Vibrations. Force Constants. Rotational Barriers

5 Molecular Vibrations. Force Constants. Rotational Barriers 

IR and Raman data for V2 to vg of solid O2F2 will be found on p. 95. The data for have been included in the following section. 

For the torsional vibration V4, a wavenumber of -160 cm was estimated from the microwave spectrum [10]. 

Wavenumbers (in cm ) of combination and overtone vibrations due to Ar matrix IR absorption studies are  

The following set of generalized valence force constants was derived from the fundamental vibrations Vg through Ve observed in an Ar matrix at 14 K and from an assumed value =1250 cm [5]. The indices R, r, a, and x pertain to the 0-0 bond, the 0-F bond, the OOF bond angle, and the torsion, respectively  

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Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

Microwave spectrometer, 219-221 Microwave spectroscopy, 130, 219-231 compilations of results of, 231 dipole-moment measurements in, 225 experimental procedures in, 219-221 frequency measurements in, 220 and molecular structure, 221-225 and rotational barriers, 226-228 and vibrational frequencies, 225-226 Mid infrared, 261 MINDO method, 71,76 and force constants, 245 and ionization potentials, 318-319 Minimal basis set, 65 Minor, 14 Modal matrix, 106 Molecular orbitals for diatomics, 58 and group theory, 418-427 for polyatomics, 66... 

Vibrational analysis, conformational stability, force constants, barriers to internal rotations, RHF, MP2 and DFT calculations of trans,trans-2,4-hexadiene87... 

Detailed studies have been made on the vibrational spectra of F3P—BH3 and F3P—BD3.18Z A force constant of 2.46 mdyn A-1 was calculated for the P—B bond stretching, while assignments of 224 cm-1 and 167 cm-1 were made for the torsional modes of the H and D compounds, respectively. These are consistent with barriers to rotation of 4.15(H), 4.31(D) kcal mol-1. 

Structure and dynamics of molecules includes the geometric structure (interatomic distances and angles) as well as vibrational frequencies, force constants (see Force Fields A General Discussion), barriers to internal rotation, ionization energies, dipole moments, etc. These are intrinsic molecular properties, independent of temperature and pressure. 

Generally, only a small number of scaling constants are needed. For example, ten scaling constants and reference values were derived for hydrocarbons from comparisons of gas phase structures, conformational energies, rotational barriers, and vibrational frequencies measured by experiment and calculated by the QMFF. For the bond and bond angle energy functions in equation (1) the same scale factor is multiplied by the QMFF quadratic, cubic, and quartic force constants. Similarly, the same scale factor is used for the one-, two-, and threefold torsion force constants, and a single scale factor is used for all cross terms. 

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