Entropy of vibration

When evaluating the entropy change in the mobile adsorption it is assumed that the rotational, vibrational and electronic degrees of freedom of the molecules are preserved. It allows considering only the translational entropy of the surface gas and the entropy of vibrations of its molecules perpendicular to the surface. These oscillations are induced by the characteristic vibration frequency of the adsorbent... 

This expression is predicated upon a few key approximations. First, we assert that the energy to form a vacancy is given by e ac and takes no account of the possible alterations in this energy that would be present if interactions between the vacancies were considered. This amounts to a low-concentration approximation, and we will see that for low temperatures, this approximation is borne out by the results. The quantity ASyn, corresponds to the change in the entropy of vibration as a result of the presence of the vacancy. In addition, the third term is the configurational entropy associated with the presence of the vacancies. Our treatment of this term assumes that there is no correlation in the positions of the vacancies, again a reflection of the presumed diluteness of the vacancies. 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

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. 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

CPR can be used to find continuous paths for complex transitions that might have hundreds of saddle points and need to be described by thousands of path points. Examples of such transitions include the quaternary transition between the R and T states of hemoglobin [57] and the reorganization of the retinoic acid receptor upon substrate entry [58]. Because CPR yields the exact saddle points as part of the path, it can also be used in conjunction with nonnal mode analysis to estimate the vibrational entropy of activation... 

To compute zero-point vibration and thermal energy corrections to total energies as well as other thermodynamic quantities of interest such and the enthalpy and entropy of the system. 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

Heating a solid increases the amplitude of vibrations, and hence, the disorder, and entropy increases. 

El0.7 Carbonyl sulfide (OCS) is a linear molecule with a moment of inertia of 137 x 10-40 g em2. The three fundamental vibrational frequencies are 521.50, 859.2, and 2050.5 cm-1, but one is degenerate and needs to be counted twice in calculating the entropy. A Third Law measurement of the entropy of OCS (ideal gas) at the normal boiling point of T = 222.87 K andp = 0.101325 MPa gives a value of 219.9 J-K- -mol"1. Use this result to decide which vibrational frequency should be given double weight. 

MMl represents the mass and moment-of-inertia term that arises from the translational and rotational partition functions EXG, which may be approximated to unity at low temperatures, arises from excitation of vibrations, and finally ZPE is the vibrational zero-point-energy term. The relation between these terms and the isotopic enthalpy and entropy differences may be written... 

Many workers have offered the opinion that the isokinetic relationship is confined to reactions in condensed phase (6, 122) or, more specially, may be attributed to solvation effects (13, 21, 37, 43, 56, 112, 116, 124, 126-130) which affect both enthalpy and entropy in the same direction. The most developed theories are based on a model of the half-specific quasi-crystalline solvation (129, 130), or of the nonideal conformal solutions (126). Other explanations have been given in terms of vibrational frequencies involving solute and solvent (13, 124), temperature dependence of solvent fluidity in the quasi-crystalline model (40), or changes of enthalpy and entropy to produce a hole in the solvent (87). 

In either case, abstraction mechanisms are direct (no long-lived collision complex is formed), have small entropy costs ( loose transition states), and typically deposit large amounts of vibrational energy in the newly formed bond while the other bonds in the system act largely as spectators. 

Of course, the converse situation, in which the entropy of the transition state is lower than that of the ground state of the reactant, can also occur (Fig. 3.11). In this case, one speaks of a tight transition state tight, because rotations, vibration or motion of the activated complex are more restricted than in the ground state of the reactant. The dissociation of molecules on a surface provides an example that we shall discuss in the next section. 

Scheffler M, Dabrowski J. 1988. Parameter-free calculations of total energies, interatomic forces and vibrational entropies of defects in semiconductors. Phil Mag A 58 107-121. 

The entropy difference A5tot between the HS and the LS states of an iron(II) SCO complex is the driving force for thermally induced spin transition [97], About one quarter of AStot is due to the multiplicity of the HS state, whereas the remaining three quarters are due to a shift of vibrational frequencies upon SCO. The part that arises from the spin multiplicity can easily be calculated. However, the vibrational contribution AS ib is less readily accessible, either experimentally or theoretically, because the vibrational spectrum of a SCO complex, such as [Fe(phen)2(NCS)2] (with 147 normal modes for the free molecule) is rather complex. Therefore, a reasonably complete assignment of modes can be achieved only by a combination of complementary spectroscopic techniques in conjunction with appropriate calculations. 

The third law of thermodynamics states that the entropy of a perfect crystal is zero at a temperature of absolute zero. Although this law appears to have limited use for polymer scientists, it is the basis for our understanding of temperature. At absolute zero (-273.14 °C = 0 K), there is no disorder or molecular movement in a perfect crystal. One caveat must be introduced for the purist - there is atomic movement at absolute zero due to vibrational motion across the bonds - a situation mandated by quantum mechanical laws. Any disorder creates a temperature higher than absolute zero in the system under consideration. This is why absolute zero is so hard to reach experimentally ... 

Many competing effects can contribute to ligand-receptor binding free energies changes in rotational, translational, conformational, and vibrational entropy of the... 

Currently, we evaluate the vibrational/rotational/translational entropy of the solute molecules using normal mode and classical statistical analyses. Although the use of a quasiharmonic analysis, as suggested by Schlitter24... 

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