Fitting databases

Analytic potential energy functions for atomistic simulation are sometimes mistakenly viewed as ad hoc mathematical expressions whose development is more art than science. Although there is perhaps some level of art in developing these expressions, the most successful potential functions are almost always based on fundamental quantum mechanics, as we have attempted to demonstrate. With the growing interest in simulating relatively large systems and long-time dynamics, development of relatively accurate and transferable analytic potential expressions will undoubtedly continue to play a central role in materials theory. 

Garrison, J. A. Harrison, J. W. Mintmire, S. B. Sinnott, and C. T. White are thanked for helpful discussions leading to some of the ideas presented here. Financial support from the Office of Naval Research, the National Science Foundation, and NASA is gratefully acknowledged. 

Cioslowski, in Reviews in Computational Chemistry, K. B. Lipkowitz and D. B. Boyd, Eds., VCH Publishers, New York, 1993, Vol. 4, pp. 1-33. Ab Initio Calculations on Large Molecules Methodology and Applications. 

Bartolotti and K. Flurchick, in Reviews in Computational Chemistry, K. B. Lipkowitz and 

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Flexibility The function should be flexible enough to accommodate inclusion of a relatively wide range of structures in a fitting database. 

Accuracy The potential function must be able to accurately reproduce quantities such as energies, bond lengths, elastic constants, and related properties that enter a fitting database. 

Transferability The function should be able to reproduce related properties that are not included in the fitting database. 

Two primary criteria must be satisfied to ensure that a cluster expansion is reliable. First, the fitting database must contain enough structures to represent fully all of the important features of the real system. Second, significant clusters necessary for describing the system must be included in the CE. One can see that if either criterion is not satisfied the CE will not be reliable if major low energy structures are missing from the database, then the CE fit to that incomplete database could potentially miss those same structures, and if major... 

The properties of these systems are obtained from published experimental data and/or the electronic structure calculations. For crystalline structures, the electronic structure calculations are performed with plane-wave DFT calculations using the software VASP (Vienna Ab initio Simulation Package) with appropriate pseudopotential and exchange-correlation functionals (US-LLDA or PAW-PBE). For molecular systems, the electronic structure calculations are performed using the Gaussian09 computational chemistry software package. Table 7.1 shows the fitting database and predicted values from the COMB potential for Cu. 

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