Potential functions parameter determination

G. Birnbaum and E. R. Cohen. Determination of molecular multipole moments and potential function parameters of non-polar molecules from far infrared spectra. Molec. Phys., 32 161, 1976. 

In the non-rigid bender approximation, we solved the inverse eigenvalue problem described by Eq. (5.4), i.e. we determined the potential function parameters given in Table 3 for NX3 (X = H, D, T). We have used the experimental infrared frequencies of transitions from the ground state to the i>2,2 2 > 2. and 41 2 inversion states and the zero-order frequencies of vibrations (Table 4). The zero-order frequencies have been obtained from the observed fundamental frequencies of NH3 [Ref. >], ND3 [Ref. °>], NTg [Refs." and [Ref.- 3)] corrected for... 

For NH2D and ND2H, only the rigid bender approximation has been used so far in the determination of the double-minimum potential function parameters ... 

Of all the vibrational degrees of freedom of H bonded polymers, the Pff and Pfi are the most interesting. Their force constants are indicative of the potential function which determines the length and angular orientation of the H bond. These force constants, if known, could be used to estimate the degree to which a H bond can be distorted to accommodate other geometrical parameters in an intramolecular H bond (e.g., in a protein). Finally, because these vibrations are the lowest in frequency, they provide an important contribution to the entropy of polymer formation. 

Determines hydrogen-bonding energies Generates an energy vs. rotation angle plot Lists all atomic coordinates Allows modification of Lennard-Jones, nonbonded potential function parameters Lists all low energy conformers Performs multi-dimensional minimization Performs random type scan of conformational hyperspace... 

An effective potential function was determined using a three-parameter (inversion coordinate, barrier height, harmonic force constant) reduced potential curve on the basis of MO calculations (ab initio MP2, CNDO/2) [15]. Another one was constructed as the sum of the pure inversion potential, Vq, and a vibrational modification, V ib. The potential Vq was described by a two-parameter (barrier height, height of the PH3 pyramid) reduced potential [14]. The vibrational modification of the inversion barrier is about 273 cm" for PH3 [32]. 

Minimization of this quantity gives a set of new coefficients and the improved instanton trajecotry. The second and third terms in the above equation require the gradient and Hessian of the potential function V(q)- For a given approximate instanton path, we choose Nr values of the parameter zn =i 2 and determine the corresponding set of Nr reference configurations qo(2n) -The values of the potential, first and second derivatives of the potential at any intermediate z, can be obtained easily by piecewise smooth cubic interpolation procedure. 

One of the disadvantages of the method is that one must determine the smoothing parameter by optimisation. When the smoothing parameter is too small (Fig. 33.16a) many potential functions of a learning class do not overlap with each other, so that the continuous surface of Fig. 33.15 is not obtained. A new object u may then have a low membership value for a class (here class K) although it clearly belongs to that class. An excessive smoothing parameter leads to a too flat surface (Fig. 33.16b), so that discrimination becomes less clear. The major task of the... 

The stretching overtones of molecules such as H20 and S02 were described in Chapter 4 by Hamiltonians of the type (7.60). If one uses the parameters determined from a fit to the data (Table 4.1), one can then calculate from Eq. (7.64) the corresponding potential function. Two examples are shown in Figures 7.1 and 7.2. 

Rigid-geometry ab initio MO calculations of 86 torsional isomers of the dimethylphosphate anion (CH30)2P02 led to the determination of parameters for the Lennard-Jones type of nonbonded interaction, two- and three-fold torsional, and electrostatic interaction potential functions (215). Extension of this approach to full relaxation ab initio and MM schemes will be extremely useful, not only for phosphorus but also for other heteroatoms. 

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. 

Figure 7.16 is the polarization curves of the pyrite electrode in dithiocarbamate solution at different concentration for dipping for 48 hours. Electrochemistry parameters determined by the computer PARcal are listed in Table 7.3. It can be seen from Fig. 7.16 and Table 7.3 that the corrosive potential of pyrite electrode decreases gradually from 187 to 160 mV and the corrosive current decreases from 10.78 to 6.01 xA/cm without or with the DDTC addition of 5 x 10 mol/L, while polarization resistance increases from 6.2 to 10.1 kfl with the increase of dithiocarbamate concentration. It indicates the formation of surface oxidation products. Comparing with xanthate, DDTC has less effect on corrosive potential, current and polarization resistance. It indicates that collector function of DDTC on pyrite is less than that of xanthate. 

Since Lennard-Jones (6-12) potential has been widely used for calcn of properties of matter in the gaseous, liquid, and solid states, Hirschfelder et al (Ref 8e, pp 162ff) discuss it in detail. They show that the parameters o and ( of the potential function may be determined by analysis of the second virial coefficient of the LJD equation of state... 

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