General Features of Potential Energy Surfaces

Most people use MM in order to find potential energy minima, which correspond to equilibrium geometries at 0 K. 

The conformation with the F and the Cl atoms trans is the global minimum. The other two conformations correspond to local minima. 

This particular potential energy surface seems very clean-cut, because there is a single minimum in the range of variables scanned. The chances are that this minimum is a local one, and a more careful scan of the potential surface with a wider range of variables would reveal many other potential minima. 

Potential energy surfaces show many fascinating features, of which the most important for chemists is a saddle point. At any stationary point, both df/dx and df /Sy are zero. For functions of two variables f(x, y) such as that above, elementary calculus texts rarely go beyond the simple observation that if the quantity 

Til explain later how we characterize such surfaces you might have noticed that (1.45) can be written as the determinant of a matrix H called the Hessian 

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In considering the dynamics of potential energy surfaces an important feature is the fact that the internal coordinates are not in general an orthogonal set. By this, one means that the Hamiltonian has cross terms in its kinetic energy part. For example, the kinetic energy of the linear triatomic (nonrotating) system. 

In the general case R denotes a set of coordinates, and Ui(R) and Uf (R) are potential energy surfaces with a high dimension. However, the essential features can be understood from the simplest case, which is that of a diatomic molecule that loses one electron. Then Ui(R) is the potential energy curve for the ground state of the molecule, and Uf(R) that of the ion (see Fig. 19.2). If the ion is stable, which will be true for outer-sphere electron-transfer reactions, Uf(R) has a stable minimum, and its general shape will be similar to that of Ui(R). We can then apply the harmonic approximation to both states, so that the nuclear Hamiltonians Hi and Hf that correspond to Ui and Uf are sums of harmonic oscillator terms. To simplify the mathematics further, we make two additional assumptions ... 

Nucleophilicity and leaving group ability 211 Effect of solvation on the gas-phase reaction 212 Mechanism of the gas-phase SN2 reaction 213 Potential energy surfaces for gas-phase SN2 reactions 214 Recent theoretical developments 218 Some examples of gas-phase SN2 reactions involving positive ions 220 Nucleophilic displacement reactions by negative ions in carbonyl systems 222 General features 222... 

General Features of Late Potential Energy Surfaces for Exothermic Reactions... 

GENERAL FEATURES OF LATE POTENTIAL ENERGY SURFACES FOR EXOTHERMIC REACTIONS... 

General features of late potential energy surfaces where the attacking atom is light... 

Figures 1.12 and 1.13 readily explain, without quantitative calculation, some key features of the photodissociation of H2O through excitation in the A and in the B absorption bands. Multi-dimensional potential energy surfaces are the cornerstones for a trustworthy analysis of molecular dynamics. Knowing the general topology of the PES often suffices for a qualitative explanation of the main experimental observations. However, in order to perform realistic calculations we need potential energy surfaces which are as accurate and complete as possible.

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