Energy Surfaces Exist

The Jablonski diagram. See text for a discussion of the various features. 

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The separation of the electronic and nuclear motion via the Born-Oppenheimer approximation leads to the concept introduced in Chapter 6, that of the potential energy surface. A potential energy surface gives the dependence of the electronic energy, plus nuclear repulsion, on the geometrical coordinates of the atomic centers of a molecule. It is only within the Born-Oppenheimer approximation that we can follow fhe dependence of the electronic energy on the atomic position coordinates, and only within the approximation does the concept of a potential energy surface exist. 

Note that the van der Waals forces tliat hold a physisorbed molecule to a surface exist for all atoms and molecules interacting with a surface. The physisorption energy is usually insignificant if the particle is attached to the surface by a much stronger chemisorption bond, as discussed below. Often, however, just before a molecule fonus a strong chemical bond to a surface, it exists in a physisorbed precursor state for a short period of time, as discussed below in section AL7.3.3. 

The use of isotopic substitution to detennine stmctures relies on the assumption that different isotopomers have the same stmcture. This is not nearly as reliable for Van der Waals complexes as for chemically bound molecules. In particular, substituting D for H in a hydride complex can often change the amplitudes of bending vibrations substantially under such circumstances, the idea that the complex has a single stmcture is no longer appropriate and it is necessary to think instead of motion on the complete potential energy surface a well defined equilibrium stmcture may still exist, but knowledge of it does not constitute an adequate description of the complex. 

Strict degeneracy between the electronic energy surfaces therefore requires the existence of points Qq at which = H b Q) and //ab (Q) = 0. These two... 

Most potential energy surfaces are extremely complex. Fiber and Karplus analyzed a 300 psec molecular dynamics trajectory of the protein myoglobin. They estimate that 2000 thermally accessible minima exist near the native protein structure. The total number of conformations is even larger. Dill derived a formula to calculate the upper bound of thermally accessible conformations in a protein. Using this formula, a protein of 150 residues (the approx-... 

As mentioned earlier, a potential energy surface may contain saddle points , that is, stationary points where there are one or more directions in which the energy is at a maximum. Asaddle point with one negative eigenvalue corresponds to a transition structure for a chemical reaction of changing isomeric form. Transition structures also exist for reactions involving separated species, for example, in a bimolecular reaction... 

A necessary condition for ion-molecule reactions that has not been considered thus far is that of continuity between reactant and product potential energy surfaces. Many reactions of ions and molecules take place with / a transition from one potential energy surface to another. If no suitable crossings between the respective surfaces exist, then obviously orbiting ion-molecule collisions cannot produce chemical reac-... 

There have a number of computational studies of hypothetical RMMR species [10-13, 40, 411. The simplest compounds are the hydrides HMMH. Some calculated structural parameters and energies of the linear and trans-bent metal-metal bonded forms of the hydrides are given in Table 1. It can be seen that in each case the frans-bent structure is lower in energy than the linear configuration. However, these structures represent stationary points on the potential energy surface, and are not the most stable forms. There also exist mono-bridged, vinylidene or doubly bridged isomers as shown in Fig. 2... 

There exist a series of beautiful spectroscopy experiments that have been carried out over a number of years in the Lineberger (1), Brauman (2), and Beauchamp (3) laboratories in which electronically stable negative molecular ions prepared in excited vibrational-rotational states are observed to eject their extra electron. For the anions considered in those experiments, it is unlikely that the anion and neutral-molecule potential energy surfaces undergo crossings at geometries accessed by their vibrational motions in these experiments, so it is believed that the mechanism of electron ejection must involve vibration-rotation... 

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. 

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