Reliable calculations of rate constants with sufficient accuracy are a challenging field in computational chemistry. So far, two main approaches have dominated the scene, that allowed the computation of such quantities in qualitative and/or quantitative agreement with experimental observations. One method is based on the Eyring equation for the calculation of rate constants. The second one is based on molecular dynamics. Both methods present somehow specular problems. On the one hand, the first approach allows calculate rate constants for systems of about thousand atoms. However, it may suffer from large inaccuracies if the model describing the nuclear dynamics (commonly the harmonic approximation) poorly resembles the physics of the system. The second method,  on the other hand, allows a full description of the system’s dynamics but, unfortunately, chemical reactions are rare events happening on a time scale that is usually not accessible in a standard simulation.

To overcome the limitations of the first approach a computational protocol that combines accurate optimization schemes and anharmonic frequency calculations using normal-modes in internal coordinates representation with hybrid MP2:DFT+D energy correction has been proposed [1, 2]. Its application to surface reactions allowed calculate rate constants within chemical accuracy with respect to experimental observations [3].

In the case of molecular dynamics, a recent work by Parrinello et al. [4] showed how to derive a variationally optimized bias potential to boost up transitions between two metastable states. This method has been applied to the study of the reaction dynamics of a prototypical organic reaction, showing how the statistical fluctuations between two free-energy basins can be enhanced even for a very high energy barrier processes.

References:

[1] G. Piccini and J. Sauer, Quantum chemical free energies: Structure optimization and vibrational frequencies in normal modes, J. Chem. Theory and Comput., 9, 5038-5045, 2013.

[2] G. Piccini and J. Sauer, Effect of anharmonicity on adsorption thermodynamics, J. Chem. Theory and Comput., 10, 2479-2487, 2014.

[3] G. Piccini, M. Alessio, and J. Sauer, Ab-initio calculation of rate constants for molecule surface reactions with chemical accuracy, Angew. Chem. Int. Ed., 55, 5235-5237, 2016.

[4] J. McCarty, O. Valsson, P. Tiwary, and M. Parrinello, Variationally optimized free-energy flooding for rate calculation, Phys. Rev. Lett., 115, 070601, 2015.