State distribution

In a final, sixth step one may also average (sum) over a thennal (or other) quantum state distribution I (and F) and obtain the usual thennal rate coefficient... 

Hamilton C E, Bierbaum V M and Leone S R 1985 Product vibrational state distributions of thermal energy charge transfer reactions determined by laser-induced fluorescence in a flowing afterglow Ar" + CC -> CC (v= 0-6) + Ar J. Chem. Rhys. 83 2284-92... 

Sonnenfroh D M and Leone S R 1989 A laser-induced fluorescence study of product rotational state distributions in the charge transfer reaction Ar <-i. i, ) + Ni Ar + MfXjat 0.28 and 0.40 eV J. them. Phys. 90 1677-85... 

However, with the advent of lasers, the teclmique of laser-induced fluorescence (LIF) has probably become the single most popular means of detennining product-state distributions an early example is the work by Zare and co-workers on Ba + FLT (X= F, Cl, Br, I) reactions [25]. Here, a tunable laser excites an electronic transition of one of the products (the BaX product in this example), and the total fluorescence is detected as a... 

Conceptually similar studies have since been carried out for the reaction of Ft atoms with Cl/Aii(l 11). More recently, quantum-state distributions have been obtamed for both the Ft + Cl/Aii(l 11)[, and M and Ft(D) + D (Ft)/Cii(l 11) systems. The results of these studies are in good qualitative agreement widi calculations. Even for the Ft(D) + D (Ft)/Cii(l 11) system [89], where we know that the incident atom caimot be significantly accommodated prior to reaction, reaction may not be direct. Detailed calculations yield much smaller cross sections for direct reaction than the overall experimental cross section, indicating that reaction may occur only after trapping of the incident atom [90]. 

Rettner C T and Auerbach D J 1996 Quantum-state distributions for the HD product of the direct reaction of H(D)/Cu(111) with D(H) incident from the gas phase J. Chem. Phys. 104 2732... 

Dobbyn A J, Stumpf M, Keller H-M and Schinke R 1996 Theoretical study of the unimolecular dissociation HO2—>H+02. II. Calculation of resonant states, dissociation rates, and O2 product state distributions J. Chem. Phys. 104 8357-81... 

Figure Bl.14.9. Imaging pulse sequence including flow and/or diflfiision encoding. Gradient pulses before and after the inversion pulse are supplemented in any of the spatial dimensions of the standard spin-echo imaging sequence. Motion weighting is achieved by switching a strong gradient pulse pair G, (see solid black line). The steady-state distribution of flow (coherent motion) as well as diffusion (spatially...

The anisotropy of the product rotational state distribution, or the polarization of the rotational angular momentum, is most conveniently parametrized tluough multipole moments of the distribution [45]. Odd multipoles, such as the dipole, describe the orientation of the angidar momentum /, i.e. which way the tips of the / vectors preferentially point. Even multipoles, such as the quadnipole, describe the aligmnent of /, i.e. the spatial distribution of the / vectors, regarded as a collection of double-headed arrows. Orr-Ewing and Zare [47] have discussed in detail the measurement of orientation and aligmnent in products of chemical reactions and what can be learned about the reaction dynamics from these measurements. 

Following the procedures outlmed above, mtemal state distributions for the products of the FI + NO2 reaction... 

Coherent anti-Stokes Raman spectroscopy (CARS) [59] has also found utility in the detemiination of the internal state distributions of products of chemical reactions. This is one of several coherent Raman spectroscopies based on the... 

Sauder D G and Dagdigian P J 1990 Determination of the internal state distribution of NC produced from the H + NG2 reaction J. Chem. Phys. 92 2389-96... 

Irvine AML, Smith I W M, Tuckett R P and Yang X-F 1990 A laser-induced fluorescence determination of the complete internal state distribution of CH produced in the reaction H + NG2 CH + NC J. Chem. Phys. 93 3177-86... 

Dagdigian P J, Varley D F, Liyanage R, Gordon R J and Field R W 1996 Detection of DCI by multiphoton ionization and determination of DCI and HCI internal state distributions J. Chem. Phys. 106 10 251-62... 

This book presents a detailed exposition of angular momentum theory in quantum mechanics, with numerous applications and problems in chemical physics. Of particular relevance to the present section is an elegant and clear discussion of molecular wavefiinctions and the detennination of populations and moments of the rotational state distributions from polarized laser fluorescence excitation experiments. 

Sinha M P, Schulz A and Zare R N 1973 Internal state distribution of alkali dimers in supersonic nozzle beams J. Chem. Phys. 58 549-56... 

The occurrence of predissociation opens up a new family of observable quantities. It is possible to measure not only linewidths or lifetimes, but also the internal state distributions of the fragments. All these quantities are sensitive to the intennolecular potential and can be used to test or refine proposed potential surfaces. 

This lineshape analysis also implies tliat electron-transfer rates should be vibrational-state dependent, which has been observed experimentally [44]- Spin-orbit relaxation has also been identified as an important factor in controlling tire identity of botli electron and vibrational-state distributions in radiationless ET reactions. 

In Figure 1, we see that there are relative shifts of the peak of the rotational distribution toward the left from f = 12 to / = 8 in the presence of the geometiic phase. Thus, for the D + Ha (v = 1, DH (v, f) - - H reaction with the same total energy 1.8 eV, we find qualitatively the same effect as found quantum mechanically. Kuppermann and Wu [46] showed that the peak of the rotational state distribution moves toward the left in the presence of a geometric phase for the process D + H2 (v = 1, J = 1) DH (v = 1,/)- -H. It is important to note the effect of the position of the conical intersection (0o) on the rotational distribution for the D + H2 reaction. Although the absolute position of the peak (from / = 10 to / = 8) obtained from the quantum mechanical calculation is different from our results, it is worthwhile to see that the peak... 

Differential cross-sections for particular final rotational states (f) of a particular vibrational state (v ) are usually smoothened by the moment expansion (M) in cosine functions mentioned in Eq, (38). Rotational state distributions for the final vibrational state v = 0 and 1 are presented in [88]. In each case, with or without GP results are shown. The peak position of the rotational state distribution for v = 0 is slightly left shifted due to the GP effect, on the contrary for v = 1, these peaks are at the same position. But both these figures clearly indicate that the absolute numbers in each case (with or without GP) are different. 

The ground state distribution of electrons in the aluminum atom is lT2T2 3T3/). The oxidation state of aluminum is +3, except at high temperatures where monovalent species such as AIQ, AIF, and AI2 have been spectrally identified At lower temperatures, these compounds disproportionate... 

After the stipulated leaching period, the waters were sampled before and after filtration through 0.05 ym Nuclepore filters and the oxidation-state distribution of plutonium in the filtrates was determined as follows PrF3 carrier precipitation for Pu(III) and (IV), PrF3 precipitation following NaHS03 reduction for total plutonium, and thenoyltrifluoroacetone (TTA) extraction... 

Because of these differences, it is not surprising that speciation differs significantly in the two systems. The contrast in oxidation-state distributions between the single-phase studies and the leaching experiments is noteworthy. In the latter,... 

Fig. 4-7 Example of a coupled reservoir system where the steady-state distribution of mass is not uniquely determined by the parameters describing the fluxes within the system but also by the initial conditions (see text).

However, with "only" 1000 Pg emitted into the system, i.e. less than 3% of the total amount of carbon in the four reservoirs, the atmospheric reservoir would still remain significantly affected (20%) at steady state. In this case the change in oceanic carbon would be only 2% and hardly noticeable. The steady-state distributions are independent of where the addition occurs. If the CO2 from fossil fuel combustion were collected and dumped into the ocean, the final distribution would still be the same. 

Note that for the determination of molecular weight, the charge-state distribution is not of great importance as it does not affect the m/z value of the ion involved and thus the calculated molecular weight. If the conformational state of the biopolymer is of interest, however, the distribution of charged states is a fundamental consideration and any parameter likely to change this distribution must be carefully controlled. 

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