Morse parameter

The substrate in these studies was restricted to be rigid, and Morse functions were used for the hydrogen-surface and two-body interactions. The parameters in the Morse functions were determined for single hydrogen atoms adsorbed on the tungsten surface by fitting to extended Huckel molecular orbital (EHMO) results, and the H2 Morse parameters were fit to gas-phase data. The Sato parameter, which enters the many-body LEPS prescription, was varied to produce a potential barrier for the desorption of H2 from the surface which matched experimental results. 

Here the simplest way to proceed is to keep the Morse parameters (Q0, / (), and a) the same for both the isolated M-A bond and each additive M-A contribution within M -A so that these contributions would differ by their bond orders x,- (i = 1,2,..., n) only. Experimentally, Q(n) increases less than linearly with n... 

It is common practice to present the cubic and quartic force constants f3 and /4 in a slightly different way, in terms of so-called Morse parameters.0 6 The Morse function is an empirical diatomic potential function of the form... 

Real molecules do not fit these formulae accurately, but it is convenient to express A and A in terms of A in a manner that draws attention to the magnitude of the discrepancy. This is done by defining two Morse parameters a3 and a4 such that... 

On the right side of Figure 3.23 is a comparison of theory and experiment [185, 186] for CO. A Morse parameter of 4.5 A-1 provides a good overall fit SSH theory, with Method B and the Lennard-Jones r0 of 3.706 A, yields the dashed curve. A summary of some older data for CO is given by Wood-mansee and Decius [187], who used a spectrophone method to measure the relaxation time of pure CO at room temperature. 

Calculate the harmonic force constant 4 and the Morse parameter j8 for the two states. Using the known r J value (0.2666 nm), plot the Morse curve for the ground electronic state of I2. Compare this with the harmonic potential calcnlated from k. ... 

Morse parameters (see Table 9.6). The second term describes the decay of zero-point energy in terms of a looseness parameter a, with a standard value of a = 1 X 10 m assumed here. The final term describes the rotational energy, with fli and ai derived in the standard manner [59]. The rotational barriers Eo as a function of / are fitted to the form Eq(/) - Eo(/ = 0) = CvJ J +... 

Figure. 1 Potential energy profiles together with some of the reactant energy levels for the H + H2O —> OH + H2 (a) and the H + H F —> F + H2 reaction (b). On panel (a) the energies of the stationary points are derived from the WSLFH PES [11], the initial energy levels for water are calculated with a DVR method using Radau coordinates, and the final levels for the products are obtained from the Morse potentials corresponding to the PES. On panel (b) the energies of the stationary points are obtained from the 6-SEC PES [13] both the initial and final energy levels are calculated from the Morse parameters obtained by fitting a Morse curve to the potential for the separated FIF and H2 oscillators.

Figure II. Three-dimensional dissociation factor Z for three values of Morse parameter bR,...

In 1963 negative-ion Morse parameters for the ground-state anions of Br2 and I2 were obtained by estimating D, re, and v from the VEa measured from charge transfer spectra and properties of the excited states of the neutral. Multiple excited states of I2(—) were characterized by D. R. Herschbach in 1966. He presented general forms for ionic Morse potential energy curves (HIMPEC). Nine total groups... 

TABLE 7.3 Morse Parameters, Dimensionless Constants, and Experimental Data for Neutral and Ionic H2 and He2(+)... 

In Table 9.1 the optimum Morse parameters for the ground states of X2( ) are compared with the 1985 values, AMB and PES and theoretical calculations... 

TABLE 9.2 Morse Parameters and Dimensionless Constants for the Neutral and Anion Morse Potentials for X2... 

The experimental Ea for 02 are assigned to bound states. The VEa for these states range from 0.9 eV to —0.75 eV. The activation energies for thermal electron attachment determined from the ECD data range from 0.05 eV to 1.9 eV. The frequencies observed in solids and the Morse parameters obtained from PES, ECD, electron swarm, and other techniques can be used to approximate the intemuclear distance and frequency of the predicted states. These give six M 2) curves (EDEA < 0, and Ea and VEa > 0) and six M( 1) curves (only Ea > 0). The PES Ea, with values of 0.430, 0.450 0.002 eV, is the most precise Ea and the Born... 

TABLE 9.5 Morse Parameters and Dimensionless Constants for Diatomic Group VA Molecules and Anions... 

TABLE 9.6 Morse Parameters and Bond Order for Homonuclear Diatomic Group IA and IB Neutral and Anions... 

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