And harmonic force field

The gas-phase molecular structures of CF3SF, CF3SCI (332), and of CFsSBr (307) were determined from electron diffraction experiments. Vibrational spectra and harmonic force field calculations were reported for CF3SCI (47). For CFsSBr an improved method of preparation from CF3SCI and HBr was developed, and a full normal coordinate analysis was performed and thermodynamic functions were derived on the basis of a modified assigiunent of the vibrational spectrum (42,307). 

The simplest way to combine electronic stnicture calculations with nuclear dynamics is to use harmonic analysis to estimate both vibrational averaging effects on physico-chemical observables and reaction rates in terms of conventional transition state theory, possibly extended to incorporate tunneling corrections. This requires, at least, the knowledge of the structures, energetics, and harmonic force fields of the relevant stationary points (i.e. energy minima and first order saddle points connecting pairs of minima). Small anq)litude vibrations around stationary points are expressed in terms of normal modes Q, which are linearly related to cartesian coordinates x... 

Highly Correlated Single-Reference Studies of the O3 Potential Surface. I. Effects of High Order Excitations on the Equilibrium Structure and Harmonic Force Field of Ozone. 

The Vibrational Frequencies and Harmonic Force Fields of Transition Metal Complexes... 

Whiteham CJ, Ozeki H, Saito S (2000) Microwave spectra of CuOD and AgOD molecular structure and harmonic force field of CuOH and AgOH. J Chem Phys 112 641-646... 

Muller HSP, Miller CE, Cohen EA (1996) Dibromine monoxide, Br20, and bromine dioxide, OBrO spectroscopic properties, molecular structures, and harmonic force fields. Angew Chem Int Ed 35 2129-2131... 

Quantum Chem. Symp., 22, 173 (1988). Calculation of Harmonic I quendes and Harmonic Force Fields by the Hartree-Fock-Slater Method. 

AB INITIO STUDIES ON POLYYNES AND POLYDIACETYLENES STRUCTURE AND HARMONIC FORCE FIELD... 

Murphy WE, Zerbetto F, Duncem JL, McKean DC (1993) Vibrational spectrum and harmonic force field of trimethylamine. J Phys Chem 97 581... 

Force constants of S2O were calculated from infrared and microwave data for a general harmonic force field using the equihbrium geometry the following data were obtained [34] (1 aj = 1 mdyn = 1 N cm ) ... 

Florian, J., Johnson, B. G., 1994, Comparison and Scahng of Hartree-Fock and Density Functional Harmonic Force Fields. 1. Formamide Monomer , J. Phys. Chem., 98, 3681. 

The revalues are distances between atoms separated by a chain of three (four) or more bonds (Section 2.1.5.). Mainly because of the introduction of the nonbonded interactions, Eq. (8) and (9) no longer represent simple harmonic force fields. We therefore denote the constants of these expressions as potential constants and not as force constants. In principle, all the constants of the force fields (2), (3), (4), (8), and (9) are different, as indicated by different indices (V FFF , U f/BFF , v = vibrational (understood in the sense of standard vibrational-spectroscopic computational techniques)). In what follows we shall be primarily concerned with force fields of the type of Eq. (8) which we therefore formulate with the simplest symbols. 

Kofraneck and coworkers24 have used the geometries and harmonic force constants calculated for tram- and gauche-butadiene and for traws-hexatriene, using the ACPF (Average Coupled Pair Functional) method to include electron correlation, to compute scaled force fields and vibrational frequencies for trans-polyenes up to 18 carbon atoms and for the infinite chain. 

The harmonic frequencies and the anharmonic constants may be obtained from experimental vibrational spectra, although their determination becomes difficult as the size of the system increases. In Table 1.10, we have listed experimental harmonic and anharmonic contributions to the AEs. These contributions may also be obtained from electronic-structure calculations of quadratic force fields (for harmonic frequencies) and cubic and quartic force fields (for anharmonic constants). For some of the larger molecules in Table 1.11, we have used ZPVEs calculated at the CCSD(T)/cc-pVTZ level or higher, see Ref. 12. In some cases, both experimental and theoretical ZPVEs are available and agree to within 0.3 kJ/mol [12, 57],... 

How one obtains the three normal mode vibrational frequencies of the water molecule corresponding to the three vibrational degrees of freedom of the water molecule will be the subject of the following section. The H20 molecule has three normal vibrational frequencies which can be determined by vibrational spectroscopy. There are four force constants in the harmonic force field that are not known (see Equation 3.6). The values of four force constants cannot be determined from three observed frequencies. One needs additional information about the potential function in order to determine all four force constants. Here comes one of the first applications of isotope effects. If one has frequencies for both H20 and D20, one knows that these frequencies result from different atomic masses vibrating on the same potential function within the Born-Oppenheimer approximation. Thus, we... 

Fig. 5.8 VPIE s of Waters and Ices. The points are experimental from various sources. The lines are calculated using an isotope independent harmonic force field consistent with spectroscopic information (Van Hook, W. A. J. Phys. Chem 72,1234 (1968))... 

Harmonic and cubic force fields of Sis were calculated using coupled-cluster (CC) theory (25) and a correlation-consistent basis set. Specifically, the CC singles and doubles (CCSD) method (24) was used in conjunction with the cc-pVTZ basis set (25) developed by Dunning and co-workers. The force... 

Table 1. Computed and experimental equilibrium geometry and harmonic force constants for HjO (all results in atomic units). The results of reference 70 were obtained by fitting 36 points on the surface to a general quartic force field the first terms of which were...

Murrell 2S6> shows theoretically that for MX6 compounds the three bond stretching force constants can be calculated sufficiently accurately from IR and Raman spectra from this the complete harmonic force field can be deduced. This is an important simplification, and bond strengths can be more conveniently calculated. Murrell shows that e.g. in WFSC1 that replacement of F by Cl strengthens the trans WF bond and weakens the cis WF bonds. 

Within the HA, the prediction of a vibrational absorption spectrum amounts to the calculation of the harmonic normal mode frequencies, vi7 and dipole strengths, Dt. The frequencies are obtained from the harmonic force field (HFF). With respect to Cartesian displacement coordinates, this is the Hessian (d2WG/dXXadXx,a,)0. Diagonalization (after mass-weighting) yields the force constants ky the frequencies, vy and the normal coordinates, <2 , i.e. the transformation matrices, SXa4. The dipole strengths depend in addition on the APTs these require calculation of (dtpG/dXXa)0. 

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