Two-state fit

The partition parameter, f, from the two-state fit (Eq.(4)) and those from the distributed fit, Eq. (5) (Fig. 12) change abruptly with temperature. The value of f drops in a sigmoidal fashion as the temperature is lowered through the transition range for the distributed fit, both the l/e -rate, k, and the distribution parameter, n, drop correspondingly through this transition. The decrease in n corresponds to broadening of the distribution in k,. 

In this method it is assumed that the molecular constants of one state are known and can be fixed while the molecular constants of the other state and the band origin are varied. The method has the advantage that all the data can be used unfortunately, however, the Hamiltonians used may not reproduce the energy levels exactly. As indicated above, the standard deviations of the constants are much smaller than for a two-state fit. The method can be used with either the upper or lower state constants fixed and is particularly useful if the ground-state rotational constants are known from microwave spectroscopy. Unfortunately, there is no case known where the excited state constants are also determined with microwave accuracy otherwise it would be possible to check the accuracy of the one-state fit method and the significance of the statistical standard errors of the rotational constants. 

One of the limitations of the two-state fit method is that it presupposes that the energy levels of both states can be fitted with comparable accuracy. To obviate this difficulty, Aslund12 has recently modified his term value approach to permit the determination of the molecular... 

Of the four methods discussed above, the two-state fit method is the most accurate if satisfactory expressions are available for the energy levels of the two states and there are no earlier precise constants available for either state (e.g., from microwave studies). This method is equivalent to the term value method with correlation included. The rotational constants in the two states are highly correlated, and it is frequently possible to change the molecular constants in a correlated manner by an order of magnitude times the standard deviations without seriously impairing the quality of the fit. If the molecular constants of one state... 

The microwave spectrum exhibits spUttings caused by torsional tuimelling between two equivalent enantiomeric minima [04Yam]. To account for torsional splitting and interaction of the torsional substates, a two-state fit was employed. Instead of the upper and lower torsional state constants the average constants and half of the differences between the values for the two states were tabulated. 

Jakubek, Z.J., Field, R.W. Core-Penetrating Rydberg Series of BaF Single-State and Two-State Fits of New Electronic States in the 4.4 [Pg.90]

The Hamiltonian provides a suitable analytic form that can be fitted to the adiabatic surfaces obtained from quantum chemical calculations. As a simple example we take the butatriene molecule. In its neutral ground state it is a planar molecule with D2/1 symmetry. The lowest two states of the radical cation, responsible for the first two bands in the photoelectron spectrum, are and... 

While there are many other aspects from which the data sets can be viewed, here we are eoneemed to fit a two-state DIFF for two measurements 5 C of collagen and 5 C of bioapatite carbonate. The approach is outlined here with fuller details in Appendix A. 

Copolymer sequence analysis follows the same procedure. A computer program (HIXCO.TRIAD) was previously written for the two-state B/B model-fitting of triad sequence distributions and applied to (unfractionated) propylene-butylene copolymers and... 

As an example of the use of MIXCO.TRIAD, an analysis of comonomer triad distribution of several ethylene-propylene copolymer samples will be delineated. The theoretical triad Intensities corresponding to the 2-state B/B and 3-state B/B/B mixture models are given In Table VI. Abls, et al (19) had earlier published the HMR triad data on ethylene-propylene samples made through continuous polymerization with heterogeneous titanium catalysts. The data can be readily fitted to the two-state B/B model. The results for samples 2 and 5 are shown In Table VII. The mean deviation (R) between the observed and the calculated Intensities Is less than 1% absolute, and certainly less than the experimental error In the HMR Intensity determination. 

In order to test higher-order or multi-site models, it is preferable to study HMR data of polymer fractions. In this work, we shall use the pairwise HMR/fractions data to fit to multi-site models. This Is carried out in the same way as in the pairwise fraction on the tactlcity data. We can either use the two-state B/B model, or even three-state B/B/B model If applicable. The comonomer sequence intensity data for the two fractions are entered Into the computer. A total of 12 entries are Involved (6 for each fraction). The equations for the three-state copolymer... 

Fig. 23. Mossbauer spectra of Fe(J-mph)NO between 84 and 319 K. Solid lines result from a fit by a two-state relaxation model based on the stochastic theory of lineshapes. According to Ref. [164]...

The 3(X) — 4.2 K relaxation rate data for the PSS-doped complex were fitted to two different theoretical models. According to the model by Hopfield [172], electron tunneling between two molecular states is considered which are only very weakly interacting. The rate of tunneling between the two states a and b,... 

For k states, a relaxation (or noise spectrum) will contain k, exponential (or Lorentzian) components. Thus, the mechanism in Eq. (6.25) above will have two states in the absence of blocker and so give rise to relaxations (or noise spectra) that can be fitted with single exponential (or Lorentzian) functions. Addition of the blocker creates an extra state (the blocked state), giving k = 3. For k = 3, the occupancy of the open state as a function of time will be described by two exponentials ... 

Gougousi et al. first attempted to explain their findings by assuming the presence of Hj ions in two vibrational states (v = 0 and v, = 1) with two different recombination coefficients, and quenching of the v, = 1 ions by H2. This two-state model did not produce a consistent, quantitative fit to the data and this interpretation was abandoned. 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

Alexa488 bound to IFABP monitored by steady-state fluorescence was fitted to a two-state reversible unfolding model. This modified protein is slightly less stable (midpoint of 4.5 M compared to 4.7 M for wild-type IFABP). 

The relaxation fits of the Mossbauer spectra of [Fe(HB(pz)3)2] yield [30] the temperature dependence of both the population of the iron(II) high-spin and low-spin states and the relaxation rate between these two states. The resulting population of the high-spin state has a striking resemblance to that of the magnetic moment shown in Fig. 1 and these populations provide clear support both for the spin-state crossover and for the difference in populations upon heating and cooling. 

Figure 4.7 shows the best fits to the experimental data using Eq. (4.11). Although the data are fit within experimental error, the two-state model is certainly just an approximation. More complex distributions of sites with different quenching constants could fit the data. The success of the two-state model is not surprising given the well-known ability of two exponentials to accurately mimic complex decay curves (see above). Further, r data indicate that a more complex model is needed for a full description. 

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