Potential energy curves computation

Tellinghuisen J A 1974 A fast quadrature method for computing diatomic RKR potential energy curves Comput. Phys. Commun. 6 221-8... 

The calculation of term values directly by treating each state as a separate variational problem is also fraught with difficulties, or rather with two difficulties. These are the problems of relativistic and correlation energy. As Figure 1 shows, the potential-energy curve computed by solution of the... 

A computational method which is suitable for studies of this nature should fulfill certain basic requirements (a) it should be sufficiently economical to allow computation of full potential-energy curves for comparatively large number of states, (b) the calculated potential curves for bound states should give rise to vibrational and rotational constants which are in reasonable agreement with experiment when a comparison is possible, (c) the calculated total energies of all the states should be of comparable accuracy, and (d) the ordering of the states should be correct. 

A potential energy curve was also computed for different values of the roci distance in the H2O-HCI complex, with HCl approaching H2O along the C2v axis. At each roci distance, optimal SCF geometry was determined and used in the subsequent SCF-MI and MCSCF-MI calculations. 

An analogous approach was employed for the study of NH3-HCI, computing a potential energy curve as a function of the distance. 

Both these potential energy curves have been computed employing 6-3IG standard basis set, see Figures 3 and 4. 

Noumerov analysis leads to more encouraging results. The energy values associated with the first 10 (v = 0-9) vibrational levels were computed. The first eight (v = 0-7) are relative to the absolute minimum of the potential energy curve employed (see Figure 5) the remaining two (v = 8-9) are relative to levels above the maximum. 

Figure 3. Computed potential energy curves for the diabatic and adiabatic state in the [HsN-H-NH ] system in the gas phase using 6-31G(d) basis set. The HF and MOVE energy profiles are overlapping.

What is next Several examples were given of modem experimental electrochemical techniques used to characterize electrode-electrolyte interactions. However, we did not mention theoretical methods used for the same purpose. Computer simulations of the dynamic processes occurring in the double layer are found abundantly in the literature of electrochemistry. Examples of topics explored in this area are investigation of lateral adsorbate-adsorbate interactions by the formulation of lattice-gas models and their solution by analytical and numerical techniques (Monte Carlo simulations) [Fig. 6.107(a)] determination of potential-energy curves for metal-ion and lateral-lateral interaction by quantum-chemical studies [Fig. 6.107(b)] and calculation of the electrostatic field and potential drop across an electric double layer by molecular dynamic simulations [Fig. 6.107(c)]. 

In the preceding sections, several potential energy curves associated with electrode reactions have been presented. Their purpose is heuristic and they are therefore schematic in nature. Nevertheless, they resemble carefully calculated curves in which molecular dynamics and computer software have been used to obtain the potential energy curves at the various displacements from equilibrium (Rose and Benjamin, 1996 Xia and Berkowitz, 1997) (Fig. 9.16). 

Fig. 1. The potential energy curves with respect of the top angle in H3 isosceles triangle as illustration of 8 coordinate of the e E JT distortion. The marked points shows the CASSCF computed values, the continuous and dashed lines corresponding to the fit with Hamiltonian of equation (3).

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