Reduced potential energy surface

HCR and co-workers carried out a number of studies by employing 3D potential energy surfaces calculated by means of highly sophisticated ab initio approaches [88,91-101]. The results of these computations are in impressive agreement with the corresponding experimental findings. The discrepancies in the order of 100 wavenumbers, as in early ab initio studies [16,17], have been reduced in the HCR studies to only a few wavenumbers. In conclusion of their paper on the ( H ) system of NH2, Gabriel et al. state We believe... 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

Ifnited atom force fields (see Ifnited versiisAll Atom Forcehiclds" on page 28 ) arc sometimes used for bioraoleciiles to decrease the number of nonbonded in teraction s and the computation time. Another reason for using a simplified poten tial is to reduce the dimensionality of the potential energy surface. This, in turn, allows for more samples of the surface. 

On the potential energy surfaces thus obtained 2D wavepacket dynamics calculations have been performed in the diabatic state representation. The reduced massses are regarded as those of CH2-ethylene system. The validity was examined by using on-the-fly ab initio molecular dynamics that were supplementarily performed. The dynamics calculations performed are composed of the following steps ... 

Thus the potential energy surface Esa does not exist and is reduced to a line for 5 = 0. On the contrary the solutions C>sb (5) and O sb (5) exist whatever 6 (at least one of them, the other one may become unstable), but the derivative of the corresponding energy surfaces are different from zero at 8 = 0. 

The topic of this review, reactions at metal surfaces, has been in general treated in a similar way to gas-phase reactivity. High level ab initio electronic structure methods are used to construct potential energy surfaces of catalytically important surface reactions in reduced dimensions. Once a chemically accurate potential surface is available, quantum or classical dynamics may be carried out in order to more deeply understand the microscopic nature of the reaction. 

The analytic potential energy surfaces, used for the Cl + CH3Clb and Cl + CHjBr trajectory studies described here, should be viewed as initial models. Future classical and quantum dynamical calculations of SN2 nucleophilic substitution should be performed on quantitative potential energy functions, derived from high-level ab initio calculations. By necessity, the quantum dynamical calculations will require reduced dimensionality models. However, by comparing the results of these reduced dimensionality classical and quantum dynamical calculations, the accuracy of the classical dynamics can be appraised. It will also be important to compare the classical and quantum reduced dimensionality and classical complete dimensionality dynamical calculations with experiment. 

Figure 6.2 Schematic diagram of the potential energy surfaces for the reduced and the oxidized state.

---