Variational transition state theory calculations

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 authors are grateful to Yuri Volobuev for participation in early stages of the DH2 analysis and to Professor Ken Leopold for helpful discussions. The quantum mechanical scattering calculations were supported in part by the National Science Foundation. The variational transition state theory calculations were supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences. 

VARIATIONAL TRANSITION STATE THEORY CALCULATIONS OF CONCERTED HYDROGEN ATOM TUNNELING IN WATER CLUSTERS AND FORMALDEHYDEAVATER CLUSTERS... 

In the present work, information about the potential energy surfaces for these systems is obtained by the BAC-MP4 method [28-33]. This method has been very successful for predicting the thermochemistry of molecules and radical species, and has been extended to calculating the potential information along reaction paths needed for the variational transition state theory calculations. In the latter case, the method has been shown to be capable of quantitative predictions for a gas phase chemical reaction [33]. In the present study our interests are in estimates of the order of magnitude of reaction rates, and in studies of qualitative trends such as the effect of cluster size on the magnitude of quantum tunneling. The methods employed here are more than adequate for these types of studies. 

The dynamics methods we employ are reviewed above, and full details are presented elsewhere. In particular, the polyatomic variational transition state theory calculations are described briefly in the original journal article [28] and in full detail in a book chapter [10]. The SCT, LCT, and xOMT tunneling methods are also explained elsewhere [7b, 17,24,25]. VTST and these multidimensional tunneling methods are also summarized in the chapter by Isaacson in the present volume. 

S. C. Tucker and D. G. Truhlar, J. Am. Chem. Soc., 112, 3338 (1990). A 6-Body Potential-Energy Surface for the Sj 2 Reaction C1 (G)- -CH3C1(G) and a Variational Transition-State-Theory Calculation of the Rate-Constant. 

A, 106,4957 (2002). Interpolated Algorithm for Large-Curvature Tunneling Calculations of Transmission Coefficients for Variational Transition State Theory Calculations of Reaction Rates. 

A noteworthy qualitative aspect of variational-transition-state-theory calculations of kinetic isotope effects is that the geometry of the variational transition state may differ for each isotopic variation of a reaction. This means that the usual methods of predicting isotope effects, based on the simplifications possible when nuclear masses are changed with fixed force fields, do not apply. Instead of using such simplifications, we perform completely independent variational calculations for each isotopic case. 

UFF (universal force field) a molecular mechanics force field unrestricted (spin unrestricted) calculation in which particles of different spins are described by different spatial functions VTST (variational transition state theory) method for predicting rate constants... 

The rate of hydrogen transfer can be calculated using the direct dynamics approach of Truhlar and co-workers which combines canonical variational transition state theory (CVT) [82, 83] with semi-classical multidimensional tunnelling corrections [84], The rate constant is calculated using [83] ... 

Calculations have identified three transition states (TS) for an SN2 reaction.4"6 Two are variational, one of which is located along the X + RY association reaction path, and the other along the XR + Y" association reaction path i.e. see Figure 1. Variational transition state theory (VTST) calculations show that the third TS is located at the central barrier.4... 

Because T -> V energy transfer does not lead to complex formation and complexes are only formed by unoriented collisions, the Cl" + CH3C1 -4 Cl"—CH3C1 association rate constant calculated from the trajectories is less than that given by an ion-molecule capture model. This is shown in Table 8, where the trajectory association rate constant is compared with the predictions of various capture models.9 The microcanonical variational transition state theory (pCVTST) rate constants calculated for PES1, with the transitional modes treated as harmonic oscillators (ho) are nearly the same as the statistical adiabatic channel model (SACM),13 pCVTST,40 and trajectory capture14 rate constants based on the ion-di-pole/ion-induced dipole potential,... 

Of course, one is not really interested in classical mechanical calculations. Thus in normal practice the partition functions used in TST, as discussed in Chapter 4, are evaluated using quantum partition functions for harmonic frequencies (extension to anharmonicity is straightforward). On the other hand rotations and translations are handled classically both in TST and in VTST, which is a standard approximation except at very low temperatures. Later, by introducing canonical partition functions one can direct the discussion towards canonical variational transition state theory (CVTST) where the statistical mechanics involves ensembles defined in terms of temperature and volume. There is also a form of variational transition state theory based on microcanonical ensembles referred to by the symbol p,. Discussion of VTST based on microcanonical ensembles pVTST is beyond the scope of the discussion here. It is only mentioned that in pVTST the dividing surface is... 

Table 6.2 Tests of Variational Transition State Theory by Comparing with Exact Quantum Calculations (Extracted from Allison, T. C. and Truhlar, D. G. Testing the accuracy of practical semiclassical methods variational transition state theory with optimized multidimensional tunneling, in Thompson, D. L., Ed. Modem methods for multidimensional dynamics computations in chemistry, World Scientific, Singapore 1998. pp 618-712. This reference quotes results on many more reactions and BO surfaces over broad temperature ranges.)The numbers in the table are ratios of the results of the approximate calculation to the quantum calculation, all at 300 K...

Table 6.3 Tests of variational transition state theory by comparing with exact quantum calculations isotope effects at 300 K. The numbers in the table are ratios of rate constants for the two selected reactions...

The most satisfactory situation for making an extrapolation of rate data to the true threshold arises when the threshold is uncertain, but we can confidently calculate the functional form of the rate-energy curve from accurate kinetic theory. For small systems, it is feasible to calculate dissociation rates by quantum methods, but this is not yet feasible for the systems of interest to us. Various approaches to variational transition-state theory (VTST) provide classical or semiclassical calculations that are feasible for large systems and seem to be accurate when carefully... 

An efficient implementation of microcanonical classical variational transition state theory was applied to Si—H bond fission in SiFF and compared with trajectory calculations on the same potential surface235. 

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