ICVT

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... 

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. 

Table 6.3 lists a few H/D isotope effects (kH/kD) for some of the examples listed in Table 6.2. It is noted with some regret that the errors in the isotope effects (kH/kD) calculated by ICVT/ p,OMT are about the same as the errors reported for kH in Table 6.1. One might have hoped to see some cancellation of error when calculating isotope effects.

Assembled from several secondary sources the 7th ICVT report (2000 van Regenmortel et al., 2000), Viper (Reddy, 1999), the Protein Data Bank (Berman et al, 2000), SwissProt (Bairoch and Apweiler, 2000), and Murphy and Kingsbury (1996). 

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).

The thermal rate constants for H + H2 that have been obtained from a variety of methods on the LSTH and PK2 surfaces are summarized in Table 2. This table indicates that on PK2, QCT underestimates the rate constant compared to CC by a factor of 3.1 at 300 K. The VTST based methods (CVT and ICVT ) do much better, with the most recent ICVTWKB/LAG results high by 21% at 300 K and 29% at 600 K. The TST-CEQB results are in comparably good agreement with CC. On the LSTH surface, CS or CC rate constants are not yet available, but the comparison with experiment indicates that QCT again is substantially low at 300 K, while the VTST based methods are quite close to experiment. Based on the PK2 comparisons, it seems unlikely that the CC rate constant on LSTH at 300 K will be above 2.3 x 10 , which... 

Table 5 summarizes the results of the experimental and theoretical results to date on Mu + H2 while Fig. 4 plots the CS, ICVT-WKB/LAC and experimental results over the range of temperatures where the experiments have been done. The Figure and Table indicate that CS,... 

ICVT-WKB/LAG and experimental results are all in excellent agreement, generally to within the experimental error bars. At low temperatures, the LAG results dip well below CS, with the difference being a factor of 6 at 300 K. This indicates that the LAG tunnelling calculation is inaccurate in the deep tunnelling regime. 

H2, a harmonic model semiclassical adiabatic (SCAD) calculation for H + H2 and D + H2, a rotationally averaged lOS (RATOS) calculationl O for D + H2> ICVT calculations using a least action (LA) tunnelling... 

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). 

ICVT)- As for the quantities discussed in the last paragraph, the ICVT approximation to the thermal rate constant may be calculated from Vmep(s) and the set of e(ot,s). 

Results obtained using the CC, lOSA, ESA-CSA, BCRLM, RBCRLM and ICVT-SCTSAG methods are compared in this Table. It can be seen that all the approximate methods overestimate the CC result apart from the RBCRLM. 

At 300K, the ESA-CSA, lOSA, RBCRLM and ICVT-SCTSAG rate constants all agree with the CC value to within a factor of two, which must be considered a very satisfactory agreement considering that the rate constant increases by a factor of 85 over the temperature range 150-30CK. ... 

---