Potential hill

The Lennard-Jones potential continues to be used in many force fields, particularly those targeted for use in large systems, e.g., biomolecular force fields. In more general force fields targeted at molecules of small to medium size, slightly more complicated functional forms, arguably having more physical justification, tend to be used (computational times for small molecules are so short dial the efficiency of the Lennard-Jones potential is of little consequence). Such forms include the Morse potential [Eq. (2.5)] and the Hill potential... 

The repulsion increases exponentially, and it is steeper than the bond length deformation potential. The attractive force is usually modeled by a 1/r6 term, while various possibilities exist for the repulsion. The functions used in modem programs include, apart from the Morse potential (Eq. 2.13), the Lennard-Jones potential (Eq. 2.25)[401 (e.g., AMBER1411), the Buckingham potential (Eq. 2.26)[421 (e.g., MOMEC[81), or a modification thereof, the Hill potential (Eq. 2.27) (e.g., MM2, MM3[1,2,231). 

Hill potential function molecular interaction fields (O steric interaction fields)... 

A steric interaction field is obtained by calculating the van der Waals interaction energy Evdw between probe and target in each grid point [Kim, 1992b]. Different potential energy functions were proposed to model van der Waals interactions between atoms. The most common are Lennard-Jones potential, Buckingham potential, and Hill potential [Leach, 1996]. 

The Hill potential function is an exponential function defined as ... 

Hill potential is an exponential-6 potential with just two parameters the minimum energy radius and the well depth e [Hill 1948] ... 

The Hill potential was originally developed to enable the more realistic exponential term to be written in terms of Lennard-Jones parameters. The coefficients 2.25,8.25 x 10 and 0.0736 in Equation (4.71) were determined by fitting to data for the rare gases and were assumed to be applicable to other non-polar gases. A Morse potential may also be used to model the van der Waals interactions in a force field, with appropriate parameters. 

Figure 2-18 (a) A rectangular-hill potential of height U and width 2a. (b) Fraction of beam... 

All calcidations have been performed within LDA+U with the same value of U as used for pure -Pu (3.13 eV) in fire fiiamework of the hill-potential linear-muffin-tin-orbital (FP-LMTO) method with von Barth-Hedin exchange-correlation potential and spin-orbit coupling. We only presait preliminary results where the antiferromagnetic configuration was not yet taken into account. 

In commercial FE-software, models for anisotropic creep are rare. One material model uses the Hill potential theory, originally developed as an anisotropic yield criterion of metal plasticity ... 

---