Thermal rate constants

These equations lead to fomis for the thermal rate constants that are perfectly similar to transition state theory, although the computations of the partition functions are different in detail. As described in figrne A3.4.7 various levels of the theory can be derived by successive approximations in this general state-selected fomr of the transition state theory in the framework of the statistical adiabatic chaimel model. We refer to the literature cited in the diagram for details. 

Wang H, Sun X and Miller W H 1998 Semiclassical approximations for the calculation of thermal rate constants for chemical reactions in complex molecular systems J. Chem. Phys. 108 9726... 

Sun X, Wang H and Miller W H 1998 Qn the semiclassical description of quantum coherence in thermal rate constants J. Chem. Phys. 109 4190... 

An exact expression for the thermal rate constant is given by ... 

Park T J and Light J C 1989 Accurate quantum thermal rate constants for the three-dimensional H + H2 reaction J. Chem. Phys. 91 974... 

Using the coordinates of special geometries, minima, and saddle points, together with the nearby values of potential energy, you can calculate spectroscopic properties and macroscopic therm ody-riatriic and kinetic parameters, sncfi as enthalpies, entropies, and thermal rate constants. HyperChem can provide the geometries and energy values for many of these ealeulatiori s. 

When this is done, the dependence of k(Ee) upon Ee is even greater than predicted by the dipole-alignment model, and the thermal rate constant predicted from this variation, extrapolated to thermal energies, is more than twice the thermal rate constant found experimentally by using the pulsing technique. 

In 1960 Tal roze and Frankevich (39) first described a pulsed mode of operation of an internal ionization source which permits the study of ion-molecule reactions at energies approaching thermal energies. In this technique a short pulse of electrons is admitted to a field-free ion source to produce the reactant ions by electron impact. A known and variable time later, a second voltage pulse is applied to withdraw the ions from the ion source for mass analysis. In the interval between the two pulses the ions react under essentially thermal conditions, and from variation of the relevant ion currents with the reaction time the thermal rate constants can be estimated. 

Using either of the above approaches we have measured the thermal rate constants for some 40 hydrogen atom and proton transfer reactions. The results are tabulated in Table II where the thermal rate constants are compared with the rate constants obtained at 10.5 volt cm.-1 (3.7 e.v. exit energy) either by the usual method of pressure variation or for concurrent reactions by the ratio-plot technique outlined in previous publications (14, 17, 36). The ion source temperature during these measurements was about 310°K. Table II also includes the thermal rate constants measured by others (12, 13, 33, 39) using similar pulsing techniques. 

As Table II shows, four separate measurements of the thermal rate constants for the reaction ... 

The ZN formulas can also be utihzed to formulate a theory for the direct evaluation of thermal rate constant of electronically nonadiabatic chemical reactions based on the idea of transition state theory [27]. This formulation can be further utilized to formulate a theory of electron transfer and an improvement of the celebrated Marcus formula can be done [28]. 

Figure 10. Arrhenius plot of the thermal rate constants for the 2D model system. Circles-full quantum results. Thick solid (dashed) curve present nonadiabatic transition state theory by using the seam surface [the minimum energy crossing point (MECP)] approximation. Thin solid and dashed curves are the same as the thick ones except that the classical partition functions are used. Taken from Ref. [27].

Figure 22 shows an application of the present method to the H3 reaction system and the thermal rate constant is calculated. The final result with tunneling effects included agree well with the quantum mechanical transition state theory calculations, although the latter is not shown here. 

We can calculate the thermal rate constants at low temperatures with the cross-sections for the HD and OH rotationally excited states, using Eqs. (34) and (35), and with the assumption that simultaneous OH and HD rotational excitation does not have a strong correlated effect on the dynamics as found in the previous quantum and classical trajectory calculations for the OH + H2 reaction on the WDSE PES.69,78 In Fig. 13, we compare the theoretical thermal rate coefficient with the experimental values from 248 to 418 K of Ravishankara et al.7A On average, the theoretical result... 

Fig. 21. Comparison of theory and experiment for the thermal rate constant of the H+H2O — H2+OH reaction and the calculated contributions from individual vibrational states of H2O.

Truong, T. N. and W. Dunkan. 1994. A new direct ab initio dynamics method for calculating thermal rate constants from density-functional theory. J. Chem. Phys. 101, 7408. 

Corcelli, S.A. Rahman, J.A. Tully, J.C., Efficient thermal rate constant calculation for rare event systems, 7. Chem. Phys. 2003,118, 1085-1088... 

Here, L total is the depth of the etched hole per pulse and is assumed to be the sum of photochemical and photothermal contributions, Tphoto and Thermal, respectively 0Ceff is the effective photon absorption coefficient of the medium and can vary with laser emission characteristics, e g., photon density Fis the incident laser fluence Fth is the medium s threshold fluence A and F are the effective frequency factor with units of pm/pulse and the effective activation energy with units of J/cm2, respectively, for the zeroth-order thermal rate constant F0, comparable in magnitude to Fth, is important only at low fluences.64 Equation (5) is obtained after assuming that the polymer temperature T in the laser-exposed region of mass mp and the thermal rate constant k are given, respectively, as... 

Experiments have also played a critical role in the development of potential energy surfaces and reaction dynamics. In the earliest days of quantum chemistry, experimentally determined thermal rate constants were available to test and improve dynamical theories. Much more detailed information can now be obtained by experimental measurement. Today experimentalists routinely use molecular beam and laser techniques to examine how reaction cross-sections depend upon collision energies, the states of the reactants and products, and scattering angles. 

In conventional transition state theory (TST) (see Chapter 4) the first approximation for the thermal rate constant k is given ... 

Table 3. 300-K Thermal Rate Constants for Hj + Hj and Its Isotopic Analogues...

J.V. Michael. Measurement of Thermal Rate Constants by Flash or Laser Photolysis in Shock Tubes Oxidation of H2 and D2. Prog. Energy Combust. Sci., 18 327-347, 1992. 

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 10. Thermal rate constants for capture of N2 by an ion (SACM calculation [33] with channels generating from rotational states N = 0, 1,2, accounting for nuclear statistical weights left figure positive ion right figure negative ion).

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