Postulate of the Arithmetical Mean and Nonbonded Interactions

Yurii. G. Papulov, Marina. G. Vinogradova and M. N. Saltykova
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Yurii. G. Papulov: Tver State University
Marina. G. Vinogradova: Tver State University
M. N. Saltykova: Tver State University

A chapter in Mathematical Modeling, 2001, pp 167-174 from Springer

Abstract: Abstract The postulate of the arithmetical mean for binary interactions of particles is formulated as the relation 1 $${p_{HX}} = \left( {1/2} \right)\left( {{p_{HH}} + {p_{XX}}} \right)$$ (interaction of unlike particles H and X is equal to one-half of the sum of the interactions of the like particles). Analogously, for ternary interactions 2 $${p_{HHX}} = \left( {1/3} \right)\left( {2{p_{HHH}} + {p_{XXX}}} \right),{p_{HXX}} = \left( {1/3} \right)\left( {{p_{HHH}} + 2{p_{XXX}}} \right);$$ and, for quaternary interactions 3 $$\begin{gathered} {p_{HHHX}} = \left( {1/4} \right)\left( {3{p_{HHHH}} + {p_{XXXX}}} \right),{p_{HXXX}} = \left( {1/4} \right)\left( {{p_{HHHH}} + 3{p_{XXXX}}} \right), \hfill \\ {p_{HHXX}} = \left( {1/4} \right)\left( {2{p_{HHHH}} + 2{p_{XXXX}}} \right) \hfill \\ \end{gathered} $$ and so on.

Keywords: Molecular Chain; Effective Interaction; Additive Scheme; Binary Interaction; Ternary Interaction (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4757-3397-6_17

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