Spectroscopic constants defined

In equation (49), which is the van t Hoff equation, —dH/de may be replaced by — AH, since these two quantities are equal for ideal-gas reactions. Relationships analogous to equation (49) may be derived for each of the equilibrium constants defined in Section A. 3, but for reactions in systems other than ideal-gas mixtures, — AH and — dH/de may not, in general, be equated in these expressions. Heats of reaction can be determined directly either by spectroscopic measurements followed by the application of statistical mechanics (for ideal-gas reactions) or by calorimetric measurements of Q (for arbitrary reactions). Since the measurement of equilibrium compositions may be simpler than either of the above procedures, in practice equation (49) is often used to obtain heats of reaction from experimental values of Kp at neighboring temperatures. 

To summarize, at the present time, no conventional ab initio calculation has been able to yield accurate spectroscopic constants for Ctj. The source of the problem is clear in general terms—more correlation is needed and the types of correlation terms needed have been at least partly defined . However, the non-empirical implementation of calculations including these terms appears to be beyond the limits of present-day technology. (See also Ref. 388.)... 

Quantal spectroscopic constants, as defined in Eq. (25), were calculated for the three reactions from fits to assigned peak energies in the finite-resolution density. Vibrationally adiabatic thresholds (the maxima in vibrationally adiabatic curves calculated using the procedure described for H 4- H2) were also least-squares fit with Eq. (25). Results are... 

The recorded time and wavelength dependent data can be related to the molecular processes within the framework of the theorie of transient spectroscopy. All time constants of the primary ET are known to be longer than 500 fs and therefore they are much longer than oszillation periods of the relevant molecular vibrations. Consequently one may assume that the absorption changes originate from intermediates with spectroscopically well defined properties. Under these conditions only exponential processes are present and the populations of the various intermediates follow a rate equation system /5/ ... 

The rate constants kTS and kST define an equilibrium constant (ATeq) connecting the singlet and triplet carbenes. An estimate of Ktq, and hence AGSX, for BA can be obtained from the experiments described above. The time resolved spectroscopic measurements indicate that BA reacts with isopropyl alcohol with a rate constant some five times slower than the diffusion limit (Table 7). This, in conjunction with the picosecond timescale measurements, gives a value for ksr. The absence of ether formation from the sensitized irradiation, when combined with the measured rate constant for reaction of 3BA with isopropyl alcohol, gives an upper limit for k-. These values give Keq and thus AGST 2 5.2 kcal mol-1 (Table 8). 

The Forster resonance energy transfer can be used as a spectroscopic ruler in the range of 10-100 A. The distance between the donor and acceptor molecules should be constant during the donor lifetime, and greater than about 10 A in order to avoid the effect of short-range interactions. The validity of such a spectroscopic ruler has been confirmed by studies on model systems in which the donor and acceptor are separated by well-defined rigid spacers. Several precautions must be taken to ensure correct use of the spectroscopic ruler, which is based on the use of Eqs (9.1) to (9.3) ... 

Most theoretical interpretations of condensed phase IE s have depended heavily on spectroscopic measurements of ZPE shifts to define limits on parameter assignments (force constant shifts). It is therefore a matter of some importance to determine the magnitude of dielectric corrections to be applied to such shifts. Fortunately dielectric corrections are larger than typical spectroscopic uncertainties in phase frequency shifts only for very intense IR bands, and therefore dielectric corrections are very often unnecessary. 

Indium orthophosphate is essentially insoluble in water, but salts of [In(P04)2]3- and [In2(P04)4]6- have been prepared,163 and a solution phase complex with the H2POj anion has been identified.164 The coordination chemistry of In3+ with the higher phosphates is at present ill defined. Stability constant measurements,9 and preparative and spectroscopic studies7 suggest that In06 is the central core of the compounds in the solid state. The same appears to be true for the complexes reported for L = fluorophosphate,165 methylphosphonate,166 dichlorophosphate,167 dimethylthiophosphate,168 diethylthiophosphinate169,170 and diisopropyl-methylphosphonate.171... 

---