• Coupled systems mechanics
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• v.7 no.3
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• pp.255-268
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• 2018

Stability of MBC1, a specific matching boundary condition, is proved for atomic simulations of a diatomic chain. The boundary condition and the Newton equations that govern the atomic dynamics form a coupled system. Energy functions that decay along with time are constructed for both the boundary with the same type atoms and the one with different type atoms. For a nonlinear chain, MBC1 is also shown stable. Numerical verifications are presented. Moreover, MBC1 is proved to be stable for a two dimensional square lattice.

• Journal of the Korean Chemical Society
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• v.53 no.3
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• pp.266-271
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• 2009

In the recently synthesized rare earth transition metal carbide $La_7O_{s4}C_9$ one finds one-dimensional organometallic $[O_{s4}C_9]^{21-}$ polymers embedded in a $La^{3+}$ ionic matrix. The electronic structure of the polymeric $[O_{s4}C_9]^{21-}$ chain was investigated by density of states (DOS) and crystal orbital overlap population (COOP), using the extended Huckel algorithm. A fragment molecular orbital analysis is used to study the bonding characteristics of the $C_2$ units in $La_7O_{s4}C_9$ containing $C_2$ units and single C atoms as well. The title compound contains partially filled Os and carbon bands leading to metallic conductivity. As the observed distances already indicated, the calculations show extensive Os-C interactions. The C-C bond distance in the diatomic $C_2$ units ($d_{C-C}$=131 pm) in the solid is significantly increased relative to $${C_2}^{2-}$$ or acetylene, because antibonding $1{\pi}_g$ orbitals are partially filled by the Os-$C_2(1\;{\pi}_g)$ bonding contribution found at and below the Fermi level.