Multidimensional interpolation approach

The second approach is based on the multidimensional interpolation approach (MIA) developed by Smolentsev, Soldatov and co-workers as well as Minuit XANes (MXAN) by Benfatto and Della Longa and co-workers... 

CVT approach is particularly attractive due to the limited amount of potential energy and Hessian information that is required to perform the calculations. Direct dynamics with CVT thus offers an efficient and cost-effective methodology. Furthermore, several theoretical reviews60,61 have indicated that CVT plus multidimensional semi-classical tunneling approximations yield accurate rate constants not only for gas-phase reactions but also for chemisorption and diffusion on metals. Computationally, it is expensive if these Hessians are to be calculated at an accurate level of ab initio molecular orbital theory. Several approaches have been proposed to reduce this computational demand. One approach is to estimate rate constants and tunneling contributions by using Interpolated CVT when the available accurate ab initio electronic structure information is very limited.62 Another way is to carry out CVT calculations with multidimensional semi-classical tunneling approximations. 

In applications to a wide range of experimental results, one needs an efficient theoretical tool allowing for quick comparison of experiment and theory, perhaps followed by adjustment of theoretical parameters to experiment. With this goal in mind, the early formulation of the SACM included a simple empirical representation of the main features of the electronic potential by a very few adjustable parameters. Furthermore, the complicated calculation of adiabatic channels by a solution of the multidimensional clamped -q- rovibrational Schrbdinger equation, which is an exceedingly demanding task even today for larger than triatomic systems, was completely circumvented by a simple channel interpolation procedure. We shall present here a very brief description of this empirical approach for simple bond fission reactions. 

Recent developments in ab initio methods for calculating potential energy surfaces will require new, systematic approaches for obtaining useful analytical representations. Progress has been made in this area using for example multidimensional splinespolynomial root interpolation, and many-body expansion.An important goal is to develop methods that can be systematically applied and that require a relatively small number of ab initio points. 

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