State-dependent

There are complicating issues in defmmg pseudopotentials, e.g. the pseudopotential in equation Al.3.78 is state dependent, orbitally dependent and the energy and spatial separations between valence and core electrons are sometimes not transparent. These are not insunnoimtable issues. The state dependence is usually weak and can be ignored. The orbital dependence requires different potentials for different angular momentum components. This can be incorporated via non-local operators. The distinction between valence and core states can be addressed by incorporating the core level in question as part of the valence shell. For... 

Simple collision theories neglect the internal quantum state dependence of a. The rate constant as a function of temperature T results as a thennal average over the Maxwell-Boltzmaim velocity distribution p Ef. 

The site specificity of reaction can also be a state-dependent site specificity, that is, molecules incident in different quantum states react more readily at different sites. This has recently been demonstrated by Kroes and co-workers for the Fl2/Cu(100) system [66]. Additionally, we can find reactivity dominated by certain sites, while inelastic collisions leading to changes in the rotational or vibrational states of the scattering molecules occur primarily at other sites. This spatial separation of the active site according to the change of state occurring (dissociation, vibrational excitation etc) is a very surface specific phenomenon. 

In the ideal case for REMPI, the efficiency of ion production is proportional to the line strength factors for 2-photon excitation [M], since the ionization step can be taken to have a wavelength- and state-mdependent efficiency. In actual practice, fragment ions can be produced upon absorption of a fouitli photon, or the ionization efficiency can be reduced tinough predissociation of the electronically excited state. It is advisable to employ experimentally measured ionization efficiency line strengdi factors to calibrate the detection sensitivity. With sufficient knowledge of the excited molecular electronic states, it is possible to understand the state dependence of these intensity factors [65]. 

Figure C2.4.3. Pressure-area isotlienn for a fatty acid. The molecules are in a gaseous, liquid or solid state, depending on tire area per molecule available. If tire pressure is furtlier increased, a mechanical instability occurs and tire film breaks down.

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. 

Chou J Z and Fiynn G W 1990 Energy dependence of the reiaxation of highiy excited NO2 donors under singie coiiision conditions vibrationai and rotationai state dependence and transiationai recoii of CO2 quencher moiecuies J. Chem. Rhys. 93 6099-101... 

Preference for endo or exo transition state depends on the substitution of the diene, dieneophile and connecting chain. 

Section 13 4 The energy required to flip the spin of a proton from the lower energy spin state to the higher state depends on the extent to which a nucleus is shielded from the external magnetic field by the molecule s electrons... 

The market penetration of synthetic fuels from biomass and wastes in the United States depends on several basic factors, eg, demand, price, performance, competitive feedstock uses, government incentives, whether estabUshed fuel is replaced by a chemically identical fuel or a different product, and cost and availabiUty of other fuels such as oil and natural gas. Detailed analyses have been performed to predict the market penetration of biomass energy well into the twenty-first century. A range of from 3 to about 21 EJ seems to characterize the results of most of these studies. 

At equihbrium, the specific composition of a concentrated phosphoric acid is a function of its P2 s content. Phosphoric acid solutions up to a concentration equivalent of about 94% H PO (68% P2O5) contain H PO as the only phosphoric acid species present. At higher concentrations, the orthophosphoric acid undergoes condensation (polymerization by dehydration) to yield a mixture of phosphoric acid species (Table 5), often referred to genericaHy as polyphosphoric or superphosphoric acid, H20/P20 = - 3, or ultraphosphoric acid, H20/P20 = - 1. At the theoretical P2O5 concentration for orthophosphoric acid of 72.4%, the solution is actually a mixture containing 13% pyrophosphoric acid and about 1% free water. Because the pyrophosphoric acid present is the result of an equihbrium state dependent on the P2 5 content of the solution, pure orthophosphoric acid can be obtained because of a shift in equihbrium back to H PO upon crystallization. 

Oxidation can also occur at the central metal atom of the phthalocyanine system (2). Mn phthalocyanine, for example, can be produced ia these different oxidation states, depending on the solvent (2,31,32). The carbon atom of the ring system and the central metal atom can be reduced (33), some reversibly, eg, ia vattiag (34—41). Phthalocyanine compounds exhibit favorable catalytic properties which makes them interesting for appHcations ia dehydrogenation, oxidation, electrocatalysis, gas-phase reactions, and fuel cells (qv) (1,2,42—49). 

The actual weight that the truck can cany in the United States depends on state-highway load limits, which in turn depend on the net vehicle weight and the number of axles on the tnu (and tractor, when a trailer arrangement is used). The accepted maximum combined total weight of vehicle and cargo is 36,200 kg (80,000 lb). In some states, this is reduced slightly, while in others it is exceeded. 

FIG. 23-17 Multiple steady states of CSTRs, stable and unstable, adiabatic except the last item, (a) First-order reaction, A and C stable, B unstable, A is no good for a reactor, the dashed line is of a reversible reaction, (h) One, two, or three steady states depending on the combination Cj, Ty). (c) The reactions A B C, with five steady states, points 1, 3, and 5 stable, (d) Isothermal operation with the rate equation = 0 /(1 -I- C y = (C o Cy/t. 

The two states have the same affinity for ATP but differ with respect to their affinity for the substrate F6P, the allosteric effector ADP and the inhibitor PEP. Because of these differences in affinity, ligand binding can shift the equilibrium between the R and T states to favor one or the other state depending on which ligand is bound. 

A variety of silicone polymers has been prepared ranging from low-viscosity fluids to rigid cross-linked resins. The bulk of such materials are based on chloromethysilanes and the gross differences in physical states depend largely on the functionality of the intermediate. 

Physical State at 20°C — the physical nature of the chemical (solid, liquid, or gas) at 20°C (i.e., room temperature). Changing the temperature may alter the physical state, depending on the magnitude and direction of the change relative to the melting and boiling points of the chemical. 

Verlet used o = 0.8 the modification of Henderson et al. is to use a state-dependent o. For hard spheres... 

All processes may be classified as batch, continuous, or semibatch depending on how materials are transferred into and out of the system. Also, the process operation may be characterized as unsteady state (i.e., transient) or steady state, depending on whether the process variables (e.g., pressure, temperature, compositions, flowrate, etc.) are changing with time or not, respectively. In a batch process, the entire feed material (i.e., charge) is added instantaneously to the system marking the beginning of the process, and all the contents of the system including the products are removed at a later time, at the end of the process. In a continuous process, the materials enter and leave the system as continuous streams, but not necessarily at the same rate. In a semibalch process, the feed may be added at once but the products removed continuously, or vice versa. It is evident that batch and semibatch processes are inherently unsteady state, whereas continuous processes may be operated in a steady or unsteady-state mode. Start-up and shut-down procedures of a steady continuous production process are examples of transient operation. 

The weathering process which eventually reduces the rock of the parent material to the inorganic constituents of soil comprises both physical and chemical changes. Size reduction from rocks to the colloidal state depends not only upon the mechanical action of natural forces but also on chemical solubilisation of certain minerals, action of plant roots, and the effects of organic substances formed by biological activity. 

The time factor in stepwise potentiostatic or potentiodynamic polarisation experiments is very important, because large differences can be caused by changes in the scanning rate. Since the steady state depends on the particular system and conditions of exposure, no set rule exists for the magnitude or frequency of potential changes. Chatfield etal. have studied the Ni/H2S04 system and have shown how becomes more passive with increase in sweep rate. 

As defined above, F consists of three operators acting simultaneously on the state G >. More generally, one may prescribe any of 10 possible time-orderings to the operators H, and. That is, specify certain intermediate state dependencies, so that, for example FilG >= (H )( G >) would in general be expected to yield results different from, say, F2 G > H( ( G>)). While we will be solely concerned with the synchronous time ordering defined above, we do not expect the qualitative results to depend critically on this choice. 

---