Quantal effects

Like Eq. (2.1), the classical ion-dipole and dipole-dipole energy expressions (2.23) and (2.25) are engagingly simple, and can be rigorously justified at sufficiently large R. However, these approximations can be expected to fail at smaller R where quantal effects become appreciable. 

Dose-Response Curves Demonstrate the relation between dose and the proportion of individuals responding widi a quantal effect (q.v.). In general, dose-response curves are S-shaped (increasing), and they have upper and lower asymptotes, usually but not always 100 and 0%. 

Quantal Effect An effect that either happens or does not happen, e.g. death. Synonym all-or-none response. 

The quantal dose-effect curve is often characterized by stating the median effective dose (ED50), which is the dose at which 50% of individuals exhibit the specified quantal effect. (Note that the abbreviation ED50 has a different meaning in this context... 

It should be clear from the earlier discussion that the measurable endpoint of toxicity could be a biochemical, physiological, or pathological change. This toxic effect will show a graded 7 increase as the dose of toxicant increases. Alternatively, the toxic effect may be an all-or-none effect such as death or the presence or absence of a tumor (which can be considered in such a way). These are also called quantal effects. In this case, an increase in the dose will result in an increase in the proportion of individuals showing the response rather than an increase in the magnitude of the effect. 

Figure 6.3 Quantal effects. Typical set of data after administration of increasing doses of drug to a group of subjects and observation of minimum dose at which each subject responds. Data shown are for 100 subjects dose increased in 0.2 mg/kg of body weight increments. Mean (ji) (and median) dose is 3.0 mg/kg standard deviation (v) is 0.8 mg/kg. Results plotted as histogram (bar graph) showing number responding at each dose smooth curve is normal distribution function calculated for ji of 3.0 and v of 0.8.

At lower temperatures, where quantal effects become appreciable for the high-frequency modes, Eq. 31 may be recast as a superposition of vibronic state-to-state processes [14],... 

At temperatures where quantal effects may be significant only for a well-defined subset of nuclear modes, a hybrid quantal-classical variant of Eqs. 35-37 may be employed, if separable quantal and classical modes are assumed, in which the summation in Eq. 35 is restricted to the quantized manifold of nuclear states. If the classical modes are assumed to be harmonic, then the modified (FCWD),., is given by [14, 100] ... 

It is curious that the striking deviations of electrochemical kinetic behavior from that expected conventionally, which are the subject of this review, have not been recognized or treated in the recent quantum-mechanical approaches, e.g., of Levich et al (e.g., see Refs. 66 and 105) to the interpretation of electrode reaction rates. The reasons for this may be traced to the emphasis which is placed in such treatments on (1) quantal effects in the energy of the system and (2) continuum modeling of the solution with consequent neglect of the specific solvational- and solvent-structure aspects that can lead, in aqueous media, to the important entropic factor in the kinetics and in other interactions in water solutions. However, the work of Hupp and Weaver, referred to on p. 153, showed that the results could be interpreted in terms of Marcus theory, with regard to potential dependence of AS, when there was a substantial net reaction entropy change in the process. 

A fixed effect model, also known as a quantal effect model, relates a certain drug concentration with the statistical likelihood of a predefined, fixed effect to be present... 

The words "canonical" and "variational" in CVT refer to the fact that in this step the dividing surface is variationally optimized for the canonical ensemble specified by T. In the third step one multiplies k (T) by a transmission coefficient k(T) to account for quantal effects on the reaction coordinate, yielding the final estimated rate constant > 2-44... 

The discovery of superdeformed rotational bands in Dy was a very impressive achievement of nuclear spectroscopy from many reasons. From the experimental point of view, it has shown that discrete y cascades can be observed from states whose excitation energy varies from 12 to 30 MeV and spin from (22) to (60) %. From the theoretical point of view, it has demonstrated that the rotation can stabilize very deformed shapes. In this way, a new possibility has been opened to study the quantal effects at very high spins. There are already >170 superdeformed bands known in the A 80, 130-140, 150, 190 mass number regions. For detailed description, see Szymanski (1983), Nilsson and Ragnarsson (1995), and Fenyes (2002). 

The ability to measure reactive scattering data for reaction products in their different quanmm states leads to a very interesting possibility of smdying quantal effects in reactive scattering. Indeed, by building PESs, vibrationally adiabatic curves, which are effective potentials for the translational motion from reactants or products, can be described by a single quantum number for the vibrational action. An example of such potentials is shown in Figure 21.15. 

It may be noted that, if we let h 0 or T oc, then K/K 1 i.e., in the classical limit there is no discrimination between isotopes, and the discrimination which actually occurs is a purely quantal effect. ... 

For hydrogen and deuterium this factor has a maximum value of 2, and since k /k often exceeds this value in practice it is clear that quantal effects are also operating. 

The term linear in A has an obvious classical correspondence, while quantal effects are represented by the term quadratic in A, which is much more significant whenever A > 1. In these cases one may retain only the highest power of A and write... 

Dose Rate The chemical s dose delivered per unit lime or the radiation dose delivered per unit time. Dose-Response Curves Demtnstrate the relation between dose and the proportion of individuals responding with a quantal effect (q.v.). In general, dose-response curves are S-shaped (increasing), and they have upper and lower asymptotes, usually but not always 1(X) and 0%. D Response Relationship The systematic relationship between the dose (or effective concentration) of a drug or xenobiotic and the magnitude (or intensity) of the response it elicits. 

After dosing the mice are observed and the responses scored either as the number showing a purgative effect (quantal effect) or as the number of wet faeces excreted per mouse (graded effect) and potency estimates with their limits of error calculated by the methods given on page 841. 

Miller and Alexander have described the conduct of the test for senna based on the quantal effect produced in mice. Healthy mice weighing 20 to 30 g are selected for test from a colony having free access to food and... 

It concerns the frequency of occurrence of a single toxic effect of a specified magnitude, referred to as a quantal effect or endpoint. Examples are death, a specific birth defect infertility, cancer, liver disease, anemia, kidney failure, or a cardiac arrhythmia. It does not concern different magnitudes of the same toxic effect nor does it involve a spectrum of toxic effects. 

To sum up, elastic scattering measurements serve as a probe of the collision dynamics and can reveal detailed information on the intermolecular potential. But to do a complete job we cannot overlook quantal effects. 

This differs from the collinear expression only in the addition of the contributions from the doubly degenerate bending motion. The V (s) barrier defined by equation (51) is also useful in interpreting the origin of variational effects when quantal effects are not included on the reaction coordinate, and we shall use it below for this purpose. 

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