Transfer, pair-wise

This process does not necessarily have to be simultaneous, but the two atoms of the dihydrogen molecule must retain a spin-spin coupling throughout the whole process. Conversely, if they are not transferred pair-wise (i. e., if the transferred hydrogen atoms stem from different dihydrogen molecules or if they lose their coupling in the course of the process), no polarization can be detected. 

If cyclopentene would react pair-wise with 2-pentene, only one product would form, namely 2,7-decadiene, and a similar result for cyclodimers etc. of cyclopentene. If somehow, the alkylidene species would be transferred one by one, we would obtain a mixture of 2,7-nonadiene, 2,7-decadiene, and 2,7-undecadiene in a 1 2 1 ratio. The latter turned out to be the case, which led the authors to propose the participation of metal-carbene (metal alkylidene) intermediates [6], Via these intermediates the alkylidene parts of the alkenes are transferred one by one to an alkene. The mechanism is depicted in Figure 16.4. In the first step the reaction of two alkylidene precursors (ethylidene -bottom- and propylidene -top) with cyclopentene is shown. In the second step the orientation of the next 2-pentene determines whether nonadiene, decadiene or undecadiene is formed. It is clear that this leads to a statistical mixture, all rates being exactly equal, which need not be the case. Sometimes the results are indeed not the statistical mixture as some combinations of metal carbene complex and reacting alkene may be preferred, but it is still believed that a metal-carbene mechanism is involved. Deuterium labelling of alkenes by Gmbbs instead of differently substituted alkenes led to the same result as the experiments with the use of 2-pentene [7],... 

The occurrence of polarization signals during homogeneous hydrogenations can be regarded as proof of the transfer of both atoms of the former parahydrogen molecule, that is, they become transferred as a pair or in a pair-wise maimer. 

Fig. 3 (a) Atomic positions in the two states before and after the pair wise charge transfer, (b) Synchronized motion between the antisymmetric vibration v and pair wise charge transfer frequency, o>, leading to COVALON conduction. 

Classical molecular simulation methods such as MC and MD represent atomistic/molecular-level modeling, which discards the electronic degrees of freedom while utilizing parameters transferred from quantum level simulation as force field information. A molecule in the simulation is composed of beads representing atoms, where the interactions are described by classical potential functions. Each bead has a dispersive pair-wise interaction as described by the Lennard-Jones (LJ) potential, ULj(Ly) ... 

CH3CH=CHCH=CHC00H)][CF3S03] is shown in a iH-PHIP experiment (see Fig. 21.10). The spectrum reveals the characteristic PFIIP polarization pattern of adsorptive and emissive lines. This polarization pattern proves the pair-wise transfer of the para-hydrogen to the substrate. The observed anti-phase coupling constant of... 

Step 5. Assigning shifts in week i, (i a 1). For each week of the schedule, a total of n shifts ate required on the weekends and N shifts on the weekdays. These requirements are met by forming n chains [Sun.-Sat.j and N-n chains [Mon.-Fri.] that are pair-wise distinct. A [dl-d2] chain, for dl < dl, is a sequence of d2 — dl -I- 1 workdays, taken from one or more employees. Two cheiins are pair-wise workday disjoint if no employee workday is a member of both chains. A d -d2 cheiin is formed by starting with an employee who works on day <71. This employee s workdays are assigned to the chain until either day d2 is reached or the employee has a day dk off, d < dk < d2). In this latter case, the chain is transferred to a new employee who works on day dk but had day dk — I off. This new employee s workdays are then assigned to the chain. This process is continued until day d2 is reached. 

The choice of the adjustable parameters used in conjunction with classical potentials can result to either effective potentials that implicitly include the nuclear quantization and can therefore be used in conjunction with classical simulations (albeit only for the conditions they were parameterized for) or transferable ones that attempt to best approximate the Born-Oppenheimer PES and should be used in nuclear quantum statistical simulations. Representative examples of effective force fields for water consist of TIP4P (Jorgensen et al. 1983), SPC/E (Berendsen et al. 1987) (pair-wise additive), and Dang-Chang (DC) (Dang and Chang 1997) (polarizable, many-body). The polarizable potentials contain - in addition to the pairwise additive term - a classical induction (polarization) term that explicitly (albeit approximately) accounts for many-body effects to infinite order. These effective potentials are fitted to reproduce bulk-phase experimental data (i.e., the enthalpy at T = 298 K and the radial distribution functions at ambient conditions) in classical molecular dynamics simulations of liquid water. Despite their simplicity, these models describe some experimental properties of liquid... 

Recently, both the MK and RVS analyses have been extended to many-body complex systems. This allows the computation of many-body effects on each energy component within the MK of RVS analyses, since rigorously only es is pair-wise additive. In the case of water trimers and tetramers it was found that polarization and charge transfer are the dominant components in the three-body energy terms. The four body term in the water tetramer was found to be negligible. 

After an extensive review of MMCT transitions involving ions in solids, it seems wise to start this paragraph with some molecular species, because many of these have been investigated in much more detail than their counterparts in non-molecular solids. It is suitable to make a distinction between outer-sphere charge-transfer (OSCT) and inner-sphere charge-transfer (ISCT) transitions [1], In the former the metal ions do not have ligands in common, in the latter they are connected by a common ligand. Studies are usually performed on metal-ion pairs in solution. 

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