Space theory

Yan Y J, Gillilan R E, Whitnell R M, Wilson K R and Mukamel S 1993 Optimal control of molecular dynamics -Liouville space theory J. Chem. Phys. 97 2320... 

The intennolecular Hamiltonian of the product fragments is used to calculate the sum of states of the transitional modes, when they are treated as rotations. The resulting model [28] is nearly identical to phase space theory [29],... 

Since the observation made in study of the formation HeH+ indicated that this product was not formed by reaction of He + with H2, it had been assumed that the exothermic heat of reaction of He+ ions with H2 is probably deposited in the product HeH + as internal energy, decomposing the product into H+ and He. This idea was cited by Light (16) in his phase space theory of ion-molecule reactions to account for the failure to observe HeH+ from reactions with He+ ions. The experimental difficulty in the mass spectrometric investigation of this process is that H + formed by electron impact tends to obscure the ion-molecule-produced H+ so that a sensitive quantitative cross-section measurement is difficult. 

Rosenstock (55) pointed out that the initial formulation of the theory failed to consider the effect of angular momentum on the decomposition of the complex. The products of reaction must surmount a potential barrier in order to separate, which is exactly analogous to the potential barrier to complex formation. Such considerations are implicit in the phase space theory of Light and co-workers (34, 36, 37). These restrictions limit the population of a given output channel of the reaction com-... 

The phase space theory in its present form suffers from the usual computational difficulties and from the fact it has thus far been developed only for treating three-body processes and a limited number of output channels. Further, to treat dissociation as occurring only through excitation of rotational levels beyond a critical value for bound vibrational states is rather artificial. Nevertheless, it is a useful framework for discussing ion-molecule reaction rates and a powerful incentive for further work. 

In contrast to the results obtained for dehydrogenation reactions, kinetic energy release distributions for alkane elimination processes can usually be fit with phase space theory. Results for the loss of methane from reaction 9 of Co + with isobutane are shown in Figure 10b. In fitting the... 

The success of the phase space theory in fitting kinetic energy release distributions for exothermic reactions which involve no barrier for the reverse reaction have led to the use of this analysis as a tool for deriving invaluable thermochemical data from endothermic reactions. This is an important addition to the studies of endothermic reactions described above. As an example of these studies, consider the decarbonylation reaction 11 of Co+ with acetone which leads to the formation of the... 

Concepts in quantum field approach have been usually implemented as a matter of fundamental ingredients a quantum formalism is strongly founded on the basis of algebraic representation (vector space) theory. This suggests that a T / 0 field theory needs a real-time operator structure. Such a theory was presented by Takahashi and Umezawa 30 years ago and they labelled it Thermofield Dynamics (TFD) (Y. Takahashi et.al., 1975). As a consequence of the real-time requirement, a doubling is defined in the original Hilbert space of the system, such that the temperature is introduced by a Bogoliubov transformation. 

To determine the optimal value of quantum correction y, several criteria have been proposed, all of which are based on the idea that an appropriate classical theory should correctly reproduce long-time hmits of the electronic populations. (Since the populations are proportional to the mean energy of the corresponding electronic oscillator, this condition also conserves the ZPE of this oscillator.) Employing phase-space theory, it has been shown that this requirement leads to the condition that the state-specihc level densities... 

The association rate data determined in this study can be used to make quite a precise binding energy estimate for the aluminum ion-benzene complex. The relation between the association rate constant and the binding energy was made with use of phase space theory (PST) to calculate as a function of E, with a convolution over the Boltzmann distribution of energies and angular momenta of the reactants (see Section VI). PST should be quite a reasonable approximation for... 

Phase space theory (PST) has been widely used for estimation of rates and energy partitioning for ion dissociations. It can be considered within the framework of transition-state theory as the limiting case of a loose transition state, in which all product degrees of freedom are statistically fully accessible at the transition state. As such, it is expected to give an upper limit for dissociation rates and to be best suited to barrierless dissociations involving reaction coordinates with simple bond cleavage character. 

Figure 3. Thermal rate constants for capture of HC1 by H3 (PST locked-dipole capture corresponding to phase-space theory, Eq. (16) SACM statistical adiabatic channel model, Eqs. (26)-(34) [15] SACMci classical SACM, Eqs. (28H31) [15] CT classical trajectories, Eqs. (26) and (27) [1]).

Figure 6. Number of open channels for the interaction between H3 and HC1 (SACM calculations from Ref. IS PST phase-space theory full curves permanent + induced dipole dashed smoothed curves permanent dipole J total angular momentum of H3-HCI complex).

Statistical phase-space theory Statistical phase-space theory Statistical phase-space theory... 

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