Parameterized Methods

The classical introduction to molecular mechanics calculations. The authors describe common components of force fields, parameterization methods, and molecular mechanics computational methods. Discusses th e application of molecular mechanics to molecules comm on in organic,and biochemistry. Several chapters deal w ith thermodynamic and chemical reaction calculations. 

There are three modihed intermediate neglect of differential overlap (MINDO) methods MINDO/1, MINDO/2, and MINDO/3. The MINDO/3 method is by far the most reliable of these. This method has yielded qualitative results for organic molecules. However its use today has been superseded by that of more accurate methods such as Austin model 1 (AMI) and parameterization method 3 (PM3). MINDO/3 is still sometimes used to obtain an initial guess for ah initio calculations. 

PLS (partial least-squares) algorithm used for 3D QSAR calculations PM3 (parameterization method three) a semiempirical method PMF (potential of mean force) a solvation method for molecular dynamics calculations... 

An series of alternative, generally parameterized methods for introducing the effects of solvent into semi-empirical calculations are termed SMr, where the value of x represents the type and quality of parameterization27-76 81. These methods have potential value in studying solvation effects on the structure, electronic spectra, and reactivity of biologically... 

Baker, B.M. Murphy, K.P. Prediction of binding energetics from structure using empirical parameterization. Methods Enzymol. 1998, 295, 294—... 

Such a procedure may not seem to be properly classified as a parameterized method, since no individual calculation incorporates a parameter, optimized or otherwise. However, in this instance it is the selection of the functional form for asymptotic behavior that may be considered to be parametric. As noted in Section 7.6.1, for certain levels of theory, like MP2, rigorous convergence behaviors have been derived, but it must be stressed that those behaviors are valid in the limit of a complete basis set, and the ability to fit points obtained with a smaller basis set to the limiting curve is by no means assured (see, for instance, Petersson and Frisch 2000). 

A parameterization method of the Hamiltonian for two electronic states which couple via nuclear distortions (vibronic coupling), based on density functional theory (DFT) and Slaters transition state method, is presented and applied to the pseudo-Jahn-Teller coupling problem in molecules with an s2-lone pair. The diagonal and off-diagonal energies of the 2X2 Hamiltonian matrix have been calculated as a function of the symmetry breaking angular distortion modes and r (Td)] of molecules with the coordination number CN = 3... 

There is ongoing work in this group to implement and test other QM methods as well, such as the more recent RM1 [59], which is a reparameterization of the AMI Hamiltonian [60], and PM6 [61], which involves modifications to the Hamiltonian as well as to the parameterization methods and training sets. It is expected that the newer methods should improve the QM results. 

The fact that the calculation of Ee as well as of its derivatives with respect to nuclear coordinates with accurate electronic-structure methods is non-trivial and often time-consuming, makes the use of simpler, parameterized methods attractive, in particular when studying larger systems of low symmetry and/or studying (very) many structures (which easily is the case when attempting to optimize the structure). With these, the total energy is given as some analytical or numerical function of the nuclear coordinates and atom types, i.e.,... 

Figures 25-27 show the results of their study. It is obvious that the various methods do not agree in many details, although, for instance the fact that the clusters are particularly stable for N = 4, N = 6, and N = 13 is found by all approaches. Moreover, with just a single exception, all methods yield the same symmetries for the clusters for all N. Thus, trends but not details seem to be accessible with most methods. It should also be mentioned that the two parameter-free methods show deviations in their predictions that are comparable with those of the parameterized methods, suggesting that the use of parameter-free methods may not necessarily give results that are particularly accurate.

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