No physical or physical-organic chemistry laboratory goes without a single instrument. To measure conductance we use conductometer, pH meter for measuring pH, colorimeter for absorbance, viscometer for viscosity, potentiometer for emf, polarimeter for angle of rotation, and several other instruments for different physical properties. But when it comes to the turn of thermodynamic or activation parameters, we don't have any meters. The only way to evaluate all the thermodynamic or activation parameters is the use of some empirical equations available in many physical chemistry text books. Most often it is very easy to interpret the enthalpy change and free energy change in thermodynamics and the corresponding activation parameters in chemical kinetics. When it comes to interpretation of change of entropy or change of entropy of activation, more often it frightens than enlightens a new teacher while teaching and the students while learning. The classical thermodynamic entropy change is well explained by Atkins [1] in terms of a sneeze in a busy street generates less additional disorder than the same sneeze in a quiet library (Figure 1) [2]. The two environments are analogues of high and low temperatures, respectively. In this article making use of Eyring equation a factor usually called 'universal factor' is derived and made use as a 'yard stick' to interpreting the change in entropy of activation for physical or physical-organic chemistry senior undergraduate and graduate students' class-room.Peter Atkins Figure 1. Keywords: entropy, universal factor, kineticsCite This Article: R. Sanjeev, D. A. Padmavathi, and V. Jagannadham, "The 'Yard Stick' to Interpret the
This paper considers the collisional excitation of 0('D) modeled by the crossing of two valence 1 IIg curves dissociating to 0{'P)+0{'P) [ V»{R)] and 0('P)+0('D) [ V22{R}]which in turn are further crossed by the C 'Ils Rydberg curve dissociating to 0('P )+0{ 'S ) [ V33(R ) ]. The role of structure in the potential curves and coupling matrix elements is quantitatively probed by the first-order functionalsensitivity densities 5lncr»(E)/51nVJ(R) of the excitation cross section o. l2(E) obtained from closecoupling calculations. The results reveal that, in spite of the well-separated nature of the crossing between the two valence curves from their crossings with the Rydberg potential curve, the excitation cross section 0. » displays considerable sensitivity to the Rydberg curve V33(R) at all energies in the range 3.0 -9.0 eV. For relative collisional energies corresponding to the higher closely spaced vibrational energy levels of the Rydberg state, the excitation cross section is found to be much more sensitive to the Rydberg state than to the two valence states themselves. At all energies, the sensitivity of the excitation cross section o. » to the coupling V»(R) between the valence states is much larger than the sensitivity to the couplings V»(R) or V»(R) with the Rydberg state. At higher energies, the large increase in the sensitivity of the cross section to the Rydberg potential is mirrored by a similar increase in sensitivity to its coupling V»(R) with the upper valence state. Due to the weak coupling between the three curves, a qualitative similarity exists between the sensitivity profiles and those predicted by the Landau-ZenerStueckelberg (LZS) theory. Quantitative departures witnessed in earlier work are, however, more pro-
The first-order functional-sensitivity densities 5o. &2(E)/5V;, (R) from close-coupling calculations are used for a quantitative probe of the role of structure in crossing diabatic curves used to model nonadiabatic collisions. Application to the excitation of Ne by He+ shows a region of significance for 5o. »(E)/6 V»(R) as a prominent Gaussian-like profile around the crossing point (R ) in accord with the 5(R -R ) idealization of the Landau-Zener-Stueckelberg (LZS) theory. Similarly, the densities 60. »(E)/6V»(R) and 5o. »(E)/5V»(R) mimic d6(R -R *)/dR-type behavior with one being the negative of the other in the neighborhood of R, in qualitative agreement with the LZS theory. However, all three sensitivity profiles identify a much broader area of importance for the curves than the loosely defined avoided-crossing region. Also, although the sensitivities themselves decrease with increasing energy, the domain of importance of the curves increases. Examination of the functional-sensitivity densities 5cr»(E)/5 V;, (R) for the chemi-ionization collision Na+ I~Na +I reveals regions of potentialfunction importance very different from that predicted by the LZS theory. The chemi-ionization cross section is about ten times more sensitive to the ionic curve than the covalent curve. Also, the domain of sensitivity of the ionic curve is larger compared to that of the covalent curve. The density 6o. »(E)/6V»(R) for chemi-ionization shows that the area of maximum potential significance is not at the crossing point itself but the regions bracketing it on both sides. Also, the dominant sign dependence of the coupling sensitivity is unexpectedly negative. The results offer other observations about the domain of validity of the intuitive pictures rooted in the LZS theory. The significance of these results to the inversion of inelastic cross-section data is briefly discussed. PACS number(s): 34.50. Pi, 34.20.Cf
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