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To construct the PES for the system with high permutation symmetry, it is essential to build the PES such a way that it remains invariant with respect to all possible permutations between identical atoms. For lower permutation symmetry this is done by expanding the data set, i.e., replicating the electronic energy for each permutations. This approach is doable for system with a lower permutation symmetry like CH2, CO2 where one has to deal with only two permutations and therefore duplicating the data set will resolve the symmetry issue. System with a high permutation symmetry, such as, CH4, where 120 permutation operations are possible, the former approach is unfeasible and one needs to come up with more efficient and convenient approach. Using the permutation invariant (PI) fitting functions is an excellent way to achieve a permutation invariant PES.
New potential energy surfaces for methane were constructed, represented as analytic fits to about 100,000 individual high-level ab initio data. Explicitly-correlated multi-reference data (MRCI-F12(AE)/CVQZ-F12) were computed and fitted using the permutation-invariant-polynomials (PIP) approach based on the interpolative moving least squares (IMLS) fitting method [1] (PIP-IMLS). The efficiency of IMLS [2, 3] method to provide a spectroscopic accurate PES is quite promising and has been applied for few van der Waals systems. Very close agreement with experiment was produced from the purely ab initio PESs.
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