Analogous to a model that predicts the linear scaling of the binding energy of a nucleus from the number of nucleons, a simple model was developed to account for the observed linear variation of the quantum-chemically computed total electronic energy
of the fully-optimized structures of a homologous series of polymers. This model was tested with both ab-initio DFT and molecular mechanics methods on the ortho-fused spiral-benzenes. Both methods predict linear scaling of total polymer energy with increasing number of repeating units added. Since this is also the case for the linear ortho-fused zigzag-benzenes and other polymers, it is postulated that the model is applicable to polymers in general. It may, therefore, be used to predict physical properties of long-chain polymers.
A unified description of i) classical phase transitions and their remnants in finite systems and ii) quantum phase transitions is presented. The ensuing discussion relies on the interplay between, on the one hand, the thermodynamic concepts of temper
ature and specific heat and on the other, the quantal ones of coupling strengths in the Hamiltonian. Our considerations are illustrated in an exactly solvable model of Plastino and Moszkowski [Il Nuovo Cimento {bf 47}, 470 (1978)].
A simple expression is obtained for the low temperature behavior of the energy and entropy of finite nuclei for $20leq Aleq 250$. The dependence on $A$ of these quantities is for the most part due to the presence of the asymmetry energy.
