Kinetic isotope effects and how to describe them

Abstract

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.

Perspective: Ring-polymer instanton theory

“…3. The rate constants predicted by the instanton method for this system are in fairly good agreement (∼35% error at 250 K) 51 with benchmark quantum dynamics results 56 using the same parametrized PES. 57 However, as the rate depends exponentially on the shape of the barrier, the PES itself may be a significant cause of error for both these approaches.…”

“…To test this assertion, instanton calculations have also been performed using on-the-fly electronic-structure [RCCSD(T)-F12a/cc-pVTZ] calculations. 48,51 At low temperatures, the calculations based on the parametrized PES underpredicted the ab initio rate by more than a factor of two. This shows that in order to obtain accurate results, the most important factor is the quality of the PES itself and that the semiclassical approximation inherent in the instanton method is of a lesser concern.…”

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

“…Kinetic isotope effects can also be easily predicted, which often provide the easiest connection to experimental data. 103 A limitation of all instanton methods is that the semiclassical approximation is not valid for liquid systems. Nonetheless, a good understanding of the instanton paths has helped in the development of a number of methods based on path-integral sampling which are applicable to reactions in solution.…”

The any particle molecular orbital approach: A short review of the theory and applications

“…These calculations are usually carried out employing the vibrational self‐consistent field method or grid based approaches such as the discrete variable representation . Alternatively, GIEs can be analyzed performing path integral molecular dynamics simulations . One limitation of the above methods when applied to the calculation of GIEs, is their reported high computational costs.…”