Postulate of the Arithmetical Mean and Nonbonded Interactions

  • Yurii. G. Papulov
  • Marina. G. Vinogradova
  • M. N. Saltykova
Chapter

Abstract

The postulate of the arithmetical mean for binary interactions of particles is formulated as the relation
$${p_{HX}} = \left( {1/2} \right)\left( {{p_{HH}} + {p_{XX}}} \right)$$
(1)
(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
$${p_{HHX}} = \left( {1/3} \right)\left( {2{p_{HHH}} + {p_{XXX}}} \right),{p_{HXX}} = \left( {1/3} \right)\left( {{p_{HHH}} + 2{p_{XXX}}} \right);$$
(2)
and, for quaternary interactions
$$\begin{gathered} {p_{HHHX}} = \left( {1/4} \right)\left( {3{p_{HHHH}} + {p_{XXXX}}} \right),{p_{HXXX}} = \left( {1/4} \right)\left( {{p_{HHHH}} + 3{p_{XXXX}}} \right), \hfill \\ {p_{HHXX}} = \left( {1/4} \right)\left( {2{p_{HHHH}} + 2{p_{XXXX}}} \right) \hfill \\ \end{gathered} $$
(3)
and so on.

Keywords

Molecular Chain Effective Interaction Additive Scheme Binary Interaction Ternary Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Yurii. G. Papulov
    • 1
  • Marina. G. Vinogradova
    • 1
  • M. N. Saltykova
    • 1
  1. 1.Tver State UniversityRussia

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