Morse potential calculation

TABLE 2. Fitted parameters of the NR potential for Fe-N bonds in the EHCF/MM method. Corresponding parameters of the Morse potential calculated by Eq. (38) are also given. 

If the straight line fit is extrapolated to zero diameter a maximum value of 26 GPa is obtained for the fibre strength. Pennings et aL consider that this is the strength in the absence of surface flaws, and point out that it compares well with a theoretical estimate of 25 GPa, obtained from Morse potential calculations of the C—C bond... 

During initialization and final analysis of the QCT calculations, the numerical values of the Morse potential paiameters that we have used aie given as... 

Results using this technique are better for force helds made to describe geometries away from equilibrium. For example, it is better to use Morse potentials than harmonic potentials to describe bond stretching. Some researchers have created force helds for a specihc reaction. These are made by htting to the potential energy surface obtained from ah initio calculations. This is useful for examining dynamics on the surface, but it is much more work than simply using ah initio methods to hnd a transition structure. 

We will now compare the numerical results obtained from our study with those obtained by other methods. Assuming a Morse potential Takayanagi (31) calculated Z 10 at 300 °K. for 02+ whereas we ob-... 

During initialization and final analysis of the QCT calculations, the numerical values of the Morse potential parameters that we have used are given as De = 4.580 eV, re = 0.7416 A, and (3 = 1.974 A-1. Moreover, the potential energy as a function of internuclear distances obtained from the analytical expression (with the above parameters) and the LSTH [75,76] surface asymptotically agreed very well. 

Various approaches have been used to model the interaction between the metal electrode and the water molecules. They range from simple Lennard-Jones or Morse potentials, which have been adjusted to give good values for experimental porperties like the energy of adsorption of a water molecule, to potentials derived from ab initio calculations performed for a cluster of metal atoms and one water molecule. 

The double degeneracy of the 0(2) case corresponds to the fact that the algebraic method describes in this case two Morse potentials related to each other by a reflection around x = 0. This is a peculiar feature of one-dimensional problems, and it does not appear in the general case of three dimensions. If one uses the 0(2) basis for calculations, this peculiarity can be simply dealt with by considering only the positive branch of M. 

The corresponding EDFs for both potentials calculated for the same test set of the Fe(II) complexes are plotted in Figs. 5, 8. The systematic errors in all cases are close to zero, as can be seen from the parameters of the EDFs for the EHCF/MM with the Morse potential — r = —0.005, (7=0.056 with the NR potential — /r =0.002, (7=0.052. However, although somewhat improved the stiffness of the Morse potential again manifests itself the systematic errors for the separate LS and HS sets do exist and only approximately cancel each other in the total set, whereas for the NR... 

Figure 5. EDF for the difference between the experimental and the EHCF/MM calcn-lated bond lengths (A) over the entire test set of Fe(II) complexes. The Morse potential is used for the Fe-N bond. The scaled Racah parameters are used for the EHCF calculations (see text).

Fig. 55. The probability that a pair of iodine atoms remain unreacted at a time f after they were formed with an initial separation of 0.7 nm. The encounter distance is 0.37 nm. A Morse potential energy getween the iodine atoms is imposed and the temperature was chosen as 300 K. The diffusion coefficient is 5 X 10 9 m2 s1 and iodine atom has a mass of 0.127 kg mol . Monte Carlo techniques were used to calculate the survival probability, with-----, toe — 2xl013s 1, cjc = 1013s l --------,...

Hynes et al. [298] and later Schell et al. [272] have developed a numerical simulation method for the recombination of iodine atoms in solution. The motions of iodine atoms was governed by a Langevin equation, though spatially dependent friction coefficients could be introduced to increase solvent structure. The force acting on iodine atoms was obtained from the mutual potential energy of interaction, represented by a Morse potential and the solvent static potential of mean force. The solvent and iodine atoms were regarded as hard spheres. The probability of reaction was calculated by following many trajectories until reaction had occurred or was most improbable. The importance of the potential of... 

A quantitative evaluation of a measured energy dependence of the ratio has been made only for the system He(23S)-Ar for which V R) and T(fl) are known, so that the evaluation leads to a determination of parameters of V+(R). In classical model calculations,43 using a semiempirically determined potential V+(R)1] that only slightly deviates from the one determined from elastic scattering30 and r( ) = 4000 exp(-R/0.36) (au), which was determined by the requirements that the total ionization cross-section curve due to Pesnelle et al.43 be reproduced with the chosen K (R), for a Morse potential V+(R) the following parameter values were determined well depth 16 meV, equilibrium distance 5.67a0, and shape... 

One can see that Emr t) < EMorse r) for all values r > r0 so that the NR potential approaches the asymptotic slower than the Morse potential. One may identify the a parameter value with the Coulomb interaction of some effective charges. These effective values in Fe(II) complexes with nitrogen-containing ligands are Q, , = 1.757 e and Qn = -0.293 e the latter is close to the real CNDO charges on the donor atoms obtained in the EHCF calculations [65]. 

Figure 13. Comparison of SDs calculated by CEL and NHDH methods. Beyond adiabatic approximation. H-bond bridge Morse potential. Grayed NHDH. Dots CEL co° = 3000 cm-1, n = 100 cm-1, Y° =0.20, y = 0.3 0, De = 0.3eV.

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