Force constants quadratic

Determination of the paiameters entering the model Hamiltonian for handling the R-T effect (quadratic force constant for the mean potential and the Renner paiameters) was carried out by fitting special forms of the functions [Eqs. (75) and (77)], as described above, and using not more than 10 electronic energies for each of the X H component states, computed at cis- and toans-planai geometries. This procedure led to the above mentioned six parameters... 

Hach molecular mechanics method has its own functional form MM+. AMBER, OPL.S, and BIO+. The functional form describes the an alytic form of each of th e term s in th e poteri tial. For exam pie, MM+h as both a quadratic and a cubic stretch term in th e poten tial whereas AMBER, OPES, and BIO+ have only c nadratic stretch term s, I h e functional form is referred to here as the force field. For exam pie, th e fun ction al form of a qu adratic stretch with force constant K, and equilibrium distance i q is ... 

A larger value for the bending force constant K0 leads to a greater tendency for the angle to remain at its equilibrium value 0g. There may be cubic, quartic, etc. terms as with the corresponding bond stretch term in addition to the quadratic term shown here. 

The functional form for bond stretching in AMBER is quadratic only and is identical to that shown in equation (11) on page 175. The bond stretching force constants are in units of kcal/mol per A and are in the file pointed to by the QuadraticStretch entry for the parameter set in the Registry or the chem.ini file, usually called =>istr.txt(dbf). 

The significance of force constants of general quadratic valence force fields application to Au(CN)2. PtCl42-, AuC14, AuBr4- and Au(CN)2Cl2. L. H. Jones, Coord. Chem. Rev., 1966,1, 351-378 (15). 

Here,/Ls and/ns are the quadratic force constants which determine the eurvature at the minima of the two curves and which are related to the corresponding vibrational frequency v resulting from IR or Raman spectra by ... 

Liu and Zhou29 have computed the quadratic force field of cis-hexatriene by a systematic scaling of ah initio force constants calculated at the planar C2V structure. Their results reproduce satisfactorily the observed spectral features of this molecule. 

With p = (Qg + Ql f being the Jahn-Teller radius, FE the linear vibronic coupling constant, GE the quadratic vibronic coupling constant, KE the force constant for the Eg normal mode of vibration, and Qo, Qe the two degenerate vibrations of eg symmetry. 

These manipulations have brought us to a familiar equation we recognize (4.23) as the Schrodinger equation (1.132) for a one-dimensional harmonic oscillator with force constant ke. Before we can conclude that (4.23) and (1.132) have the same solutions, we must verify that the boundary conditions are the same. For quadratic integrability, we require that S(q) vanish for q = oo. Also, since the radial factor F(R) in the nuclear wave function is... 

A simple proof of principle13-16 which has been used by most workers is to represent the energy of a occ bond as a quadratic function of the C—C distance, r, as in eq 2 where ka is the stretching force constant. 

For the sake of argument, we will assume that both the it- and the a-energies are quadratic in the distortion coordinate, with respective force constants Ajt and ka.34 This leads to the following expression for the displacement of the ground state (ARgs) relative... 

To this end the theory is enriched by the following set of parameters the harmonic force constants Kee (fCtt), the linear vibronic constants Xe (Xt) and eventually the quadratic ones, and the tetragonal (trigonal) distortion energy Atetr (Atrig). 

These equations are obtained from the energy expression Ef = fefQf/2 of a harmonic oscillator when shifting the parabola in the Ef, Q, plane [ 19]1. The force constant kf belonging to this state is connected to one of the quadratic contributions in the third term of Eq. (1) by... 

Fig. 6a, b. Calculated emission spectra showing the effects of changing the force constant of the initial wave packet placed on the quadratically coupled surface with dx = 1.44, and Ay = 1.53. The excited state force constants are a 540 cm 1 and b 135 cm 1... 

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