Entropy molecular representation

FIGURE 3.7 A molecular representation of entropy. Bottom Entropy is low when only a few energy levels are populated. Top Entropy is higher when larger numbers of energy levels are populated... 

The next steps are the following Step 1 Passage to the entropy representation and specification of the dissipative thermodynamic forces and the dissipative potential E. Step 2 Specification of the thermodynamic potential o. Step 3 Recasting of the equation governing the time evolution of the np-particle distribution function/ p into a Liouville equation corresponding to the time evolution of np particles (or p quasi-particles, Up > iip —see the point 4 below) that then represent the governing equations of direct molecular simulations. 

The ultimate goal of a thermodynamic description of molecular systems, however, is to determine the horizontal displacements of the electronic structure (see Section 7), i.e., transitions from one v-representable molecular density to another. In order to relate the information entropy H[p], possibly involving also the reference densities (equation (92)), to the system energetic parameters one uses the generalized variational principle in the entropy representation [108] ... 

As we have demonstrated in this survey, there is a wide range of problems in the theory of electronic structure and chemical reactivity, which can be tackled using concepts and techniques of the density functional and information theories. These two descriptions are complementary in character, providing the energy and entropy representations of molecular systems, respectively. Together they constitute the... 

There are two modes that are not applied to the above statistical treatment of thermodynamic properties that may be a major factor in some molecular species. The first is contribution to entropy, S, and heat capacity, Cp(T) from internal rotors, which for some species can be significant. Molecular species that do not have internal rotors are represented by the above statistical analysis representation. However, for molecular species that have hindered internal rotors, the contributions to S and Cp(T) need to be separately calculated and incorporated into the thermodynamic properties. One method to estimate the hinder rotor contributions is by using the vibration frequency for the torsion. 

In addition to its use in quantum mechanics for the past 20 years, SE analysis has more recently been applied to molecular dynamics simulations and conformational analysis. An algorithm has been developed to calculate SE values from dynamics trajectories, and it was shown that entropies of conformational energies of test molecules correlated linearly with their experimental thermodynamic entropies." Using 2-D-lattices and simplified (two-state i.e., hydrophilic-hydrophobic) protein chain representations, SE values for energy distributions produced by different pair-wise interactions were calculated. Potentials leading to their discrimination on the basis of differences in information content were developed. ... 

---