One-dimensional potential energy curves

The reaction of hydrogen gas with a metal is called the absorption process and can be described in terms of a simplified one-dimensional potential energy curve (onedimensional Lennard-Jones potential) [30] (Figure 5.22). 

Many previous studies using ab initio, - > >- 3.58 molecular simulations - > >24.2939 and experimental methods,2°-2i.6o-63 jjave reported first shell structures and ion-water binding energies. In the next sections we present DFT results corresponding to the one-dimensional potential energy curve for the interaction ion/water, when the ion interacts with one and with six water molecules. Li, Na Be", Mg, Al" and were considered, and the results compared to previous calculations and experiments. 

Figure 2. A typical example of a one-dimensional potential energy curve where there are the two local points and the saddle point.

Figure 1. Various one-dimensional potential energy curves for the proton motion in AH- -B...

The one-dimensional potential energy curve describes precisely the electronic term of a system only in the simple case of diatomic molecules. With A H bonds, where A is part of a multiatom molecule, the diatomic approximation is valid. But in the general case the potential energy as a function of the A H bond length, F(r), should be expressed using a polynomial expansion... 

The discussion up till now has been concerned with two colliding atomic particles, the motion of which can be described on one-dimensional potential energy curves. If however, one or both of the colliding particles are molecules, the collision process takes place on multidimensional potential surfaces. If N > 2 atoms are involved, we have s 3N — 6 independent relative... 

Figure 8.2 Energy levels for a one-dimensional potential energy curve. The levels are shape resonances and are broadened by tunneling through the potential energy barrier.

Figure n.9 One-dimensional potential energy curve for the explanation of vibrational relaxation process observed by TR SEP FD [31], (Reproduced with permission from Elsevier.)... 

Figure 8 Experimental luminescence spectrum of crystalline fraw5-Re02(ethylenediamine)2Cl at room temperature. The calculated spectra were obtained from the one-dimensional potential energy curve calculated by DFT and from the harmonic curve, both shown in Figure 7.

FIGURE 23 One-dimensional potential energy curves for dissociative adsorption through a precursor or physisorbed state (a) adsorption into the stable state with no activation energy and (b) adsorption into the chemisorption well with activation energy A E. ... 

Fig. 6. One-dimensional potential energy curves for the two excited states, A2 and of H2S. The two HS separations, Hhs. varied symmetrically. Note the different vertical axes for the different HSH bond angles a. The wave function in the ground electronic state is indicated on the horizontal axis and the circles for a = 92° mark the two conical intersections. Reprinted, with permission of the American Institute of Physics, from Ref. 49.

Fig. 1.16 A one-dimensional potential energy curve Pot a diatomic molecule, indicating possible electronic, vibrational, vibrational-rotational and rotational transitions...

The adsorption of H is conveniently described in terms of simplified one dimensional potential energy curves for an H2 molecule and for 2H atoms on a metal surface (Fig. 1). Far from the surface the two curves are separated by the heat of dissociation Ed = 218 kJ/mol H. The flat minimum in the H2 + M curve corresponds to physisorbed H2 (heat of physi-sorption Ep 10 kJ/mol H) and the deep minimum in the 2H + M curve describes chemisorbed H (heat of chemisorption E 50 kJ/mol H). If the two curves intersect above the zero energy level, the chemisorption requires an activation energy E. In further steps the chemisorbed H atoms penetrate the surface and are then dissolved exothermically or endothermically in the bulk where hydrides can be formed. There is now experimental and theoretical evidence that not all chemisorbed H necessarily stays on top of the first metal atom layer, but also below it as a so called subsurface H (two step chemisorption). 

FIG U RE 1.1 Three kinds of tunneling phenomena schematically depicted by one-dimensional potential energy curves (a) mnneling splitting, (b) decay of metastable state, and (c) tunneling in reaction. 

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