Energy partition

It is also instructive to start from the expression for entropy S = log(g(A( m)) for a specific energy partition between the two-state system and the reservoir. Using the result for g N, m) in section A2.2.2. and noting that E = one gets (using the Stirling approximation A (2kN)2N e ). 

Since E = - 2 iU)tn., a given spin excess value 2m. implies a given energy partition. The free energy for such a specific energy partition is... 

Mullin A S, Park J, Chou J Z, Flynn G W and Weston R E Jr 1993 Some rotations like it hot seleotive energy partitioning in the state resolved dynamios of oollisions between COj and highly vibrationally exoited pyrazine Chem. Phys. 175 53-70... 

The energy partition between blast wave energy and fragment kinetic energy is as described in paragraph I. 

The nearest excited electronic state of NCT is more than 10,000 cm-1 above the ground electronic state. Because of the large energy difference, energy partitioning into the excited electronic states will not take place until the temperature is very very high. 

Glendening, E. D., Streitwieser, A., 1994, Natural Energy Decomposition Analysis An Energy Partitioning Procedure for Molecular Interactions With Apphcation to Weak Hydrogen Bonding, Strong Ionic, and Moderate Donor-Acceptor Interactions , J. Chem. Phys., 100, 2900. 

Korchowiec J, Uchimaru T (2000) New energy partitioning scheme based on the self-consistent charge and configuration method for subsystems application to water dimer system. J Chem Phys 112(4) 1623—1633... 

PHASE FNF.RCiY - Adsorption energy - Partition energy <3C LC ... 

FIGURE 3.5 Energy partition among the track entities (spurs, blobs, and short tracks) as a function of electron energy in liquid water. Data from Pimblott et at. (1990), with permission of Am. Chem. Soc. ... 

To calculate the energy partition between the core and the envelope, Mozumder et al. (1968) considered the equipartition of deposited energy between glancing and knock-on collisions (Sect. 2.3.4). Of the ejected electrons... 

The quantities defined by Eqs. (2)—(7) plus Vs max, Vs min, and the positive and negative areas, A and, enable detailed characterization of the electrostatic potential on a molecular surface. Over the past ten years, we have shown that subsets of these quantities can be used to represent analytically a variety of liquid-, solid-, and solution-phase properties that depend on noncovalent interactions [14-17, 84] these include boiling points and critical constants, heats of vaporization, sublimation and fusion, solubilities and solvation energies, partition coefficients, diffusion constants, viscosities, surface tensions, and liquid and crystal densities. 

A semiempirical predictor of homoaromaticity has been developed based on the interactions between atoms obtained from an energy partitioning scheme (Williams et al., 1988). This technique correlates the energy lowering two-centre interactions of two non-bonded atoms with homoaromaticity. A second part of the predictor is the demonstration of the necessity of including at least a minimal 2x2 configuration interaction (Cl) treatment. This semiempirical predictor has been verified by correctly interpreting the interactions in cycloheptatriene [5], 1,6-... 

Fig. 3. Energy partitioning in (LiHe)+ obtained by first-order perturbation theory. (Basis set ...

In order to leam more about the nature of the intermolecular forces we will start with partitioning of the total molecular energy, AE, into individual contri butions, which are as close as possible to those we defined in intermolecular perturbation theory. Attempts to split AE into suitable parts were undertaken independently by several groups 83-85>. The most detailed scheme of energy partitioning within the framework of MO theory was proposed by Morokuma 85> and his definitions are discussed here ). This analysis starts from antisymmetrized wave functions of the isolated molecules, a and 3, as well as from the complete Hamiltonian of the interacting complex AB. Four different approximative wave functions are used to describe the whole system ... 

W Another type of energy partitioning in MO theory was proposed by Clementi 86>. This kind of partitioning called Bond Energy Analysis" (BEA) was found to be particularly useful in larger molecular clusters 87-90) Since the individual contributions of BEA are not directly related to the quantities discussed in intermolecular perturbation theory, dementi s technique will not be used here (see Chapter V). 

---