Force-density method

Schek, H.J. (1974) The force densities method for form finding and computation of general networks. Computer Methods in Applied Mechanics and Engineering, S.115-134. 

The Gordon-Kim interaction functions may be compared with empirical potential functions derived by energy- or net-force minimization methods using known crystal structures. The O—O Gordon-Kim potentials are more repulsive, as illustrated in Fig. 9.2. Spackman points out that the empirical potentials likely contain a significant attractive component because of the inadequate allowance for electrostatic interactions in their derivation. This attractive component is included in the electrostatic interaction in the density functional model. 

Vibrational frequencies of 1,4-benzodioxin using the density functional theory (DFT) method, as well as the conventional HF and MM3 force-field methods, were calculated to evaluate the frequency prediction capability of each computational method and get a better understanding of the vibrational spectra . 

AI, ab initio molecular orbital methods DF, density functional methods SE, semiempirical molecular orbital methods FF, force field methods. 

Again, assume uniform particle density, I = r, and that the overhead of neighborhood construction is very small. We write down the volume, Vy, that the improved force calculation method will search on average ... 

Additive fuzzy density fragment force (AFDFF) method. ... 

Density functional calculations were used to determine protonation enthalpies, geometric parameters, and dipole moments of pyridazine (94T2405) as well as the total energy values for 4,5-dichloro-2-methyl-3(2//)-pyridazinone [94H(38)1957].The same physical properties were calculated also by MM3 force-field methods (93JA11906) and by statistical methods based on spectroscopic data (94JIC195). 

It has recently become possible to compute rather accurate dielectric boundary forces from finite difference solutions of the PB equations.50 The method is based on the finite difference discretization of the second term of the force density expression (Eq. [35]), together with the use of dielectric boundary smoothing. A full description of the method and accuracy testing is beyond the scope of the present chapter. However, the results of a sample calculation may be instructive. 

The force calculation method described here promises to be of value in a variety of molecular mechanics simulations. It should be particularly useful in calculations on systems of high charge density, such as nucleic acids and lipid bilayers, where the accurate treatment of solvent by means of the explicit treatment of water molecules and ions is most computationally challenging. Preliminary calculations on small molecules show that the method can readily be incorporated into standard energy minimization and molecular dynamics computations. 

Thus the method of force-densities immediately leads to the solution of fig.l B above. 

Although the modularity has been improved, there are unavoidable interdependencies. Chapters 3,4 and 5 contain the essentials of electronic structure theory, and most would include Chapter 6 describing density functional methods. Chapter 2 contains a description of empirical force field methods, and this is tightly coupled to the simulation methods in Chapter 14, which of course leans on the statistical mechanics in Chapter 13. Chapter 1 on fundamental issues is of a more philosophical nature, and can be skipped. Chapter 16 on mathematical techniques is mainly for those not already familiar with this, and Chapter 17 on statistical meUiods may be skipped as well. 

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