Stillinger

The distribution fimctions also satisfy a second moment condition, as first shown by Stillinger and Lovett... 

Stillinger F H and Lovett R 1968 General restriction on the distribution of ions in electrolytes J. Chem. Phys. 48 1991... 

Stillinger F 1973 Structure in aqueous solutions from the standpoint of scaled particle theory J. Solution Chem. 2 141 Widom B 1967 Intermolecular forces and the nature of the liquid state Sc/e/ ce 375 157 Longuet-Higgins H C and Widom B 1964 A rigid sphere model for the melting of argon Mol. Phys. 8 549... 

Mitchell D J, McQuarrie D A, Szabo A and Groeneveld J 1977 On the second-moment condition of Stillinger and Lovett J. Stat. Phys. 17 1977... 

Weber T A and Stillinger F FI 1990 Dynamioal branohing during fluorination of the dimerized Si (100) surfaoe a moleoular dynamios study J. Chem Phys. 92 6239-45... 

Rahman, A., Stillinger, F.H. Molecular dynamics study of liquid water. J. Chem. Phys. 55 (1971) 3336-3359. 

The function/c is a smoothing function with the value 1 up to some distance Yy (typically chosen to include just the first neighbour shell) and then smoothly tapers to zero at the cutoff distance, by is the bond-order term, which incorporates an angular term dependent upon the bond angle 6yk- The Tersoff pofenfial is more broadly applicable than the Stillinger-Weber potential, but does contain more parameters. 

Stillinger F H and A Rahman 1974. Improved Simulation of Liquid Water by Molecular Dynamics. Journal of Chemical Physics 60 1545-1557. 

Stillinger F H and T A Weber 1985. Computer Simulation of Local Order in Condensed Phases of Silicon. Physical Review 831 5262-5271. 

Interatomic potentials began with empirical formulations (empirical in the sense that analytical calculations based on them... no computers were being used yet... gave reasonable agreement with experiments). The most famous of these was the Lennard-Jones (1924) potential for noble gas atoms these were essentially van der Waals interactions. Another is the Weber potential for covalent interactions between silicon atoms (Stillinger and Weber 1985) to take into account the directed covalent bonds, interactions between three atoms have to be considered. This potential is well-tested and provides a good description of both the crystalline and... 

Thermodynamic properties. A molecular-dynamics simulation method (using a steepest decent method) with Stillinger-Weber potential is employed to optimize structures and to obtain the cohesive en-... 

Fig. 4. Optimized toroidal structures (a) torus and (b) torus C24o Pentagons and heptagons are shaded. The diameters of the tube of the stable torus determined by optimization using molecular dynamics with Stillinger-Weber poiemial[211, is 8.8 A. The diameter of the hole is 7.8 A, which is quite close to the diameter of fullerence Qy.

A full-scale treatment of crystal growth, however, requires methods adapted for larger scales on top of these quantum-mechanical methods, such as effective potential methods like the embedded atom method (EAM) [11] or Stillinger-Weber potentials [10] with three-body forces necessary. The potentials are obtained from quantum mechanical calculations and then used in Monte Carlo or molecular dynamics methods, to be discussed below. 

Here is an extract from the synopsis to the original paper by Rahman and Stillinger ... 

Molecular Dynamics Study of Liquid Water Aneesur Rahman and Frank H. Stillinger The Journal of Chemical Physics 55 (1972) 3336-3359... 

In Chapter 2, I mentioned that there was great interest in water as a solvent, and explained about the pioneering calculations of Rahman and Stillinger (1972). Many molecular mechanics (MM), Monte Carlo (MC) and molecular dynamics (MD) studies have been made based on their box of 216 water molecules. A good starting point is the work of Jorgensen and coworkers. 

Different results were obtained in the case of the Stillinger-Weber (SW) potential for silicon (10). In this case, material deposited on the (ill) orientation was disordered, without distinct layers of atoms. Growth on the (100) face did produce about ten distinct layers at sufficiently high temperatures, although it is not clear whether thicker deposits would retain this order since some degeneration was observed as successive layers were deposited. 

Stillinger FH (1979) Dynamics and ensemble averages for the polarization models of molecular interactions. J Chem Phys 71(4) 1647... 

Stillinger FH, David CW (1978) Polarization model for water and its ionic dissociation products. J Chem Phys 69(4) 1473... 

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