Orbiting transition state theory

Phase space orbiting transition state theory works much better for the calculation of KERDs than for that of the rate constants, thereby demonstrating that the former are controlled by the long-range part of the potential whereas the latter are governed by its shorter range. In addition, Klots has introduced a set of effective temperatures to parametrize the observed distributions. The SACM has also demonstrated its usefulness in the case of weakly bonded species. 

Carbenes A Testing Ground for Electronic Structure Methods Complete Active Space Self-consistent Field (CASSCF) Second-order Perturbation Theory (CASPT2) Configuration Interaction Mpller-Plesset Perturbation Theory Natural Orbitals Transition State Theory Unimolecu-lar Reaction Dynamics. 

Equation (5-69) is an important result. It was first obtained by Marcus " in the context of electron-transfer reactions. Marcus derivation is completely different from the one given here. In electron transfer from one molecule (or ion) to another, no bonds are broken or formed, so the transition state theory does not seem to be applicable. Marcus assumed negligible orbital overlap in the electron-transfer transition state, but he later obtained the same equation for group transfer reactions requiring significant overlap. Many applications have been made to proton transfers and nucleophilic displacements. ... 

Periodic boundary conditions, Monte Carlo heat flow simulation, nonequilibrium molecular dynamics, 79—81 Periodic-orbit dividing surface (PODS) geometric transition state theory, 196-201 transition state trajectory, 202-213 Perturbation theory, transition state trajectory, deterministically moving manifolds, 224-228... 

DFT has come to the fore in molecular calculations as providing a relatively cheap and effective method for including important correlation effects in the initial and final states. ADFT methods have been used, but by far the most popular approach is that based on Slater s half electron transition state theory [73] and its developments. Unlike Hartree-Fock theory, DFT has no Koopmans theorem that relates the orbital energies to an ionisation potential, instead it has been shown that the orbital energy (e,) is related to the gradient of the total energy E(N) of an N-electron system, with respect to the occupation number of the 2th orbital ( , ) [74],... 

UNIMOLECULAR BIMOLECULAR TRANSITION-STATE THEORY ELEMENTARY REACTION MOLECULAR MECHANICS CALCULATIONS MOLECULAR ORBITALS MOLECULAR REARRANGEMENT MOLECULAR SIMILARITY Molecular stoichiometry of an elementary reaction,... 

Felipe M.A., Xiao Y., and Kubickl J.D. (2001) Molecular orbital modeling and transition state theory in geochemistry. Rev. Mineral. Geochem. 42, 485-531. 

In addition to this type of empirical approach, there are several other approaches that are related more directly to specific properties of the organic, such as the C-H bond dissociation enthalpies (Heicklen, 1981 Jolly et a.L, 1985), ionization energy (Gaffney and Levine, 1979), or NMR shifts (Hodson, 1988). In addition, molecular orbital calculations (Klamt, 1993) and transition state theory (Cohen and Benson, 1987) have been applied. 

It is seen from this table that the rate of reaction increases -CH2C(CH3)20H < CH2OH < C(CH3)HOH < (TCI I3)2OI I despite the fact that the exothermicity of the reaction decreases in the same direction. This unexpected behavior has been discussed in terms of the charge and spin polarization in the transition state, as determined by the AIM analysis, and in terms of orbital interaction theory (Reid et al. 2002). Rate constants, calculated by transition state theory, were in good agreement with the experimental data. 

Different practical procedures for computing r) have been proposed, that range from the computation of the difference between the energy values of the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals [8,9], to the atom in molecules based models [10, 11], to the charge sensitivity analysis [12, 13], to the use of Slater transition state theory [14], to the Janak s extension of DFT for fractional occupancies [15, 16]. Recently, Neshev and Mineva have proposed a scheme for the construction of the internally resolved hardness tensor in... 

Recent mechanistic discussions of unimolecular decompositions of organic ions have invoked ion—molecule complexes as reaction intermediates [102, 105, 361, 634]. The complexes are proposed to be bound by long-range ion—dipole forces and to be sufficiently long-lived to allow hydrogen rearrangements to occur. The question of lifetime aside, there is more than a close similarity between the proposed ion—dipole intermediate and the assumed loose or orbiting transition state of phase space theory. 

Natural Atomic Orbital and Natural Bond Orbital Analysis 230 9.7 Computational Considerations 232 9.8 Examples 232 References 234 10 Molecular Properties 235 104 Examples 236 References 294 12 Transition State Theory and Statistical Mechanics 296 12.1 Transition State Theory 296 12.2 Statistical Mechanics 298 12.2.1 ans 299 12.2.2 300... 

So here, the term theory will be used in a way that embraces the typical named theories of chemistry such things as molecular orbital theory, valence shell electron pair repulsion theory, transition state theory of reactions, and Debye Hiickel theory of electrolyte solutions. No decisive distinction will be made between theory, model, and other similar terms. But there is one distinction that we do make. The term theory is considered in an epistemological sense—as an expression of oin best knowledge and belief about the way chemical systems work. 

In our recent work [89], the reaction of HO2 with CIO has been investigated by ab initio molecular orbital and variational transition state theory calculations. The geometric parameters of the reaction system HO2 + CIO were optimized at the B3LYP and BH HLYP levels of theory with the basis set, 6-311+G(3df,2p), which can be found in Ref. [89]. Both singlet and triplet potential energy surfaces were predicted by the G2M method, as shown in Fig. 24. 

The mechanism for the reaction CIO + OCIO has been investigated by ab initio molecular orbital and transition state theory calculations [140]. Nine stable isomers of CI2O3 (including optical isomers) are located at the B3LYP/6-311+G(3df) level. The transition states between pairs of isomers... 

The idea that the vibrational enhancement of the rate is due to the attractive potential for excited vibrational states of the reactant is closely related to the observation made long ago based on transition state theory [25,26]. Poliak [25] found that for vibrationally highly excited reactants the repulsive pods (periodic orbit dividing snrface) is way out in the reactant valley, and the corresponding adiabatic barrier is shallow Based on this theory one can explain why dynamical thresholds are observed in reactions with vibrationally excited reactants. The simplicity of the theory and its snccess for mostly collinear reactions has a real appeal. However, to reconcile the existence of a vibrationally adiabatic barrier with the captnre-type behavior - which seems to be supported by the agreement of the calculated and experimental rate coefficients [23] -needs further study. 

PHASE SPACE THEORY AND ORBITING TRANSITION STATE PHASE SPACE THEORY... 

Orbiting Transition State Phase Space Theory... 

Chesnavich and Bowers (1977a,b 1979) modified the phase space theory model by assuming (a) an orbiting transition state located at the centrifugal barrier, and (b) that orbital rotational energy at this transition state is converted into relative translational energy of the products. The Hamiltonian used for this orbiting transition state/phase... 

Figure 11. Kinetic energy release distribution for metastable loss of CH4 from nascent Co(C3Hg)+ collision complexes. The "unrestricted" phase space theory curve assumes the entrance channel contains only an orbiting transition state, the exit channel has only an orbiting transition state (no reverse activation barrier), and there are no intermediate tight transition states that affect the dynamics. The "restricted" phase space theory calculation includes a tight transition state for insertion into a C-H bond located 0.08 eV below the asymptotic energy of the reactants.

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