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Although there are usually many more non-bonded than bonded interactions, because of the more complicated functional forms the effort for the bonded part can still be an appreciable fraction of the total. Recognizing this, many research groups have put considerable effort into speeding up the calculation of internal coordinates and derivatives for stretch and other chemically bonded interactions (see, for example, [1418]).

Our group has found it most advantageous computationally to take advantage of the highly connected nature of the bond networks for the systems we simulate [8-11]. For example, in a diamondoid bond network one bond stretch can be part of as many as six different bend interactions and 24 different torsion interactions. It therefore makes sense to use two- and three-body internal coordinates and derivatives as intermediates for those for three- and four-body interactions. A bond distance and its derivatives can be used as intermediates for bond angles and their derivatives, thus avoiding duplicate calculations, most especially square roots. For example,

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