Improved canonical variational theory

Several VTST techniques exist. Canonical variational theory (CVT), improved canonical variational theory (ICVT), and microcanonical variational theory (pVT) are the most frequently used. The microcanonical theory tends to be the most accurate, and canonical theory the least accurate. All these techniques tend to lose accuracy at higher temperatures. At higher temperatures, excited states, which are more difficult to compute accurately, play an increasingly important role, as do trajectories far from the transition structure. For very small molecules, errors at room temperature are often less than 10%. At high temperatures, computed reaction rates could be in error by an order of magnitude. 

ICVT (improved canonical variational theory) a variational transition state theory technique... 

Figure 27.6 Rate constants as a function of temperature forthe collinear Cl + HBr reaction. Accurate quantum mechanical rate constants (solid line with bullets) are compared with those computed using improved canonical variational theory (ICVT) with tunneling included by SCSAG (dotted line) and LCG3 and LAG (long dashed line).

B. C. Garrett and D. G. Truhlar, Improved canonical variational theory for chemical reaction rates. Classical mechanical theory and applications to collinear reactions, J. Phys. Chem. 84 805 (1980). 

TST = conventional Transition State Theory, ICVT = Improved Canonical Variational Transition state theory, ICVT/SCT = ICVT/Small Curvature Tunneling, ICVT/p,OMT = ICVT/Microcanonical Optimized Multidimensional Tunneling. 

ICVTST improved canonical variational transition-state theory... 

A more sophisticated reaction path approach is to replace in eq. (40) by 8jjq(sJj This is the essence of the approach taken by Garrett and Truhlar and generalized by Miller et al. and Skodje and Truhlar for polyatomic reactions. Truhlar and coworkers have proposed one-dimensional paths which deviate from the reaction path in order to compute accurate tunneling probabilities from which transmission coefficients (see below) are then used to correct their version of variational transition state theory, the so-called improved canonical variational [transition state] theory (ICVT) (also see below). 

When the canonical variational transition state is strongly dependent on temperature, a more consistent theory is provided by improved canonical variational transition state theory (ICVTST or, for short. 

The partition functions and numbers of accessible states can all be calculated from the reaction path data, (j) and F(s), assuming harmonic vibrations and separation of vibration and rigid-body rotation. The vibrational partition function may be improved in accuracy by accounting for anharmonicity in some modes. This has been done simply in a separable mode approximation (e.g., Morse stretches and quartic terms in the bending potentials) [129-131]. There are now a number of examples of applications of various forms of canonical variational transition-state theory using ab initio reaction path calculations [15,106,108,112,131-142]. 

Variational transition-state theory has been formulated on various levels [5, 23-27]. At first, there is the group of canonical VTST (CVTST) treatments, which correspond to the search for a maximum of the free energy AG(r) along the reaction path r [23, 24]. It was noticed early that for barri-erless potentials this approach leads to an overestimate of the rate constant because, in the language of SACM, channels are included that are closed. Therefore, an improved version (ICVTST) was proposed [25] that truncates Q at the position r of the minimum of (t(r) by including only states... 

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