Optimization empiric parameters

Keywords, protein folding, tertiary structure, potential energy surface, global optimization, empirical potential, residue potential, surface potential, parameter estimation, density estimation, cluster analysis, quadratic programming... 

Tliroughout this chapter and in Table 1 the inclusion of QM results as target data is evident, with the use of such data in the optimization of empirical forces fields leading to many improvements. Use of QM data alone, however, is insufficient for the optimization of parameters for condensed phase simulations. This is due to limitations in the ability to perform QM calculations at an adequate level combined with limitations in empirical force fields. As discussed above, QM data are insufficient for the treatment of dispersion... 

It is the main aim of semiempirical chromatographic models to couple the empirical parameters of retention with the established thermodynamic quantities generally used in physical chemistry. The validity of a model for chromatographic practice can hardly be overestimated, because it often and successfully helps to overcome the old trial-and-error approach to running the analyses, especially when incorporated in the separation selectivity oriented optimization strategy. 

J. J. P. Stewart, Optimization of parameters for semi-empirical methods 1. Method, J. Comput. Chem. 10 209 (1989). 

Perhaps the most widely discussed source of uncertainty in electrostatic calculations is the location of the solute/solvent boundary. The most common treatment is to place the boundary at the surface of a set of overlapping spheres centered at the nuclei. But what radius should one use for those spheres One common answer is van der Waals radii times I.2.46 In our own quantum mechanical solvation models,12 27 and those of several others59, 69, these radii are empirical parameters. Recently Barone et al.70 have modified the PCM to use charge-dependent united-atom spheres instead of all-atom spheres, and they optimized the electrostatic radii for a... 

It is also important to take into account that one of the main issues with the carbon fiber paper or cloth used as the DL is the uncontrolled variation in porosity (and other localized properties) of these manufactured conventional diffusion layers that is, the porosity characteristics between carbon papers are not repeatable [57]. These materials are difficult to improve because only average pore sizes and volume densities can be measured and much of the development has been based on empirical parameters. Thus, extensive work has focused on optimizing the MPL in order to reduce the differences within carbon paper fiber and cloth diffusion layers. 

Here, is the distance between atoms i andj, C(/ is a dispersion coefficient for atoms i andj, which can be calculated directly from tabulated properties of the individual atoms, and /dampF y) is a damping function to avoid unphysical behavior of the dispersion term for small distances. The only empirical parameter in this expression is S, a scaling factor that is applied uniformly to all pairs of atoms. In applications of DFT-D, this scaling factor has been estimated separately for each functional of interest by optimizing its value with respect to collections of molecular complexes in which dispersion interactions are important. There are no fundamental barriers to applying the ideas of DFT-D within plane-wave DFT calculations. In the work by Neumann and Perrin mentioned above, they showed that adding dispersion corrections to forces... 

HCTH Hamprecht. Cohen. Tozer. and Handy GGA exchange-coiTelation functional based on a reoptimization/extension of empirical parameters in B97 and a removal of HF exchange. Now a family of functionals with optimizations over different numbers of test-set molecules, typically denoted HCTH/w where n is the number of molecules in the test set, e.g., HCTH/93, HCTH/120, HCTH/147, and HCTH/407. Hamprecht, F. A., Cohen, A. J., Tozer, D. J., and Handy, N. C. 1998. 7. Chem. Phys., 109, 6264. (Most recent refinement, Boese, A. D., Martin, J. M. L., and Handy, N. C. 2003. 7. Chem. Phys., 119, 3005.)... 

Studies of isoelectronic sequences are very useful and fruitful in theoretical, semi-empirical and experimental investigations of atomic spectra. They reveal important regularities and pecularities in the behaviour of various physical characteristics of many-electron atoms and ions, help to identify and classify their energy levels with an optimal coupling scheme, find initial values of semi-empirical parameters, etc. 

A promising development in the latter direction was the implementation of a multicon-figurational DFT approach [52] with empirical parameters (in addition to those already contained in the mixed density functionals). This method can yield accurate potential energy surfaces of excited states, and has recently been adapted to perform spin-orbit Cl calculations [53], but the lack of analytic gradients has up to now prevented its use in the simulation of molecular dynamics and in geometry optimizations. A more classically... 

In fact, the distinction between two-step and direct dynamics is rather fuzzy. The basic issue is what kind and amount of preliminary work is needed before starting a dynamical calculation. Direct ab initio dynamics [90,97-101] requires a minimum of preparation some tests to choose basis sets and other options may suffice. For large systems, however, fully ab initio calculations are impractical, and one has to resort to QM/MM or PCM approaches but then, a host of empirical parameters are introduced, which may need some readjustement to avoid artefacts and to improve the accuracy before starting the dynamical calculations. The same holds for the semiempirical methods in order to represent at best the excited states, one has to re-parameterize the hamiltonian. In particular, our FOMO-SCF-CI method [56-58] differs considerably from the normal SCF or SCF+CIS procedures, so that the standard parameters need to be modified. However, the parameter sets are fairly transferable, and their optimization can be limited to the atoms belonging to the chromophore. In the two-step strategies one fits the ab... 

In a computation of the kind of clustering reactions, between molecules you need the positions of the atoms for each ligand, that is the distances and the angles (and even that you can nowadays optimize if you wish). That is one input the other input is the basis set, namely the linear combination of atomic orbitals in terms of which you decide to develop your molecular orbitals. Now this is not an empirical parameter, it is a choice you decide that you ate going to express your molecular orbitals as a linear combination of a certain set of... 

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