Correlated exchange

Most of the potential energy surfaces reviewed so far have been based on effective pair potentials. It is assumed that the parameterization is such as to account for nonadditive interactions, but in a nonexplicit way. A simple example is the use of a charge distribution with a dipole moment of 2.ID in the ST2 model. However, it is well known that there are significant non-pairwise additive interactions in liquid water and several attempts have been made to include them explicitly in simulations. Nonadditivity can arise in several ways. We have already discussed induced dipole interactions, which are a consequence of the permanent diple moment and polarizability of the molecules. A second type of nonadditive interaction arises from the deformation of the molecules in a condensed phase. Some contributions from such terms are implicitly included in calculations based on flexible molecule potentials. Other contributions arises from electron correlation, exchange, and similar effects. A good example is the Axilrod-Teller three-body dispersion interaction ... 

Figure 4. Exchange-correlation, exchange-only and correlation Kohn-Sham potentials.

Application of the overlap model to calculating correlated exchange energies ... 

TABLE 3.20 Molecular Kinetic, Exchange, Correlation, Exchange-Correlation, and Total Energies (in Hartrees) From Various Schemes of Computations... 

The terms s are the Kohn-Sham orbital energies. The correlation exchange potential, Vxc, is the functional derivative of the exchange-correlation energy. 

A two-dimensional experiment has been described for correlating the chemical shifts of nuclei undergoing chemical exchange (Jeener ef al., 1979 Macura et al., 1981). The pulse sequence for generating a homonuclear correlated exchange spectrum is shown in Fig. 20. At the end of the... 

Cross-peaks, correlating exchanging nuclei A and X, will only be observed when the exchange rate constant k is slow on the NMR time scale, that is, Kx Va - Vxl-... 

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