More Advanced Empirical Potentials

More often than not, the following spectroscopic constants are available for a diatomic molecule  

There are a number of three- to five-parameter potential functions in the literature, of which the Morse potential is the most popular a typical five-parameter potential is the Linnett function (Linnett, 1940, 1942)  

0eXs the anharmonicity constant (sometimes equated to xe only) 

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Three types of surface are in use for water simulations. The first consists of simple empirical models based on the LJ-C potential. There seems to be no purpose in continuing to develop and use such models as they give little, if any, new information. A second group attempts to improve the accuracy of the potential using semiempirical methods based on a comprehensive set of experimental data. These models allow for physical phenomena such as intramolecular relaxation, electrostatic induced terms, and many-body interactions, all of which are difficult to incorporate correctly in liquid water theories. There is room for much more work in these areas. The third group makes use of the most advanced ab initio methods to develop accurate potentials from first principles. Such calculations are now converging with parameterized surfaces based on accurate semiempirical models. Over the next few years it seems very likely that the continued application of the second and third approaches will result in a potential energy surface that achieves quantitative accuracy for water in the condensed phase. 

These five issues provide a useful yardstick against which the theory can be measured repeatedly as it continues to evolve. At this juncture, of course, neither schema theory nor any other cognitive theory is yet sufficiently developed to explicate them fully. However, schema theory does have something to contribute to each of them, and more importantly, it generates hypotheses about these issues that may be empirically tested and that have the potential of contributing to further theoretical advances. 

In spite of recent advances in computer technology and electronic structure theory, only for the simplest molecules can potential energy surfaces be calculated with spectroscopic accuracy by employing purely ab initio approaches (2). For more complicated systems, empirical approaches are often used to invert spectra from experimental observables (3-10). This process is shown schematically by following the arrows up in Fig. 1. This new potential can then be used to predict the spectroscopy and dynamics for previously unobserved states and thereby help direct future experiments (11,12). This latter process corresponds to following the down arrows in Fig. 1. 

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