Potential energy function parameters

We can state, in conclusion, that optimization of the potential energy function parameters on experimental data of small model compounds has led to a parameter set that gives an overall improvement of the accuracy of postdiction and, by implication, of the validity of prediction. The improvement is most marked in the most flexible substance. 

Derive an expression for the elastic modulus of an ionic solid in terms of the potential energy function parameters a, b, and n. 

Figure 7 Schematic representation of the empirical method for deriving short-range potential energy function parameters p, are the computed properties for the system, observed properties, and S the sum of squared deviations from target values p and C,y are potential parameters of Eq. [13] K and fCy are shell model parameters, and qi and qj the charges of component species.

The interacting ions with their mass and charges is presented in Table 3.1, and the potential energy function parameters for adsorbed molecules is presented in Table 3.2. Table 3.3 shows the respective potential parameters used for quartz and wollastonite mineral systems. 

Potential Energy Function Parameters for Adsorbed Molecules... 

This word shall be synonymous with "potential energy function parameters , and its meaning shall be those quantities of a potential energy function which are unchanged from one molecule to another within the same series of minimisation or within one iteration in optimisation. 

CHARMM is the first program system published which deserves the designation "molecular mechanics , in the sense that it treats static, kinematic and dynamic properties. All other programs available are much more limited in scope. A few warnings for the uninitiated are in place The more complicated a system is, and here I mean only modern well-structured and well-documented systems, the more attention is required to maintain and operate it, and that cannot be left solely to the computer people. Also, know-how does not come by itself or on a tape. For many prospective applications, potential energy function parameters, or even the functions themselves, are lacking, just as for the simpler systems. Parameters must be found by trial and error, as is usual, or, preferably, by optimisation, which cannot be done in CHARMM a program of the consistent force field family is necessary. 

Let p be a vector whose components are the current values of those potential energy function parameters we want to optimise ... 

Z is the Jacobian matrix of partial derivatives of observables with respect to potential energy function parameters ... 

The elements of the Jacobian or Z matrix are the partial derivatives of observables with respect to potential energy function parameters. Some classes of them are rather laborious to obtain this Is the price we have to pay for being able to optimise simultaneously on many classes of observables. 

The interdependence of the potential energy function parameters cannot be judged by inspection of the correlation coefficients as is usual in optimisation because of the methods employed here the modified Z matrix is not diagonalised. For the same reason, an estimate of the standard deviation is not possible either ... 

The two C-C-C-C torsions, in n-butane g and cyclohexane, cannot be compared in this way. They are very important in optimisation especially for the determination of non-bonded potential energy function parameters. 

A few notes on how the selected data are used in optimisation are relevant. As an example, let us look at the C-C bond in alkanes and cycloalkanes. The constancy of the C-C bond length does not mean that we have here a good value for the potential energy function parameter b. The C-C bond length in an actual molecule is in our model determined by other parameters as well, most clearly illustrated in ethane where H-----H non-bonded interactions are equally... 

If we then turn to ethers, we see that the C-C bond is shorter in the normal straight-chain and cyclic ethers than in alkanes. This must be taken care of in the optimisation of potential energy function parameters different parameter values cannot be accepted, if the overall goal of a simple potential energy function for many classes of substances is to be attained. 

For optimisation on lattice observables we need partial derivatives of each type of observable with respect to potential energy function parameters. So far, we have two types of observables conformation. Including lattice constants, and lattice energy. 

All members of the consistent force field family of programs are available, from QCPE or from the authors they are described under section 3.4 They are all singular in a way they allow for optimisation of potential energy function parameters on many types of observable, and are therefore splendid tools in the hands of a skilled worker. 

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