 molecule. Values for the two [IrFJ" fundamentals, V4 and v, not known from our experimental data, were estimated from values for IrFj (ref. 19) and the difference in the other bending frequency, Vj, between IrFj and [IrFg]". The estimated values, V4 = 274 cm." and Vj = 204 cm.", should be within ca. 20 cm." of the true values. The six frequencies were then used to solve for the valence-field force-constants, applying the approximation introduced by Claasen. ... 

The valence force field for XeF, contains 20 force constants, but only nine fundamentals are observed the system is clearly underdetermined, and some assumptions must be made about the force field. Our approach initially involved the transfer of interaction constants from related molecules. A detailed treatment by Curtis has given uncertainty limits for the force constants of IF, and XeOF, moreover, frU is usually assumed to be zero in systems with massive central atoms. IF, was also considered since it has unusual vibrational properties (v,> vi> v,y, the most noticeable feature of its force field is f <0. Good agreement with the experimental frequencies of XeF was obtained in calculations using a simple seven parameter force field / = 4.3, /, = 4.0,... 

The molecular structure Is that derived from electron-diffraction data by Akishin et al. ( 3). Observed vibrational frequencies are those reported by Buchler et al. (1 ) from Infrared spectra of the vapor at 1000-1200 K. These frequencies are confirmed by Infrared spectra of AlFg Isolated In matrlcles of neon, argon and krypton (1, 16). Drake and Rosenblatt (17) have estimated the Raraan-actlve fundamentals based on a correlation of vibrational frequencies and internuclear distances for the Group IIIA trihalides. They estimated v, = 685 cm" which would decrease S (298,15 K) by 0.05 cal k" raol" from our adopted value. We adopt Vj 650 50 cm as derived from three other methods (a) calculation of the force constant k from v and v (b) comparison of k,(XY,)/k(XY) for X = B, Al and Y = F, Cl, and Br and (c) extrapolation of v,(BY )/v-(AlY ) to Y F from Y=C1, Br... 

The fundamental ground state vibrational frequencies are those from a re-analysis of infra-red and Raman spectra by Guenther and Stoicheff, referenced by Kleman ( ) as a private communication. Several sets of anharmonicity constants and/or rotational constants have been published (2, 4-9). Some are corrected for Fermi resonance to some degree in some manner (6, 7, 9), others are not 2, 4). We adopt the x j, and g22 terms determined from the least-square estimates of the force... 

All five fundamental vibrational frequencies are calculated by the modified valence force method ( ) from estimated force constants which are interpolated from those of Cgig (5) CH=CP (6), CH=CC1 (6), CHsCBr (6), and C2D2 (4). 

As it is seen on Table 1, the vibrational frequencies of ammonia are adequately reproduced by the PES given in Eqs. 4, 5, and in Table 2, both for the fundamentals, the highly excited inversion levels, and the overtones and combinations of all vibrational modes. From a comparison with our preceding work [13] it is seen that some of the force constants for ammonia are different from our previous work. This is... 

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