Spectroscopic constants for bound states

J. Oddershede, N. Elander, Spectroscopic Constants and Radiative Lifetimes for Valence-Excited Bound States, J. Chem. Phys. 56 (1972) 3495. 

The third column of table 1 contains the spectroscopic constants of the four E states, based on the corrected adiabatic potentials. Apart from the D, Tt and 7/j=oo energies, which are bound to coincide with the experimental values, we observe a remarkable improvement in the computed vibrational levels of the B E state. The A 1 and R values here presented for the barrier and outer minimum of this potential curve are probably the best estimates available to date. The vibrational levels belonging to the C E" " state are much less accurately determined, the energy differences AE(calc. — exp.) ranging from -58 to -280 cm. The only previous determination of this potential energy curve leads to overestimate the same levels by 200-600 cm (the same holds for the lowest electronic states, and may be partly due to a poor interpolation, i.e. to an insufficient number of points on the potential curves). No comparison with previous determinations is possible for the E" " state. 

However, when we spectroscopically examine a host-guest system, we are observing its free and the bound states. For example, for an NMR analysis we may be examining the free and bound signals for a particular guest proton. Thus, we are directly concerned with the observed rate constants (ka and b) for the exchange between the free and bound states (25). 

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

Heat capacity between that of ice and liquid water ACpi - - 0.2 cal K-1 g 1 Normalization of pK at 0.05 gg-1. Knee in adsorption isotherm. Native state very stable At 0.07 gg-1 transition in surface water, from disordered to ordered and/or from dispersed to clustered state seen in IR and EPR spectroscopic and thermodynamic properties associated with completion of charged group hydration Water mobility ca. 100 x less than for bulk water increased motion with increased hydration. Bound ligand mobility r constant from 0-0.2gg-1 t = 4x10-9s. Enzymatic activity negligible. 

---