OVERVIEW OF THEORETICAL METHODS USED

One of the first methods to be applied to CPs to elucidate structure/property or theory/experiment relationships was the semi-empirical extended Hiickel (EH) 

The most widely applied, and apparently the most practical in terms of theory/-experiment correlation and predictive capability, has been the Valence Effective Hamiltonian (VEH) method propounded by Br6das and others [18, 217], which also commonly uses an initial ab initio optimization of monomer or oligomer geometry ( ab initio parametrization ), or less frequently, experimental geometries, prior to calculation. The VEH method has been used to arrive at ionization potentials, bandwidths, and, in the coplanar approximation, bandgaps, which reasonably follow experimental trends. 

Other semi-empirical methods used have included the AMI method of Dewar et al. [218], and the CND02/S3 method (a variant of the complete neglect of differential overlap method) applied with some success to P(Ac) and P(Py) [219, 220]. These have in nearly all cases been used in conjunction with initial or following ab initio calculations. 

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In this section, we give a brief overview of theoretical methods used to perform tribological simulations. We restrict the discussion to methods that are based on an atomic-level description of the system. We begin by discussing generic models, such as the Prandtl-Tomlinson model. Below we explore the use of force fields in MD simulations. Then we discuss the use of quantum chemical methods in tribological simulations. Finally, we briefly discuss multiscale methods that incorporate multiple levels of theory into a single calculation. 

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