Enthalpy motional

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

The above treatment has made some assumptions, such as harmonic frequencies and sufficiently small energy spacing between the rotational levels. If a more elaborate treatment is required, the summation for the partition functions must be carried out explicitly. Many molecules also have internal rotations with quite small barriers, hi the above they are assumed to be described by simple harmonic vibrations, which may be a poor approximation. Calculating the energy levels for a hindered rotor is somewhat complicated, and is rarely done. If the barrier is very low, the motion may be treated as a free rotor, in which case it contributes a constant factor of RT to the enthalpy and R/2 to the entropy. 

Table 2 gives our calculated results for the equilibrium volume Vq, bulk modulus Bq, and enthalpy of formation AH. Theoretical results refer to T=0, uncorrected for zero point motion, whereas experimental values refer to room temperature. Note that the extensive quantities AH and Vq arc reported per atom in the present paper, i.e., divided by the total number of atoms. As well known the LDA underestimates the volume. Comparing the bulk modulus for T3 and D8s we see that the addition of Si to pure Ti has a large (26 %) effect on the bulk modulus, indicating that p electrons of Si have a strong effect on the bonding in this system. 

Though solid electrolytes for multivalent ions offer the advantage of a larger charge transfer, their conductivities are much lower than those of monovalent ions at ambient temperature because of a higher activation enthalpy for the ionic motion... 

The thermal energy needed for an ionic jump is the motional enthalpy AH . It has two components, a barrier energy AHb for the ion to hop when the receptor and donor sites are at the same energy and a relaxation energy AH, that must be supplied to make energetically equal the receptor and donor sites. AH, is present because the time it takes for an ion to hop over the barrier energy AHb is long compared to the time it takes the immobile ions to relax to their equilibrium positions, which are different at the empty and occupied sites. In... 

From these simple phenomenological considerations, it is clear that the two dominant considerations in the design of a solid electrolyte are the creation of a temperature-independent (l — n ) with approaching its optimum value of 0.5 and a minimisation of the motional enthalpy AH and minimisation of the energy E appearing in an exponent must demand priority. 

These parameters (AG, A//, and A5 ) differ slightly from normal standard parameters in that the contribution of motion along the reaction coordinate toward the transition state is not included. The values are the difference in free energy, enthalpy, and entropy between 1 mole of activated complex and 1 mole of each reactant, all substances being at their standard-state concentrations (usually 1 M). 

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