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... 

It can clearly be seen that the CISD curve is worse than either of the other two, which are essentially identical out to a AR of 1.3 A. The size inconsistency of the CISD method also has consequences for the energy curve when the bond is only half broken. Figure 11.11 illustrates why the use of Cl methods has declined over the years, it normally gives less accurate results compared with MP or CC methods, but at a similar or Irigher computational cost. Furthermore, it is difficult to include the important triply excited configurations in Cl methods (CISDT scales as M ), but it is relatively easy to include them in MP or CC methods (MP4 and CCSD(T) scales as M ). 

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. 

Many different procedures have been published, all of them aimed at finding the characteristic values of the parameters m, ]i and A = R2(E — l/i )/2, needed to produce acceptable solutions to the coupled equations. With the allowed values of m known, the procedure consists in finding the relation that must exist between A and ]i to produce an acceptable solution of the r] equation, and using this relation to calculate from the equation characteristic values of A and hence of the energy. The computational details are less important and have often been reduced to reliable computer routines that yield the precise results[85], best represented in terms of binding energy curves, such as those shown below for the ground and first excited states. 

The first microscopical computation of a free energy curve for a chemical reaction in solution was performed by the Jorgensen s group [41,52,53] ten years ago. They studied the degenerate SN2 reaction of chloride anion with methyl chloride in gas phase, in aqueous solution and in dimethylformamide (DMF) ... 

The computed results of free energy as a function of the solvent coordinate, u-ul (where ug is the value of u at the crossing point of the free energy curves at the overpotential, q =0) for Fe and are given in Fig. 9. The free energy of activation AG from the crossing point of this plot is found to be 0.6 eV, which correlates well with the experimental result of 0.59 eV. Furthermore, simple calculations using the continuum theory expression show that AG (continuum) = 0.23 eV, which is... 

Following the early studies on the pure interface, chemical and electrochemical processes at the interface between two immiscible liquids have been studied using the molecular dynamics method. The most important processes for electrochemical research involve charge transfer reactions. Molecular dynamics computer simulations have been used to study the rate and the mechanism of ion transfer across the water/1,2-dichloroethane interface and of ion transfer across a simple model of a liquid/liquid interface, where a direct comparison of the rate with the prediction of simple diffusion models has been made. ° ° Charge transfer of several types has also been studied, including the calculations of free energy curves for electron transfer reactions at a model liquid/liquid... 

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. 

In Fig. 16.3 we show the two lowest A states as a function of R for optimum values of the Rz and parameters, and in Fig. 16.4 we show the path by giving Rz and as functions of R. Qualitatively, the two energy curves have the classic appearance of an avoided crossing between two diabatic states. The dashed lines in Fig. 16.3 are not computed, but have been added to guide the eye. 

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