Potential energy functions and chemical reactions

A topographical contour map is a 2D plot of the height as a function of longitude and latitude. We plot the potential as a function of the two bond distances. Computers easily allow you to make a three-dimensional perspective plot of the potential as a function of two variables. Even for the triatomic ABC system what we really want is to view the potential as a fimction of three variables. We know of no easy way for doing so. 

The mountain pass en route from the reactants to products (along tiie minimum energy route) is a dominant feature of such a surface, explaining why the energy threshold for reaction is often much smaller than a bond dissociation energy. As pointed out by Eyring, Polanyi, and Evans in tiie early 1930s, a chemical reaction, say 

Because the reaction path passes through the local minima of the surface, the potential energy increases when we deviate sideways from the path. Hence, near the barrier the potential surface has the form of a saddle. The location of the barrier is thus referred to as the saddle point of the surface (sometimes as the cot). The configurations about the saddle point are the transition state region. 

The height of the barrier along the mmimum reaction path is the lowest maximum of the potential between the reactants and products valleys. In classical mechanics this height is therefore the minimal energy for a trajectory to go over. Such a trajectory represents a possible motion of the nuclei during a reactive collision. Of course, in an actual collision the three atoms need not be confined to move on a line. The trajectory needs to be computed using the potential when all three bond distances are allowed to move independently, subject of course to the forces. 

It is not invariably the case that the reaction is concerted with the new bond forming as the old bond is being broken. Organic chemists are famihar with 

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Our multireference M0Uer-Plesset (MRMP) perturbation method [1-4] and MC-QDPT quasi-degenerate perturbation theory (QDPT) with multiconfiguration self-consistent field reference functions (MC-QDPT) [5,6] are perturbation methods of such a type. Using these perturbation methods, we have clarified electronic stmctures of various systems and demonstrated that they are powerful tools for investigating excitation spectra and potential energy surfaces of chemical reactions [7-10]. In the present section, we review these multireference perturbation methods as well as a method for interpreting the electronic structure in terms of valence-bond resonance structure based on the CASSCF wavefunction. 

However, even the best experimental technique typically does not provide a detailed mechanistic picture of a chemical reaction. Computational quantum chemical methods such as the ab initio molecular orbital and density functional theory (DFT) " methods allow chemists to obtain a detailed picture of reaction potential energy surfaces and to elucidate important reaction-driving forces. Moreover, these methods can provide valuable kinetic and thermodynamic information (i.e., heats of formation, enthalpies, and free energies) for reactions and species for which reactivity and conditions make experiments difficult, thereby providing a powerful means to complement experimental data. 

A great deal of recent success has been achieved in writing simple analytic potential energy expressions which capture the essence of chemical bonding. Much of the inspiration for these efforts has come from the desire to realistically model reactions in condensed phases and at surfaces. As computer simulations grow in importance, continued progress in the development of new potential energy functions will be needed. 

A common and important problem in theoretical chemistry and in condensed matter physics is the calculation of the rate of transitions, for example chemical reactions or diffusion events. In either case, the configuration of atoms is changed in some way during the transition. The interaction between the atoms can be obtained from an (approximate) solution of the Schrodinger equation describing the electrons, or from an otherwise determined potential energy function. Most often, it is sufficient to treat the motion of the atoms using classical mechanics,... 

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