Potential-based methods

There are many computational techniques available, covering many orders of magnitude of length and time-scales, as shown schematically in Figure 11.1. Potential-based methods depend on the use of analytical expressions for the interaction energies between the atoms in the molecule or solid under study. These are parametrized by fitting either to experiment or to the results of quantum mechanical... 

We start in this chapter with potential-based methods, the computationally cheapest approach, which can be applied to large assemblies of molecules. We then move on to the use of quantum mechanical techniques, as used for problems involving smaller numbers of atoms. The aim is to give a brief overview of the subject and its applications, and to show what type of information can be obtained from the different methods. The reader is referred to specialist texts for fuller details. 

Two broad classes of technique are available for modeling matter at the atomic level. The first avoids the explicit solution of the Schrodinger equation by using interatomic potentials (IP), which express the energy of the system as a function of nuclear coordinates. Such methods are fast and effective within their domain of applicability and good interatomic potential functions are available for many materials. They are, however, limited as they cannot describe any properties and processes, which depend explicitly on the electronic structme of the material. In contrast, electronic structure calculations solve the Schrodinger equation at some level of approximation allowing direct simulation of, for example, spectroscopic properties and reaction mechanisms. We now present an introduction to interatomic potential-based methods (often referred to as atomistic simulations). 

Gennard et al. have calculated the surface energies of the (011) and (111) faces of both ceria and zirconia. They hnd that interatomic potential-based methods provide a correct estimate of the surface relaxations and the correct order of stability of the two faces examined, with the energy difference between the (Oil) and the (111) surfaces being approximately I J/m, as found in the QM study. However, interatomic potential-based methods do not discriminate adequately between the properties of the two materials. It was also found that geometric and electronic relaxations in the (111) surface are confined to the outermost oxygen ions, while in ihe (Oil) slabs they are more important and extend to the subsurface layers in a columnar way. The unsaturation of the surface ions in the (011) face may have important implications for catalytic activity. 

Ten years ago when I attended a Faraday Discussion on Solid State Chemistry New Opportunities from Computer Simulations, interatomic potential methods were well developed and the use of ab initio methods starting to become widespread. In his Introductory Lecture Prof. C. R. A. Catlow asked With the continuing growth of the applicability of electronic structure techniques, can we see them as replacing interatomic potential based methods His reply then was there will be a continuing role for interatomic based potential based methods as the field moves to more complex systems. Over the last decade, ab initio electronic structure methods have progressed rapidly and for many applications plane-wave ab initio methods are now the first choice for calculations. Nevertheless that reply still holds true. 

Well-Behaved Electrostatic Potential Based Method Using Charge Restraints for Deriving Atomic Charges The RESP Model. 

C. Bayly, P. Cieplak, W. Cornell, and P. A. Kollman, A well-behaved electrostatic potential based method using charge restraints for deriving atomic point changes The RESP model, J. Phys Chem. 97 10269 (1993). 

Bayly C1, P Cieplak, W D Cornell and P A Kollman 1993. A Well-Behaved Electrostatic Potential Based Method for Deriving Atomic Charges - The RESP Model. Journal of Physical Chemistry 97 10269-10280. 

Bayly, C. 1., Cieplak, R, Cornell, W. D., and Kollman, P. A. (1993). A well-behaved electrostatic potential base method using charge restraints for deriving atomic charges the RESP method, /. Phys. Chem. 97, pp. 10269-10280. 

Estimation of the Raman phonon intensities is even more complex, though a model has been proposed for this quantity that is suitable for potential based methods (Kleinman and Spitzer 1962). The electric susceptibility tensor is given by ... 

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